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At least 1,711 records · Page 95

Technical Note: Impact of the geometry dependence of the ion chamber detector response function on a convolution-based method to address the volume averaging effect

Purpose: To investigate the geometry dependence of the detector response function (DRF) of three commonly used scanning ionization chambers and its impact on a convolution-based method to address the volume averaging effect (VAE). Methods: A convolution-based approach has been proposed recently to address the ionization chamber VAE. It simulates the VAE in the treatment planning system (TPS) by iteratively convolving the calculated beam profiles with the DRF while optimizing the beam model. Since the convolved and the measured profiles are subject to the same VAE, the calculated profiles match the implicit “real” ones when the optimization converges. Three DRFs (Gaussian, Lorentzian, and parabolic function) were used for three ionization chambers (CC04, CC13, and SNC125c) in this study. Geometry dependent/independent DRFs were obtained by minimizing the difference between the ionization chamber-measured profiles and the diode-measured profiles convolved with the DRFs. These DRFs were used to obtain eighteen beam models for a commercial TPS. Accuracy of the beam models were evaluated by assessing the 20%–80% penumbra width difference (PWD) between the computed and diode-measured beam profiles. Results: The convolution-based approach was found to be effective for all three ionization chambers with significant improvement for all beam models. Up to 17% geometry dependence of the three DRFs was observed for the studied ionization chambers. With geometry dependent DRFs, the PWD was within 0.80 mm for the parabolic function and CC04 combination and within 0.50 mm for other combinations; with geometry independent DRFs, the PWD was within 1.00 mm for all cases. When using the Gaussian function as the DRF, accounting for geometry dependence led to marginal improvement (PWD < 0.20 mm) for CC04; the improvement ranged from 0.38 to 0.65 mm for CC13; for SNC125c, the improvement was slightly above 0.50 mm. Conclusions: Although all three DRFs were found adequate to represent the response of the studied ionization chambers, the Gaussian function was favored due to its superior overall performance. The geometry dependence of the DRFs can be significant for clinical applications involving small fields such as stereotactic radiotherapy.

60 APPLIED LIFE SCIENCES↗

New Mathematical Functions for Vacuum System Analysis

A new bivariate function has been found that provides solutions of integrals having the form u (sup minus eta) e (sup u) du which arise when developing predictions for the behavior of pressure within a rigid volume under high vacuum conditions in the presence of venting as well as sources characterized by power law transient decay over the range [0,1] for eta and for u greater than or equal to 0. A few properties of the new function are explored in this work. For instance the eta equals 1/2 case reproduces the Dawson function. In addition, a slight variation of the solution technique reproduces the exponential integral for eta equals 1. The technique used to generate these functions leads to an approach for solving a more general class of nonlinear ordinary differential equations, with the potential for identifying other new functions that solve other integrals.

Dawson Function↗

Linking plant functional trait plasticity and the large increase in forest water use efficiency

Elevated atmospheric CO 2 concentrations are anticipated to enhance photosynthesis and reduce stomatal conductance, thus increasing plant water use efficiency. A recent study based on eddy covariance flux observations from Northern Hemisphere forests showed a large increase in inherent water use efficiency (IWUE). Here we used an updated version of the same data set and robust uncertainty quantification to revisit these contemporary IWUE trends. We tested the hypothesis that the observed IWUE increase could be attributed to interannual trends in plant functional traits, potentially triggered by environmental change. We postulate that IWUE increased by ~1.3% yr -1 , which is less than previously reported but still larger than theoretical expectations. Numerical simulations with the Tethys-Chloris ecosystem model using temporally static plant functional traits cannot explain this increase. Simulations with plant functional trait plasticity, i.e., temporal changes in model parameters such as specific leaf area and maximum Rubisco capacity, match the observed trends in IWUE. Our results show that trends in plant functional traits, equal to 1.0% yr -1 , can explain the observed IWUE trends. Thus, at decadal or longer time scales, trait plasticity could potentially influence forest water, carbon, and energy fluxes with profound implications for both the monitoring of temporal changes in plant functional traits and their representation in Earth system models.

