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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Reversible vector ratchets for skyrmion systems

In this paper, we show that ac driven skyrmions interacting with an asymmetric substrate provide a realization of a class of ratchet system which we call a vector ratchet that arises due to the effect of the Magnus term on the skyrmion dynamics. In a vector ratchet, the dc motion induced by the ac drive can be described as a vector that can be rotated clockwise or counterclockwise relative to the substrate asymmetry direction. Up to a full 360° rotation is possible for varied ac amplitudes or skyrmion densities. In contrast to overdamped systems, in which ratchet motion is always parallel to the substrate asymmetry direction, vector ratchets allow the ratchet motion to be in any direction relative to the substrate asymmetry. It is also possible to obtain a reversal in the direction of rotation of the vector ratchet, permitting the creation of a reversible vector ratchet. We examine vector ratchets for ac drives applied parallel or perpendicular to the substrate asymmetry direction, and show that reverse ratchet motion can be produced by collective effects. No reversals occur for an isolated skyrmion on an asymmetric substrate. Finally, since a vector ratchet can produce motion in any direction, it could represent a method for controlling skyrmion motion for spintronic applications.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Principal fiber bundle description of number scaling for scalars and vectors: application to gauge theory

The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value are combined in the usual representations of number structures. This is valid as long as one structure of each number type is being considered. It is not valid when different structures of each number type are being considered. Elements of base sets of number structures, considered by themselves, have no meaning. They acquire meaning or value as elements of a number structure. Fiber bundles over a space or space time manifold, M, are described. The fiber consists of a collection of many real or complex scaling factor, s. A vector space at a fiber level, s, has as scalars, real or complex number structures at the same level. Connections are described that relate scalar and vector space structures at both neighbor M locations and at neighbor scaling levels. Scalar and vector structure valued fields are described and covariant derivatives of these fields are obtained. Two complex vector fields, each with one real and one imaginary field, appear, with one complex field associated with positions in M and the other with position dependent scaling factors. A derivation of the covariant derivative for scalar and vector values fields gives the same vector fields. The derivation shoes that complex vector field associated with scaling fiber levels is the gradient of a complex scalar field. Use of these results in gauge theory shows that the imaginary part of the vector field associated with M positions acts like the electromagnetic field. The physical relevance of the other three fields, if any, is not known.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Construction and Evaluation of Novel Rhesus Monkey Adenovirus Vaccine Vectors

Adenovirus vectors are widely used as vaccine candidates for a variety of pathogens, including HIV-1. To date, human and chimpanzee adenoviruses have been explored in detail as vaccine vectors. Furthermore, the phylogeny of human and chimpanzee adenoviruses is overlapping, and preexisting humoral and cellular immunity to both are exhibited in human populations worldwide. More distantly related adenoviruses may therefore offer advantages as vaccine vectors. We describe the primary isolation and vectorization of three novel adenoviruses from rhesus monkeys. The seroprevalence of these novel rhesus monkey adenovirus vectors was extremely low in sub-Saharan Africa human populations, and these vectors proved to have immunogenicity comparable to that of human and chimpanzee adenovirus vaccine vectors in mice. These rhesus monkey adenoviruses phylogenetically clustered with the poorly described adenovirus species G and robustly stimulated innate immune responses. These novel adenoviruses represent a new class of candidate vaccine vectors.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

