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At least 793 records · Page 44

Recent Progress in the Electroweak Structure of Light Nuclei Using Quantum Monte Carlo Methods

Nuclei will play a prominent role in searches for physics beyond the Standard Model as the active material in experiments. In order to reliably interpret new physics signals, one needs an accurate model of the underlying nuclear dynamics. In this review, we discuss recent progress made with quantum Monte Carlo approaches for calculating the electroweak structure of light nuclei. We place particular emphasis on recent β decay, muon capture, neutrinoless double β decay, and electron scattering results.

Physics↗

Structural analysis of molten materials by a remote fiber optic Raman sensor

This study presents a novel in situ high-temperature fiber optic Raman probe that enables the study of the physical properties and structure of molten samples at temperatures up to 1400 °C. To demonstrate the functionality of the high-temperature fiber optic Raman probe, different composition mold fluxes were evaluated in this report. The Raman spectra at flux molten temperature were successfully collected and analyzed. A deconvolution algorithm was employed to identify peaks in the spectra associated with the molecular structure of the components in each sample. Here, the experimental results demonstrate that the composition-dependent Raman signal shift can be detected at high temperatures, indicating that molten materials analysis using a high-temperature Raman system shows significant promise. This flexible and reliable high-temperature Raman measurement method has great potential for various applications, such as materials development, composition and structure monitoring during high-temperature processing, chemical identification, and process monitoring in industrial production.

47 OTHER INSTRUMENTATION↗

Structured back gates for high-mobility two-dimensional electron systems using oxygen ion implantation

We present a reliable method to obtain patterned back gates compatible with high mobility molecular beam epitaxy via local oxygen ion implantation that suppresses the conductivity of an 80 nm thick silicon doped GaAs epilayer. Our technique was optimized to circumvent several constraints of other gating and implantation methods. The ion-implanted surface remains atomically flat which allows unperturbed epitaxial overgrowth. We demonstrate the practical application of this gating technique by using magneto-transport spectroscopy on a two-dimensional electron system (2DES) with a mobility exceeding 20 × 10{sup 6} cm{sup 2}/V s. The back gate was spatially separated from the Ohmic contacts of the 2DES, thus minimizing the probability for electrical shorts or leakage and permitting simple contacting schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Calibration of a distributed flood forecasting model with input uncertainty using a Bayesian framework

In the process of calibrating distributed hydrological models, accounting for input uncertainty is important, yet challenging. In this study, we develop a Bayesian model to estimate parameters associated with a geomorphology‐based hydrological model (GBHM). The GBHM model uses geomorphic characteristics to simplify model structure and physically based methods to represent hydrological processes. We divide the observed discharge into low‐ and high‐flow data, and use the first‐order autoregressive model to describe their temporal dependence. We consider relative errors in rainfall as spatially distributed variables and estimate them jointly with the GBHM parameters. The joint posterior probability distribution is explored using Markov chain Monte Carlo methods, which include Metropolis‐Hastings, delay rejection adaptive Metropolis, and Gibbs sampling methods. We evaluate the Bayesian model using both synthetic and field data sets. The synthetic case study demonstrates that the developed method generally is effective in calibrating GBHM parameters and in estimating their associated uncertainty. The calibration ignoring input errors has lower accuracy and lower reliability compared to the calibration that includes estimation of the input errors, especially under model structure uncertainty. The field case study shows that calibration of GBHM parameters under complex field conditions remains a challenge. Although jointly estimating input errors and GBHM parameters improves the continuous ranked probability score and the consistency of the predictive distribution with the observed data, the improvement is incremental. To better calibrate parameters in a distributed model, such as GBHM here, we need to develop a more complex model and incorporate much more information.

