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Integrations over solid angle and frequency are performed in the expressions for the radiant heat flux and local energy loss of a line in a region of strong variations of the source function in one direction. Approximations are given for coefficients and kernels in the resulting forms which involve integrals over the physical coordinate.
In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.
Purpose: To develop and validate an automated technique for evaluating the spatial resolution characteristics of clinical computed tomography (CT) images. Methods: Twenty one chest and abdominopelvic clinical CT datasets were examined in this study. An algorithm was developed to extract a CT resolution index (RI) analogous to the modulation transfer function from clinical CT images by measuring the edge-spread function (ESF) across the patient’s skin. A polygon mesh of the air-skin boundary was created. The faces of the mesh were then used to measure the ESF across the air-skin interface. The ESF was differentiated to obtain the line-spread function (LSF), and the LSF was Fourier transformed to obtain the RI. The algorithm’s ability to detect the radial dependence of the RI was investigated. RIs measured with the proposed method were compared with a conventional phantom-based method across two reconstruction algorithms (FBP and iterative) using the spatial frequency at 50% RI, f{sub 50}, as the metric for comparison. Three reconstruction kernels were investigated for each reconstruction algorithm. Finally, an observer study was conducted to determine if observers could visually perceive the differences in the measured blurriness of images reconstructed with a given reconstruction method. Results: RI measurements performed with the proposed technique exhibited the expected dependencies on the image reconstruction. The measured f{sub 50} values increased with harder kernels for both FBP and iterative reconstruction. Furthermore, the proposed algorithm was able to detect the radial dependence of the RI. Patient-specific measurements of the RI were comparable to the phantom-based technique, but the patient data exhibited a large spread in the measured f{sub 50}, indicating that some datasets were blurrier than others even when the projection data were reconstructed with the same reconstruction algorithm and kernel. Results from the observer study substantiated this finding. Conclusions: Clinically informed, patient-specific spatial resolution can be measured from clinical datasets. The method is sufficiently sensitive to reflect changes in spatial resolution due to different reconstruction parameters. The method can be applied to automatically assess the spatial resolution of patient images and quantify dependencies that may not be captured in phantom data.
Maize rough endosperm (rgh) mutants have defective kernels with a rough, etched, or pitted endosperm surface. Molecular genetic analysis of this mutant class has identified multiple RNA processing proteins critical to endosperm development. Here, we report on the developmental and molecular function of the rgh6 locus. The rgh6 mutant was isolated from the UniformMu transposon tagging population. Mutant kernels have reduced endosperm size and defective embryos that develop in a more apical position than typical for defective embryos. TB translocation crosses revealed that rgh6 mutant endosperm inhibits normal embryo development. Positional cloning of the rgh6 locus found that it encodes a predicted DEAD-box RNA helicase. Consistent with a predicted function for RNA processing, transient expression of a RGH6-GFP fusion protein is localized to nucleolus and nuclear speckles in Nicotiana benthamiana leaves. Rgh6 transcripts are highly expressed in endosperm epidermal cell types such as the aleurone, basal endosperm cell layer, embryo surrounding region, and endosperm adjacent to scutellum. Markers of these cell types show increased levels in rgh6 mutant kernels. Mutant endosperm tissues have increased precursor microRNA (pre-miRNA) and decreased mature miRNA relative to normal sibling endosperm, indicating that rgh6 is required for miRNA processing. The transcript levels for most miRNA target genes accumulate to a higher level in rgh6 mutant tissue. These results suggest that miRNA processing and regulation of miRNA target genes are required for normal endosperm development.
In this work, we study a molecular emitter above a silver surface in the framework of macroscopic quantum electrodynamics and explore the population dynamics including non-Markovian effects. The theory we present is general for molecular fluorescence in the presence of dielectrics with any space-dependent, frequency-dependent, or complex dielectric functions. Furthermore, the proposed theory allows us to calculate the memory kernel of polaritons using computational electrodynamics packages. In the limit of a high vibration frequency, the different strengths of exciton-polariton couplings lead to distinct characteristics in the population dynamics, e.g., Franck-Condon-Rabi oscillation. (The frequency of Rabi oscillation is dependent on the Franck-Condon factor.) Additionally, in a specific condition, we derive a parameter-free formula that can be used to estimate the exciton-polariton coupling between a molecular emitter and a nanocavity, and the coupling estimated by our theory is in good agreement with the reported experimental results.
The central role played by pseudodifferential operators in relativistic dynamics is known very well. In this work, operators like the Schrodinger one (e.g., square root) are treated from the point of view of the non-local pseudodifferential Green functions. Starting from the explicit construction of the Green (semigroup) theoretical kernel, a theorem linking the integrability conditions and their dependence on the spacetime dimensions is given. Relativistic wave equations with arbitrary spin and the causality problem are discussed with the algebraic interpretation of the radical operator and their relation with coherent and squeezed states. Also we perform by means of pure theoretical procedures (based in physical concepts and symmetry) the relativistic position operator which satisfies the conditions of integrability: it is a non-local, Lorentz invariant and does not have the same problems as the “local”position operator proposed by Newton and Wigner. Physical examples, as zitterbewegung and rogue waves, are presented and deeply analyzed in this theoretical framework.
