Derived Response Functions Research Articles

Spectral response between particle and fluid kinetic energy in decaying homogeneous isotropic turbulence

In particle-laden turbulence, the Fourier Lagrangian spectrum of each phase is regularly computed, and analytically derived response functions relate the Lagrangian spectrum of the fluid and the particle phase. However, due to the periodic nature of the Fourier basis, the analysis is restricted to statistically stationary flows. In the present work, utilizing the bases of time-focalized proper orthogonal decomposition (POD), this analysis is extended to temporally non-stationary turbulence. Studying two-way coupled particle-laden decaying homogeneous isotropic turbulence for various Stokes numbers, it is demonstrated that the temporal POD modes extracted from the dispersed phase may be used for the expansion of both fluid and particle velocities. The POD Lagrangian spectrum of each phase may thus be computed from the same set of modal building blocks, allowing the evaluation of response functions in a POD frame of reference. Based on empirical evaluations, a model for response functions in non-stationary flows is proposed. The related energies of the two phases is well approximated by simple analytical expressions dependent on the particle Stokes number. It is found that the analytical expressions closely resemble those derived through the Fourier analysis of statistically stationary flows. These results suggest the existence of an inherent spectral symmetry underlying the dynamical systems consisting of particle-laden turbulence, a symmetry which spans across stationary/non-stationary particle-laden flow states.

Exploring new strategies for ozone-risk assessment: A dynamic-threshold case study

Tropospheric ozone is a dangerous atmospheric pollutant for forest ecosystems when it penetrates stomata. Thresholds for ozone-risk assessment are based on accumulated stomatal ozone fluxes such as the Phytotoxic Ozone Dose (POD). In order to identify the effect of ozone on a Holm oak forest in central Italy, four flux-based ozone impact response functions were implemented and tested in a multi-layer canopy model AIRTREE and evaluated against Gross Primary Productivity (GPP) obtained from observations of Eddy Covariance fluxes of CO2. To evaluate if a clear phytotoxic threshold exists and if it changes during the year, six different detoxifying thresholds ranging between 0 and 5 nmol O3 m−2 s−1 were tested.The use of species-specific rather than more general response functions based on plant functional types (PFT) increased model accuracy (RMSE reduced by up to 8.5%). In the case of linear response functions, a threshold of 1 nmol m−2 s−2 produced the best results for simulations of the whole year, although the tolerance to ozone changed seasonally, with higher tolerance (5 nmol m−2 s−1 or no ozone impact) for Winter and Spring and lower thresholds in Summer and Fall (0–1 nmol m−2 s−1). A “dynamic threshold” obtained by extracting the best daily threshold values from a range of different simulations helped reduce model overestimation of GPP by 213 g C m−2 y−1 and reduce RMSE up to 7.7%. Finally, a nonlinear ozone correction based on manipulative experiments produced the best results when no detoxifying threshold was applied (0 nmol O3 m−2 s−1), suggesting that nonlinear functions fully account for ozone detoxification. The evidence of seasonal changes in ozone tolerance points to the need for seasonal thresholds to predict ozone damage and highlights the importance of performing more species-specific manipulative experiments to derive response functions for a broad range of plant species.

Kinetic energy density of nearly free electrons. I. Response functionals of the external potential

Free electrons have a uniform kinetic energy density (KED), which evolves into a spatially varying quantity as the electrons respond to the gradual imposition of an external potential. In this paper and a companion paper, we examine two sets of functionals for describing the local, non-negative KED that emerges after such a perturbation. In this paper, we emphasize potential functionals, deriving the first- and second-order deviations from the free-electron KED as functionals of the perturbing potential, also reconsidering the analogous functionals for the local density of states and the electron density. (In the second paper, we use these results to re-express the KED response in terms of functionals of the induced electron density.) We develop reciprocal-space formulations of the response kernels to complement previously known real-space forms. The first-order function is straightforward to obtain, but the second-order function requires considerable effort. To manage the derivations, we relate the KED response to that of the one-electron Green function, and then examine the latter in detail. Finally, we provide extensive validation of the derived response functions based on asymptotic analysis of an integral representation, numerical integration of the same generating integral, and application to the linear potential model.