54 ENVIRONMENTAL SCIENCES↗

Marginal Cost Pricing in a World without Perfect Competition: Implications for Electricity Markets with High Shares of Low Marginal Cost Resources

A common approach to regulating electricity is through auction-based competitive wholesale markets. The goal of this approach is to provide a reliable supply of power at the lowest reasonable cost to the consumer. This necessitates market structures and operating rules that ensure revenue sufficiency for all generators needed for resource adequacy purposes. Wholesale electricity markets employ marginal-cost pricing to provide cost-effective dispatch such that resources are compensated for their operational costs. However, marginal-cost pricing alone cannot guarantee cost recovery outside of perfect competition, and electricity markets have at least six attributes that preclude them from functioning as perfectly competitive markets. These attributes include market power, externalities, public good attributes, lack of storage, wholesale price caps, and ineffective demand curve. Until (and unless) these failures are ameliorated, some form of corrective action(s) will be necessary to improve market efficiency so that prices can correctly reflect the needed level of system reliability. Many of these options necessarily involve some form of administrative or out-of-market actions, such as scarcity pricing, capacity payments, bilateral or other out-of-market contracts, or some hybrid combination. A key focus with these options is to create a connection between the electricity market and long-term reliability/loss-of-load expectation targets, which are inherently disconnected in the native markets because of the aforementioned market failures. The addition of variable generation resources can exacerbate revenue sufficiency and resource adequacy concerns caused by these underlying market failures. Because variable generation resources have near-zero marginal costs, they effectively suppress energy prices and reduce the capacity factors of conventional generators through the merit-order effect in the simplest case of a convex market; non-convexities can also suppress prices.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Misoriented grain boundaries vicinal to the (111) <11¯0> twin in nickel part II: Thermodynamics of hydrogen segregation

Grain boundary engineered materials are of immense interest for their resistance to hydrogen embrittlement. This work builds on the work undertaken in Part I on the thermodynamic stability and structure of misoriented grain boundaries vicinal to the Σ3 (111) <11¯0> (coherent-twin) boundary to examine hydrogen segregation to those boundaries. The segregation of hydrogen reflects the asymmetry of the boundary structure with the sense of rotation of the grains about the coherent-twin boundary, and the temperature-dependent structural transition present in one sense of misorientation. This work also finds that the presence of hydrogen affects a change in structure of the boundaries with increasing concentration. The structural change effects only one sense of misorientation and results in the reduction in length of the emitted stacking faults. Moreover, the structural change results in the generation of occupied sites populated by more strongly bound hydrogen. The improved understanding of misoriented twin grain boundary structure and the effect on hydrogen segregation resulting from this work is relevant to higher length-scale models. To that end, we examine commonly used metrics such as free volume and atomic stress at the boundary. In conclusion, free volume is found not to be useful as a surrogate for predicting the degree of hydrogen segregation, whereas the volumetric virial stress reliably predicts the locations of hydrogen segregation and exclusion at concentrations below saturation or the point where structural changes are induced by increasing hydrogen concentration.

36 MATERIALS SCIENCE↗

Single Atom Catalysts: A Review of Characterization Methods

Abstract Single atom catalysts (SACs) harbor a potential to exceed nanoparticle catalysts in terms of activity, stability and selectivity in a growing number of chemical reactions. Although their investigation is attracting significant attention, important fundamental questions focusing on key physicochemical properties of SACs (e. g., structure – property relationships, structural dynamics, reaction‐driven restructuring) remain unanswered. A main challenge for research in the field is how to reliably characterize the environments of single atoms in the presence of complicating factors such as low weight loadings, strong metal‐support interactions, and atomic and multiscale heterogeneity of bonding in the single atom sites. This review addresses this challenge – identifying catalytically relevant features of physicochemical properties of single atoms (charge state, electronic structure, atomic configuration, bonding interactions with a support) and surveying advanced tools/methods for characterizing them. The review places a strong emphasis on multimodal methods exploiting X‐ray absorption, emission and photoelectron spectroscopies, and provides several examples from the authors’ research that demonstrate their use as powerful tools for SAC characterization.

Kottwitz, Matthew↗

Covalently-Bonded Laminar Assembly of Van der Waals Semiconductors with Polymers: Toward High-Performance Flexible Devices

Van der Waals semiconductors (vdWS) offer superior mechanical and electrical properties and are promising for flexible microelectronics when combined with polymer substrates. However, the self-passivated vdWS surfaces and their weak adhesion to polymers tend to cause interfacial sliding and wrinkling, and thus, are still challenging the reliability of vdWS-based flexible devices. Here, in this study, an effective covalent vdWS–polymer lamination method with high stretch tolerance and excellent electronic performance is reported. Using molybdenum disulfide (MoS 2 ) and polydimethylsiloxane (PDMS) as a case study, gold–chalcogen bonding and mercapto silane bridges are leveraged. The resulting composite structures exhibit more uniform and stronger interfacial adhesion. This enhanced coupling also enables the observation of a theoretically predicted tension-induced band structure transition in MoS 2 . Moreover, no obvious degradation in the devices’ structural and electrical properties is identified after numerous mechanical cycle tests. This high-quality lamination enhances the reliability of vdWS-based flexible microelectronics, accelerating their practical applications in biomedical research and consumer electronics.

