Analytical Parameterization Research Articles

The energy loss and nuclear absorption effects in semi-inclusive deep inelastic scattering on nucleus

Semi-inclusive deep inelastic lepton-nucleus scattering provides a good opportunity to investigate the cold nuclear effects on quark propagation and hadronization. Considering the nuclear modification of the quark energy loss and nuclear absorption effects in final state, the leading-order computations on hadron multiplicity ratios for both hadronization occurring outside and inside the medium are performed with the nuclear geometry effect of the path length L of the struck quark in the medium. By fitting the HERMES two-dimensional data on the multiplicity ratios for positively and negatively charged pions and kaons produced on neon, the hadron–nucleon inelastic cross section for different identified hadrons is determined, respectively. It is found that our predictions obtained with the analytic parameterizations of quenching weights based on BDMPS formalism and the nuclear absorption factor are in good agreement with the experimental measurements. This indicates that the energy loss and nuclear absorption are the main nuclear effects inducing a reduction of the hadron yield for quark hadronization occurring outside and inside the nucleus, respectively.

Evaluation of a scattering correction method for high energy tomography

One of the main drawbacks of Cone Beam Computed Tomography (CBCT) is the contribution of the scattered photons due to the object and the detector. Scattered photons are deflected from their original path after their interaction with the object. This additional contribution of the scattered photons results in increased measured intensities, since the scattered intensity simply adds to the transmitted intensity. This effect is seen as an overestimation in the measured intensity thus corresponding to an underestimation of absorption. This results in artifacts like cupping, shading, streaks etc. on the reconstructed images. Moreover, the scattered radiation provides a bias for the quantitative tomography reconstruction (for example atomic number and volumic mass measurement with dual-energy technique). The effect can be significant and difficult in the range of MeV energy using large objects due to higher Scatter to Primary Ratio (SPR). Additionally, the incident high energy photons which are scattered by the Compton effect are more forward directed and hence more likely to reach the detector. Moreover, for MeV energy range, the contribution of the photons produced by pair production and Bremsstrahlung process also becomes important. We propose an evaluation of a scattering correction technique based on the method named Scatter Kernel Superposition (SKS). The algorithm uses a continuously thickness-adapted kernels method. The analytical parameterizations of the scatter kernels are derived in terms of material thickness, to form continuously thickness-adapted kernel maps in order to correct the projections. This approach has proved to be efficient in producing better sampling of the kernels with respect to the object thickness. This technique offers applicability over a wide range of imaging conditions and gives users an additional advantage. Moreover, since no extra hardware is required by this approach, it forms a major advantage especially in those cases where experimental complexities must be avoided. This approach has been previously tested successfully in the energy range of 100 keV – 6 MeV. In this paper, the kernels are simulated using MCNP in order to take into account both photons and electronic processes in scattering radiation contribution. We present scatter correction results on a large object scanned with a 9 MeV linear accelerator.

Influence of a West Antarctic mantle plume on ice sheet basal conditions

AbstractThe possibility that a deep mantle plume manifests Pliocene and Quaternary volcanism and potential elevated heat flux in West Antarctica has been studied for more than 30 years. Recent seismic images support the plume hypothesis as the cause of Marie Byrd Land (MBL) volcanism and geophysical structure. Mantle plumes may more than double the geothermal heat flux above nominal continental values. A dearth of in situ ice sheet basal data exists that samples the heat flux. Consequently, we examine a realistic distribution of heat flux associated with a possible late Cenozoic mantle plume in West Antarctica and explore its impact on thermal and melt conditions at the ice sheet base. We use a simple analytical mantle plume parameterization to produce geothermal heat flux at the base of the ice sheet. The three‐dimensional ice flow model includes an enthalpy framework and full‐Stokes stress balance. As both the putative plume location and extent are uncertain, we perform broadly scoped experiments to characterize the impact of the plume on geothermal heat flux and ice sheet basal conditions. The experiments show that mantle plumes have an important local impact on the ice sheet, with basal melting rates reaching several centimeters per year directly above the hotspot. In order to be consistent with observations of basal hydrology in MBL, the upper bound on the plume‐derived geothermal heat flux is 150 mW/m2. In contrast, the active lake system of the lower part of Whillans Ice Stream suggests a widespread anomalous mantle heat flux, linked to a rift source.