Histologically derived fiber response functions for diffusion MRI vary across white matter fibers-An ex vivo validation study in the squirrel monkey brain.

Understanding the relationship between the diffusion-weighted MRI signal and the arrangement of white matter fibers is fundamental for accurate voxel-wise reconstruction of the fiber orientation distribution (FOD) and subsequent fiber tractography. Spherical deconvolution reconstruction techniques model the diffusion signal as the convolution of the FOD with a response function that represents the signal profile of a single fiber orientation. Thus, given the signal and a fiber response function, the FOD can be estimated in every imaging voxel by deconvolution. However, the selection of the appropriate response function remains relatively under-studied, and requires further validation. In this work, using 3D histologically defined FODs and the corresponding diffusion signal from three ex vivo squirrel monkey brains, we derive the ground truth response functions. We find that the histologically derived response functions differ from those conventionally used. Next, we find that response functions statistically vary across brain regions, which suggests that the practice of using the same kernel throughout the brain is not optimal. We show that different kernels lead to different FOD reconstructions, which in turn can lead to different tractography results depending on algorithmic parameters, with large variations in the accuracy of resulting reconstructions. Together, these results suggest there is room for improvement in estimating and understanding the relationship between the diffusion signal and the underlying FOD.

Electrons in GEO Measured With the ESA Multifunctional Spectrometer During the January 2014 SEP

The multifunctional spectrometer (MFS) is a radiation monitor installed on the X panel of the Alphasat satellite, in geostationary orbit (GEO) since July 2013. The MFS was specially tailored to characterize the space radiation environment in GEO and it is expected to acquire scientific data during a total lifetime of five years. An end-to-end Geant4 simulation of the MFS flight model based on the full geometry of the MFS, imported from computer-aided design (CAD) to geometry description markup language, was implemented and validated with the MFS ground-test results obtained in Paul Scherrer Institute facilities in 2010. The MFS simulation was then used to derive response functions for the MFS electron and proton channels. This paper describes the implementation of a maximum likelihood fit method to reconstruct particle spectra from MFS data, and its application to the reconstruction of the electron spectra for a 20-day period centered on the occurrence of January 2, 2014, solar energetic particle event. The obtained electron integral fluxes for this period are in reasonable agreement with GOES-15 public data and with the predictions of the AE8MIN update and IGE-2006 models.

A method for the direct measurement of electronic site populations in a molecular aggregate using two-dimensional electronic-vibrational spectroscopy

Two dimensional electronic spectroscopy has proved to be a valuable experimental technique to reveal electronic excitation dynamics in photosynthetic pigment-protein complexes, nanoscale semiconductors, organic photovoltaic materials, and many other types of systems. It does not, however, provide direct information concerning the spatial structure and dynamics of excitons. 2D infrared spectroscopy has become a widely used tool for studying structural dynamics but is incapable of directly providing information concerning electronic excited states. 2D electronic-vibrational (2DEV) spectroscopy provides a link between these domains, directly connecting the electronic excitation with the vibrational structure of the system under study. In this work, we derive response functions for the 2DEV spectrum of a molecular dimer and propose a method by which 2DEV spectra could be used to directly measure the electronic site populations as a function of time following the initial electronic excitation. We present results from the response function simulations which show that our proposed approach is substantially valid. This method provides, to our knowledge, the first direct experimental method for measuring the electronic excited state dynamics in the spatial domain, on the molecular scale.

Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers.