A formulation for integrating the gradient of the thin wire kernel is presented. This approach employs a new expression for the gradient of the thin wire kernel derived from a recent technique for numerically evaluating the exact thin wire kernel. This approach should provide essentially arbitrary accuracy and may be used with higher-order elements and basis functions using the procedure described in [4].When the source and observation points are close, the potential integrals over wire segments involving the wire kernel are split into parts to handle the singular behavior of the integrand [1]. The singularity characteristics of the gradient of the wire kernel are different than those of the wire kernel, and the axial and radial components have different singularities. The characteristics of the gradient of the wire kernel are discussed in [2]. To evaluate the near electric and magnetic fields of a wire, the integration of the gradient of the wire kernel needs to be calculated over the source wire. Since the vector bases for current have constant direction on linear wire segments, these integrals reduce to integrals of the form
Parton distribution functions (PDFs) at large x are challenging to extract from experimental data, yet they are essential for understanding hadron structure and searching for new physics beyond the Standard Model. Within the framework of the large momentum P z expansion of lattice quasi-PDFs, we investigate large x PDFs, where the matching coefficient is factorized into the hard kernel, related to the active quark momentum xP z , and the threshold soft function, associated with the spectator momentum (1 − x)P z . The renormalization group equation of the soft function enables the resummation of the threshold double logarithms α k ln 2k (1 − x), which is crucial for a reliable and controllable calculation of large x PDFs. Our analysis with pion valence PDFs indicates that perturbative matching breaks down when the spectator momentum (1 − x)P z approaches Λ QCD , but remains valid when both xP z and (1 − x)P z are much larger than Λ QCD . Additionally, we incorporate leading renormalon resummation within the threshold framework, demonstrating good perturbative convergence in the region where both spectator and active quark momenta are perturbative scales.
Purpose: The GEANT4-DNA physics models are upgraded by a more accurate set of electron cross sections for ionization and excitation in liquid water. The impact of the new developments on low-energy electron transport simulations by the GEANT4 Monte Carlo toolkit is examined for improving its performance in dosimetry applications at the subcellular and nanometer level. Methods: The authors provide an algorithm for an improved implementation of the Emfietzoglou model dielectric response function of liquid water used in the GEANT4-DNA existing model. The algorithm redistributes the imaginary part of the dielectric function to ensure a physically motivated behavior at the binding energies, while retaining all the advantages of the original formulation, e.g., the analytic properties and the fulfillment of the f-sum-rule. In addition, refinements in the exchange and perturbation corrections to the Born approximation used in the GEANT4-DNA existing model are also made. Results: The new ionization and excitation cross sections are significantly different from those of the GEANT4-DNA existing model. In particular, excitations are strongly enhanced relative to ionizations, resulting in higher W-values and less diffusive dose-point-kernels at sub-keV electron energies. Conclusions: An improved energy-loss model for the excitation and ionization of liquid water by low-energy electrons has been implemented in GEANT4-DNA. The suspiciously low W-values and the unphysical long tail in the dose-point-kernel have been corrected owing to a different partitioning of the dielectric function.
Purpose: The RavenQA system (LAP Laser, Germany) is a QA device with a phosphor screen detector for performing the QA tasks of TG-142. This study tested if it is feasible to use the system for the patient specific QA of the Volumetric Modulated Arc Therapy (VMAT). Methods: Water equivalent material (5cm) is attached to the front of the detector plate of the RavenQA for dosimetry purpose. Then the plate is attached to the gantry to synchronize the movement between the detector and the gantry. Since the detector moves together with gantry, The ’Reset gantry to 0’ function of the Eclipse planning system (Varian, CA) is used to simulate the measurement situation when calculating dose of the detector plate. The same gantry setup is used when delivering the treatment beam for feasibility test purposes. Cumulative dose is acquired for each arc. The optical scatter component of each captured image from the CCD camera is corrected by deconvolving the 2D spatial invariant optical scatter kernel (OSK). We assume that the OSK is a 2D isotropic point spread function with inverse-squared decrease as a function of radius from the center. Results: Three cases of VMAT plans including head & neck, whole pelvis and abdomen-pelvis are tested. Setup time for measurements was less than 5 minutes. Passing rates of absolute gamma were 99.3, 98.2, 95.9 respectively for 3%/3mm criteria and 96.2, 97.1, 86.4 for 2%/2mm criteria. The abdomen-pelvis field has long treatment fields, 37cm, which are longer than the detector plate (25cm). This plan showed relatively lower passing rate than other plans. Conclusion: An algorithm for IMRT/VMAT verification using the RavenQA has been developed and tested. The model of spatially invariant OSK works well for deconvolution purpose. It is proved that the RavenQA can be used for the patient specific verification of VMAT. This work is funded in part by a Maryland Industrial Partnership Program grant to University of Maryland and to JPLC who owns the Raven technology. John Wong is a co-founder of JPLC.
