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At least 361 records · Page 20

Calculations of Beam-Beam Effect and Luminosity for Crab Dynamics Simulations in JLEIC

Crab crossing is an integral part of the Jefferson Lab Electron-Ion Collider (JLEIC) design to achieve high luminosity while meeting the detection and physics pro-gram requirements. The crab crossing scheme provides a head-on beam-beam collision for beams with a nonzero crossing angle. Simulations of crabbing dynamics currently do not include beam-beam effects. We describe a framework for accurate simulation of beam-beam effects on crabbing dynamics by applying a numerical calculation of the Bassetti-Erskine analytic solution to symplectic particle tracking codes. The numerical calculation is benchmarked against the analytic solution by calculating the luminosity reduction for several colliding beam scenarios. Benchmarking results show good agreement be-tween the numerical calculation and analytic solution, paving the way for implementation of the beam-beam kick to Elegant tracking simulations.

Huang, He↗

Development, verification, and validation of comprehensive acoustic fluid-structure interaction capabilities in an open-source computational platform

The acoustic fluid-structure interaction (FSI) formulation is a practical numerical approach for the seismic analysis of fluid-filled tanks. However, there are no verification and validation studies reported in the literature that demonstrate the ability of an acoustic FSI numerical model to predict responses important to structural and mechanical design for intense translational and rotational earthquake inputs. Herein, an acoustic FSI formulation is implemented in the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE), and is formally verified and validated using analytical solutions and code-to-code verification, and experimental data, respectively. The analytical solutions are for small amplitude, unidirectional seismic inputs. The code-to-code verification utilizes a previously verified and validated Arbitrary Lagrangian-Eulerian (ALE) numerical model in the commercial finite element code LS-DYNA. The validation studies utilize a comprehensive data set assembled from results of 3D earthquake-simulator tests of a fluid-filled vessel. The acoustic numerical model in MOOSE is verified and validated for hydrodynamic pressures and support reactions except for cases that involve significant convective response. For small amplitude inputs, numerically predicted wave heights match those of the analytical solutions. The numerical model is not verified and validated for wave height calculations under intense 3D seismic inputs. The run times for the acoustic FSI simulations in MOOSE are an order of magnitude, or more, shorter than for the corresponding ALE simulations in LS-DYNA. The utility of the MOOSE acoustic FSI implementation is demonstrated by seismic analysis of a building equipped with a fluid-filled, advanced nuclear reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Feasibility study of real-time planning for stereotactic radiosurgery

Purpose: 3D rotational setup errors in radiotherapy are often ignored by most clinics due to inability to correct or simulate them accurately and efficiently. There are two types of rotation-related problems in a clinical setting. One is to assess the affected dose distribution in real-time if correction is not applied and the other one is to correct the rotational setup errors prior to the initiation of the treatment. Here, the authors present the analytical solutions to both problems. Methods: (1) To assess the real-time dose distribution, eight stereotactic radiosurgery (SRS) cases were used as examples. For each plan, two new sets of beams with different table, gantry, and collimator angles were given in analytical forms as a function of patient rotational errors. The new beams simulate the rotational effects of the patient during the treatment setup. By using one arbitrary set of beams, SRS plans were recomputed with a series of different combinations of patient rotational errors, ranging from (-5 Degree-Sign , -5 Degree-Sign , -5 Degree-Sign ) to (5 Degree-Sign , 5 Degree-Sign , 5 Degree-Sign ) (roll, pitch, and yaw) with an increment of 1 Degree-Sign and compared with those without rotational errors. For each set of rotational errors, its corresponding equivalent beams were computed using the analytical solutions and then used for dose calculation. (2) To correct for the rotational errors, two new sets of table, gantry, and collimator angles were derived analytically to validate the previously published derivation. However, in the derivation, a novel methodology was developed and two sets of table, gantry, and collimator angles were obtained in analytical forms. The solutions provide an alternative approach to rotational error correction by rotating the couch, gantry, and collimator rather than the patient. Results: For demonstration purpose, the above-derived new beams were implemented in a treatment planning system (TPS) to study the rotational effects on the SRS cases. For each case, the authors have generated ten additional plans that accounted for different rotations of the patient. They have found that rotations have an insignificant effect on the minimal, maximum, mean doses, and V{sub 80%} of the planning target volume (PTV) when the rotations were relatively small. This was particularly true for the small and near-spherical targets. They, however, did change V{sub 95%} significantly when the rotations approached 5 Degree-Sign . The theory has been validated with clinical SRS cases and proven to be practical and viable. The preliminary results demonstrate that the rotational effects are patient-specific and depend on several important factors, such as the PTV size, the PTV location, and the beam configuration. The solutions given in this paper are of great potential values in clinical applications. Conclusions: They have derived the analytical solutions to a new set of table, gantry, and collimator angles for a given treatment beam configuration as a function of patient rotational errors. One solution was used to assess the dosimetric effects of an imperfect patient setup and the other one was used to correct for the setup errors without rotating the patient. Compared to the widely adopted method of rotation effect assessment by importing the rotational CT images into TPS, the equivalent beam approach is simple and accurate. The analytical solutions to correcting for rotational setup errors prior to treatment were also derived. Based on the initial clinical investigations, they firmly believe that clinically viable real-time treatment planning and adaptive radiation therapy are feasible with this novel method.

