Analytical Response Functions Research Articles

Unfolding of mono-energy neutron spectra using artificial neural network based on LMBP training algorithm

In this work, neutron spectra are unfolded using artificial neural networks (ANNs). The neutron response of the NE213 scintillator detector, characterized by the pulse height distribution, is calculated to obtain the necessary data for unfolding the energy spectrum. This is achieved using both analytical response functions and response functions generated by the MCNPX-PHOTRACK code. In this query, the Levenberg-Marquardt method (LMM), which has a high computational speed in the learning method, is used to train the network. The performance of the ANN for unfolding the neutron energy spectrum of the NE213 scintillation detector was evaluated by comparing its results to the established Gravel method. The ANN method consistently produced spectra with a single peak closely matching the incident energy, while the Gravel method showed additional peaks and distortions. Quantitative analysis revealed a lower relative energy peak difference (indicating higher accuracy) for the ANN method compared to Gravel, particularly when noise was introduced into the data. These results suggest that ANNs offer a more robust and accurate approach for neutron spectrum unfolding.

DeSIRe: Departure coefficient aided Stokes Inversion based on Response functions

Future ground-based telescopes, such as the 4-metre class facilities DKIST and EST, will dramatically improve on current capabilities for simultaneous multi-line polarimetric observations in a wide range of wavelength bands, from the near-ultraviolet to the near-infrared. As a result, there will be an increasing demand for fast diagnostic tools, i.e., inversion codes, that can infer the physical properties of the solar atmosphere from the vast amount of data these observatories will produce. The advent of substantially larger apertures, with the concomitant increase in polarimetric sensitivity, will drive an increased interest in observing chromospheric spectral lines. Accordingly, pertinent inversion codes will need to take account of line formation under general non-local thermodynamic equilibrium (NLTE) conditions. Several currently available codes can already accomplish this, but they have a common practical limitation that impairs the speed at which they can invert polarised spectra, namely that they employ numerical evaluation of the so-called response functions to changes in the atmospheric parameters, which makes them less suitable for the analysis of very large data volumes. Here we present DeSIRe (Departure coefficient aided Stokes Inversion based on Response functions), an inversion code that integrates the well-known inversion code SIR with the NLTE radiative transfer solver RH. The DeSIRe runtime benefits from employing analytical response functions computed in local thermodynamic equilibrium (through SIR), modified with fixed departure coefficients to incorporate NLTE effects in chromospheric spectral lines. This publication describes the operating fundamentals of DeSIRe and describes its behaviour, robustness, stability, and speed. The code is ready to be used by the solar community and is being made publicly available.

Analytical modeling of the neutron response function of the NE213 organic liquid scintillator in the energy range of 0.2 MeV to 148 MeV

Determination of the neutron response function is essential for measuring the energy of neutrons emitted from natural and artificial neutron sources and nuclear reactions. This paper presents the calculation procedure of generating a neutron analytical response function for NE213 scintillation detectors in the energy range of 0.2–148 MeV. To obtain the analytical response function, the available neutron experimental response functions were grouped according to their behavior in different energy ranges. Different analytical functions were fitted to the experimental data of the detector response function for each neutron energy range. The function which best fits the experimental data was selected. Then a computer program was written for calculating the parameters of the analytical function by using the fitting functions and their parameters for each desired energy, and generating the analytical response functions. A comparison of the results shows that the analytical response functions are much faster and more consistent with the experimental response functions than the generated response functions of stand-alone codes and general-purpose Monte Carlo codes.

Model-based monitoring of temperatures and heat flows in the milling cutter

The quantification of the heat flow distribution in the cutting zone is still an unsolved problem from an analytical as well as experimental perspective. Yet the heat flows into the tool and the time-variant temperature fields in the tool significantly influence the tool wear rate. This publication shows the results of a model extended measuring approach in order to monitor as well as investigate heat flows and their partitioning in the milling process under dry conditions. Therefore, the cutting power in the process was measured by means of a dynamometer as well as the temperature in the tool by an embedded thermocouple. The time response of the embedded thermocouple was accounted by an analytical time response function. By further data post processing of the temperature, the heat flow into the tool was inversely determined by comparison of the measured temperature trend at a distinct point with an analytically modeled, transient temperature as a solution of the heat conduction equations by a Green’s function. As input into the analytical model, an iteratively determined partition of the measured time-variant cutting power signal was used. The results showed a decreasing heat partition into the tool with rising cutting velocity. The introduced approach is a valuable tool not only to determine the heat partition in the milling process but also to understand and monitor the comprehensive thermo-mechanical conditions in the cutting zone. Understanding and monitoring thermo-mechanical conditions in the cutting process finally enable the exploitation of economic and ecologic process potentials.