We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye (KLT) relations in string theory. For this purpose, explicit bases of twisted cycles and cocycles are worked out whose orthonormality simplifies the coaction. We present methods to efficiently perform and organize the expansions of configuration-space integrals in the inverse string tension α' or the dimensional-regularization parameter ϵ of Feynman integrals. Generating-function techniques open up a new perspective on the coaction of multiple polylogarithms in any number of variables and analytic continuations in the unintegrated punctures. We present a compact recursion for a generalized KLT kernel and discuss its origin from intersection numbers of Stasheff polytopes and its implications for correlation functions of two-dimensional conformal field theories. We find a non-trivial example of correlation functions in (p, 2) minimal models, which can be normalized to become uniformly transcendental in the p → ∞ limit.
Modeling results used to assess the fuel performance of the TRISO-coated fuel particles as a function of kernel/buffer volume fraction include SiC tangential stress, formation of the buffer/IPyC gap, particle temperature profile, internal particle pressure, fission gas released from the kernel, probability of fuel particle failure, and fission product diffusion. These results were evaluated at two burnup levels and irradiation temperatures to bound expected steady-state irradiation conditions. In general, increasing the kernel/buffer volume fraction increases the SiC stress and subsequently the failure probability of a fuel particle when compared to the AGR designed particle. There was little impact on the fission product diffusion through the particle as the kernel/buffer volume fraction increased.
Abstract Physics‐driven discovery in an autonomous experiment has emerged as a dream application of machine learning in physical sciences. Here, this work develops and experimentally implements a deep kernel learning (DKL) workflow combining the correlative prediction of the target functional response and its uncertainty from the structure, and physics‐based selection of acquisition function, which autonomously guides the navigation of the image space. Compared to classical Bayesian optimization (BO) methods, this approach allows to capture the complex spatial features present in the images of realistic materials, and dynamically learn structure–property relationships. In combination with the flexible scalarizer function that allows to ascribe the degree of physical interest to predicted spectra, this enables physical discovery in automated experiment. Here, this approach is illustrated for nanoplasmonic studies of nanoparticles and experimentally implemented in a truly autonomous fashion for bulk‐ and edge plasmon discovery in MnPS 3 , a lesser‐known beam‐sensitive layered 2D material. This approach is universal, can be directly used as‐is with any specimen, and is expected to be applicable to any probe‐based microscopic techniques including other STEM modalities, scanning probe microscopies, chemical, and optical imaging.
We consider the reflected entropy and the associated entanglement spectrum for free fermions reduced to two intervals in 1 + 1 dimensions. Working directly in the continuum theory the reflected entropy can be extracted from the spectrum of a singular integral equation whose kernel is determined by the known free fermion modular evolved correlation function. We find the spectrum numerically and analytically in certain limits. For intervals that almost touch the reflected entanglement spectrum approaches the spectrum of the thermal density matrix. This suggests that the reflected entanglement spectrum is well suited to the task of extracting physical data of the theory directly from the ground state wave function.
We extend the results of [1], computing one loop partition functions for massive fields with spin half in AdS 2 using the quasinormal mode method proposed by Denef, Hartnoll, and Sachdev [2]. We find the finite representations of SO(2,1) for spin zero and spin half, consisting of a highest weight state |hi and descendants with non-unitary values of h. These finite representations capture the poles and zeroes of the one loop determinants. Together with the asymptotic behavior of the partition functions (which can be easily computed using a large mass heat kernel expansion), these are sufficient to determine the full answer for the one loop determinants. We also discuss extensions to higher dimensional AdS 2n and higher spins.
Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of partial differential equations (PDEs) in an entirely self-supervised manner. In this work we analyze the training dynamics of deep operator networks (DeepONets) through the lens of Neural Tangent Kernel theory, and reveal a bias that favors the approximation of functions with larger magnitudes. To correct this bias we propose to adaptively re-weight the importance of each training example, and demonstrate how this procedure can effectively balance the magnitude of back-propagated gradients during training via gradient descent. We also propose a novel network architecture that is more resilient to vanishing gradient pathologies. Taken together, our developments provide new insights into the training of DeepONets and consistently improve their predictive accuracy by a factor of 10-50x, demonstrated in the challenging setting of learning PDE solution operators in the absence of paired input-output observations.
This paper presents a probabilistic data-driven method to model the uncertainty of distributed photovoltaic (PV) generation to enhance the observability of distribution grids with a high penetration of renewable resources. The proposed method employs a kernel density estimation (KDE) technique to develop the conditional probability density function (PDF) of PV outputs given the time of the day, using the measurement data from observed PV systems. Then time series of output power of unmeasured PV generators, located at the same grid, are generated according to the corresponding PDF and used as pseudo-measurements in distribution system state estimation (DSSE). The proposed model has been tested and verified using real PV data and utility networks.
Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.