Representation Of Fluxes Research Articles

On invariant structures of black hole charges

Abstract We study “minimal degree” complete bases of duality- and “horizontal”- invariant homogeneous polynomials in the flux representation of two-centered black hole solutions in two classes of D = 4 Einstein supergravity models with symmetric vector multiplets’ scalar manifolds. Both classes exhibit an SL(2, $ \mathbb{R} $ ) “horizontal” symmetry which mixes the two centers. The first class encompasses $ \mathcal{N} = {2} $ and $ \mathcal{N} = {4} $ matter-coupled theories, with semisimple U-duality given by SL(2, $ \mathbb{R} $ ) × SO(m,n); the analysis is carried out in the so-called Calabi-Vesentini symplectic frame (exhibiting maximal manifest covariance) and until order six in the fluxes included. The second class, exhibiting a non-trivial “horizontal” stabilizer SO(2), includes $ \mathcal{N} = {2} $ minimally coupled and $ \mathcal{N} = 3 $ matter coupled theories, with U-duality given by the pseudounitary group U(r,s) (related to complex flux representations). Finally, we comment on the formulation of special Kähler geometry in terms of “generalized” groups of type E 7.

Flux simulation of the SU(3) spin model at finite chemical potential

We present a Monte Carlo simulation of an effective theory for local Polyakov loops at finite temperature and density. The sign problem is overcome by mapping the partition sum to a flux representation. We determine the phase diagram of the model as a function of the temperature and the chemical potential.

The QCD deconfinement transition for heavy quarks and all baryon chemical potentials

Using combined strong coupling and hopping parameter expansions, we derive an effective three-dimensional theory from thermal lattice QCD with heavy Wilson quarks. The theory depends on traced Polyakov loops only and correctly reflects the centre symmetry of the pure gauge sector as well as its breaking by finite mass quarks. It is valid up to certain orders in the lattice gauge coupling and hopping parameter, which can be systematically improved. To its current order it is controlled for lattices up to N_\tau\sim 6 at finite temperature. For nonzero quark chemical potentials, the effective theory has a fermionic sign problem which is mild enough to carry out simulations up to large chemical potentials. Moreover, by going to a flux representation of the partition function, the sign problem can be solved. As an application, we determine the deconfinement transition and its critical end point as a function of quark mass and all chemical potentials.

Optimal representation of source-sink fluxes for mesoscale carbon dioxide inversion with synthetic data

[1] The inversion of CO2 surface fluxes from atmospheric concentration measurements involves discretizing the flux domain in time and space. The resolution choice is usually guided by technical considerations despite its impact on the solution to the inversion problem. In our previous studies, a Bayesian formalism has recently been introduced to describe the discretization of the parameter space over a large dictionary of adaptive multiscale grids. In this paper, we exploit this new framework to construct optimal space-time representations of carbon fluxes for mesoscale inversions. Inversions are performed using synthetic continuous hourly CO2 concentration data in the context of the Ring 2 experiment in support of the North American Carbon Program Mid Continent Intensive (MCI). Compared with the regular grid at finest scale, optimal representations can have similar inversion performance with far fewer grid cells. These optimal representations are obtained by maximizing the number of degrees of freedom for the signal (DFS) that measures the information gain from observations to resolve the unknown fluxes. Consequently information from observations can be better propagated within the domain through these optimal representations. For the Ring 2 network of eight towers, in most cases, the DFS value is relatively small compared to the number of observations d (DFS/d < 20%). In this multiscale setting, scale-dependent aggregation errors are identified and explicitly formulated for more reliable inversions. It is recommended that the aggregation errors should be taken into account, especially when the correlations in the errors of a priori fluxes are physically unrealistic. The optimal multiscale grids allow to adaptively mitigate the aggregation errors.

Assessing the impact of internal conductance to CO 2 in a land-surface scheme: Measurement and modelling of photosynthesis in Populus nigra