59 BASIC BIOLOGICAL SCIENCES↗

Versatile Surface Functionalization of Metal-Organic Frameworks through Direct Metal Coordination with a Phenolic Lipid Enables Diverse Applications

A novel strategy for the versatile functionalization of the external surface of metal-organic frameworks (MOFs) has been developed based on the direct coordination of a phenolic-inspired lipid molecule DPGG (1,2-dipalmitoyl-sn-glycero-3-galloyl) with metal nodes/sites surrounding MOF surface. X-ray diffraction and Argon sorption analysis prove that the modified MOF particles retain their structural integrity and porosity after surface modification. Density functional theory calculations reveal that strong chelation strength between the metal sites and the galloyl head group of DPGG is the basic prerequisite for successful coating. Due to the pH-responsive nature of metal-phenol complexation, the modification process is reversible by simple washing in weak acidic water, showing an excellent regeneration ability for water-stable MOFs. Moreover, the colloidal stability of the modified MOFs in the nonpolar solvent allows them to be further organized into 2 dimensional MOF or MOF/polymer monolayers by evaporation-induced interfacial assembly conducted on an air/water interface. Lastly, the easy fusion of a second functional layer onto DPGG-modified MOF cores, enabled a series of MOF-based functional nanoarchitectures, such as MOFs encapsulated within hybrid supported lipid bilayers (so-called protocells), polyhedral core-shell structures, hybrid lipid-modified-plasmonic vesicles and multicomponent supraparticles with target functionalities, to be generated. for a wide range of applications.

36 MATERIALS SCIENCE↗

Functional Materials Under Stress: In Situ TEM Observations of Structural Evolution

The operating conditions of functional materials usually involve varying stress fields, resulting in structural changes, whether intentional or undesirable. Complex multiscale microstructures including defects, domains, and new phases, can be induced by mechanical loading in functional materials, providing fundamental insight into the deformation process of the involved materials. On the other hand, these microstructures, if induced in a controllable fashion, can be used to tune the functional properties or to enhance certain performance. In situ nanomechanical tests conducted in scanning/transmission electron microscopes (STEM/TEM) provide a critical tool for understanding the microstructural evolution in functional materials. In our study, select results on a variety of functional material systems in the field are presented, with a brief introduction into some newly developed multichannel experimental capabilities to demonstrate the impact of these techniques.

36 MATERIALS SCIENCE↗

Potential and limitations of inferring ecosystem photosynthetic capacity from leaf functional traits

Abstract The aim of this study was to systematically analyze the potential and limitations of using plant functional trait observations from global databases versus in situ data to improve our understanding of vegetation impacts on ecosystem functional properties ( EFP s). Using ecosystem photosynthetic capacity as an example, we first provide an objective approach to derive robust EFP estimates from gross primary productivity ( GPP ) obtained from eddy covariance flux measurements. Second, we investigate the impact of synchronizing EFP s and plant functional traits in time and space to evaluate their relationships, and the extent to which we can benefit from global plant trait databases to explain the variability of ecosystem photosynthetic capacity. Finally, we identify a set of plant functional traits controlling ecosystem photosynthetic capacity at selected sites. Suitable estimates of the ecosystem photosynthetic capacity can be derived from light response curve of GPP responding to radiation (photosynthetically active radiation or absorbed photosynthetically active radiation). Although the effect of climate is minimized in these calculations, the estimates indicate substantial interannual variation of the photosynthetic capacity, even after removing site‐years with confounding factors like disturbance such as fire events. The relationships between foliar nitrogen concentration and ecosystem photosynthetic capacity are tighter when both of the measurements are synchronized in space and time. When using multiple plant traits simultaneously as predictors for ecosystem photosynthetic capacity variation, the combination of leaf carbon to nitrogen ratio with leaf phosphorus content explains the variance of ecosystem photosynthetic capacity best (adjusted R 2 = 0.55). Overall, this study provides an objective approach to identify links between leaf level traits and canopy level processes and highlights the relevance of the dynamic nature of ecosystems. Synchronizing measurements of eddy covariance fluxes and plant traits in time and space is shown to be highly relevant to better understand the importance of intra‐ and interspecific trait variation on ecosystem functioning.

