Atomic response function.
Response functions of atoms, excited in external field of given frequency and of wavelength larger than atomic dimensions
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Response functions of atoms, excited in external field of given frequency and of wavelength larger than atomic dimensions
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Here, we present calculations of the 40 Ca transverse response function obtained from coupled-cluster theory used in conjunction with the Lorentz integral transform method. We employ nuclear forces derived at next-to-next-to leading order in chiral effective field theory with and without Δ degrees of freedom. We first benchmark this approach on the 4 He nucleus and compare both the transverse sum rule and the response function to earlier calculations based on different methods. As expected from the power counting of the chiral expansion of electromagnetic currents and from previous studies, our results retaining only one-body term underestimate the experimental data for 4 He by about 20%. However, when the method is applied to 40 Ca at the same order of the expansion, response functions do not lack strength and agree well with the world electron scattering data. We discuss various sources of theoretical uncertainties and comment on the comparison of our results with the available experiments.
We apply the linear response function method to investigate the most excitable mode of the September Arctic sea ice and its corresponding remote oceanic forcing in climate models. The method is useful in identifying the fundamental, dynamical and causal relationship between the remote forcing and sea ice response. We find that the most excitable mode of the September Arctic sea ice preferentially takes place over the Pacic side of the Arctic and its remote forcing corresponds to a dipole pattern of precipitation anomaly in the tropics with an increase of precipitation over the western and central tropical and subtropical Pacic ocean while a decrease over the Maritime Continent. The tropical precipitation anomaly likely drives a Rossby wave train propagating toward higher latitudes and leads to a ridge anomaly over the Pacic side of the Arctic, resulting in poleward atmospheric heat transport, enhanced downward longwave radiation and thus melting of the sea ice. In addition, a good agreement is found with the leading tropical Arctic teleconnection mode detected in a pre-industrial control simulation, which supports the usefulness and robustness of the linear response function method and the importance of tropical forcing in shaping the sea ice variability.
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Response functions of quantum systems, such as electron Green’s functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and quantum computing and measured directly in experiment. Further, response functions are intrinsically causal. In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain. Since response functions define an inner product on a Hilbert space and thereby induce a positive definite function, the properties of this function can be used to reduce noise in measured data and, in equilibrium and steady state, to construct positive definite extensions for data known on finite time intervals, which are then guaranteed to correspond to positive spectra.
Many computer models output functional data, and in some cases, these functional data have similar, but misaligned, shape characteristics. In this paper, we introduce a general approach for building emulators for computer models that output misaligned functional data when key values in the functional response (landmarks) can be easily identified. This approach has two main parts: modeling the aligned (using the landmarks) functional data, and modeling the functions that map the misaligned data to the aligned space (warping functions). As the warping functions are required to be monotonic, we give special attention to modeling monotonic functional response data. We discuss how our approach can be easily applied for a variety of typical emulators, such as Gaussian processes, Bayesian multivariate adaptive regression splines, and Bayesian additive regression trees, and how sensitivity analysis can be performed. We demonstrate our approach by building emulators for two applications: (1) a high-energy-density physics computer model used to simulate inertial confinement fusion ignition experiments, where model outputs are highly misaligned, and (2) a multiphysics continuum hydrocode used to simulate high-velocity impact experiments, where model outputs are only slightly misaligned. In case (1) traditional methods cannot be applied, while in (2) they can be applied, but the proposed method performs significantly better.
The ability of center/surround response functions to make explicit high resolution spatial information in optical images was investigated by performing convolutions of two dimensional response functions and image intensity functions (mainly edges). The center/surround function was found to have the unique property of separating edge contrast from shape variations and of providing a direct basis for determining contrast and subsequently shape of edges in images. Computationally simple measures of contrast and shape were constructed for potential use in cybernetic vision systems. For one class of response functions these measures were found to be reasonably resilient for a range of scan direction and displacements of the response functions relative to shaped edges. A pathological range of scan directions was also defined and methods for detecting and handling these cases were developed. The relationship of these results to biological vision is discussed speculatively.
