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At least 991 records · Page 55

Plant terpene specialized metabolism: complex networks or simple linear pathways?

From the perspectives of pathway evolution, discovery and engineering of plant specialized metabolism, the nature of the biosynthetic routes represents a critical aspect. Classical models depict biosynthesis typically from an end-point angle and as linear, for example, connecting central and specialized metabolism. As the number of functionally elucidated routes increased, the enzymatic foundation of complex plant chemistries became increasingly well understood. The perception of linear pathway models has been severely challenged. With a focus on plant terpenoid specialized metabolism, we review here illustrative examples supporting that plants have evolved complex networks driving chemical diversification. The completion of several diterpene, sesquiterpene and monoterpene routes shows complex formation of scaffolds and their subsequent functionalization. These networks show that branch points, including multiple sub-routes, mean that metabolic grids are the rule rather than the exception. This concept presents significant implications for biotechnological production.

60 APPLIED LIFE SCIENCES↗

A Novel Approach for Computing Rigid Body Motion Using Linear Accelerations

Here, a novel approach is presented for computing general rigid body motion based on a few known linear accelerations. This method utilizes linear acceleration data obtained from three distinct points on the body, all within a body-fixed reference frame. The only requirement is that the three chosen points must not be collinear. A system of differential-algebraic equations is derived, combining principles of rigid body kinematics with theory of the rotation group SO(3). These equations provide a framework for numerically computing various motion parameters, including angular velocity, angular acceleration, body orientation, velocity field, acceleration field, and displacement field. By numerically solving this system of equations, we can fully characterize rigid body motion in three-dimensional space. A numerical example is provided to demonstrate the practical implementation and efficacy of the proposed technique, illustrating its potential for accurate motion computation in various applications.

42 ENGINEERING↗

SU-E-T-78: Comparison of Dose-Averaged Linear Energy Transfer Calculation Methods Used in Monte Carlo Simulations of Clinical Proton Beams

Purpose: To evaluate the differences in dose-averaged linear energy transfer (LETd) maps calculated in water by means of different strategies found in the literature in proton therapy Monte Carlo simulations and to compare their values with dose-mean lineal energy microdosimetry calculations. Methods: The Geant4 toolkit (version 9.6.2) was used. Dose and LETd maps in water were scored for primary protons with cylindrical voxels defined around the beam axis. Three LETd calculation methods were implemented. First, the LETd values were computed by calculating the unrestricted linear energy transfer (LET) associated to each single step weighted by the energy deposition (including delta-rays) along the step. Second, the LETd was obtained for each voxel by computing the LET along all the steps simulated for each proton track within the voxel, weighted by the energy deposition of those steps. Third, the LETd was scored as the quotient between the second momentum of the LET distribution, calculated per proton track, over the first momentum. These calculations were made with various voxel thicknesses (0.2 – 2.0 mm) for a 160 MeV proton beamlet and spread-out Bragg Peaks (SOBP). The dose-mean lineal energy was calculated in a uniformly-irradiated water sphere, 0.005 mm radius. Results: The value of the LETd changed systematically with the voxel thickness due to delta-ray emission and the enlargement of the LET distribution spread, especially at shallow depths. Differences of up to a factor 1.8 were found at the depth of maximum dose, leading to similar differences at the central and distal depths of the SOBPs. The third LETd calculation method gave better agreement with microdosimetry calculations around the Bragg Peak. Conclusion: Significant differences were found between LETd map Monte Carlo calculations due to both the calculation strategy and the voxel thickness used. This could have a significant impact in radiobiologically-optimized proton therapy treatments.

07 ISOTOPE AND RADIATION SOURCES↗

TH-E-BRE-02: A Forward Scattering Approximation to Dose Calculation Using the Linear Boltzmann Transport Equation

Purpose: To investigate the use of the linear Boltzmann transport equation as a dose calculation tool which can account for interface effects, while still having faster computation times than Monte Carlo methods. In particular, we introduce a forward scattering approximation, in hopes of improving calculation time without a significant hindrance to accuracy. Methods: Two coupled Boltzmann transport equations were constructed, one representing the fluence of photons within the medium, and the other, the fluence of electrons. We neglect the scattering term within the electron transport equation, resulting in an extreme forward scattering approximation to reduce computational complexity. These equations were then solved using a numerical technique for solving partial differential equations, known as a finite difference scheme, where the fluence at each discrete point in space is calculated based on the fluence at the previous point in the particle's path. Using this scheme, it is possible to develop a solution to the Boltzmann transport equations by beginning with boundary conditions and iterating across the entire medium. The fluence of electrons can then be used to find the dose at any point within the medium. Results: Comparisons with Monte Carlo simulations indicate that even simplistic techniques for solving the linear Boltzmann transport equation yield expected interface effects, which many popular dose calculation algorithms are not capable of predicting. Implementation of a forward scattering approximation does not appear to drastically reduce the accuracy of this algorithm. Conclusion: Optimized implementations of this algorithm have been shown to be very accurate when compared with Monte Carlo simulations, even in build up regions where many models fail. Use of a forward scattering approximation could potentially give a reasonably accurate dose distribution in a shorter amount of time for situations where a completely accurate dose distribution is not required, such as in certain optimization algorithms.