60 APPLIED LIFE SCIENCES↗

Free-standing gold elliptical nanoantenna with tunable wavelength in near-infrared region for enhanced Raman spectroscopy

The purpose of this work is to present a surface-enhanced Raman scattering (SERS) amplifying antenna for the possible usage in the near-infrared region. Instead of the visible-light range amplifying antenna such as a bowtie, the finite-difference time-domain (FDTD) simulation results indicate that elliptical antenna could provide large electromagnetic field enhancement at near-infrared wavelength by combining the free-standing enhancement property with large aspect ratios of the ellipse geometry. The simulation results consist with the enhancement factors characterized by SERS measurements at the excited wavelength of 785 nm for different aspect ratios and periodicities. In addition to the redshift of the resonance wavelength as the aspect ratio of ellipse increases, the free-standing structure modifies the resonance behavior and the dielectric environment of antenna by elevating the elliptical disk from the substrate. To interpret the simulation results, the analytical solution of resonance wavelength for ellipsoid dimmer is derived based on Lorentz–Mie theory, and comparisons are made between the analytical solution and simulation results. The quasi-static analytical solution provides a way to characterize the resonance behavior of two ellipsoid particles as a function of the gap distance, aspect ratio, and dielectric environment. In conclusion, the electrodynamic analysis for the periodic structure was performed in our FDTD simulations.

47 OTHER INSTRUMENTATION↗

Sierra/SolidMechanics Verification Report

This document presents the Sierra/SolidMechanics (Sierra/SM) verification plan. This plan centers on the tests in the Sierra/SM verification test suite, a subset of which are documented in the Sierra/SM Verification Tests Manual. Most of these tests are run nightly with the Sierra/SM code suite, and the results of the tests are checked against analytic solutions. For each of the tests presented in the Verification Tests Manual, the test setup, a description of the analytic solution, and comparison of the Sierra/SM code results to the analytic solution is provided. Mesh convergence is also checked on a nightly basis for several of these tests. This verification plan discusses these various types of tests and what they mean for Sierra/SM verification. Many other activities also contribute to Sierra/SM quality. These address code and solution quality and range from low-level unit tests, run nightly, up to full-fidelity acceptance tests, used to verify release stability. This acceptance test suite checks that new versions of Sierra/SM continue to yield the same answers for high-resolution analyst problems. Further code quality measures include an extensive suite of intermediate-size regression tests and automated nightly code quality checks. While these additional activities do not fall under a strict definition of verification, they greatly add to the quality, stability, and reliability of Sierra/SM, and are discussed here as well.