36 MATERIALS SCIENCE↗

Multi-fidelity Uncertainty Quantification for Homogenization Problems in Structure-Property Relationships from Crystal Plasticity Finite Elements

Crystal plasticity finite element method (CPFEM) has been an integrated computational materials engineering (ICME) workhorse to study materials behaviors and structure-property relationships for the last few decades. These relations are mappings from the microstructure space to the materials properties space. Due to the stochastic and random nature of microstructures, there is always some uncertainty associated with materials properties, for example, in homogenized stress-strain curves. For critical applications with strong reliability needs, it is often desirable to quantify the microstructure-induced uncertainty in the context of structure-property relationships. However, this uncertainty quantification (UQ) problem often incurs a large computational cost because many statistically equivalent representative volume elements (SERVEs) are needed. In this article, we apply a multi-level Monte Carlo (MLMC) method to CPFEM to study the uncertainty in stress-strain curves, given an ensemble of SERVEs at multiple mesh resolutions. By using the information at coarse meshes, we show that it is possible to approximate the response at fine meshes with a much reduced computational cost. We focus on problems where the model output is multi-dimensional, which requires us to track multiple quantities of interest (QoIs) at the same time. In conclusion, our numerical results show that MLMC can accelerate UQ tasks around 2.23x, compared to the classical Monte Carlo (MC) method, which is widely known as ensemble average in the CPFEM literature.

36 MATERIALS SCIENCE↗

Polymorphism and melt in high-pressure tantalum. II. Orthorhombic phases

Continuing uncertainty in the high-pressure melt curves of bcc transition metals has spawned renewed research interest in the phase diagrams of these materials, with tantalum becoming an important prototype. Here, the present paper extends the quantum-based investigation of high- T, P polymorphism and melt in Ta that was begun in Paper I [Haskins et al., Phys. Rev. B 86, 224104 (2012)] on five candidate cubic and hexagonal structures (bcc, A15, fcc, hcp, and hex-ω) to here treat four promising orthorhombic structures (Pnma, Fddd, Pmma, and α-U). Using DFT-based MGPT multi-ion potentials that allow accurate MD simulations of large systems, we showed in Paper I that the mechanically unstable fcc, hcp, and hex-ω structures can only be stabilized at high- T , P by large anharmonic vibrational effects, requiring systems of ~500 atoms to produce size-independent melt curves and reliable calculations of thermodynamic stability. This reversed a previous small-cell quantum-simulation prediction of a high- T , P hex-ω phase. Subsequent DFT calculations have now suggested a more energetically favorable and mechanically stable Pnma structure, which again small-cell quantum simulations predict could be a high- T , P phase. Our present MGPT total-energy and phonon calculations show that not only Pnma, but all four orthorhombic structures considered here, are similarly energetically favorable, and that Fddd in addition to Pnma is mechanically stable at T = 0 up to 420 GPa. MGPT-MD simulations further reveal spontaneous temperature-induced Pnma → bcc and Fddd → bcc transformations at modest temperatures, peaking at ~1450 K near 100 GPa. At high temperatures near melt, we find T -dependent c / a and b / a axial ratios and large stabilizing anharmonicity present in all four orthorhombic structures. The anharmonicity drives significantly larger melt size effects, requiring systems of ~1000 – 4000 atoms to produce converged melt curves for reliable predictions of relative thermodynamic stability. In the large-cell limit, with ~40000 solid-phase atoms and accurate two-phase MGPT-MD melt simulation, we find that Pnma, Fddd and α-U have melt temperatures that are equal to bcc over small pressure ranges in the vicinity of 100 GPa, but that the orthorhombic melt temperatures never exceed bcc up to 420 GPa. This finding suggests that Pnma, Fddd, and α-U remain highly competitive metastable phases that could coexist with bcc and possibly be observed experimentally. Finally, to add additional insight into our results we have constructed global Helmholtz free energies for the A15, Pnma, and Fddd phases of Ta, complementing previous free energies obtained for the bcc, fcc, and liquid phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