Vegetation plays a key role in both the global carbon and water cycles. Therefore, the representation of leaf-level fluxes of carbon and water in process-based land-surface schemes is central to accurately predicting these surface exchanges on a larger scale. Leaf-level models of photosynthesis used in such schemes are commonly based on the equations of Farquhar et al. (1980), which were founded on the assumption that differences in the drawdown of CO 2 from sub-stomatal cavities ( c i ) to the site of carboxylation inside chloroplasts ( c c ) were negligible. Recent research, however, indicates an important role for this additional internal pathway of CO 2 transfer ( g i ) in photosynthesis. This work therefore combined fieldwork and modelling to assess the impact of g i on estimation of key photosynthetic parameters, and on the accuracy of simulated photosynthesis ( A net ) and stomatal conductance ( g s ) in a coupled model of leaf-level A net and g s embedded in a land-surface scheme. It was shown that, in a fast growing poplar genotype ( Populus nigra), the photosynthetic parameter V max was sensitive to g i . Determination of V max under the assumption of finite g i led to estimates of V max in well-watered trees that were, on average, 52% higher than values calculated on a c i basis. Drought induced declines in all key photosynthetic parameters measured were observed ( V max , J max and g i ), in addition to a two-fold increase in photosynthetic biochemical capacity upon re-watering. Reasons for this and the implications for land-surface modelling are discussed. It was shown that inclusion of a constant (non-water stressed) internal conductance to CO 2 in a coupled model of leaf-level A net and g s did not improve the accuracy of these simulated fluxes. It was concluded that, for application within a land-surface scheme, currently, accurate calibration of V max potentially has a greater impact on simulated A net and g s than the inclusion of additional, fine-scale leaf-level processes such as g i .

Non-commutative flux representation for loop quantum gravity

The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. It has long been believed that this non-commutativity prevents a dual flux (or triad) representation of loop quantum gravity to exist. We show here, instead, that such a representation can be explicitly defined, by means of a non-commutative Fourier transform defined on the loop gravity state space. In this dual representation, flux operators act by ⋆-multiplication and holonomy operators act by translation. We describe the gauge invariant dual states and discuss their geometrical meaning. Finally, we apply the construction to the simpler case of a U(1) gauge group and compare the resulting flux representation with the triad representation used in loop quantum cosmology.

Hamiltonian formalism in the equilibrium problem for a plasma with islands

Hamiltonian formalism is applied to the equilibrium problem for a plasma with islands by using an analogy between the equilibrium problem for a plasma with one island and the nonlinear mechanics of a physical pendulum. A relationship is established between magnetic flux coordinates with straightened magnetic field lines and the action-angle variables. The flux and current representations of a magnetic field with islands are obtained, and the solution to the equilibrium problem for a narrow island is presented.

QCD Phase Diagram According to the Center Group

We study an effective theory for QCD at finite temperature and density which contains the leading center symmetric and center symmetry breaking terms. The effective theory is studied in a flux representation where the complex phase problem is absent and the model becomes accessible to Monte Carlo techniques also at finite chemical potential. We simulate the system by using a generalized Prokof'ev-Svistunov worm algorithm and compare the results to a low temperature expansion. The phase diagram is determined as a function of temperature, chemical potential, and quark mass. The shape and quark mass dependence of the phase boundaries are as expected for QCD. The transition into the deconfined phase is smooth throughout, without any discontinuities or critical points.

A generalized power law approximation for fluvial incision of bedrock channels

Sediment flux is known to influence bedrock incision rates in mountain rivers. Although the widely used stream power incision model lacks any explicit representation of sediment flux, the model appears to work in a variety of real settings. We address this apparent contradiction using numerical experiments to explore the morphology of fluvial landscapes evolved with four different incision models, three of which include the influence of sediment flux on incision rate. The numerical landscapes have different spatial patterns of uplift and are at steady state. We analyze these landscape using the common “stream power” approach, which views incision rates to be primarily a function of the local channel gradient S and the upstream drainage area A. We find that incision rates I for these landscapes are well described by an empirical power law equation I = K′Am′Sn′. This equation is functionally equivalent to the widely used stream power model, with the important distinction that the parameters K′, m′, and n′ are entirely empirical. These parameters take on constant values within a single landscape, but can otherwise be quite different between landscapes mainly due to differences in the pattern of rock uplift within the drainage. In particular, the parameters m′ and n′ decrease as the rate of rock uplift becomes more focused in the upland part of a mountain belt. The parameter m′ is particularly important in that it describes the sensitivity of a tectonically active mountain belt to changes in precipitation or tectonic accretion. It also defines how incision rates will change as the discharge becomes flashier.