Abstract How predators respond to changes in prey abundance (i.e., functional responses) is foundational to consumer–resource interactions, predator–prey dynamics, and the stability of predator–prey systems. Predation by piscivorous waterbirds on out‐migrating juvenile steelhead trout ( Oncorhynchus mykiss ) is considered a factor affecting the recovery of multiple Endangered Species Act‐listed steelhead populations in the Columbia River basin. Waterbird functional responses, however, may vary by predator species and location, with important implications to predator management strategies. We used a 13‐year dataset on waterbird abundance across seven breeding colonies (three Caspian tern [ Hydroprogne caspia ], two double‐crested cormorant [ Nannopterum auritum ], and two California and ring‐billed gull [ Larus californicus and Larus delawarensis ] colonies) and steelhead tag‐recovery data (>645,000 tagged and >32,000 recovered steelhead) to quantify weekly predation probabilities and functional responses across waterbird species, colonies, and years. Weekly predation probabilities were highly variable, ranging from 0.01 to 0.30 at tern colonies, 0.01 to 0.20 at cormorant colonies, and 0.03 to 0.13 at gull colonies. Per capita predation probabilities were an order of magnitude higher at inland tern and cormorant colonies relative to estuary colonies of the same species. Terns displayed Type II functional responses across colonies and years, where predation probabilities peaked at low steelhead abundances and declined as steelhead abundance increased (i.e., predator swamping). Cormorants nesting at the large estuary colony (several thousand birds) displayed a Type III functional response, but cormorants nesting at the smaller inland colony (several hundred birds) displayed a Type II response. Consumption probabilities of steelhead by gulls remained consistent across a large range of steelhead availability, suggesting a Type I or a Type III functional response, but a lack of colony abundance data prevented quantifying functional responses. The level of tern predation combined with Type II functional responses indicate possible population‐level impacts that could destabilize small or declining prey populations. Conversely, the apparent Type III functional responses of gulls and estuary nesting cormorants are indicative of prey switching behaviors targeted at periods of high steelhead abundance. Our results illustrate the complexity of predator–prey interactions and the importance of quantifying predator‐ and location‐specific functional responses when predicting the efficacy of management strategies to enhance prey populations.
The hybrid stochastic deterministic transport code COMET, based on the incident response expansion theory, is used to model reactor cores with high fidelity and formidable computational speed. COMET models a reactor core using a library of incident flux response expansion coefficients that are pre computed for all the unique lattice cells (e.g., fuel assemblies, reflector blocks, etc.) in the core. In order to further improve its computational efficiency in pre-calculating the response library a new response function generation method is developed to compute the response functions for the composite coarse meshes made of a smaller set of unique lattices on the fly within the COMET's deterministic transport core sweep. The efficiency is achieved by eliminating a number of unique lattices that can be made up from the reduced set of unique meshes on the fly. The numerical process consists of the following steps. First, the boundary condition on composite coarse mesh boundaries is projected onto the expansion basis to compute the incident flux moments on external surfaces of all the basic (reduced set of unique) coarse meshes. Secondly, the deterministic sweeping solver in COMET is used to converge on the outgoing/incoming flux expansion moments crossing interfaces between the basic coarse meshes. Thirdly, the response functions for the composite coarse meshes are constructed as a superposition on the fly. The new response function generation method was tested on 88 composite coarse meshes consisting of CANDU fuel bundles and moderator blocks. It was found that response functions generated by the new method agree very well with those generated by direct Monte Carlo calculations. The average and maximum relative differences in the surface-to-surface response coefficients computed by the two methods are 0.10% and 0.20%, respectively. Similarly, the average and maximum relative differences in the response fission densities are 0.13% and 0.43%, respectively. These discrepancies are within one standard deviation of the stochastic uncertainties. The new method is five times faster than the original direct Monte Carlo method. The size of the response function library for the new method is five times smaller than that for the original method, leading to significantly less requirement for the computer hard drive space and memory. (authors)
Response functions are a key quantity to describe the near-equilibrium dynamics of strongly interacting many-body systems. Recent techniques that attempt to overcome the challenges of calculating these ab initio have employed expansions in terms of orthogonal polynomials. We employ a neural network prediction algorithm to reconstruct a response function 𝑆(𝜔) defined over a range in frequencies 𝜔. Here, we represent the calculated response function as a truncated Chebyshev series whose coefficients can be optimized to reduce the representation error. We compare the quality of response functions obtained using coefficients calculated using a neural network (NN) algorithm with those computed using the Gaussian integral transform (GIT) method. In the regime where only a small number of terms in the Chebyshev series are retained, we find that the NN scheme outperforms the GIT method.