Parameterization of the Aerosol Upscatter Fraction as Function of the Backscatter Fraction and Their Relationships to the Asymmetry Parameter for Radiative Transfer Calculations

Simple analytical approximations for aerosol radiative forcing generally contain the aerosol upscatter fraction (the fraction of scattered light that is scattered into the upper hemisphere), while ambient measurements generally yield the backscatter fraction, and theoretical calculations of scattering phase functions often yield the asymmetry parameter. Therefore, simple analytical relationships and parameterizations relating these three parameters are very valuable for radiative transfer calculations. Here, we review published parameterizations, mostly based on the Henyey-Greenstein phase function, and evaluate their goodness and range of validity. In addition, we give new parameterizations that are valid over the full range of backscatter fractions that are possibly encountered in the ambient atmosphere (i.e., 0 to 0.5).

Monte Carlo Electron Track Structure Calculations in Liquid Water Using a New Model Dielectric Response Function.

Monte Carlo track structure codes provide valuable information for understanding radiation effects down to the DNA level, where experimental measurements are most difficult or unavailable. It is well recognized that the performance of such codes, especially at low energies and/or subcellular level, critically depends on the reliability of the interaction cross sections that are used as input in the simulation. For biological media such as liquid water, one of the most challenging issues is the role of condensed-phase effects. For inelastic scattering, such effects can be conveniently accounted for through the complex dielectric response function of the media. However, for this function to be useful it must fulfill some important sum rules and have a simple analytic form for arbitrary energy- and momentum-transfer. The Emfietzoglou-Cucinotta-Nikjoo (ECN) model offers a practical, self-consistent and fully analytic parameterization of the dielectric function of liquid water based on the best available experimental data. An important feature of the ECN model is that it includes, in a phenomenological manner, exchange and correlation effects among the screening electrons, thus, going beyond the random-phase approximation implicit in earlier models. In this work, inelastic cross sections beyond the plane wave Born approximation are calculated for low-energy electrons (10 eV-10 keV) based on the ECN model, and used for Monte Carlo track structure simulations of physical quantities relevant to the microdosimetry of low-energy electrons in liquid water. Important new developments in the physics of inelastic scattering are discussed and their effect on electron track structure is investigated by a comparison against simulations (under otherwise identical conditions) using the Born approximation and a simpler form of the dielectric function based on the Oak Ridge National Laboratory model. The results reveal that both the dielectric function and the corrections to the Born approximation may have a sizeable effect on track structure calculations at the nanometer scale (DNA level), where the details of inelastic scattering and the role of low-energy electrons are most critical.

Bed Shear Stresses Parameterization in Wave–Current Interaction by k − ω Turbulence Model

For a flow generated by the wave–current interaction (WCI), an accurate estimate of the maximum ([Formula: see text]) and the mean ([Formula: see text]) bed shear stresses is important for the sediment transport calculation. These two parameters are usually estimated by numerical modeling which can prove to be difficult to implement and very costly in CPU time. This paper then proposes analytic parameterization of [Formula: see text] and [Formula: see text] by simple relationship depending on the current and wave shear stresses ([Formula: see text] and [Formula: see text]).The proposed parameterization was performed in two steps: the first step is to build a numerical database of [Formula: see text] and [Formula: see text] for different combinations of flow variables. This step was carried out by an one-dimensional vertical (1DV) model of turbulent bottom boundary layer using the [Formula: see text] turbulence model. The second step is to represent this database by predefined analytical relations. This step was performed by an optimization procedure adopting the GlobalSearch (GS) (function of Matlab software).The proposed parameterization based on the “[Formula: see text]/GS” combination provides very good estimations of [Formula: see text] and [Formula: see text]. These estimations are similar to those proposed by other authors who have studied the WCI by analytical models widely used by the marine science community.

A Resilient Approach to Distributed Filter Design for Time-Varying Systems Under Stochastic Nonlinearities and Sensor Degradation

This paper is concerned with the distributed filtering problem for a class of discrete time-varying systems with stochastic nonlinearities and sensor degradation over a finite horizon. A two-step distributed filter algorithm is proposed where the sensor nodes collaboratively estimate the states of the plant by exploiting the information from both the local and the neighboring nodes. The goal of this paper is to design the distributed filters over a wireless sensor network subject to given sporadic communication topology. Moreover, a resilient operation is guaranteed to suppress random perturbations on the actually implemented filter gains. An upper bound is first derived for the filtering error covariance by utilizing an inductive method and such an upper bound is subsequently minimized via iteratively solving a quadratic optimization problem. To account for the topological information of the sensor networks, a novel matrix simplification technique is utilized to preserve the sparsity of the gain matrices in accordance with the given topology, and the analytical parameterization is obtained for the gain matrices of the desired suboptimal filter. Furthermore, a sufficient condition is established to guarantee the mean-square boundedness of the estimation errors. Numerical simulation is carried out to verify the effectiveness of the proposed filtering algorithm.