Exploring flux representations of complex kinetics networks

AbstractTo extract meaningful information from complex kinetic models involving a large number of species and reactions, advanced computational techniques are required. In this work, new approaches have been proposed based on element flux calculations for systematic kinetic analysis of complex reaction models. These approaches quantify element transformation flux between species to determine a metric that accurately captures the production and consumption of species. Furthermore, a graph searching procedure is employed to retrieve all possible reaction pathways from the highly complex reaction networks. Element fluxes involved in these pathways provide an indicator to quantitatively evaluate pathway activities. Based on pathway activities, a novel approach is proposed to project the totality of the information contained in pathway weights onto a single scalar, reactivity status indicator, which enables a compact representation of local chemistry. The proposed approaches are illustrated with highly complex kinetic mechanisms describing oxidation of n‐pentane, n‐heptane, and a biodiesel surrogate methyl‐butanoate. © 2011 American Institute of Chemical Engineers AIChE J, 2012

Flux representation of an effective Polyakov loop model for QCD thermodynamics

We discuss an effective Polyakov loop model for QCD thermodynamics with a chemical potential. Using high temperature expansion techniques the partition sum is mapped exactly onto the partition sum of a flux model. In the flux representation the complex action problem is resolved and a simulation with worm-type algorithms becomes possible also at finite chemical potential.

Modelling of block-scale macrodispersion as a random function

Numerical modelling of solute dispersion in natural heterogeneous porous media is facing several challenges. Amongst these we highlight the challenge of accounting for high-frequency variability that is filtered out by homogenization at the subgrid scale and the uncertainty in the dispersive flux for transport under non-ergodic conditions. These two effects when combined lead to inaccurate representation of the dispersive fluxes. We propose to compensate for this deficiency by defining a block-scale dispersion tensor and modelling it as a random space function ℳij. The derived dispersion tensor is a function of several length scales and time. Grid blocks will be assigned dispersion coefficients generated from the ℳijdistribution. We will show the dependence of ℳijon the spatial variability of the conductivity field, on the contaminant source size, on the travel time and on the grid-block scale. For an ergodic source, a statistically uniform conductivity field and very large grid blocks, ℳijis equal to the macrodispersion coefficients proposed by Dagan (J. Fluid Mech., vol. 145, 1984, p. 151) with zero variance. For an ergodic source and non-uniform conductivity field with a finite-size grid block, ℳijapproaches the model proposed by Rubinet al. (J. Fluid Mech., vol. 395, 1999, p. 161). In both cases, ℳijis defined by its mean value with zero variance. ℳijis subject to uncertainty when the source is non-ergodic and when the grid block is defined by a finite scale. When the grid-block scale approaches zero, which means that the spatial variability is captured completely on the numerical grid, ℳijapproaches zero with zero variance. In addition, we provide a complete statistical characterization of ℳijby invoking the concept of minimum relative entropy, thus providing upper bounds on the uncertainty associated with ℳij.

Modelling of block-scale macrodispersion as a random function

Numerical modelling of solute dispersion in natural heterogeneous porous media is facing several challenges. Amongst these we highlight the challenge of accounting for high-frequency variability that is filtered out by homogenization at the subgrid scale and the uncertainty in the dispersive flux for transport under non-ergodic conditions. These two effects when combined lead to inaccurate representation of the dispersive fluxes. We propose to compensate for this deficiency by defining a block-scale dispersion tensor and modelling it as a random space function ℳij. The derived dispersion tensor is a function of several length scales and time. Grid blocks will be assigned dispersion coefficients generated from the ℳij distribution. We will show the dependence of ℳij on the spatial variability of the conductivity field, on the contaminant source size, on the travel time and on the grid-block scale. For an ergodic source, a statistically uniform conductivity field and very large grid blocks, ℳij is equal to the macrodispersion coefficients proposed by Dagan (J. Fluid Mech., vol. 145, 1984, p. 151) with zero variance. For an ergodic source and non-uniform conductivity field with a finite-size grid block, ℳij approaches the model proposed by Rubin et al. (J. Fluid Mech., vol. 395, 1999, p. 161). In both cases, ℳij is defined by its mean value with zero variance. ℳij is subject to uncertainty when the source is non-ergodic and when the grid block is defined by a finite scale. When the grid-block scale approaches zero, which means that the spatial variability is captured completely on the numerical grid, ℳij approaches zero with zero variance. In addition, we provide a complete statistical characterization of ℳij by invoking the concept of minimum relative entropy, thus providing upper bounds on the uncertainty associated with ℳij.