54 ENVIRONMENTAL SCIENCES↗

Effect of XC functionals and dispersion corrections on the DFT‐computed structural and vibrational properties of SrCl 2 –NaCl and ZrF 4 –LiF

Density functional theory (DFT) calculations were performed to examine the impact of exchange–correlation (XC) functionals and van der Waals corrections (specifically the D3 method) on the structural and vibrational properties of the SrCl 2 –NaCl and ZrF 4 –LiF salt systems. Multiple XC functionals, including the local density approximation (LDA), the generalized gradient approximation using the Perdew–Burke–Ernzerhof (PBE) model, and its modified form suitable for solids (PBEsol), the dispersion-corrected PBE-D3 and PBEsol-D3, were considered. Of these functionals, LDA was found to exhibit the highest degree of error, while PBEsol and PBE-D3 displayed the least error. Underestimated lattice parameters compared with experimental values were observed to result in higher force constants, leading to an overprediction of vibrational frequencies. Conversely, an overestimation of lattice parameters was associated with lower vibrational frequencies. The methodology presented in this study yielded results that are in good agreement with experiment, irrespective of the method (finite differences vs. density functional perturbation theory) employed for calculating infrared and Raman spectra. It was further demonstrated that for alkali halides with weak Raman scattering, utilizing a supercell constructed from primitive cells better predicts Raman features than does the use of conventional cells.

Raman↗

Status of genome function annotation in model organisms and crops

Abstract Since the entry into genome‐enabled biology several decades ago, much progress has been made in determining, describing, and disseminating the functions of genes and their products. Yet, this information is still difficult to access for many scientists and for most genomes. To provide easy access and a graphical summary of the status of genome function annotation for model organisms and bioenergy and food crop species, we created a web application ( https://genomeannotation.rheelab.org ) to visualize, search, and download genome annotation data for 28 species. The summary graphics and data tables will be updated semi‐annually, and snapshots will be archived to provide a historical record of the progress of genome function annotation efforts. Clear and simple visualization of up‐to‐date genome function annotation status, including the extent of what is unknown, will help address the grand challenge of elucidating the functions of all genes in organisms.

59 BASIC BIOLOGICAL SCIENCES↗

DNA Crystals as a Template for Patterned Functional Materials

DNA nanotechnology offers a wide toolkit of molecular functionalities and scales, including intricate motifs less than 10 nm and periodic structures exceeding 100 µm. At larger scales, however, there are often significant tradeoffs for DNA structures, namely stability and mechanical strength. This work describes the design, synthesis, and characterization of a functionalized DNA crystal. Using a ligated DNA crystal grants significant freedom for various functional materials to be applied, in this case, semiconducting cadmium sulfide and palladium metal. Properties investigated in this study include stability, mechanical strength, and optoelectronic properties such as photoluminescence (PL) and electric conductivity. Significant changes are observed based on the functional material applied to DNA crystals. The Young's modulus of the crystal varies by about five orders of magnitude when functionalized with palladium. PL and semiconductive behaviors were observed when cadmium sulfide was attached. These crystals represent an expansion of the capabilities of DNA structures at these length scales, and additionally a platform for future studies exchanging the materials or altering the ligation scheme.