Modeling the evolution of pulse-like perturbations in atmospheric carbon and carbon isotopes: the role of weathering–sedimentation imbalances

Abstract. Measurements of carbon isotope variations in climate archives and isotope-enabled climate modeling advance the understanding of the carbon cycle. Perturbations in atmospheric CO2 and in its isotopic ratios (δ13C, Δ14C) are removed by different processes acting on different timescales. We investigate these differences on timescales of up to 100 000 years in pulse-release experiments with the Bern3D-LPX Earth system model of intermediate complexity and by analytical solutions from a box model. On timescales from years to many centuries, the atmospheric perturbations in CO2 and δ13CO2 are reduced by air–sea gas exchange, physical transport from the surface to the deep ocean, and by the land biosphere. Isotopic perturbations are initially removed much faster from the atmosphere than perturbations in CO2 as explained by aquatic carbonate chemistry. On multimillennial timescales, the CO2 perturbation is removed by carbonate compensation and silicate rock weathering. In contrast, the δ13C perturbation is removed by the relentless flux of organic and calcium carbonate particles buried in sediments. The associated removal rate is significantly modified by spatial δ13C gradients within the ocean, influencing the isotopic perturbation of the burial flux. Space-time variations in ocean δ13C perturbations are captured by principal components and empirical orthogonal functions. Analytical impulse response functions for atmospheric CO2 and δ13CO2 are provided. Results suggest that changes in terrestrial carbon storage were not the sole cause for the abrupt, centennial-scale CO2 and δ13CO2 variations recorded in ice during Heinrich stadials HS1 and HS4, though model and data uncertainties prevent a firm conclusion. The δ13C offset between the Penultimate Glacial Maximum and Last Glacial Maximum reconstructed for the ocean and atmosphere is most likely caused by imbalances between weathering, volcanism, and burial fluxes. Our study highlights the importance of isotopic fluxes connected to weathering–sedimentation imbalances, which so far have been often neglected on glacial–interglacial timescales.

Multispectral incoherent holography based on measurement of differential wavefront curvature

We propose a technique of multispectral incoherent holography. The differential wavefront curvature is measured, and the principle of Fourier transform spectrometry is applied to provide a set of spectral components of three-dimensional images and continuous spectra for spatially incoherent, polychromatic objects. This paper presents the mathematical formulation of the principle and the experimental results. Three-dimensional imaging properties are investigated based on an analytical impulse response function. The experimental and theoretical results agree well.

Noise-induced chaos and signal detection by the nonisochronous Hopf oscillator.

The Hopf oscillator has been shown to capture many phenomena of the auditory and vestibular systems. These systems exhibit remarkable temporal resolution and sensitivity to weak signals, as they are able to detect sounds that induce motion in the angstrom regime. In the present work, we find the analytic response function of a nonisochronous Hopf oscillator to a step stimulus and show that the system is most sensitive in the regime where noise induces chaotic dynamics. We show that this regime also provides a faster response and enhanced temporal resolution. Thus, the system can detect a very brief, low-amplitude pulse. Finally, we subject the oscillator to periodic delta-function forcing, mimicking a spike train, and find the exact analytic expressions for the stroboscopic maps. Using these maps, we find a period-doubling cascade to chaos with increasing force strength.

Arbitrary order exceptional point induced by photonic spin\u2013orbit interaction in coupled resonators

Many novel properties of non-Hermitian systems are found at or near the exceptional points—branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce. In particular, higher-order exceptional points can result in optical structures that are ultrasensitive to external perturbations. Here we show that an arbitrary order exceptional point can be achieved in a simple system consisting of identical resonators placed near a waveguide. Unidirectional coupling between any two chiral dipolar states of the resonators mediated by the waveguide mode leads to the exceptional point, which is protected by the transverse spin–momentum locking of the guided wave and is independent of the positions of the resonators. Various analytic response functions of the resonators at the exceptional points are experimentally manifested in the microwave regime. The enhancement of sensitivity to external perturbations near the exceptional point is also numerically and analytically demonstrated.

Various Response Functions in Lattice Domes Reliability Via Analytical Integration and Finite Element Method

The main aim of this work is to verify an influence of the response function type in direct symbolic derivation of the probabilistic moments and coefficients of the structural state variables of axisymmetric spherical steel dome structures. The second purpose is to compare four various types of domes (ribbed, Schwedler, geodesic as well as diamatic) in the context of time-independent reliability assessment in the presence of an uncertainty in the structural steel Young modulus. We have considered various analytical response functions to approximate fundamental eigenfrequencies, critical load multiplier, global extreme vertical and horizontal displacements as well as local deformations. Particular values of the reliability indices calculated here can be of further assistance in the reliability assessment by comparing the minimal one with its counterpart given in the Eurocode depending upon the durability class, reference period and the given limit state type.