Stellar electron capture rates on neutron-rich nuclei and their impact on stellar core collapse

During the late stages of gravitational core-collapse of massive stars, extreme isospin asymmetries are reached within the core. Due to the lack of microscopic calculations of electron capture (EC) rates for all relevant nuclei, in general simple analytic parameterizations are employed. We study here several extensions of these parameterizations, allowing for a temperature, electron density and isospin dependence as well as for odd-even effects. The latter extra degrees of freedom considerably improve the agreement with large scale microscopic rate calculations. We find, in particular, that the isospin dependence leads to a significant reduction of the global EC rates during core collapse with respect to fiducial results, where rates optimized on calculations of stable $fp$-shell nuclei are used. Our results indicate that systematic microscopic calculations and experimental measurements in the $N\approx 50$ neutron rich region are desirable for realistic simulations of the core-collapse.

Temperature parameters in the fragmentation of carbon ions at the energy of 0.6 GeV/nucleon

Momentum distributions of nuclear fragments at an angle of 3.5° in the interaction of 0.6-GeV/nucleon carbon ions with a beryllium target are measured in the FRAGM experiment on the ITEP-TWAC facility. The measured spectra are used for testing predictions of four ion–ion interaction models: BC, QMD, INCL, and LAQGSM03.03, and for comparison with the analytical parameterization within the thermodynamic concept of fragmentation.

A generalized description of the signal size in extensive air shower detectors and its applications

The number as well as the energy and angular distributions of particles in extensive air showers (EAS) depend on the stage of the shower development and the distance to the shower axis. In this work we derive an analytic parameterization of the particle distributions at ground from air shower simulations convolved with the response of a surface detector array. Shower particles are classified into four components according to the shower component they belong to: the muonic component, the electromagnetic component stemming from muon interactions and muon decay, the purely electromagnetic component, and the newly introduced electromagnetic component from low-energy hadrons. Using this scheme, we will show that the total signal at ground level for different surface detectors can be described with minimal fluctuations with parameterizations depending on the primary energy, position of the shower maximum, and the overall number of muons in the shower. The simulation results for different combinations of primaries and hadronic interaction models are reproduced with an accuracy better than 5–10% in the range from 100 m to 2000 m from the shower core. This parameterization is then used as a Lateral Distribution ansatz to reconstruct showers in current EAS experiments. Since this ansatz depends on physical parameters, it opens the possibility to infer them from data.

Large eddy simulations and parameterisation of roughness element orientation and flow direction effects in rough wall boundary layers

ABSTRACTWe conduct a series of large eddy simulations (LES) of turbulent boundary layers over arrays of cuboidal roughness elements at arbitrary orientation angles (non-frontal orientations with the incident flow). Flow response to changing roughness orientation is systematically studied at two ground coverage densities, λp = 0.06 and 0.11. As expected, the effective roughness heights zo measured from LES are higher for λp = 0.11 than for λp = 0.06, although appreciable changes both in zo and wall shear stress (friction velocity) are observed at both ground coverage densities as the roughness orientation angle changes. This suggests the necessity of accounting for detailed rough wall topology (including more information than just λp, λf) when relating rough wall morphology to its aerodynamic properties. To this end, a recently developed analytical rough wall parameterisation is used to predict the aerodynamic properties of the simulated rough surfaces. In this rough wall model, wake interactions among roughness elements are explicitly modelled using the concept of sheltering height and exponential attenuation coefficient. As a result, the parameterisation is responsive to detailed ground roughness arrangements and flow conditions, including roughness height variations, element orientation, incident flow direction, transverse displacements, etc. Model-predicted effective roughness heights, wall stress, mean velocity at the height of the roughness, and in some cases displacement height, are compared against the LES measurements from this study as well as numerical/experiment measurements from other authors. The predictions from the model are found to agree well with the measurements both in trends and in absolute values, thus extending the applicability of the analytical rough wall model to more general surfaces than those previously tested.

SU-G-TeP1-02: Analytical Stopping Power and Range Parameterization for Therapeutic Energy Intervals