Imaginary-time response functions of finite-temperature quantum systems are often obtained with methods that exhibit stochastic or systematic errors. Reducing these errors comes at a large computational cost—in quantum Monte Carlo simulations, the reduction of noise by a factor of two incurs a simulation cost of a factor of four. In this paper, we relate certain imaginary-time response functions to an inner product on the space of linear operators on Fock space. We then show that data with noise typically does not respect the positive definiteness of its associated Gramian. The Gramian has the structure of a Hankel matrix. As a method for denoising noisy data, we introduce an alternating projection algorithm that finds the closest positive definite Hankel matrix consistent with noisy data. We test our methodology at the example of fermion Green's functions for continuous-time quantum Monte Carlo data and show remarkable improvements of the error, reducing noise by a factor of up to 20 in practical examples. We argue that Hankel projections should be used whenever finite-temperature imaginary-time data of response functions with errors is analyzed, be it in the context of quantum Monte Carlo, quantum computing, or in approximate semianalytic methodologies. Published by the American Physical Society 2024
The radiation effects community needs clear, well-documented, neutron energy-dependent responses that can be used in assessing radiation-induced material damage to GaAs semiconductors and for correlating observed radiation-induced changes in the GaAs electronic properties with computed damage metrics. In support of the objective, this document provides: a) a clearly defined set of relevant neutron response functions for use in dosimetry applications; b) clear mathematical expressions for the defined response functions; and c) updated quantitative values for the energy- dependent response functions that reflect the best current nuclear data and modelling. This document recaps the legacy response functions. It then surveys the latest nuclear data and updates the recommended response function to support current GaAs damage studies. A detailed tabulation for six of the energy-dependent response functions is provided in an Appendix.
Recent work has shown that it is possible to circumvent the calculation of the spectral density and directly generate the coefficients of the discretized influence functionals using data from classical trajectory simulations. However, the accuracy of this procedure depends on the validity of the high temperature approximation. In this work, an alternative derivation based on the Kubo formalism is provided. This enables the calculation of additional correction terms that increases the range of applicability of the procedure to lower temperatures. Because it is based on the Kubo-transformed correlation function, this approach allows the direct use of correlation functions obtained from methods such as ring-polymer molecular dynamics and centroid molecular dynamics in determining the influence functional coefficients for subsequent system-solvent simulations. The accuracy of the original procedure and the corrected procedure is investigated across a range of parameters. It is interesting that the correction term comes at zero additional cost. Furthermore, it is possible to improve upon the correction using zero-cost physical intuition and heuristics making the method even more accurate.
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We use large datasets from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) to derive AIRS spatial response functions and study their potential variations over the mission. The new reconstructed spatial response functions can be used to reduce errors in the radiances in non-uniform scenes and improve products generated using both AIRS and MODIS data. AIRS spatial response functions are distinct for each of its 2378 channels and each of its 90 scan angles. We develop the mathematical model and the optimization framework for deriving spatial response functions for two AIRS channels with low water vapor absorption and various scan angles. We quantify uncertainties in the derived reconstructions and study how they differ from pre-flight spatial response functions. We show that our approach generates reconstructions that agree with the data more accurately compared to pre-flight spatial responses. We derive spatial response functions using data collected during successive dates in order to ascertain the repeatability of the reconstructed spatial response functions. We also compare the derived spatial response functions based on data collected in the beginning, the middle, and at the current state of the mission in order to study changes in reconstructions over time.
In this study, we have extended the detector response function toolkit (DRiFT) to provide modeling capabilities of semiconductor sensors. DRiFT provides realistic nuclear instrumentation response by post-processing Monte-Carlo N-particle (MCNP®) radiation transport outputs. MCNP® is capable of modeling radiation transport in complex environments, but has limited detector physics and readout electronics modeling capabilities. Semiconductor detector response can be calculated with a high-fidelity for a flexible range of environments by utilizing MCNP® to simulate radiation interactions inside of detector volumes, and then using DRiFT to model charge transport and signal formation in the semiconductor, as well as the readout electronics. DRiFT models charge transport in the semiconductor, the preamplifier, shaping amplifier, pulse pile-up, and electronic noise to generate detector response. The semiconductor application in DRiFT can model a range of semiconductor materials, shapes, and sizes; and is demonstrated here for a large volume coaxial high-purity germanium (HPGe) detector. Here, we compare detector response functions of a coaxial HPGe detector with measurement of 60 Co, 133 Ba, and 137 Cs at varying count rates, and we conduct a parameter study to demonstrate the effect of changing parameters in the DRiFT simulation. The HPGe detector response function shows excellent agreement with measurements of difference sources with varying dead times and count rates.
An empirical response function model was developed for ammonium perchlorate propellants to supplant T-burner testing at the preliminary design stage. The model was developed by fitting a limited T-burner data base, in terms of oxidizer size and concentration, to an analytical two parameter response function expression. Multiple peaks are predicted, but the primary effect is of a single peak for most formulations, with notable bulges for the various AP size fractions. The model was extended to velocity coupling with the assumption that dynamic response was controlled primarily by the solid phase described by the two parameter model. The magnitude of velocity coupling was then scaled using an erosive burning law. Routine use of the model for stability predictions on a number of propulsion units indicates that the model tends to overpredict propellant response. It is concluded that the model represents a generally conservative prediction tool, suited especially for the preliminary design stage when T-burner data may not be readily available. The model work included development of a rigorous summation technique for pseudopropellant properties and of a concept for modeling ordered packing of particulates.