Theoretical analysis of angular distribution of scattering in nozzle components using a response-function method for proton spot-scanning therapy

In spot-scanning proton therapy, highly precise beam control is required in the treatment nozzle such that the proton beam does not spread out during transportation by restraining the divergence of the beam angle and spot size, simultaneously. In order to evaluate the beam-broadening behaviour induced by passing through the various nozzle components, we have developed a new method to calculate the angular divergence profile of a proton beam in the nozzle. The angular divergence of the proton beam for each nozzle component is calculated by the Monte Carlo simulation code, Geant4, assuming that the initial beam has no divergence. The angular divergence profiles generated in the various nozzle components are then fitted by the analytic function formula with triple Gaussian distributions. The fitted profiles can be treated like analytic response functions and the angular divergence profile in the nozzle can be easily and systematically calculated by using a convolution theorem. The beam-broadening behaviour during transportation in the nozzle is carefully evaluated. The beam profiles are well-characterized by the proposed angular divergence analysis, i.e. triple Gaussian profile analysis. The primary Gaussian part of the beam profile is mainly generated by air and dose monitors with plate electrode components. The secondary and tertiary Gaussian parts are so-called wide-angle scattering and generated mainly by spot-position and profile monitors with metal window and wire components. The scattering of the nozzle component can be analysed using the proposed response function method for the angular distribution. Multiple convolved angular scattering can be determined from the response function of the individual nozzle components. The angular distribution from small to large angle regions can then be quantitatively evaluated by the proposed method. The method is quite simple and generalized, and is a straightforward way to understand the nozzle and component characteristics related to the beam-broadening behaviour.

Generalised relative and cumulative response functions for electromagnetic induction conductivity meters operating at low induction numbers

ABSTRACTRelative and cumulative analytical response functions have been widely used as a powerful tool for forward modelling and interpretation of measurements obtained by electromagnetic induction conductivity meters operating at low induction numbers for one‐dimensional layered earth models. These well‐known functions were derived and should be used for the instruments laid on the surface of the earth. In this paper, we extended the response functions and obtained new generalised analytical expressions, which can be used for instruments carried at any height from the surface. The proposed new equations were compared with numerically constructed functions, obtained using the full solution of Maxwell's equations, and proved to be in very good agreement at low induction numbers. Quantitative analyses of the behaviour of the relative response and the depth of investigation of electromagnetic induction instruments, when raised from the ground, could also be done using the generalised functions.

A time-series analysis framework for the flood-wave method to estimate groundwater model parameters

The flood-wave method is implemented within the framework of time-series analysis to estimate aquifer parameters for use in a groundwater model. The resulting extended flood-wave method is applicable to situations where groundwater fluctuations are affected significantly by time-varying precipitation and evaporation. Response functions for time-series analysis are generated with an analytic groundwater model describing stream–aquifer interaction. Analytical response functions play the same role as the well function in a pumping test, which is to translate observed head variations into groundwater model parameters by means of a parsimonious model equation. An important difference as compared to the traditional flood-wave method and pumping tests is that aquifer parameters are inferred from the combined effects of precipitation, evaporation, and stream stage fluctuations. Naturally occurring fluctuations are separated in contributions from different stresses. The proposed method is illustrated with data collected near a lowland river in the Netherlands. Special emphasis is put on the interpretation of the streambed resistance. The resistance of the streambed is the result of stream-line contraction instead of a semi-pervious streambed, which is concluded through comparison with the head loss calculated with an analytical two-dimensional cross-section model.

3D spatial resolution and spectral resolution of interferometric 3D imaging spectrometry.

Recently developed interferometric 3D imaging spectrometry (J. Opt. Soc. Am A18, 765 [2001]1084-7529JOAOD610.1364/JOSAA.18.000765) enables obtainment of the spectral information and 3D spatial information for incoherently illuminated or self-luminous object simultaneously. Using this method, we can obtain multispectral components of complex holograms, which correspond directly to the phase distribution of the wavefronts propagated from the polychromatic object. This paper focuses on the analysis of spectral resolution and 3D spatial resolution in interferometric 3D imaging spectrometry. Our analysis is based on a novel analytical impulse response function defined over four-dimensional space. We found that the experimental results agree well with the theoretical prediction. This work also suggests a new criterion and estimate method regarding 3D spatial resolution of digital holography.

