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At least 271 records · Page 15

Kinetics of subdiffusive growth of new phase particles in supersaturated solid solutions

The kinetics of the subdiffusion-limited growth of spherical precipitates is studied. The process is described by the equation of anomalous diffusion with a fractional derivative with respect to time. It is shown that a decrease in the concentration of monomers is described by the law exp(−kt{sup 3α/2}) at the initial stage and the power law t{sup −α} at large times, where 0 < α ≤ 1 is the dispersion parameter coinciding with the order of time derivative in the subdiffusion equation. The time dependence of the size of a spherical precipitate is obtained. The results generalize the Ham diffusion theory and are in agreement with the Monte Carlo simulation data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Increasing ROI Using Your Digital Twin for Model Based Engineering

The purpose of this work is to identify innovative ways of using the plant reference simulator or digital twin differently than it has traditionally been used in the past. This paper will identify reasons that the plant reference simulator will support varying levels of model based design and engineering. I will point out real world examples in which the plant reference simulator was used to identify problems with engineering designs, digital control systems and plant modifications. The earlier these issues can be identified and resolved, the less impact they have on the plant modification or upgrade. By using the plant reference simulator earlier in the engineering process, utilities and engineering organizations can minimize costly outage extensions and increase the return on the investment made in the simulator.

42 ENGINEERING↗

Annual Research Briefs, 2002: Center for Turbulence Research

Turbulent combustion remains the largest component of the CTR's core program. This program and several related activities at CTR are supported by NASA's Ultra Efficient Engine Technology Program. It is also intimately connected with the Department of Energy's ASCI program at Stanford which develops the technology for numerical simulation of realistic aircraft engines using state of the art massively parallel computers. In combustion modeling the attention has been directed to the modeling of higher levels of complexity such as spray dynamics, radiation and soot formation. Major aircraft engine manufacturers have shown considerable interest in this program; in particular, a significant active collaboration exists between CTR and the Pratt & Whitney Corporation. CTR's combustion program is essentially based on the large-eddy simulation technique, LES, which is actively being pursued at CTR for this and many other applications. Important accomplishments in LES included simulations with three-dimensional filters which result in grid independent calculations (that is why we call it "true" LES), and the development of the methodology for integration of LES and Reynolds Averaged computations. Optimization techniques are being studied and used for the important problem of wall boundary conditions for LES as well as for optimal shape design for aeroacoustic and aerodynamic performance gains.

ULTRA EFFICIENT ENGINE TECHNOLOGY↗

On the Validity of Linear Response Theory in High-Dimensional Deterministic Dynamical Systems

This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory’s assumptions. Here we provide a proof of concept for the validity of linear response theory in high-dimensional deterministic systems for large-scale observables. We introduce an exemplary model in which observables of resolved degrees of freedom are weakly coupled to a large, inhomogeneous collection of unresolved chaotic degrees of freedom. By employing statistical limit laws we give conditions under which such systems obey linear response theory even if all the degrees of freedom individually violate linear response. We corroborate our result with numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dependence of Strain Rate Sensitivity on the Slip System: A Molecular Dynamics Simulation

The strain rate of deformation might affect mechanical properties of metallic materials, especially at elevated temperatures. Due to the nature of dislocation slip, it is anticipated that strain rate sensitivity (SRS) depends on the slip system. While the dependency of SRS on the temperature and strain rate of the deformation is well recognized, its dependence on the slip system is not well understood. Accordingly, the molecular dynamics simulation was used to investigate the dependence of strain rate sensitivity of pure Al single crystals on the slip system. In this study, the embedded atom method (EAM) potential for Al was employed. SRS and shear strength of the material were studied in four different slip systems and at two temperatures of 300 and 500 K. It was found that SRS of the material depends on the slip system in addition to the temperature, and SRS was higher in less compact systems with more difficult slip. The dislocation theories were used to rationalize the simulation results.