The direct and indirect effects of copper on vector-borne disease dynamics

Metal pollution is a growing concern that affects the health of humans and animals globally. Copper is an essential insect micronutrient required for respiration, pigmentation and oxidative stress protection but can also act as a potentially toxic trace element. While several studies have focused on the negative fitness effects of copper on the aquatic larvae of mosquitoes, the effects of larval copper exposure on adult mosquito fitness (i.e., survival and fecundity) and their ability to transmit parasites (i.e., vector competence) remains unclear. Here, using a well-studied model vector-parasite system, the mosquito Aedes aegypti and parasite Dirofilaria immitis, we show that sublethal copper exposure in larval mosquitoes alters adult female fecundity and vector competence. Specifically, mosquitoes exposed to copper had a hormetic fecundity response and mosquitoes exposed to 600 μg/L of copper had significantly fewer infective parasite larvae than control mosquitoes not exposed to copper. Therefore, exposure of mosquito larvae to copper levels far below EPA-mandated safe drinking water limits (1300 μg/L) can impact vector-borne disease dynamics not only by reducing mosquito abundance (through increased larval mortality), but also by reducing parasite transmission risk. Our results also demonstrated that larval copper is retained through metamorphosis to adulthood in mosquitoes, indicating that these insects could transfer copper from aquatic to terrestrial foodwebs, especially in urban areas where they are abundant. To our knowledge this is the first study to directly link metal exposure with vector competence (i.e., ability to transmit parasites) in any vector-parasite system. Additionally, it also demonstrates unequivocally that mosquitoes can transfer contaminants from aquatic to terrestrial ecosystems. These results have broad implications for public health because they directly linking contaminants and vector-borne disease dynamics, as well as linking mosquitoes and contaminant dynamics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements

Within finite element models of fluids, vector-valued fields such as velocity or momentum variables are commonly discretised using the Raviart-Thomas elements. However, when using the lowest-order quadrilateral Raviart-Thomas elements, standard finite element discretisations of the vector transport equation typically have a low order of spatial accuracy. This paper describes two schemes that improve the accuracy of transporting such vector-valued fields on two-dimensional curved manifolds. The first scheme that is presented reconstructs the transported field in a higher-order function space, where the transport equation is then solved. The second scheme applies a mixed finite element formulation to the vector transport equation, simultaneously solving for the transported field and its vorticity. In this work, an approach to stabilising this mixed vector-vorticity formulation is presented that uses a Streamline Upwind Petrov-Galerkin (SUPG) method. These schemes are then demonstrated, along with their accuracy properties, through some numerical tests. Two new test cases are used to assess the transport of vector-valued fields on curved manifolds, solving the vector transport equation in isolation. The improvement of the schemes is also shown through two standard test cases for rotating shallow-water models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The development of Gibbs's dyadic and implications for the gradient of a vector field

In this paper, we review the history of the dyadic as developed by Gibbs. This mathematical construct appeared in the second part of Gibbs's pamphlet on vector analysis (published in 1884), and it represented the first known development of a Cartesian theory of tensors. Gibbs made extensive use of the dyadic to express his theory of linear vector functions, that is, functions that acted on vectors and mapped them to new vectors. The dyadic proved to be a capable vehicle in Gibbs's hands, and his theory for dyadics (which we would now call second-order Cartesian tensors) was relatively advanced. The theory detailed notions such as the decomposition of vectors and conditions under which a tensor would have an inverse. While Gibbs's theory for linear operators expressed by dyadics was robust, it did not seem to garner the attention that the more conventional vector analysis (published in the first half of his pamphlet in 1881) did. Perhaps in part because of the general unfamiliarity with the dyadic, two distinct and conflicting definitions of the gradient of a vector field have arisen in the literature. The details of these differences in notation, possible reasons for the difference, and a potential resolution are proposed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A Fiber-Optic Borehole Seismic Vector Sensor System for Geothermal Site Characterization and Monitoring