97 MATHEMATICS AND COMPUTING↗

The electromechanical behavior of piezoelectric thin film composite diaphragms possessing in-plane stresses

Many piezoelectric microelectromechanical systems (MEMS) measure or generate acoustic signals via the motion of radially non-uniform, thin film composite plates. The composite layers provide piezoelectric actuation, structural support, electrode metallization, passivation, etc. Often, the layers are non-uniform over the plate and contain residual stresses introduced during the fabrication process. Accurate models of non-uniform composite plate mechanics are crucial for predicting and optimizing device performance. In this paper, an analytical solution for a radially non-uniform, piezoelectric, circular composite plate incorporating residual stress is derived. The analytical solution is compared to experimental measurements of a MEMS piezoelectric diaphragm. The results show the improved accuracy of the analytical model when including film stress, the speed of the analytical solution as compared to finite element analysis, the sensitivity of device performance to residual stress and the importance of accurate film stresses as model inputs. Finally, the analytical model presented is useful as a design optimization tool given the efficiency of the computational time, shown to be 275 times less than a comparable finite element analysis.

42 ENGINEERING↗

AN ANALYTIC MODEL OF DUSTY, STRATIFIED, SPHERICAL H ii REGIONS

We study analytically the effect of radiation pressure (associated with photoionization processes and with dust absorption) on spherical, hydrostatic H ii regions. We consider two basic equations, one for the hydrostatic balance between the radiation-pressure components and the gas pressure, and another for the balance among the recombination rate, the dust absorption, and the ionizing photon rate. Based on appropriate mathematical approximations, we find a simple analytic solution for the density stratification of the nebula, which is defined by specifying the radius of the external boundary, the cross section of dust absorption, and the luminosity of the central star. We compare the analytic solution with numerical integrations of the model equations of Draine, and find a wide range of the physical parameters for which the analytic solution is accurate.

79 ASTRONOMY AND ASTROPHYSICS↗

Phase transformations in metastable liquids combined with polymerization

Here, we report on the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymerization degree is formulated. The exact steady-state analytical solutions are found. In the case of unsteady-state crystallization with polymerization, the particle-size distribution function is determined analytically for different space–time regions by means of the Laplace transform. Two functional integro-differential equations governing the dimensionless temperature and polymerization degree are deduced. These equations are solved by means of the saddle-point technique for the evaluation of a Laplace-type integral. The time-dependent distribution function, temperature and polymerization degree at different polymerization rates and nucleation kinetics are derived with allowance for the main contribution to the Laplace-type integral. In addition, the general analytical solution by means of the saddle-point technique and an example showing how to construct the analytical solutions in particular cases are given in the appendices. The analytical method developed in this paper can be used to describe the similar phase transition phenomena in the presence of chemical reactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Soliton solutions of the 3D Gross-Pitaevskii equation by a potential control method

We present a class of three-dimensional solitary waves solutions of the Gross-Pitaevskii (GP) equation, which governs the dynamics of Bose-Einstein condensates (BECs). By imposing an external controlling potential, a desired time-dependent shape of the localized BEC excitation is obtained. The stability of some obtained localized solutions is checked by solving the time-dependent GP equation numerically with analytic solutions as initial conditions. The analytic solutions can be used to design external potentials to control the localized BECs in experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Solving the Grad–Shafranov equation using spectral elements for tokamak equilibrium with toroidal rotation

The Grad–Shafranov equation is solved using spectral elements for tokamak equilibrium with toroidal rotation. The Grad–Shafranov solver builds upon and extends the NIMEQ code (Howell and Sovinec, 2014) previously developed for static tokamak equilibria. Both geometric and algebraic convergence are achieved as the polynomial degree of the spectral-element basis increases. A new analytical solution to the Grad–Shafranov equation is obtained for Solov’ev equilibrium in presence of rigid toroidal rotation, in addition to a previously obtained analytical solution for a different set of equilibrium and rotation profiles. The numerical solutions from the extended NIMEQ are benchmarked with the analytical solutions, with good agreements. Besides, the extended NIMEQ code is benchmarked with the FLOW code (Guazzotto et al., 2004). The modification of pressure profile induced by toroidal flow is investigated. The relative change of pressure profile is found significant around the edge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Improved procedures for mass matrix-reductions in eigenvalue solutions

Analytical models of three structures were used to test mass matrix-reduction schemes. Accuracy of four mode shapes and frequencies was tracked through successive mass matrix-reductions with diminishing numbers of indicator degrees of freedom. Results were consistently disappointing. Two new procedures were developed in attempt to improve accuracy.