CdS↗

A Short Note on the Scaling Function Constant Problem in the Two-Dimensional Ising Model

We provide a simple derivation of the constant factor in the short-distance asymptotics of the tau-function associated with the 2-point function of the two-dimensional Ising model. This factor was first computed by Tracy (Commun Math Phys 142:297–311, 1991) via an exponential series expansion of the correlation function. Further simplifications in the analysis are due to Tracy and Widom (Commun Math Phys 190:697–721, 1998) using Fredholm determinant representations of the correlation function and Wiener–Hopf approximation results for the underlying resolvent operator. Our method relies on an action integral representation of the tau-function and asymptotic results for the underlying Painlevé-III transcendent from McCoy et al. (J Math Phys 18:1058–1092, 1977).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the Depth of k-Valued Logic Functions Over Arbitrary Bases

The behavior of the Shannon function of the depth of k-valued logic functions realized by circuits over an arbitrary complete basis is examined. For all k, k ≥ 3, for an arbitrary basis of k-valued logic functions, the existence of the asymptotic behavior of the Shannon function of the depth is established. The asymptotic behavior is linear for finite bases and it is constant or logarithmic for infinite bases. Thus, the complete picture of asymptotic behavior of the Shannon function of the depth is obtained for all k, k ≥ 2.

97 MATHEMATICS AND COMPUTING↗

A filled function method for global optimization with inequality constraints

In this paper, we propose a new filled function method for finding a global minimizer of global optimization with inequality constraints. The proposed filled function is a continuously differentiable function with only one parameter. Then, we can use classical local optimization methods to find a better minimizer of the proposed filled function with a few parameter adjustment. The numerical experiments are made and the results show that the proposed filled function method is effective.

97 MATHEMATICS AND COMPUTING↗

Computational aspects of the continuum quaternionic wave functions for hydrogen

Over the past few years considerable attention has been given to the role played by the Hydrogen Continuum Wave Functions (HCWFs) in quantum theory. The HCWFs arise via the method of separation of variables for the time-independent Schrödinger equation in spherical coordinates. The HCWFs are composed of products of a radial part involving associated Laguerre polynomials multiplied by exponential factors and an angular part that is the spherical harmonics. In the present paper we introduce the continuum wave functions for hydrogen within quaternionic analysis ((R)QHCWFs), a result which is not available in the existing literature. In particular, the underlying functions are of three real variables and take on either values in the reduced and full quaternions (identified, respectively, with R{sup 3} and R{sup 4}). We prove that the (R)QHCWFs are orthonormal to one another. The representation of these functions in terms of the HCWFs are explicitly given, from which several recurrence formulae for fast computer implementations can be derived. A summary of fundamental properties and further computation of the hydrogen-like atom transforms of the (R)QHCWFs are also discussed. We address all the above and explore some basic facts of the arising quaternionic function theory. As an application, we provide the reader with plot simulations that demonstrate the effectiveness of our approach. (R)QHCWFs are new in the literature and have some consequences that are now under investigation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Wigner function in the relativistic quantum mechanics

A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation. - Highlights: • We study the Wigner function for a quantum spinless relativistic particle. • We discuss the relativistic Wigner function introduced by Zavialov and Malokostov. • We introduce relativistic Wigner function based on the standard definition. • We find analytic expressions for relativistic Wigner functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Physics and the choice of regulators in functional renormalisation group flows