97 MATHEMATICS AND COMPUTING↗

A deterministic solution of the first order linear Boltzmann transport equation in the presence of external magnetic fields

Purpose: Accurate radiotherapy dose calculation algorithms are essential to any successful radiotherapy program, considering the high level of dose conformity and modulation in many of today’s treatment plans. As technology continues to progress, such as is the case with novel MRI-guided radiotherapy systems, the necessity for dose calculation algorithms to accurately predict delivered dose in increasingly challenging scenarios is vital. To this end, a novel deterministic solution has been developed to the first order linear Boltzmann transport equation which accurately calculates x-ray based radiotherapy doses in the presence of magnetic fields. Methods: The deterministic formalism discussed here with the inclusion of magnetic fields is outlined mathematically using a discrete ordinates angular discretization in an attempt to leverage existing deterministic codes. It is compared against the EGSnrc Monte Carlo code, utilizing the emf-macros addition which calculates the effects of electromagnetic fields. This comparison is performed in an inhomogeneous phantom that was designed to present a challenging calculation for deterministic calculations in 0, 0.6, and 3 T magnetic fields oriented parallel and perpendicular to the radiation beam. The accuracy of the formalism discussed here against Monte Carlo was evaluated with a gamma comparison using a standard 2%/2 mm and a more stringent 1%/1 mm criterion for a standard reference 10 × 10 cm{sup 2} field as well as a smaller 2 × 2 cm{sup 2} field. Results: Greater than 99.8% (94.8%) of all points analyzed passed a 2%/2 mm (1%/1 mm) gamma criterion for all magnetic field strengths and orientations investigated. All dosimetric changes resulting from the inclusion of magnetic fields were accurately calculated using the deterministic formalism. However, despite the algorithm’s high degree of accuracy, it is noticed that this formalism was not unconditionally stable using a discrete ordinate angular discretization. Conclusions: The feasibility of including magnetic field effects in a deterministic solution to the first order linear Boltzmann transport equation is shown. The results show a high degree of accuracy when compared against Monte Carlo calculations in all magnetic field strengths and orientations tested.

60 APPLIED LIFE SCIENCES↗

Discontinuous finite element space-angle treatment of the first order linear Boltzmann transport equation with magnetic fields: Application to MRI-guided radiotherapy

Purpose: The advent of magnetic resonance imaging (MRI) guided radiotherapy systems demands the incorporation of the magnetic field into dose calculation algorithms of treatment planning systems. This is due to the fact that the Lorentz force of the magnetic field perturbs the path of the relativistic electrons, hence altering the dose deposited by them. Building on the previous work, the authors have developed a discontinuous finite element space-angle treatment of the linear Boltzmann transport equation to accurately account for the effects of magnetic fields on radiotherapy doses. Methods: The authors present a detailed description of their new formalism and compare its accuracy to GEANT4 Monte Carlo calculations for magnetic fields parallel and perpendicular to the radiation beam at field strengths of 0.5 and 3 T for an inhomogeneous 3D slab geometry phantom comprising water, bone, and air or lung. The accuracy of the authors’ new formalism was determined using a gamma analysis with a 2%/2 mm criterion. Results: Greater than 98.9% of all points analyzed passed the 2%/2 mm gamma criterion for the field strengths and orientations tested. The authors have benchmarked their new formalism against Monte Carlo in a challenging radiation transport problem with a high density material (bone) directly adjacent to a very low density material (dry air at STP) where the effects of the magnetic field dominate collisions. Conclusions: A discontinuous finite element space-angle approach has been proven to be an accurate method for solving the linear Boltzmann transport equation with magnetic fields for cases relevant to MRI guided radiotherapy. The authors have validated the accuracy of this novel technique against GEANT4, even in cases of strong magnetic field strengths and low density air.