Levy, R.↗

Applications of the Space-Time Conservation Element and Solution Element (CE/SE) Method to Computational Aeroacoustic Benchmark Problems

The Internal Propagation problems, Fan Noise problem, and Turbomachinery Noise problems are solved using the space-time conservation element and solution element (CE/SE) method. The problems in internal propagation problems address the propagation of sound waves through a nozzle. Both the nonlinear and linear quasi 1D Euler equations are solved. Numerical solutions are presented and compared with the analytical solution. The fan noise problem concerns the effect of the sweep angle on the acoustic field generated by the interaction of a convected gust with a cascade of 3D flat plates. A parallel version of the 3D CE/SE Euler solver is developed and employed to obtain numerical solutions for a family of swept flat plates. Numerical solutions for sweep angles of 0, 5, 10, and 15 deg are presented. The turbomachinery problems describe the interaction of a 2D vortical gust with a cascade of flat-plate airfoils with/without a downstream moving grid. The 2D nonlinear Euler Equations are solved and the converged numerical solutions are presented and compared with the corresponding analytical solution. All the comparisons demonstrate that the CE/SE method is capable of solving aeroacoustic problems with/without shock waves in a simple and efficient manner. Furthermore, the simple non-reflecting boundary condition used in the CE/SE method which is not based on the characteristic theory works very well in 1D, 2D and 3D problems.

Wang, Xiao-Yen↗

Lattice strains and diffraction elastic constants of cubic polycrystals

In situ synchrotron X-ray and neutron diffraction experiments provide a powerful approach to measure lattice strains in bulk polycrystalline materials. They are being increasingly used for quantitative characterization of microscale deformation within and between grains and phases. Here we use a self-consistent micromechanics model to obtain a general analytic solution of the grain-level lattice strains and diffraction elastic constants for a broad class of elastically isotropic polycrystals with cubic crystal symmetry. This analytic solution reveals a direct linear relationship between the reciprocal of the elastic diffraction constant and the orientation index parameter along the direction of any diffraction vector, including tensile loading and transverse directions. The straightforward numerical implementation of this solution provides diffraction elastic constants for 26 representative cubic polycrystals. Finally, analytic solutions of this kind can serve to benchmark in situ diffraction measurements of lattice strains and also facilitate high-throughput studies of microscale stresses and diffraction elastic constants in polycrystalline materials.

36 MATERIALS SCIENCE↗

Overshooting thunderstorm cloud top dynamics as approximated by a linear Lagrangian parcel model with analytic exact solutions

Results are presented from a linear Lagrangian entraining parcel model of an overshooting thunderstorm cloud top. The model, which is similar to that of Adler and Mack (1986), gives analytic exact solutions for vertical velocity and temperature by representing mixing with Rayleigh damping instead of nonlinearly. Model results are presented for various combinations of stratospheric lapse rate, drag intensity, and mixing strength. The results are compared to those of Adler and Mack.

Schlesinger, Robert E.↗

Development and application of a three dimensional numerical model for predicting pollutant and sediment transport using an Eulerian-Lagrangian marker particle technique

A computer coded Lagrangian marker particle in Eulerian finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.