Seismic techniques are the dominant geophysical techniques for the characterization of subsurface structures and stratigraphy. The seismic techniques also dominate the monitoring and mapping of reservoir injection and production processes. Borehole seismology, of all the seismic techniques, despite its current shortcomings, has been shown to provide the highest resolution characterization and most precise monitoring results because it generates higher signal to noise ratio and higher frequency data than surface seismic techniques. The operational environments for borehole seismic instruments are however much more demanding than for surface seismic instruments making both the instruments and the installation much more expensive. The current state-of-the-art borehole seismic instruments have not been robust enough for long term monitoring compounding the problems with expensive instruments and installations. Furthermore, they have also not been able to record the large bandwidth data available in boreholes or having the sensitivity allowing them to record small high frequency micro seismic events with high vector fidelity. To reliably achieve high resolution characterization and long term monitoring of Enhanced Geothermal Systems (EGS) sites a new generation of borehole seismic instruments must therefore be developed and deployed. To address the critical site characterization and monitoring needs for EGS programs, US Department of Energy (DOE) funded Paulsson, Inc. in 2010 to develop a fiber optic based ultra-large bandwidth clamped borehole seismic vector array capable of deploying up to one thousand 3C sensor pods suitable for deployment into ultra-high temperature and high pressure boreholes. Tests of the fiber optic seismic vector sensors developed on the DOE funding have shown that the new borehole seismic sensor technology is capable of generating outstanding high vector fidelity data with extremely large bandwidth: 0.01 – 6,000 Hz. Field tests have shown that the system can record events at magnitudes much smaller than M-2.6 at frequencies up to 2,000 Hz. The sensors have also proved to be about 100 times more sensitive than the regular coil geophones that are used in borehole seismic systems today. The fiber optic seismic sensors have furthermore been qualified to operate at temperatures over 300°C (572°F). Simultaneously with the fiber optic based seismic 3C vector sensors we are using the lead-in fiber to acquire Distributed Acoustic Sensor (DAS) data from the surface to the bottom of the vector array. While the DAS data is of much lower quality than the vector sensor data it provides a 1 m spatial sampling of the downgoing wavefield which will be used to build the high resolution velocity model which is an essential component in high resolution imaging and monitoring.

15 GEOTHERMAL ENERGY↗
DOE OSTI2016

Divergence preserving reconstruction of the nodal components of a vector field from its normal components to edges

We have developed a new divergence preserving method for the reconstruction of the Cartesian components of a vector field from the orthogonal projection of a vector field to the normals to edges in two dimensional. In this method, discrete divergences computed from the nodal components and from the normal ones are exactly the same. Our new method consists of two stages. At the first stage, we use an extended version of the local procedure described in [J. Comput. Phys., 139:406–409, 1998] to obtain a ‘reference’ nodal vector. This local procedure is exact for linear vector fields; however, the discrete divergence is not preserved. Then, we formulate a constrained optimization problem, in which this reference vector plays the role of a target, and the divergence constraints are enforced by using Lagrange multipliers. It leads to the solution of ‘elliptic’ like discrete equations for the cell-centered Lagrange multipliers. The new global divergence preserving method is exact for linear vector fields. Here in this paper, we describe all details of our new method and present numerical results, which confirm our theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Search for single production of vector-like quarks decaying to a top quark and a $\mathrm {W} $ boson in proton–proton collisions at $\sqrt{s} = 13 \,\text {TeV} $

A search is presented for the single production of vector-like quarks in proton–proton collisions at $\sqrt{s}=13\,\text {TeV} $. The data, corresponding to an integrated luminosity of 35.9 $\,\text {fb}^{-1}$, were recorded with the CMS experiment at the LHC. The analysis focuses on the vector-like quark decay into a top quark and a $\mathrm {W} $ boson, with one muon or electron in the final state. The mass of the vector-like quark candidate is reconstructed from hadronic jets, the lepton, and the missing transverse momentum. Methods for the identification of $\mathrm {b}$ quarks and of highly Lorentz boosted hadronically decaying top quarks and $\mathrm {W} $ bosons are exploited in this search. No significant deviation from the standard model background expectation is observed. Exclusion limits at 95% confidence level are set on the product of the production cross section and branching fraction as a function of the vector-like quark mass, which range from 0.3 to 0.03 $\,\text {pb}$ for vector-like quark masses of 700 to 2000 $\,\text {GeV}$. Mass exclusion limits up to 1660 $\,\text {GeV}$ are obtained, depending on the vector-like quark type, coupling, and decay width. Furthermore, these represent the most stringent exclusion limits for the single production of vector-like quarks in this channel.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Consistent Feature Extraction From Vector Fields: Combinatorial Representations and Analysis Under Local Reference Frames