CORROSION RESISTANCE OF LASER-INTERFERENCE STRUCTURED ALUMINUM ALLOY 2024 COATED WITH MIL-PRF-85582 PRIMER

The use of aluminum alloys in aerospace industry requires more effective and reliable joining techniques. The lubricant contaminants from prior rolling operations affect surface energies and the quality of coating adhe-sion and adhesive bonded joints. In this study, a new laser-based technique is investigated as a surface treatment for coating applications. The laser interference power profile was created by splitting the beam and guiding both beams towards the specimen and overlapping them on the specimen surface, creating a line-interference pattern on the specimen surface. The laser-interference structuring (LIS) was used without any chemical treatments, such as those in chemical conversion coating (CCC) and sulfuric acid anodizing (SAA), which is a much simpler process than those chemical-based. To assess the effect of LIS on corrosion re-sistance of coating, Al 2024 panels prepared by LIS, CCC and SAA were coated with MIL-PRF-85582, Type I, Class N primer and exposed to salt spray environment according to ASTM B117. The exposure is currently in progress and the corrosion attack on the coated panels will be evaluated by the degree of blister formation and rust creepage.

Sabau, Adrian↗

Surface reaction for efficient and stable inverted perovskite solar cells

We report perovskite solar cells (PSCs) with an inverted structure (often referred to as the p-i-n architecture) are attractive for future commercialization due to their easily scalable fabrication, reliable operation, and compatibility with a wide range of perovskite-based tandem device architectures. However, the power conversion efficiency (PCE) of p-i-n PSCs falls behind n-i-p (or normal) structure counterparts. This large performance gap could undermine efforts to adopt p-i-n architectures, despite their other advantages. Given the remarkable advances in perovskite bulk materials optimization over the past decade, interface engineering has become the most important strategy to push PSC performance to its limit. Here, we report a reactive surface engineering approach based on a simple post-growth treatment of 3-(Aminomethyl)pyridine (3-APy) on top of a perovskite thin film. First, the 3-APy molecule selectively reacts with surface FA+, reducing perovskite surface roughness and surface potential fluctuations associated with surface steps/terraces. Second, the reaction product on the perovskite surface decreases the formation energy of charged iodine-vacancies, leading to effective n-type doping with a reduced work function in the surface region. With this reactive surface engineering, the resulting p-i-n PSCs obtained a PCE over 25%, along with retaining 87% of the initial PCE after over 2400 h of one-sun operation at about 55 degrees C in air.

14 SOLAR ENERGY↗

Leveraging Structures in Fault Diagnosis for Lithium-Ion Battery Packs

Lithium-ion battery systems consist of a varying number of single cells, designed to meet specific application requirements for output voltage and capacity. Effective fault diagnosis in these battery systems is an essential prerequisite for ensuring their safe and reliable operation. To address this need, we introduce a novel model-based fault diagnosis approach that distinguishes itself by leveraging informative structures inherent in battery systems such as architecture, uniformity among the constituent cells, and sparsity of fault occurrences to enhance its fault diagnosis capabilities. The proposed approach formulates a moving horizon estimation (MHE) problem, incorporating such structural information to estimate different fault signals—specifically, internal short circuits, external short circuits, and voltage and current sensors faults. We conduct various simulations to evaluate the performance of the proposed approach under different fault types and magnitudes. The obtained results validate the proposed approach and promise effective fault diagnosis for battery systems.