36 MATERIALS SCIENCE↗

Combination of the pair density approximation and the Takahashi–Imada approximation for path integral Monte Carlo simulations

We construct an accurate imaginary time propagator for path integral Monte Carlo simulations for heterogeneous systems consisting of a mixture of atoms and molecules. We combine the pair density approximation, which is highly accurate but feasible only for the isotropic interactions between atoms, with the Takahashi–Imada approximation for general interactions. We present finite temperature simulations results for energy and structure of molecules–helium clusters X{sup 4}He{sub 20} (X=HCCH and LiH) which show a marked improvement over the Trotter approximation which has a 2nd-order time step bias. We show that the 4th-order corrections of the Takahashi–Imada approximation can also be applied perturbatively to a 2nd-order simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Rossby wave radiation by an eddy on a beta-plane: Experiments with laboratory altimetry

Results from the laboratory experiments on the evolution of vortices (eddies) generated in a rotating tank with topographic β-effect are presented. The focus of the experiments is on the far-field flow which contains Rossby waves emitted by travelling vortices. The surface elevation and velocity fields are measured by the altimetric imaging velocimetry. The experiments are supplemented by shallow water numerical simulations as well as a linear theory which describes the Rossby wave radiation by travelling vortices. The cyclonic vortices observed in the experiments travel to the northwest and continuously radiate Rossby waves. Measurements show that initially axisymmetric vortices develop a dipolar component which enables them to perform translational motion. A pattern of alternating zonal jets to the west of the vortex is created by Rossby waves with approximately zonal crests. Energy spectra of the flows in the wavenumber space indicate that a wavenumber similar to that introduced by Rhines for turbulent flows on the β-plane can be introduced here. The wavenumber is based on the translational speed of a vortex rather than on the root-mean-square velocity of a turbulent flow. The comparison between the experiments and numerical simulations demonstrates that evolving vortices also emit inertial waves. While these essentially three-dimensional non-hydrostatic waves can be observed in the altimetric data, they are not accounted for in the shallow water simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SIMULATIONS OF THE SPATIAL AND TEMPORAL INVARIANCE IN THE SPECTRA OF GRADUAL SOLAR ENERGETIC PARTICLE EVENTS

The spatial and temporal invariance in the spectra of energetic particles in gradual solar events is reproduced in simulations. Based on a numerical solution of the focused transport equation, we obtain the intensity time profiles of solar energetic particles (SEPs) accelerated by an interplanetary shock in three-dimensional interplanetary space. The shock is treated as a moving source of energetic particles with a distribution function. The time profiles of particle fluxes with different energies are calculated in the ecliptic at 1 AU. According to our model, we find that shock acceleration strength, parallel diffusion, and adiabatic cooling are the main factors in forming the spatial invariance in SEP spectra, and perpendicular diffusion is a secondary factor. In addition, the temporal invariance in SEP spectra is mainly due to the effects of adiabatic cooling. Furthermore, a spectra invariant region, which agrees with observations but is different from the one suggested by Reames et al. is proposed based on our simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

From wires to cosmology

We provide a statistical framework for characterizing stochastic particle production in the early universe via a precise correspondence to current conduction in wires with impurities. Our approach is particularly useful when the microphysics is uncertain and the dynamics are complex, but only coarse-grained information is of interest. We study scenarios with multiple interacting fields and derive the evolution of the particle occupation numbers from a Fokker-Planck equation. At late times, the typical occupation numbers grow exponentially which is the analog of Anderson localization for disordered wires. Some statistical features of the occupation numbers show hints of universality in the limit of a large number of interactions and/or a large number of fields. For test cases, excellent agreement is found between our analytic results and numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

Anomalous structural evolution and √(3)×√(3) reconstruction of a clean Si(111) surface observed after thermal desorption of thallium