This dissertation presents research on addressing some of the contemporary challenges in the analysis of vector fields—an important type of scientific data useful for representing a multitude of physical phenomena, such as wind flow and ocean currents. In particular, new theories and computational frameworks to enable consistent feature extraction from vector fields are presented. One of the most fundamental challenges in the analysis of vector fields is that their features are defined with respect to reference frames. Unfortunately, there is no single “correct” reference frame for analysis, and an unsuitable frame may cause features of interest to remain undetected, thus creating serious physical consequences. This work develops new reference frames that enable extraction of localized features that other techniques and frames fail to detect. As a result, these reference frames objectify the notion of “correctness” of features for certain goals by revealing the phenomena of importance from the underlying data. An important consequence of using these local frames is that the analysis of unsteady (time-varying) vector fields can be reduced to the analysis of sequences of steady (timeindependent) vector fields, which can be performed using simpler and scalable techniques that allow better data management by accessing the data on a per-time-step basis. Nevertheless, the state-of-the-art analysis of steady vector fields is not robust, as most techniques are numerical in nature. The residing numerical errors can violate consistency with the underlying theory by breaching important fundamental laws, which may lead to serious physical consequences. This dissertation considers consistency as the most fundamental characteristic of computational analysis that must always be preserved, and presents a new discrete theory that uses combinatorial representations and algorithms to provide consistency guarantees during vector field analysis along with the uncertainty visualization of unavoidable discretization errors. Together, the two main contributions of this dissertation address two important concerns regarding feature extraction from scientific data: correctness and precision. The work presented here also opens new avenues for further research by exploring more-general reference frames and more-sophisticated domain discretizations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Episomal DNA vectors for plant genetic engineering

This disclosure pertains to a novel platform for genetic engineering of chloroplasts. The disclosure provides episomal DNA vectors containing a chloroplast origin of replication. These vectors remain extra-plastomic and sustainably and autonomously replicate in chloroplasts of the plant cells transformed with the vectors and in the plants regenerated from the transformed plant cells. The episomal DNA vectors do not contain any sequence that shares sequence homology with the plastome DNA and, thus, do not get integrated into the plastome DNA. The vectors can also comprise one or more genes of interest that confer desirable characteristics to the transformed plant cells. The disclosure also provides methods of transforming plant cells with the episomal DNA vectors and regenerating from the transformed plant cells plants having desirable characteristics. The vectors and methods disclosed herein provide a significant advancement in speed, flexibility, and prospects of introducing genes into plant cells for effective metabolic engineering.

Lenaghan, Scott C.↗
DOE OSTI2023

Vectorization of CMSSW offline software

The CMS experiment has been utilizing vectorization, or SIMD, in parts of its data processing applications for over a decade. On x86 platforms the vectorization level is still SSE3. In the past attempts to use wider vector instruction sets such as AVX or AVX-512 have, in practice, not resulted in improvements in the overall event processing throughput, because the CPUs scale down their frequency when processing AVX instructions. In addition, a notable part of the global pool of CMS’ resources has been old systems either not supporting AVX, or where the CPU frequency downscaling impacts all cores of the CPU. CMS has nevertheless continued to vectorize more of its application code, and in this work we review profiling methods we have found effective to find out pieces of code that would benefit from vectorization, and techniques to transform those codes such that the GCC compiler is able to auto-vectorize those codes. The build system used for CMSSW, Scram, has also been enha nced to be able to build code for multiple CPU microarchitectures such that the shared libraries of desired microarchitecture level can be loaded based on the CPU of the system. This multi-microarchitecture setup is invisible to the workflow management system, which makes its deployment straightforward. We describe in detail how this multi-microarchitecture build is set up, and measure the impact of using wider vector units than SSE3 on the event processing throughput of CMS applications such as simulation and reconstruction on recent x86 CPUs.