The Chladni nodal line patterns and resonant frequencies for a thin plate excited by an electronically controlled mechanical oscillator are experimentally measured. Experimental results reveal that the resonant frequencies can be fairly obtained by means of probing the variation of the effective impedance of the exciter with and without the thin plate. The influence of the extra mass from the central exciter is confirmed to be insignificant in measuring the resonant frequencies of the present system. In the theoretical aspect, the inhomogeneous Helmholtz equation is exploited to derive the response function as a function of the driving wave number for reconstructing experimental Chladni patterns. The resonant wave numbers are theoretically identified with the maximum coupling efficiency as well as the maximum entropy principle. Substituting the theoretical resonant wave numbers into the derived response function, all experimental Chladni patterns can be excellently reconstructed. More importantly, the dispersion relationship for the flexural wave of the vibrating plate can be determined with the experimental resonant frequencies and the theoretical resonant wave numbers. The determined dispersion relationship is confirmed to agree very well with the formula of the Kirchhoff-Love plate theory.

Ozone effects on wheat grain quality – A summary

We synthesized the effects of ozone on wheat quality based on 42 experiments performed in Asia, Europe and North America. Data were analysed using meta-analysis and by deriving response functions between observed effects and daytime ozone concentration. There was a strong negative effect on 1000-grain weight and weaker but significant negative effects on starch concentration and volume weight. For protein and several nutritionally important minerals (K, Mg, Ca, P, Zn, Mn, Cu) concentration was significantly increased, but yields were significantly decreased by ozone. For other minerals (Fe, S, Na) effects were not significant or results inconclusive. The concentration and yield of potentially toxic Cd were negatively affected by ozone. Some baking properties (Zeleny value, Hagberg falling number) were positively influenced by ozone. Effects were similar in different exposure systems and for spring and winter wheat. Ozone effects on quality should be considered in future assessments of food security/safety.

CO2 dose–response functions for wheat grain, protein and mineral yield based on FACE and open-top chamber experiments

Data from three Swedish open-top chamber and four German FACE experiments were combined to derive response functions for elevated CO2 (eCO2) effects on Cd, Zn, Mn, protein, grain yield, grain mass and grain number of wheat. Grain yield and grain number were increased by ∼6% and ∼7%, respectively, per 100 ppm CO2; the former effect was linked to plant nitrogen status. Grain mass was not influenced by eCO2, whereas Cd concentration was reduced. Unlike Zn, Mn and protein, effects on Cd yield were not related to effects on grain yield. Yields of Mn, Zn and (weakly) protein were positively affected by eCO2. For protein, grain yield, grain mass and grain number, the results were consistent among the FACE and OTC experiments. A key conclusion was that yields of essential nutrients were enhanced (Mn > Zn > protein), although less than grain yield, which would not be expected from a simple dilution model.

Systems biology. Conditional density-based analysis of T cell signaling in single-cell data.

Cellular circuits sense the environment, process signals, and compute decisions using networks of interacting proteins. To model such a system, the abundance of each activated protein species can be described as a stochastic function of the abundance of other proteins. High-dimensional single-cell technologies, such as mass cytometry, offer an opportunity to characterize signaling circuit-wide. However, the challenge of developing and applying computational approaches to interpret such complex data remains. Here, we developed computational methods, based on established statistical concepts, to characterize signaling network relationships by quantifying the strengths of network edges and deriving signaling response functions. In comparing signaling between naïve and antigen-exposed CD4(+) T lymphocytes, we find that although these two cell subtypes had similarly wired networks, naïve cells transmitted more information along a key signaling cascade than did antigen-exposed cells. We validated our characterization on mice lacking the extracellular-regulated mitogen-activated protein kinase (MAPK) ERK2, which showed stronger influence of pERK on pS6 (phosphorylated-ribosomal protein S6), in naïve cells as compared with antigen-exposed cells, as predicted. We demonstrate that by using cell-to-cell variation inherent in single-cell data, we can derive response functions underlying molecular circuits and drive the understanding of how cells process signals.

Combined treatment of relaxation and fluctuation dynamics in the calculation of two-dimensional electronic spectra.