Prediction of tonal ducted fan noise

This study introduces an analytical model aiming at predicting the tonal acoustic sources generated and radiated by the rotor–stator interaction in a fan stage. This model is able to cope with complex three-dimensional stator geometries and it fully accounts for cascade effects, characteristic of modern fan stages. It is based on a proper description of the rotor wake coupled with an analytic cascade response function and with an acoustic analogy. The proposed model is validated for the first time against acoustic sources and sound power measurements, on the Advanced Noise Control Fan from NASA. On this configuration representative of an actual fan stage, the model is shown to predict tonal sources and powers accurately, in function of the rotational velocity and of the stator-vane count. Another realistic configuration, namely the low-pressure CME2 research compressor, is then considered in order to demonstrate the suitability of the model to be used as a design tool in an industrial context. A parametric study concerning both the stator vane sweep and lean angles is performed on this rotor–stator stage. The model produces predictions consistent with studies from literature, quantifying the effectiveness of swept and leaned vanes as a tonal noise reduction mechanism. This parametric study allows defining an optimal stator design for minimal noise emission.

Preliminary measurements of the Bremsstrahlung doubly differential cross section for electrons between 20 and 100 keV in Au

SynopsisElectron Bremsstrahlung cross sections were experimentally determined, for five kinetic energies, unfolding the measured photon spectra with an analytical detector response function.

A PET detector prototype based on digital SiPMs and GAGG scintillators

Silicon Photomultipliers (SiPM) are interesting light sensors for Positron Emission Tomography (PET). The detector signal of analog SiPMs is the total charge of all fired cells. Energy and time information have to be determined with dedicated readout electronics. Philips Digital Photon Counting has developed a SiPM with added electronics on cell level delivering a digital value of the time stamp and number of fired cells. These so called Digital Photon Counters (DPC) are fully digital devices. In this study, the feasibility of using DPCs in combination with LYSO (Lutetium Yttrium Oxyorthosilicate) and GAGG (Gadolinium Aluminum Gallium Garnet) scintillators for PET is tested. Each DPC module has 64 channels with 3.2 × 3.8775 mm2, comprising 3200 cells each. GAGG is a recently developed scintillator (Zeff = 54, 6.63 g cm−3, 520 nm peak emission, 46 000 photons MeV−1, 88 ns (92%) and 230 ns (8%) decay times, non-hygroscopic, chemically and mechanically stable). Individual crystals of 2 × 2 × 6 mm3 were coupled onto each DPC pixel. LYSO coupled to the DPC results in a coincidence time resolution (CTR) of 171 ps FWHM and an energy resolution of 12.6% FWHM at 511 keV. Using GAGG, coincidence timing is 310 ps FWHM and energy resolution is 8.5% FWHM. A PET detector prototype with 2 DPCs equipped with a GAGG array matching the pixel size (3.2 × 3.8775 × 8 mm3) was assembled. To emulate a ring of 10 modules, objects are rotated in the field of view. CTR of the PET is 619 ps and energy resolution is 9.2% FWHM. The iterative MLEM reconstruction is based on system matrices calculated with an analytical detector response function model. A phantom with rods of different diameters filled with 18F was used for tomographic tests.

Two-dimensional Fourier transform electronic spectroscopy at a conical intersection

We report measurement and modeling of two-dimensional (2D) electronic spectra of a silicon naphthalocyanine (SiNc) in benzonitrile, a system for which the polarization anisotropy reveals passage through a square-symmetric Jahn-Teller conical intersection in ∼100 fs [D. A. Farrow, W. Qian, E. R. Smith, A. A. Ferro, and D. M. Jonas, J. Chem. Phys. 128, 144510 (2008)]. The measured 2D Fourier transform (FT) spectra indicate loss of electronic coherence on a similar timescale. The 2D spectra arising from femtosecond vibronic dynamics through the conical funnel are modeled by full non-adiabatic treatment of the coupled electronic and vibrational dynamics for a pair of un-damped Jahn-Teller active vibrations responsible for both electronic decoherence and population transfer. Additional damped Jahn-Teller active modes that can cause only decoherence or population transfer are treated with analytical response functions that can be incorporated into the numerical non-adiabatic calculation by exploiting symmetry assignment of degenerate vibronic eigenstates to one of two electronic states. Franck-Condon active totally symmetric modes are incorporated analytically. The calculations reveal that these conical intersection dynamics alone are incapable of destroying the coherence of the initially prepared wavepacket on the experimentally observed timescale and predict an unobserved recurrence in the photon echo slice at ∼200 fs. Agreement with the experimental two-dimensional electronic spectra necessitates a role for totally symmetric vibrational dynamics in causing the echo slice to decay on a ∼100 fs timescale. This extended model also reproduces the ∼100 fs ultrafast electronic anisotropy decay in SiNc when an "asymmetric solvation mode" with a small stabilization energy of ∼2 cm(-1) is included. Although calculations show that inhomogeneities in the energy gap between excited states can broaden the anti-diagonal 2D lineshape, the anti-diagonal width is dominated by totally symmetric vibrational motions in SiNc. For this shallow conical intersection, the non-adiabatic dynamics destroy electronic coherence more slowly than they destroy electronic alignment.