61 RADIATION PROTECTION AND DOSIMETRY↗

Linear rheology and structure of molecular bottlebrushes with short side chains

We investigate the microstructure and linear viscoelasticity of model molecular bottlebrushes (BBs) using rheological and small-angle X-ray and neutron scattering measurements. Our polymers have short atactic polypropylene (aPP) side chains of molecular weight ranging from 119 g/mol to 259 g/mol and narrow molecular weight distribution (M{sub w}/M{sub n} 1.02–1.05). The side chain molecular weights are a small fraction of the entanglement molecular weight of the corresponding linear polymer (M{sub e,aPP}= 7.05 kg/mol), and as such, they are unentangled. The morphology of the aPP BBs is characterized as semiflexible thick chains with small side chain interdigitation. Their dynamic master curves, obtained by time-temperature superposition, reveal two sequential relaxation processes corresponding to the segmental relaxation and the relaxation of the BB backbone. Due to the short length of the side chains, their fast relaxation could not be distinguished from the glassy relaxation. The fractional free volume is an increasing function of the side chain length (N{sub SC}). Therefore, the glassy behavior of these polymers as well as their molecular friction and dynamic properties are influenced by their N{sub SC} values. The apparent flow activation energies are a decreasing function of N{sub SC}, and their values explain the differences in zero-shear viscosity measured at different temperatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Kinematic dust viscosity effect on linear and nonlinear dust-acoustic waves in space dusty plasmas with nonthermal ions

Linear and nonlinear dust-acoustic (DA) waves are studied in a collisionless, unmagnetized and dissipative dusty plasma consisting of negatively charged dust grains, Boltzmann-distributed electrons, and nonthermal ions. The normal mode analysis is used to obtain a linear dispersion relation illustrating the dependence of the wave damping rate on the carrier wave number, the dust viscosity coefficient, the ratio of the ion temperature to the electron temperatures, and the nonthermal parameter. The plasma system is analyzed nonlinearly via the reductive perturbation method that gives the KdV-Burgers equation. Some interesting physical solutions are obtained to study the nonlinear waves. These solutions are related to soliton, a combination between a shock and a soliton, and monotonic and oscillatory shock waves. Their behaviors are illustrated and shown graphically. The characteristics of the DA solitary and shock waves are significantly modified by the presence of nonthermal (fast) ions, the ratio of the ion temperature to the electron temperature, and the dust kinematic viscosity. The topology of the phase portrait and the potential diagram of the KdV-Burgers equation is illustrated, whose advantage is the ability to predict different classes of traveling wave solutions according to different phase orbits. The energy of the soliton wave and the electric field are calculated. The results in this paper can be generalized to analyze the nature of plasma waves in both space and laboratory plasma systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Submicrosecond linear pulse transformer for 800 kV voltage with modular low-inductance primary power supply

A pulsed power source with voltage amplitude up to 800 kV for fast charging (350–400 ns) of the forming line of a high-current nanosecond accelerator is developed. The source includes capacitive energy storage and a linear pulse transformer. The linear transformer consists of a set of 20 inductors with circular ferromagnetic cores surrounded by primary windings inside of which a common stock adder of voltage with film-glycerol insulation is placed. The primary energy storage consists of ten modules, each of which is a low-inductance assembly of two capacitors with a capacitance of 0.35 μF and one gas switch mounted in the same frame. The total energy stored in capacitors is 5.5 kJ at the operating voltage of 40 kV. According to test results, the parameters of the equivalent circuit of the source are the following: shock capacitance = 17.5 nF, inductance = 2 μH, resistance = 3.2 Ω.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Surface wave and linear operating mode of a plasma antenna

The relation between the propagation conditions of a surface electromagnetic wave along a finiteradius plasma cylinder and the linear operating mode of a plasma antenna is investigated. The solution to the dispersion relation for a surface wave propagating along a finite-radius plasma cylinder is analyzed for weakly and strongly collisional plasmas. Computer simulations of an asymmetrical plasma dipole antenna are performed using the KARAT code, wherein the dielectric properties of plasma are described in terms of the Drude model. The plasma parameters corresponding to the linear operating mode of a plasma antenna are determined. It is demonstrated that the characteristics of the plasma antenna in this mode are close to those of an analogous metal antenna.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On the theory of the two-photon linear photovoltaic effect in n-GaP

A quantitative theory of the diagonal (ballistic) and nondiagonal (shift) band index contributions to the two-photon current of the linear photovoltaic effect in a semiconductor with a complex band due to the asymmetry of events of electron scattering at phonons and photons is developed. It is shown that processes caused by the simultaneous absorption of two photons do not contribute to the ballistic photocurrent in n-GaP. This is due to the fact that, in this case, there is no asymmetric distribution of the momentum of electrons excited with photons; this distribution arises upon the sequential absorption of two photons with the involvement of LO phonons. It is demonstrated that the temperature dependence of the shift contribution to the two-photon photocurrent in n-GaP is determined by the temperature dependence of the light-absorption coefficient caused by direct optical transitions of electrons between subbands X{sub 1} and X{sub 3}. It is shown that the spectral dependence of the photocurrent has a feature in the light frequency range ω → Δ/2ℏ, which is related to the hump-like shape of subband X{sub 1} in n-GaP{sup 1} and the root-type singularity of the state density determined as k{sub ω}{sup -1}= (2ℏω–Δ){sup –1/2}, where Δ is the energy gap between subbands X{sub 1} and X{sub 3}. The spectral and temperature dependences of the coefficient of absorption of linearly polarized light in n-GaP are obtained with regard to the cone-shaped lower subband of the conduction band.