While the theoretical description of population transfer subsequent to electronic excitation in combination with a line shape function description of vibrational dynamics in the context of 2D-spectroscopy is well-developed under the assumption of different timescales of population transfer and fluctuation dynamics, the treatment of the interplay between both kinds of processes lacks a comprehensive description. To bridge this gap, we use the cumulant expansion approach to derive response functions, which account for fluctuation dynamics and population transfer simultaneously. We compare 2D-spectra of a model system under different assumptions about correlations between fluctuations and point out under which conditions a simplified treatment is justified. Our study shows that population transfer and dissipative fluctuation dynamics cannot be described independent of each other in general. Advantages and limitations of the proposed calculation method and its compatibility with the modified Redfield description are discussed.

Optimizing production from water drive gas reservoirs based on desirability concept

There are various factors which determine the optimization and economic production from water drive gas reservoirs. These factors play an important role in designing an effective reservoir development plan. The present study, in the first step, investigates the relation between recovery factor, volumetric sweep efficiency and cumulative water production with six different engineering and geologic factors using design of experiments (DOE) and response surface methodology (RSM). Next, all derived response functions are optimized simultaneously based on the concept of desirability. In this manner, part of water drive gas reservoirs is simulated using Box–Behnken design. Important factors that have been studied include reservoir horizontal permeability (Kh), permeability anisotropy (Kv/Kh), aquifer size (Vaq), gas production rate (Qg), perforated thickness (Hp) and tubing head pressure (THP). The results indicate that by combining various levels of factors and considering relative importance of each response function, optimized conditions could be raised in order to maximizing recovery factor, volumetric sweep efficiency and minimizing cumulative water production. Also high rates of gas production result poor volumetric sweep efficiency and early water breakthrough, hence ultimate recovery factor decreases by 3.2–8.4%.

Stability Issues in Supply Chain Networks: Implications for Coordination Mechanisms

With supply chains evolving into complex networks of diverse and independent economic entities, supply chain coordination has emerged as a key management capability for improving overall performance of the network. For long term sustainability, it is important that such networks remain stable with little incentive for players to sever their linkages, especially in supply chains with participative constraints on their members. While topic of coordination has received vast attention from both academia and practitioners, the issues related to network stability have not been addressed adequately. In order to bridge this gap in the literature, we focus on a two tier supply chain network competing with independent producers. The network involves a marketing agent that coordinates activities among the network producers via a price and pro t sharing based coordination mechanism.We develop a (noncooperative) game theoretic model and analyze the impact of the coordination mechanism on stability of the network. In particular, we focus on three factors: cost parameters, number of producers vis-a-vis level of competition, and profit sharing. We derive response functions for the players involved and show that optimal decisions by coordination leads to Nash equilibrium for the supply chain. In addition, we develop structural results to characterize stability of the network. Our results show, that while profit sharing parameter of the coordination mechanism has no impact on network surplus, it has implications for network stability. These results bring out relationship between the factors of interest and provide insights for determining the decision parameters of the coordination mechanism.

Practical method to derive nonlinear response functions of cameras for scientific imaging

We developed a practical method to derive response functions that convert the amount of incident light to the counts of analog-to-digital conversion (A/D) of cameras for scientific imaging. In this method, we need a mechanism to accurately control the amount of incident light into cameras just within a limited dynamic range and at a limited number of steps. A variable brightness light source, which supplies the incident light into cameras, is also necessary, but we do not need to know its accurate brightness. Thus, this method enables us to derive the nonlinear response functions accurately with such a simple setup.

A density matrix-based quasienergy formulation of the Kohn–Sham density functional response theory using perturbation- and time-dependent basis sets

A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability.

Estimates of compression at low and high frequencies using masking additivity in normal and impaired ears.