Development and evaluation of a LOR-based image reconstruction with 3D system response modeling for a PET insert with dual-layer offset crystal design

In this study we present a method of 3D system response calculation for analytical computer simulation and statistical image reconstruction for a magnetic resonance imaging (MRI) compatible positron emission tomography (PET) insert system that uses a dual-layer offset (DLO) crystal design. The general analytical system response functions (SRFs) for detector geometric and inter-crystal penetration of coincident crystal pairs are derived first. We implemented a 3D ray-tracing algorithm with 4π sampling for calculating the SRFs of coincident pairs of individual DLO crystals. The determination of which detector blocks are intersected by a gamma ray is made by calculating the intersection of the ray with virtual cylinders with radii just inside the inner surface and just outside the outer-edge of each crystal layer of the detector ring. For efficient ray-tracing computation, the detector block and ray to be traced are then rotated so that the crystals are aligned along the X-axis, facilitating calculation of ray/crystal boundary intersection points. This algorithm can be applied to any system geometry using either single-layer (SL) or multi-layer array design with or without offset crystals. For effective data organization, a direct lines of response (LOR)-based indexed histogram-mode method is also presented in this work. SRF calculation is performed on-the-fly in both forward and back projection procedures during each iteration of image reconstruction, with acceleration through use of eight-fold geometric symmetry and multi-threaded parallel computation. To validate the proposed methods, we performed a series of analytical and Monte Carlo computer simulations for different system geometry and detector designs. The full-width-at-half-maximum of the numerical SRFs in both radial and tangential directions are calculated and compared for various system designs. By inspecting the sinograms obtained for different detector geometries, it can be seen that the DLO crystal design can provide better sampling density than SL or dual-layer no-offset system designs with the same total crystal length. The results of the image reconstruction with SRFs modeling for phantom studies exhibit promising image recovery capability for crystal widths of 1.27–1.43 mm and top/bottom layer lengths of 4/6 mm. In conclusion, we have developed efficient algorithms for system response modeling of our proposed PET insert with DLO crystal arrays. This provides an effective method for both 3D computer simulation and quantitative image reconstruction, and will aid in the optimization of our PET insert system with various crystal designs.

Design optimization of magnetorheological fluid valves using response surface method

A new design optimization methodology for the optimal design of a single-coil annular magnetorheological valve constrained in a specific volume inside a magnetorheological damper has been presented in this article. The methodology combines the finite element model, with the design of experiments and response surface techniques in order to develop approximate response surface functions for the magnetic field intensity across the activation length of a magnetorheological valve orifice with respect to identified design variables. The accuracy of the developed response surface functions over the entire design space has been verified. The developed analytical response functions have then been used in Bingham plastic model, which is based on the steady behavior of a magnetorheological fluid in order to derive the field-dependent performance functions of the magnetorheological damper, which can be effectively used in the design optimization problems. The design optimization problem has been formulated for single- and multiobjective performance functions using sequential quadratic programming technique and the genetic algorithm to find the global optimum geometrical parameters of the magnetorheological valve. Finally, a proportional–integral–derivative controller has been designed to evaluate the closed-loop performance of the optimally designed magnetorheological valve confined in a magnetorheological damper used in a quarter-car suspension model.

On the use of an analytical cascade response function to predict sound transmission through an annular cascade

The present study aims at developing and assessing an analytical model for the sound transmission through an annular stator row in a configuration without mean flow. The model reformulates a three-dimensional annular model dedicated to turbulence interaction noise to deal with the case of an incident acoustic mode of an annular duct. It is a strip theory approach coupled with a previously published analytical formulation for the unsteady vane loading in a rectilinear cascade. Three formulations are developed on the basis of different definitions of the incident acoustic waves impinging on the rectilinear cascade. The latter are designed to match most of the properties of the incident mode in the annular case. The formulations are compared with a finite element method solution and with a rectilinear cascade model in configurations with no mean flow. The benchmarks consist in four annular ducts from very high (0.98) to moderate (0.5) hub-to-tip ratio containing a possibly staggered annular cascade. The frequency and the radial mode order of the incident mode are varied. Both pressure field and pressure coefficients are compared.