Purpose: To develop a simple, analytic parameterization of stopping power and range, which covers a wide energy interval and is applicable to many species of projectile ions and target materials, with less than 15% disagreement in linear stopping power and 1 mm in range. Methods: The new parameterization was required to be analytically integrable from stopping power to range, and continuous across the range interval of 1 µm to 50 cm. The model parameters were determined from stopping power and range data for hydrogen, carbon, iron, and uranium ions incident on water, carbon, aluminum, lead and copper. Stopping power and range data was taken from SRIM. A stochastic minimization algorithm was used to find model parameters, with 10 data points per energy decade. Additionally, fitting was performed with 2 and 26 data points per energy decade to test the model's robustness to sparse Results: 6 free parameters were sufficient to cover the therapeutic energy range for each projectile ion species (e.g. 1 keV – 300 MeV for protons). The model agrees with stopping power and range data well, with less than 9% relative stopping power difference and 0.5 mm difference in range. As few as, 4 bins per decade were required to achieve comparable fitting results to the full data set. Conclusion: This study successfully demonstrated that a simple analytic function can be used to fit the entire energy interval of therapeutic ion beams of hydrogen and heavier elements. Advantages of this model were the small number (6) of free parameters, and that the model calculates both stopping power and range. Applications of this model include GPU-based dose calculation algorithms and Monte Carlo simulations, where available memory is limited. This work was supported in part by a research agreement between United States Naval Academy and Louisiana State University: Contract No N00189-13-P-0786. In addition, this work was accepted for presentation at the American Nuclear Society Annual Meeting 2016.

Exploring central opacity and asymptotic scenarios in elastic hadron scattering

In the absence of a global description of the experimental data on elastic and soft diffractive scattering from the first principles of QCD, model-independent analyses may provide useful phenomenological insights for the development of the theory in the soft sector. With that in mind, we present an empirical study on the energy dependence of the ratio X between the elastic and total cross sections; a quantity related to the evolution of the hadronic central opacity. The dataset comprises all the experimental information available on proton–proton and antiproton–proton scattering in the c.m. energy interval 5 GeV–8 TeV. Generalizing previous works, we discuss four model-independent analytical parameterizations for X, consisting of sigmoid functions composed with elementary functions of the energy and three distinct asymptotic scenarios: either the standard black disk limit or scenarios above or below that limit. Our two main conclusions are the following: (1) although consistent with the experimental data, the black disk does not represent an unique solution; (2) the data reductions favor a semi-transparent scenario, with asymptotic average value for the ratio X¯=0.30±0.12. In this case, within the uncertainty, the asymptotic regime may already be reached around 1000 TeV. We present a comparative study of the two scenarios, including predictions for the inelastic channel (diffraction dissociation) and the ratio associated with the total cross-section and the elastic slope. Details on the selection of our empirical ansatz for X and physical aspects related to a change of curvature in this quantity at 80–100 GeV, indicating the beginning of a saturation effect, are also presented and discussed.

MONTE CARLO STUDY OF THE CARDIAC ABSORBED DOSE DURING X-RAY EXAMINATION OF AN ADULT PATIENT.

The computational voxel phantom 'High-Definition Reference Korean-Man (HDRK-Man)' was implemented into the Monte Carlo transport toolkit Geant4. The voxel model, adjusted to the Reference Korean Man, is 171 cm in height and 68 kg in weight and composed of ∼30 million voxels whose size is 1.981 × 1.981 × 2.0854 mm3 The Geant4 code is then utilised to compute the dose conversion coefficients (DCCs) expressed in absorbed dose per air kerma free in air for >30 tissues and organs, including almost all organs required in the new recommendation of the ICRP 103, due to a broad parallel beam of monoenergetic photons impinging in antero-postero direction with energy ranging from 10 to 150 keV. The computed DCCs of different organs are found to be in good agreement with data published using other simulation codes. Also, the influence of patient size on DCC values was investigated for a representative body size of the adult Korean patient population. The study was performed using five different sizes covering the range of 0.8-1.2 magnification order of the original HDRK-Man. It focussed on the computation of DCC for the human heart. Moreover, the provided DCCs were used to present an analytical parameterisation for the calculation of the cardiac absorbed dose for any arbitrary X-ray spectrum and for those patient sizes. Thus, the present work can be considered as an enhancement of the continuous studies performed by medical physicist as part of quality control tests and radiation protection dosimetry.

The small and the beautiful: how the star formation law affects galactic disc structure

We investigate the influence of different analytical parameterizations and fit functions for the local star formation rate in AMR simulations of an isolated disk galaxy with the Nyx code. Such parameterizations express the star formation efficiency as function of the local turbulent Mach number and virial parameter. By employing the method of adaptively refined large eddy simulations, we are able to evaluate these physical parameters from the numerically unresolved turbulent energy associated with the grid scale. We consider both single and multi free-fall variants of star formation laws proposed by Padoan & Nordlund, Hennebelle & Chabrier, and Krumholz & McKee, summarised and tested recently with numerical simulations by Federrath & Klessen. We find that the global star formation rate and the relation between the local star formation rate and the gas column density is reproduced in agreement with observational constraints by all multi free-fall models of star formation. Some models with obsolete calibration or a single free-fall time scale, however, result in an overly clumpy disk that does not resemble the structure of observed spirals.