Farakhor, Amir↗

High-Performance First-Principles Molecular Dynamics for Predictive Theory and Modeling

This project focused on developing high-performance software tools for First-Principles Molecular Dynamics (FPMD) simulations, and applying them in investigations of materials relevant to energy conversion processes. FPMD is an atomistic simulation method that combines a quantum-mechanical description of electronic structure with the statistical description provided by molecular dynamics (MD) simulations. This reliance on fundamental principles allows FPMD simulations to provide a consistent description of structural, dynamical and electronic properties of a material. This is particularly useful in systems for which reliable empirical models are lacking. FPMD simulations are increasingly used as a predictive tool for applications such as batteries, solar energy conversion, light-emitting devices, electro-chemical energy conversion devices and other materials. During the course of the project, several new features were developed and added to the open-source Qbox FPMD code. The code was further optimized for scalable operation of large-scale, Leadership-Class DOE computers. When combined with Many-Body Perturbation Theory (MBPT) calculations, this infrastructure was used to investigate structural and electronic properties of liquid water, ice, aqueous solutions, nanoparticles and solid-liquid interfaces. Computing both ionic trajectories and electronic structure in a consistent manner enabled the simulation of several spectroscopic properties, such as Raman spectra, infrared spectra, and sum-frequency generation spectra. The accuracy of the approximations used allowed for direct comparisons of results with experimental data such as optical spectra, X-ray and neutron diffraction spectra. The software infrastructure developed in this project, as applied to various investigations of solids, liquids and interfaces, demonstrates that FPMD simulations can provide a detailed, atomic-scale picture of structural, vibrational and electronic properties of complex systems relevant to energy conversion devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Extending DFT-based genetic algorithms by atom-to-place re-assignment via perturbation theory: A systematic and unbiased approach to structures of mixed-metallic clusters

Energy surfaces of metal clusters usually show a large variety of local minima. For homo-metallic species the energetically lowest can be found reliably with genetic algorithms, in combination with density functional theory without system-specific parameters. For mixed-metallic clusters this is much more difficult, as for a given arrangement of nuclei one has to find additionally the best of many possibilities of assigning different metal types to the individual positions. In the framework of electronic structure methods this second issue is treatable at comparably low cost at least for elements with similar atomic number by means of first-order perturbation theory, as shown previously [F. Weigend, C. Schrodt, and R. Ahlrichs, J. Chem. Phys. 121, 10380 (2004)]. In the present contribution the extension of a genetic algorithm with the re-assignment of atom types to atom sites is proposed and tested for the search of the global minima of PtHf{sub 12} and [LaPb{sub 7}Bi{sub 7}]{sup 4−}. For both cases the (putative) global minimum is reliably found with the extended technique, which is not the case for the “pure” genetic algorithm.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Initial implementation of the conversion from the energy-subtracted CT number to electron density in tissue inhomogeneity corrections: An anthropomorphic phantom study of radiotherapy treatment planning

Purpose: To achieve accurate tissue inhomogeneity corrections in radiotherapy treatment planning, the authors had previously proposed a novel conversion of the energy-subtracted computed tomography (CT) number to an electron density (ΔHU–ρ{sub e} conversion), which provides a single linear relationship between ΔHU and ρ{sub e} over a wide range of ρ{sub e}. The purpose of this study is to present an initial implementation of the ΔHU–ρ{sub e} conversion method for a treatment planning system (TPS). In this paper, two example radiotherapy plans are used to evaluate the reliability of dose calculations in the ΔHU–ρ{sub e} conversion method. Methods: CT images were acquired using a clinical dual-source CT (DSCT) scanner operated in the dual-energy mode with two tube potential pairs and an additional tin (Sn) filter for the high-kV tube (80–140 kV/Sn and 100–140 kV/Sn). Single-energy CT using the same DSCT scanner was also performed at 120 kV to compare the ΔHU–ρ{sub e} conversion method with a conventional conversion from a CT number to ρ{sub e} (Hounsfield units, HU–ρ{sub e} conversion). Lookup tables for ρ{sub e} calibration were obtained from the CT image acquisitions for tissue substitutes in an electron density phantom (EDP). To investigate the beam-hardening effect on dosimetric uncertainties, two EDPs with different sizes (a body EDP and a head EDP) were used for the ρ{sub e} calibration. Each acquired lookup table was applied to two radiotherapy plans designed using the XiO TPS with the superposition algorithm for an anthropomorphic phantom. The first radiotherapy plan was for an oral cavity tumor and the second was for a lung tumor. Results: In both treatment plans, the performance of the ΔHU–ρ{sub e} conversion was superior to that of the conventional HU–ρ{sub e} conversion in terms of the reliability of dose calculations. Especially, for the oral tumor plan, which dealt with dentition and bony structures, treatment planning with the HU–ρ{sub e} conversion exhibited apparent discrepancies between the dose distributions and dose–volume histograms (DVHs) of the body-EDP and head-EDP calibrations. In contrast, the dose distributions and DVHs of the body-EDP and head-EDP calibrations coincided with each other almost perfectly in the ΔHU–ρ{sub e} conversion for 100–140 kV/Sn. The difference between the V{sub 100}’s (the mean planning target volume receiving 100% of the prescribed dose; a DVH parameter) of the body-EDP and head-EDP calibrations could be reduced to less than 1% using the ΔHU–ρ{sub e} conversion, but exceeded 11% for the HU–ρ{sub e} conversion. Conclusions: The ΔHU–ρ{sub e} conversion can be implemented for currently available TPS’s without any modifications or extensions. The ΔHU–ρ{sub e} conversion appears to be a promising method for providing an accurate and reliable inhomogeneity correction in treatment planning for any ill-conditioned scans that include (i) the use of a calibration EDP that is nonequivalent to the patient’s body tissues, (ii) a mismatch between the size of the patient and the calibration EDP, or (iii) a large quantity of high-density and high-atomic-number tissue structures.