The Renormalisation Group is a versatile tool for the study of many systems where scale-dependent behaviour is important. Its functional formulation can be cast into the form of an exact flow equation for the scale-dependent effective action in the presence of an infrared regularisation. The functional RG flow for the scale-dependent effective action depends explicitly on the choice of regulator, while the physics does not. In this work, we systematically investigate three key aspects of how the regulator choice affects RG flows: (i) We study flow trajectories along closed loops in the space of action functionals varying both, the regulator scale and shape function. Such a flow does not vanish in the presence of truncations. Based on a definition of the length of an RG trajectory, we suggest a constructive procedure for devising optimised regularisation schemes within a truncation. (ii) In systems with various field variables, a choice of relative cutoff scales is required. At the example of relativistic bosonic two-field models, we study the impact of this choice as well as its truncation dependence. We show that a crossover between different universality classes can be induced and conclude that the relative cutoff scale has to be chosen carefully for a reliable description of a physical system. (iii) Non-relativistic continuum models of coupled fermionic and bosonic fields exhibit also dependencies on relative cutoff scales and regulator shapes. At the example of the Fermi polaron problem in three spatial dimensions, we illustrate such dependencies and show how they can be interpreted in physical terms. - Highlights: • We show the regulator dependence of functional renormalisation (FRG) group equations. • Solving FRG equations along closed loops provides a distance between two regulators. • We suggest a practical procedure for devising optimal regulators. • A universality class crossover can be induced by changing relative cutoff scales. • We examine the regulator dependence explicitly in the Fermi polaron problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Scalar field in Reissner–Nordström spacetime: Bound state and scattering state (with appendix on eliminating oscillation in partial sum approximation of periodic function)

Highlights: • Bound-state and scattering-state solutions of massive scalar fields in R-N spacetime. • Bound-state wave functions and eigenvalues of massive scalar fields in R-N spacetime. • Solving explicit expressions of scattering phase shifts by integral equation methods. • Introducing tortoise coordinates for R-N spacetime. • Eliminating oscillations in the partial sum approximation of periodic functions. In this paper, we solve the massive scalar field in the Reissner–Nordström spacetime. The scalar field in the Reissner–Nordström spacetime has both bound states and scattering states. For bound states, we solve the bound-state wave function and the eigenvalue spectrum. For scattering states, we solve the scattering wave function and give an explicit expression for scattering phase shift by the integral equation method. Especially, we introduce the tortoise coordinate for the Reissner–Nordström spacetime. Moreover, in the calculation of scattering cross sections, we encounter a difficulty in partial sum approximation. If the sum of partial waves cannot be performed exactly, one has to turn to the partial sum approximation which approximates a function by the first several terms of the series. However, in the partial sum approximation there exists an incorrect oscillation which cannot be eliminated by keeping more terms. In the appendix we suggest an approach for eliminating such oscillations in the partial sum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Impact of functional groups on the electrocatalytic hydrogenation of aromatic carbonyls to alcohols

We report that electrocatalytic hydrogenation (ECH) of biomass-derived feedstocks has a critical dependence on the molecular structure of the organic and its adsorption on the electrode surface. In this study, we investigated the role of functional groups in the adsorption of the organic molecule on the charged Pd (111) surface and its subsequent effect on organic reduction in electrochemical hydrogenation of organic molecules. With three aromatic carbonyls of benzaldehyde (BZD), acetophenone (ACE), and vanillin (VAN), we rationalize molecular-scale adsorption and interfacial charge transfer processes by employing density-functional-theory based ab initio molecular dynamics simulations. We observe that the functional group and electrode charge strongly affect the proximity of organic molecule to the Pd (111) surface, where distances of aromatic ring and carbonyl group of the organic on the electrode change distinctively with functional groups and charge state of electrode, which strongly impact reduction of organics on the surface. Calculations of differential electron density show the strongest reduction with benzaldehyde via interfacial electron transfer from the charged Pd surface. We also observe that the interaction between the functional groups and solvent (VAN > BZD > ACE) significantly influence the organic interaction with the charged electrode (BZD > VAN > ACE), resulting in the net interaction energy between the organic and the electrode in the order of BZD > ACE > VAN. Experimental measurement of ECH rate also show the same trend of the net interaction energy. These results demonstrate the significance of solvent effect on the reducibility of organic molecules on electrodes.

36 MATERIALS SCIENCE↗

Coulomb wave functions in momentum space

We present an algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space. The arguments are the Sommerfeld parameter η, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p → q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of vertical bar eta vertical bar in the range of 10 -1 to 10, and thus is particularly suited for momentum space calculations of nuclear reactions.

97 MATHEMATICS AND COMPUTING↗