Analytical parametrization of self-consistent polycrystal mechanics: Fast calculation of upper mantle anisotropy

Progressive deformation of upper mantle rocks via dislocation creep causes their constituent crystals to take on a non-random orientation distribution (crystallographic preferred orientation or CPO) whose observable signatures include shear-wave splitting and azimuthal dependence of surface wave speeds. Comparison of these signatures with mantle flow models thus allows mantle dynamics to be unraveled on global and regional scales. However, existing self-consistent models of CPO evolution are computationally expensive when used in 3-D and/or time-dependent convection models. Here we propose a new method, called ANPAR, which is based on an analytical parameterisation of the crystallographic spin predicted by the second-order (SO) self-consistent theory. Our parameterisation runs approximately 2-3 x 10^4 times faster than the SO model and fits its predictions for CPO and crystallographic spin with a variance reduction > 99%. We illustrate the ANPAR model predictions for three uniform deformations (uniaxial compression, pure shear, simple shear) and for a corner-flow model of a spreading ridge.

Nuclear geometry effect and transport coefficient in semi-inclusive lepton-production of hadrons off nuclei

Hadron production in semi-inclusive deep-inelastic scattering of leptons from nuclei is an ideal tool to determine and constrain the transport coefficient in cold nuclear matter. The leading-order computations for hadron multiplicity ratios are performed by means of the SW quenching weights and the analytic parameterizations of quenching weights based on BDMPS formalism. The theoretical results are compared to the HERMES positively charged pions production data with the quarks hadronization occurring outside the nucleus. With considering the nuclear geometry effect on hadron production, our predictions are in good agreement with the experimental measurements. The extracted transport parameter from the global fit is shown to be qˆ=0.74±0.03 GeV2/fm for the SW quenching weight without the finite energy corrections. As for the analytic parameterization of BDMPS quenching weight without the quark energy E dependence, the computed transport coefficient is qˆ=0.20±0.02 GeV2/fm. It is found that the nuclear geometry effect has a significant impact on the transport coefficient in cold nuclear matter. It is necessary to consider the detailed nuclear geometry in studying the semi-inclusive hadron production in deep inelastic scattering on nuclear targets.

The radio emission pattern of air showers as measured with LOFAR—a tool for the reconstruction of the energy and the shower maximum

The pattern of the radio emission of air showers is finely sampled with the Low-Frequency ARray (LOFAR). A set of 382 measured air showers is used to test a fast, analytic parameterization of the distribution of pulse powers. Using this parameterization we are able to reconstruct the shower axis and give estimators for the energy of the air shower as well as the distance to the shower maximum.

A theory of ventilation estimate over hypothetical urban areas

Urban roughness is a major factor governing the flows and scalar transport in the atmospheric boundary layer (ABL) but our understanding is rather limited. The ventilation and pollutant removal of hypothetical urban areas consisting of various types of street canyons are examined using computational fluid dynamics (CFD). The aerodynamic resistance, ventilation efficiency, and pollutant removal are measured by the friction factor f, air exchange rate (ACH), and pollutant exchange rate (PCH), respectively. Two source configurations of passive tracer, ground-level-only (Tracer 0) and all-solid-boundary (Tracer 1) are employed to contrast their transport behavior. It is found that the ventilation and pollutant removal are largely attributed to their turbulent components (over 60%). Moreover, with a consistent support from analytical solution and CFD results, the turbulent ACH is a linear function of the square root of the friction factor (ACH′∝f1/2) regardless of building geometry. Tracer 0 and Tracer 1 exhibit diversified removal behavior as functions of friction factor so analytical parameterizations have not yet been developed. In view of the large portion of aged air removal by turbulence, it is proposed that the aerodynamic resistance can serve as an estimate to the minimum ventilation efficiency of urban areas.

PT-symmetry-induced wave confinement and guiding inε-near-zero metamaterials

Inspired by the parity-time symmetry concept, we show that a judicious spatial modulation of gain and loss in epsilon-near-zero metamaterials can induce the propagation of exponentially-bound interface modes characterized by zero attenuation. With specific reference to a bi-layer configuration, via analytical studies and parameterization of the dispersion equation, we show that this waveguiding mechanism can be sustained in the presence of moderate gain/loss levels, and it becomes leaky (i.e., radiative) below a gain/loss threshold. Moreover, we explore a possible rod-based metamaterial implementation, based on realistic material constituents, which captures the essential features of the waveguiding mechanism, in good agreement with our theoretical predictions. Our results may open up new possibilities for the design of optical devices and reconfigurable nanophotonics platforms.