Pavish, D. L.↗

Modeling of Chill Down in Cryogenic Transfer Lines

A numerical model to predict chill down in cryogenic transfer lines has been developed. Three chill down cases using hydrogen as the working fluid are solved: 1) a simplified model amenable to analytical solution, 2) a realistic model of superheated vapor flow, and 3) a realistic model of initially subcooled liquid flow. The first case compares a numerical model with an analytical solution with very good agreement between the two. Additionally, the analytical solution provides a convenient way to look at parametric effects on the chill down. The second and third cases are numerical models which provide temperature histories of the fluid and solid tube wall during chill down as well as several other quantities of interest such as pressure and mass flow rate. Of great interest is the ability to predict accurate values of chill down time (the time required to achieve steady-state cryogenic flow). The models predict that a 26 in. long, 3/16 in. ID aluminum tube has a shorter chill down time (approx. equal to 100 sec) and uses less hydrogen with superheated vapor flow than with initially subcooled liquid flow (greater than 200 sec for chill down).

Cross, Matthew F.↗

A Limiting Case of Constant Counterion Electrochemical Potentials in the Membrane for Examining Ion Transfer at Ion-Exchange Membranes and Patches

We present that ion passage through ion-exchange membranes is vital in electrodialysis desalination, batteries and fuel cells, and water splitting. Simplified models of ion transport through such membranes frequently assume complete exclusion of coions (ions with the same sign of charge as the fixed charge in the membrane) from the membrane. However, a second assumption of constant counterion electrochemical potentials across the membrane leads to simple analytical expressions for ion fluxes and transmembrane potentials. Moreover, linear corrections to account for a small membrane electrical resistance yield analytical expressions with a wider applicability. For bi-ionic potential measurements and current-induced concentration polarization at low salt concentrations, these analytical solutions match the fluxes and potentials obtained numerically without the limiting assumptions. This gives confidence in both the limiting assumptions (under appropriate conditions) and the numerical solutions. At low ion concentrations, the analytical solutions may enable rapid characterization of membrane coatings or boundary layers in solution, and such boundary layers are important in many applications of ion-exchange membranes. In fact, the assumption of complete coion exclusion is sometimes more limiting than the constraint of constant electrochemical potentials of counterions across the membrane. Remarkably, this limiting case readily yields the ion accumulation and depletion regions above “ion-exchange patches” that reside beneath a solution with an applied electric field. Finally, such regions are important for sample pre-concentration in microfluidic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Symmetry Determining Equations of the Rankine-Hugoniot Equations for Variable Velocity Shock Waves

The “constant velocity piston” problem (Fig. 1), also known as the “piston problem,” is a standard model for a one dimensional, in our case linear, symmetric shock wave moving through an inviscid, perfect gas. The model can be divided into two regions - a perturbed section on the left and an unperturbed section on the right - by a moving shock wave moving left to right. Both the perturbed and unperturbed sections, i.e. the shocked and unshocked regions, respectively, obey the Eulerian conservation equations; however, at the exact location of the shock, there is a mathematical discontinuity not satisfied by the Euler equations. To ensure continuity and conservation of certain quantities when crossing between the unshocked and shocked regions, we evoke a series of equations derived from the Eulerian conservation equations, called the Rankine-Hugoniot equations, or “jump” equations as it is often referred to in the literature on the topic. The classical constant-velocity piston problem assumes the piston features a constant driving velocity (among many other willing suspensions of belief required in the pursuit of a first principles equation model); consequent to this assumption is a constant-velocity shock and a constant-velocity shocked flow state. However, using Lie Group Theory (LGT), also known as symmetry analysis, we can attempt to reinterpret the model with a shock wave of variable velocity in time and space. An extension of the model in this way opens up the possibility for obtaining new analytical solutions to the piston problem for certain shock velocity models. In this report, we use LGT to derive the symmetry determining equations (SDEs), whose solutions are Lie groups, which permit analytical solutions. In the future, we can then use the SDEs to define constraint equations on the shock velocity model and what the successive solutions to the Euler equations might be based off such constraints. This report is structured as follows: Section 2 provides a brief derivation of the Rankine-Hugoniot (“jump”) equations; Section 3 gives an overview of Lie group theory; Section 4 derives the SDEs of the jump equations; Section 5 derives the Euler conservation equations for fluids; and Section 6 presents concluding remarks and opportunities for future studies.

42 ENGINEERING↗