36 MATERIALS SCIENCE↗

Synthesis and Tests of a 1-m{sup 3} Scintillator Based on Linear Alkylbenzene

The stability of a liquid organic scintillator based on linear alkylbenzene in a volume of 1 m{sup 3} was measured. The measurements were performed using an iDREAM reactor antineutrino detector at the National Research Center Kurchatov Institute. No systemic degradation of the scintillator light yield within an observation time of 225 days was observed. These long-term stability measurements of a large-volume liquid organic scintillator based on linear alkylbenzene are the first in Russia.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Goal-Oriented Optimal Approximations of Bayesian Linear Inverse Problems

We propose optimal dimensionality reduction techniques for the solution of goal-oriented linear-Gaussian inverse problems, where the quantity of interest (QoI) is a function of the inversion parameters. These approximations are suitable for large-scale applications. In particular, we study the approximation of the posterior covariance of the QoI as a low-rank negative update of its prior covariance and prove optimality of this update with respect to the natural geodesic distance on the manifold of symmetric positive definite matrices. Assuming exact knowledge of the posterior mean of the QoI, the optimality results extend to optimality in distribution with respect to the Kullback--Leibler divergence and the Hellinger distance between the associated distributions. We also propose the approximation of the posterior mean of the QoI as a low-rank linear function of the data and prove optimality of this approximation with respect to a weighted Bayes risk. Both of these optimal approximations avoid the explicit computation of the full posterior distribution of the parameters and instead focus on directions that are well informed by the data and relevant to the QoI. These directions stem from a balance among all the components of the goal-oriented inverse problem: prior information, forward model, measurement noise, and ultimate goals. We illustrate the theory using a high-dimensional inverse problem in heat transfer.

97 MATHEMATICS AND COMPUTING↗

Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

We consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error [A. Mugler and H.-J. Starkloff, ESAIM Math. Model. Numer. Anal., 47 (2013), pp. 1237--1263]. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weighted $\ell^2$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $\ell^2$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.

97 MATHEMATICS AND COMPUTING↗

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

Fully implicit Runge--Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). Additionally, this framework also naturally applies to discontinuous Galerkin discretizations in time. Under quite general assumptions on the spatial discretization that yield stable time integration, the preconditioned operator is proven to have condition number bounded by a small, order-one constant, independent of the spatial mesh and time-step size, and with only weak dependence on number of stages/polynomial order; for example, the preconditioned operator for 10th-order Gauss IRK has condition number less than two, independent of the spatial discretization and time step. The new method can be used with arbitrary existing preconditioners for backward Euler-type time-stepping schemes and is amenable to the use of three-term recursion Krylov methods when the underlying spatial discretization is symmetric. The new method is demonstrated to be effective on various high-order finite-difference and finite element discretizations of linear parabolic and hyperbolic problems, demonstrating fast, scalable solution of up to 10th-order accuracy. The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications and wallclock time as required using standard diagonally IRK methods.

97 MATHEMATICS AND COMPUTING↗

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗

Potential linear and angular momentum in the scalar diquark model

We present an analytic two-loop calculation within the scalar diquark model of the potential linear and angular momenta, defined as the difference between the Jaffe-Manohar and Ji notions of linear and angular momenta. As expected by parity and time-reversal symmetries, a direct calculation confirms that the potential transverse momentum coincides with the Jaffe-Manohar (or canonical) definition of average quark transverse momentum, also known as the quark Sivers shift. We examine whether initial/final-state interactions at the origin of the Sivers asymmetry can also generate a potential angular momentum in the scalar diquark model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Luminosity Limitations of Linear Colliders Based on Plasma Acceleration

Particle acceleration in plasma creates a possibility of exceptionally high accelerating gradients and appears as a very attractive option for future linear electron-positron and/or photon-photon colliders. These high accelerating gradients were already demonstrated in a number of experiments. Furthermore, a linear collider requires exceptionally high beam brightness which still needs to be demonstrated. In this article we discuss major phenomena which limit the beam brightness of accelerated beam and, consequently, the collider luminosity.

43 PARTICLE ACCELERATORS↗