Gartung, Patrick↗
DOE OSTI2021

Towards a Unified theory of Fractional and Nonlocal Vector Calculus

Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or anomalous behavior. This has driven a desire for a vector calculus that includes nonlocal and fractional gradient, divergence and Laplacian type operators, as well as tools such as Green’s identities, to model subsurface transport, turbulence, and conservation laws. In the literature, several independent definitions and theories of nonlocal and fractional vector calculus have been put forward. Some have been studied rigorously and in depth, while others have been introduced ad-hoc for specific applications. The goal of this work is to provide foundations for a unified vector calculus by (1) consolidating fractional vector calculus as a special case of nonlocal vector calculus, (2) relating unweighted and weighted Laplacian operators by introducing an equivalence kernel, and (3) proving a form of Green’s identity to unify the corresponding variational frameworks for the resulting nonlocal volume-constrained problems. Here, the proposed framework goes beyond the analysis of nonlocal equations by supporting new model discovery, establishing theory and interpretation for a broad class of operators, and providing useful analogues of standard tools from the classical vector calculus.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Unified Theory of Fractional Nonlocal and Weighted Nonlocal Vector Calculus

Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or anomalous behavior. This has driven a desire for a vector calculus that includes nonlocal and fractional gradient, divergence and Laplacian type operators, as well as tools such as Green's identities, to model subsurface transport, turbulence, and conservation laws. In the literature, several independent definitions and theories of nonlocal and fractional vector calculus have been put forward. Some have been studied rigorously and in depth, while others have been introduced ad-hoc for specific applications. The goal of this work is to provide foundations for a unified vector calculus by (1) consolidating fractional vector calculus as a special case of nonlocal vector calculus, (2) relating unweighted and weighted Laplacian operators by introducing an equivalence kernel, and (3) proving a form of Green's identity to unify the corresponding variational frameworks for the resulting nonlocal volume-constrained problems. The proposed framework goes beyond the analysis of nonlocal equations by supporting new model discovery, establishing theory and interpretation for a broad class of operators, and providing useful analogues of standard tools from the classical vector calculus.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Transition, coexistence, and interaction of vector localized waves arising from higher-order effects

We study vector localized waves on continuous wave background with higher-order effects in a two-mode optical fiber. The striking properties of transition, coexistence, and interaction of these localized waves arising from higher-order effects are revealed in combination with corresponding modulation instability (MI) characteristics. It shows that these vector localized wave properties have no analogues in the case without higher-order effects. Specifically, compared to the scalar case, an intriguing transition between bright–dark rogue waves and w-shaped–anti-w-shaped solitons, which occurs as a result of the attenuation of MI growth rate to vanishing in the zero-frequency perturbation region, is exhibited with the relative background frequency. In particular, our results show that the w-shaped–anti-w-shaped solitons can coexist with breathers, coinciding with the MI analysis where the coexistence condition is a mixture of a modulation stability and MI region. It is interesting that their interaction is inelastic and describes a fusion process. In addition, we demonstrate an annihilation phenomenon for the interaction of two w-shaped solitons which is identified essentially as an inelastic collision in this system. -- Highlights: •Vector rogue wave properties induced by higher-order effects are studied. •A transition between vector rogue waves and solitons is obtained. •The link between the transition and modulation instability (MI) is demonstrated. •The coexistence of vector solitons and breathers coincides with the MI features. •An annihilation phenomenon for the vector two w-shaped solitons is presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

How random is a random vector?