Cross-evaluation of measurements of peatland methane emissions on microform and ecosystem scales using high-resolution landcover classification and source weight modelling

The methane exchange in an oligotrophic mire complex was measured on the ecosystem and microform scale with the eddy covariance (EC) and the closed chamber technique, respectively. Information about the distribution of three distinct microform types in the area of interest and in each 30 min EC flux source area was derived from a high-resolution (1 m 2) landcover map in combination with an analytical source weight model ( Kormann and Meixner, 2001). The mean weighted coverage of flark, lawn and hummock microforms in the EC source area (0.3% : 57% : 43%) closely mirrors the overall distribution in the area of interest (0.5% : 50.1% : 49.4%), despite great differences in microform coverage between individual 30 min EC source areas. The measured ecosystem flux was fitted to the sum of three microform flux models based on environmental variables and weighted by their fractional coverage in the EC source area. This method resulted in a better representation of the ecosystem flux compared to an approach based on only one flux model for the whole ecosystem ( R 2 = 0.87, RMSE = 0.44 vs. R 2 = 0.74, RMSE = 0.61, n = 5181) and thus constitutes a successful down-scaling of measured ecosystem scale flux to the microform scale. A comparison of down-scaled and measured microform fluxes reveals a good agreement for lawn microforms and systematic differences for flark and hummock microforms. Reasons for the differences are thought to be the limited resolution of the landcover classification and the systematic underestimation of hummock fluxes by the closed chamber technique. As a result, hummock fluxes derived by down-scaling of EC fluxes are considered to be more dependable than closed chamber fluxes. The seasonal ecosystem methane budget from gap-filled EC measurements was 9.4 ± 0.2 g CH 4 m −2; the budget derived from up-scaled microform measurements was 8.0 ± 0.8 g CH 4 m −2. The lower value of the latter budget is attributed to the underestimation of flark and hummock fluxes by closed chamber measurements and to the microform gap-filling procedure. Generally, estimates from up-scaled microform measurements are found to be less certain than estimates from EC measurements.

Ekman heat transport for slab oceans

A series of schemes designed to include various representations of the Ekman-driven heat fluxes in slab-ocean models is introduced. They work by computing an Ekman mass flux, then deducing heat fluxes by the surface flow and an opposite deep return flow. The schemes differ by the computation of the return flow temperature: either diagnosed from the SST or given by an active second layer. Both schemes conserve energy, and use as few parameters as possible. Simulations in an aquaplanet setting show that the schemes reproduce well the structure of the meridional heat transport by the ocean. Compared to a diffusive slab-ocean, the simulated SST is more flat in the tropics, and presents a relative minimum at the equator, shifting the ITCZ into the summer hemisphere. In a realistic setting with continents, the slab model simulates correctly the mean state in many regions, especially in the tropics. The lack of other dynamical features, such as barotropic gyres, means that an optimal mean-state in regions such as the mid-latitudes will require additional flux corrections. © 2011 Springer-Verlag.

Improvement of Tone's Method with Two-Term Rational Approximation

An improvement of Tone's method, which is a resonance calculation method based on the equivalence theory, is proposed. In order to increase calculation accuracy, the two-term rational approximation is incorporated for the representation of neutron flux. Furthermore, some theoretical aspects of Tone's method, i.e., its inherent approximation and choice of adequate multigroup cross section for collision probability estimation, are also discussed. The validity of improved Tone's method is confirmed through a verification calculation in an irregular lattice geometry, which represents part of an LWR fuel assembly. The calculation result clarifies the validity of the present method.

Numerical Simulation of 3D Density Flow by an Improved EASM Model

Reynolds stress turbulence models are still an effective method to solve thermal density flow in reservoir. Presently, these turbulence models have extensive research and play an important role in the project. However, the pursuit of a more general, economic and accurate Reynolds stress model is still necessary for buoyant turbulent flow. In this paper, an improved explicit algebraic Reynolds stress model was established accounting for buoyancy. The tensor representation of the Reynolds stresses are divided into two parts, the former is composed of EASM derived by Wallin & Johansson (2000) and latter is the formulations of buoyant stress. In the derivation of explicit algebraic active scalar flux model, WWJ (Wikström, Wallin and Johansson, 2000) model only for explicit tensor representation of passive scalar flux is improved by affiliating external buoyancy effects terms. The current EASM is discretized on three-dimensional unstructured grids and compared with experimental data of 3D thermal density flow. The calculations show that the model yields better results than LAHM and LARM. In addition, EASM model also has good stability and relative economic calculation CPU time-consuming. The current model would be promising in hydraulic engineering and environmental engineering.