Auditory compression was estimated at 250 and 4000 Hz by using the additivity of forward masking technique, which measures the effects on signal threshold of combining two temporally nonoverlapping forward maskers. The increase in threshold in the combined-masker condition compared to the individual-masker conditions can be used to estimate compression. The signal was a 250 or 4000 Hz tone burst and the maskers (M1 and M2) were bands of noise. Signal thresholds were measured in the presence of M1 and M2 alone and combined for a range of masker levels. The results were used to derive response functions at each frequency. The procedure was conducted with normal-hearing and hearing-impaired listeners. The results suggest that the response function in normal ears is similar at 250 and 4000 Hz with a mid level compression exponent of about 0.2. However, compression extends over a smaller range of levels at 250 Hz. The results confirm previous estimates of compression using temporal masking curves (TMCs) without assuming a linear off-frequency reference as in the TMC procedure. The impaired ears generally showed less compression. Importantly, some impaired ears showed a linear response at 250 Hz, providing a further indication that low-frequency compression originates in the cochlea.

Use of response functions in selecting lodgepole pine populations for future climates

AbstractAlthough growth response functions have previously been developed for lodgepole pine (Pinus contorta Dougl. ex Loud.) populations in British Columbia, new analyses were conducted: (1) to demonstrate the merit of a new local climate model in genecological analysis; (2) to highlight new methods for deriving response functions; and (3) to evaluate the impacts of management options for existing geographically defined seed planning units (SPUs) for reforestation. Results of this study suggest that new methods for anchoring population response functions, and a multivariate approach for incorporating climate variables into a single model, considerably improve the reliability of these functions. These functions identified a small number of populations in central areas of the species distribution with greater growth potential over a wide range of mean annual temperature (MAT). Average productivity of lodgepole pine is predicted to increase (up to 7%) if moderate warming (∼2°C MAT) occurs in the next few decades as predicted, although productivity would substantially decline in some SPUs in southern BC. Severe global warming (>3°C MAT) would result in either a drastic decline in productivity or local populations being extirpated in southern SPUs. New deployment strategies using the best seed sources for future reforestation may not only be able to mitigate the negative impact of global warming, but may even be able to increase productivity in some areas.

Response theory for vibrational wave functions

A formalism for deriving and implementing response functions for vibrational wave functions is described. The formalism utilizes a recently developed second-quantization formulation of many-mode dynamics to define nonredundant parameterizations for different types of approximate vibrational wave functions. The derived response functions cover the cases of an exact state, a vibrational self-consistent field state, and a vibrational configuration interaction state. Sample calculations are presented for the linear-response function and response excitation energies for a two-mode model system and for formaldehyde employing a quartic force field. The advantages and disadvantages of the response theoretical approach for describing excitation energies using different parameterizations are discussed.

Momentum conservation and local field corrections for the response of interacting fermi gases

We reanalyzed the recently derived response function for interacting systems in relaxation-time approximation respecting density, momentum, and energy conservation. We find that momentum conservation leads exactly to the local-field corrections for both cases respecting only density conservation and respecting density and energy conservation. This rewriting simplifies the former formulas dramatically. We discuss the small wave vector expansion and find that the response function shows a high-frequency dependence of omega(-5), which allows to fulfill higher-order sum rules. The momentum conservation also resolves a puzzle about the conductivity, which should only be finite in multicomponent systems.

Timescales of Land Surface Evapotranspiration Response

Abstract Soil and vegetation exert strong control over the evapotranspiration rate, which couples the land surface water and energy balances. A method is presented to quantify the timescale of this surface control using daily general circulation model (GCM) simulation values of evapotranspiration and precipitation. By equating the time history of evaporation efficiency (ratio of actual to potential evapotranspiration) to the convolution of precipitation and a unit kernel (temporal weighting function), response functions are generated that can be used to characterize the timescales of evapotranspiration response for the land surface model (LSM) component of GCMs. The technique is applied to the output of two multiyear simulations of a GCM, one using a Surface-Vegetation-Atmosphere-Transfer (SVAT) scheme and the other a Bucket LSM. The derived response functions show that the Bucket LSM’s response is significantly slower than that of the SVAT across the globe. The analysis also shows how the timescales of i...