Over 80 years ago Samuel Wilks proposed that the “generalized variance” of a random vector is the determinant of its covariance matrix. To date, the notion and use of the generalized variance is confined only to very specific niches in statistics. In this paper we establish that the “Wilks standard deviation” –the square root of the generalized variance–is indeed the standard deviation of a random vector. We further establish that the “uncorrelation index” –a derivative of the Wilks standard deviation–is a measure of the overall correlation between the components of a random vector. Both the Wilks standard deviation and the uncorrelation index are, respectively, special cases of two general notions that we introduce: “randomness measures” and “independence indices” of random vectors. In turn, these general notions give rise to “randomness diagrams”—tangible planar visualizations that answer the question: How random is a random vector? The notion of “independence indices” yields a novel measure of correlation for Lévy laws. In general, the concepts and results presented in this paper are applicable to any field of science and engineering with random-vectors empirical data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Vector tomography for reconstructing electric fields with non-zero divergence in bounded domains

In vector tomography (VT), the aim is to reconstruct an unknown multi-dimensional vector field using line integral data. In the case of a 2-dimensional VT, two types of line integral data are usually required. These data correspond to integration of the parallel and perpendicular projection of the vector field along the integration lines and are called the longitudinal and transverse measurements, respectively. In most cases, however, the transverse measurements cannot be physically acquired. Therefore, the VT methods are typically used to reconstruct divergence-free (or source-free) velocity and flow fields that can be reconstructed solely from the longitudinal measurements. In this paper, we show how vector fields with non-zero divergence in a bounded domain can also be reconstructed from the longitudinal measurements without the need of explicitly evaluating the transverse measurements. To the best of our knowledge, VT has not previously been used for this purpose. In particular, we study low-frequency, time-harmonic electric fields generated by dipole sources in convex bounded domains which arise, for example, in electroencephalography (EEG) source imaging. We explain in detail the theoretical background, the derivation of the electric field inverse problem and the numerical approximation of the line integrals. We show that fields with non-zero divergence can be reconstructed from the longitudinal measurements with the help of two sparsity constraints that are constructed from the transverse measurements and the vector Laplace operator. As a comparison to EEG source imaging, we note that VT does not require mathematical modeling of the sources. By numerical simulations, we show that the pattern of the electric field can be correctly estimated using VT and the location of the source activity can be determined accurately from the reconstructed magnitudes of the field. - Highlights: • Vector tomography is used to reconstruct electric fields generated by dipole sources. • Inverse solutions are based on longitudinal and transverse line integral measurements. • Transverse line integral measurements are used as a sparsity constraint. • Numerical procedure to approximate the line integrals is described in detail. • Patterns of the studied electric fields are correctly estimated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Vector-model-supported approach in prostate plan optimization

Lengthy time consumed in traditional manual plan optimization can limit the use of step-and-shoot intensity-modulated radiotherapy/volumetric-modulated radiotherapy (S&S IMRT/VMAT). A vector model base, retrieving similar radiotherapy cases, was developed with respect to the structural and physiologic features extracted from the Digital Imaging and Communications in Medicine (DICOM) files. Planning parameters were retrieved from the selected similar reference case and applied to the test case to bypass the gradual adjustment of planning parameters. Therefore, the planning time spent on the traditional trial-and-error manual optimization approach in the beginning of optimization could be reduced. Each S&S IMRT/VMAT prostate reference database comprised 100 previously treated cases. Prostate cases were replanned with both traditional optimization and vector-model-supported optimization based on the oncologists' clinical dose prescriptions. A total of 360 plans, which consisted of 30 cases of S&S IMRT, 30 cases of 1-arc VMAT, and 30 cases of 2-arc VMAT plans including first optimization and final optimization with/without vector-model-supported optimization, were compared using the 2-sided t-test and paired Wilcoxon signed rank test, with a significance level of 0.05 and a false discovery rate of less than 0.05. For S&S IMRT, 1-arc VMAT, and 2-arc VMAT prostate plans, there was a significant reduction in the planning time and iteration with vector-model-supported optimization by almost 50%. When the first optimization plans were compared, 2-arc VMAT prostate plans had better plan quality than 1-arc VMAT plans. The volume receiving 35 Gy in the femoral head for 2-arc VMAT plans was reduced with the vector-model-supported optimization compared with the traditional manual optimization approach. Otherwise, the quality of plans from both approaches was comparable. Vector-model-supported optimization was shown to offer much shortened planning time and iteration number without compromising the plan quality.

61 RADIATION PROTECTION AND DOSIMETRY↗