An assessment of the surface climate in the NCEP climate forecast system reanalysis

This paper analyzes surface climate variability in the climate forecast system reanalysis (CFSR) recently completed at the National Centers for Environmental Prediction (NCEP). The CFSR represents a new generation of reanalysis effort with first guess from a coupled atmosphere–ocean–sea ice–land forecast system. This study focuses on the analysis of climate variability for a set of surface variables including precipitation, surface air 2-m temperature (T2m), and surface heat fluxes. None of these quantities are assimilated directly and thus an assessment of their variability provides an independent measure of the accuracy. The CFSR is compared with observational estimates and three previous reanalyses (the NCEP/NCAR reanalysis or R1, the NCEP/DOE reanalysis or R2, and the ERA40 produced by the European Centre for Medium-Range Weather Forecasts). The CFSR has improved time-mean precipitation distribution over various regions compared to the three previous reanalyses, leading to a better representation of freshwater flux (evaporation minus precipitation). For interannual variability, the CFSR shows improved precipitation correlation with observations over the Indian Ocean, Maritime Continent, and western Pacific. The T2m of the CFSR is superior to R1 and R2 with more realistic interannual variability and long-term trend. On the other hand, the CFSR overestimates downward solar radiation flux over the tropical Western Hemisphere warm pool, consistent with a negative cloudiness bias and a positive sea surface temperature bias. Meanwhile, the evaporative latent heat flux in CFSR appears to be larger than other observational estimates over most of the globe. A few deficiencies in the long-term variations are identified in the CFSR. Firstly, dramatic changes are found around 1998–2001 in the global average of a number of variables, possibly related to the changes in the assimilated satellite observations. Secondly, the use of multiple streams for the CFSR induces spurious jumps in soil moisture between adjacent streams. Thirdly, there is an inconsistency in long-term sea ice extent variations over the Arctic regions between the CFSR and other observations with the CFSR showing smaller sea ice extent before 1997 and larger extent starting in 1997. These deficiencies may have impacts on the application of the CFSR for climate diagnoses and predictions. Relationships between surface heat fluxes and SST tendency and between SST and precipitation are analyzed and compared with observational estimates and other reanalyses. Global mean fields of surface heat and water fluxes together with radiation fluxes at the top of the atmosphere are documented and presented over the entire globe, and for the ocean and land separately.

Electromagnetic geophysics: Notes from the past and the road ahead

During the last century, electrical geophysics has been transformed from a simple resistivity method to a modern technology that uses complex data-acquisition systems and high-performance computers for enhanced data modeling and interpretation. Not only the methods and equipment have changed but also our ideas about the geoelectrical models used for interpretation have been modified tremendously. This paper describes the evolution of the conceptual and technical foundations of EM methods. It outlines a framework for further development, which should focus on multitransmitter and multireceiver surveys, analogous to seismic data-acquisition systems. Important potential topics of future research efforts are in the areas of multidimensional modeling and inversion, including a new approach to the formulation and understanding of EM fields based on flux and voltage representation, which corresponds well to geophysical experiments involving the measurement of voltage and flux of electric and magnetic fields.

Latent heat in soil heat flux measurements

The surface energy balance includes a term for soil heat flux. Soil heat flux is difficult to measure because it includes conduction and convection heat transfer processes. Accurate representation of soil heat flux is an important consideration in many modeling and measurement applications. Yet, there remains uncertainty about what comprises soil heat flux and how surface and subsurface heat fluxes are linked in energy balance closure. The objective of this study is to demonstrate the presence of a subsurface latent heat sink, which must be considered in order to accurately link subsurface heat fluxes between depths near and at the soil surface. Measurements were performed under effectively bare surface conditions in a silty clay loam soil near Ames, IA. Soil heat flux was measured with heat-pulse sensors using the gradient heat flux approach at 1-, 3-, and 6-cm soil depths. Independent estimates of the daily latent heat sink were obtained by measuring the change of mass of microlysimeters. Heat flux measurements at the 1-cm depth deviated from heat flux measurements at other depths, even after calorimetric adjustment was made. This deviation was most pronounced shortly after rainfall, where the 1-cm soil heat flux measurement exceeded 400 W m −2. Cumulative soil heat flux measurements at the 1-cm depth exceeded measurements at the 3-cm depth by >75% over a 7-day rain-free period, whereas calorimetric adjustment allowed 3- and 6-cm depth measurements to converge. Latent heat sink estimates from the microlysimeters accounted for nearly all of the differences between the 1- and 3-cm depth heat flux measurements, indicating that the latent heat sink was distributed between the 1- and 3-cm depths shortly after the rainfall event. Results demonstrate the importance of including latent heat when attempts are made to link or extrapolate subsurface soil heat flux measurements to the surface soil heat flux.