60 APPLIED LIFE SCIENCES↗

An Interface–Type Memristive Device for Artificial Synapse and Neuromorphic Computing

Interface-type (IT) metal/oxide Schottky memristive devices have attracted considerable attention over filament-type (FT) devices for neuromorphic computing because of their uniform, filament-free, and analog resistive switching (RS) characteristics. The most recent IT devices are based on oxygen ions and vacancies movement to alter interfacial Schottky barrier parameters and thereby control RS properties. However, the reliability and stability of these devices have been significantly affected by the undesired diffusion of ionic species. Herein, a reliable interface-dominated memristive device is demonstrated using a simple Au/Nb-doped SrTiO 3 (Nb:STO) Schottky structure. The Au/Nb:STO Schottky barrier modulation by charge trapping and detrapping is responsible for the analog resistive switching characteristics. Because of its interface-controlled RS, the proposed device shows low device-to-device, cell-to-cell, and cycle-to-cycle variability while maintaining high repeatability and stability during endurance and retention tests. Furthermore, the Au/Nb:STO IT memristive device exhibits versatile synaptic functions with an excellent uniformity, programmability, and reliability. A simulated artificial neural network with Au/Nb:STO synapses achieves a high recognition accuracy of 94.72% for large digit recognition from MNIST database. These results suggest that IT resistive switching can be potentially used for artificial synapses to build next-generation neuromorphic computing.

36 MATERIALS SCIENCE↗

SU-C-18A-04: 3D Markerless Registration of Lung Based On Coherent Point Drift: Application in Image Guided Radiotherapy

Purpose: This study evaluated a new probabilistic non-rigid registration method called coherent point drift for real time 3D markerless registration of the lung motion during radiotherapy. Method: 4DCT image datasets Dir-lab (www.dir-lab.com) have been used for creating 3D boundary element model of the lungs. For the first step, the 3D surface of the lungs in respiration phases T0 and T50 were segmented and divided into a finite number of linear triangular elements. Each triangle is a two dimensional object which has three vertices (each vertex has three degree of freedom). One of the main features of the lungs motion is velocity coherence so the vertices that creating the mesh of the lungs should also have features and degree of freedom of lung structure. This means that the vertices close to each other tend to move coherently. In the next step, we implemented a probabilistic non-rigid registration method called coherent point drift to calculate nonlinear displacement of vertices between different expiratory phases. Results: The method has been applied to images of 10-patients in Dir-lab dataset. The normal distribution of vertices to the origin for each expiratory stage were calculated. The results shows that the maximum error of registration between different expiratory phases is less than 0.4 mm (0.38 SI, 0.33 mm AP, 0.29 mm RL direction). This method is a reliable method for calculating the vector of displacement, and the degrees of freedom (DOFs) of lung structure in radiotherapy. Conclusions: We evaluated a new 3D registration method for distribution set of vertices inside lungs mesh. In this technique, lungs motion considering velocity coherence are inserted as a penalty in regularization function. The results indicate that high registration accuracy is achievable with CPD. This method is helpful for calculating of displacement vector and analyzing possible physiological and anatomical changes during treatment.

60 APPLIED LIFE SCIENCES↗