The authors have observed anomalous structural evolution of a clean Si(111) surface, which was prepared first by thallium (Tl) deposition on a Si(111)7 × 7 surface, leading to incomplete formation of a Tl/Si(111)1 × 1 structure at 300 °C and subsequent desorption of Tl at 350 °C. Thus prepared clean Si(111) surfaces exhibit structural changes with increase of temperature: 2×1→(√(3)×√(3))R30°→2×1→5×5→7×7, as observed by low-energy electron diffraction and scanning tunneling microscopy. Among the above structures, the (√(3)×√(3))R30° formed at 450–550 °C is found not to be a simple adatom structure. Instead, by means of ab-initio calculations a new metastable (√(3)×√(3))R30° reconstruction was found, having analogous structural features and formation origin to a 2 × 1 reconstruction known as the Pandey chain model. This new (√(3)×√(3))R30° model is 0.09 eV per surface atom less favorable than the 2 × 1 reconstruction. A reason for the anomalous occurrence of the (√(3)×√(3))R30° structure is explored with an aid of Monte Carlo simulations.

42 ENGINEERING↗

Poster — Thur Eve — 53: Novel Technique for the Measurement of Ultra-Superficial Doses Using Gafchromic Film

Purpose: Dose build-up and electron contamination are two closely related quantities with important implications in radiotherapy, yet they are quite difficult to measure with great certainty. We present a novel technique for measuring ultra-superficial doses. Method and Materials: We used Gafchromic EBT-3 film which have an effective point of measurement of roughly 153 micros (effective depth in water). By peeling off one of the polyester layers, the active layer becomes the top layer and we obtain a film with a effective point of measurement of 15 microns (effective depth in water). A film calibration was performed using a 180 kVp orthovoltage beam. Since the active layer of the film may have been compressed or perturbed during the peeling of clear polyester we use a triple-channel film calibration technique to minimize the effects of non-uniformity in the active layer. We measured surface doses of orthovoltage beams with lead cutouts in place to introduce contaminant photoelectrons. Results: Our measurements show that the dose enhancement near the edges of the lead were about 125% relative to central axis for 6 cm diameter cutouts up to 170% for 2 cm diameter cutouts, which were within 5% of our EGSnrc based Monte Carlo simulations.

60 APPLIED LIFE SCIENCES↗

SU-E-T-546: Modeling and Validation of the a New Proton Therapy System Using a Monte-Carlo Environment Optimized for Protons

8 particle histories were run. Results: Range measurements of the Monte-Carlo simulations matched the measured data within 1mm. Distal fall-off of the simulated fields matched within <1mm. Lateral penumbra and field size measurements of the standard-sized square and half-beam blocked fields matched within 1mm at all three planes compared. A small difference was seen in the in-air profiles at doses <0%. The suspected cause of the difference was the aperture shape. The measured data utilized a divergent aperture. The Monte-Carlo calculation used a non-divergent aperture. Conclusion: The validation measurements indicate that we were able to accurately model the MEVION s250 Proton therapy system using Monte-Carlo Calculations. This may reduce the commissioning time for future users. Purpose: Monte-Carlo modeling is an important tool for understanding the behavior of therapeutic proton beams in a heterogeneous media such as the patient. To gain confidence that a Monte-Carlo model is accurate in complex geometries and media, it must first be compared with measurement in simple situations. This study documents the validation of our Monte-Carlo Model. Methods: A model of the MEVION s250 Proton therapy system was created in the TOPAS Monte-Carlo environment using machine geometry and field shaping system information provided by the vendor. For each of 24 options, validation of the TOPAS model was performed by comparing the dose scored by TOPAS to the dose measurements obtained during the commissioning of the treatment planning system. The measurements compared consisted of: pristine peak depth-dose profiles, in-air profiles for a standard-sized square field (20cm×20cm or 10cm×10cm depending on the maximum field size for each option) at isocenter and at 20cm upstream and downstream of isocenter, and in-air profiles with a half-beam blocked aperture at isocenter and at 20cm upstream and downstream of isocenter. For all Monte-Carlo simulations,.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Dynamics of a high-current relativistic electron beam

The dynamics of a high-current relativistic electron beam is studied experimentally and by numerical simulation. The beam is formed in a magnetically insulated diode with a transverse-blade explosive-emission cathode. It is found experimentally that the radius of a 500-keV beam with a current of 2 kA and duration of 500 ns decreases with time during the beam current pulse. The same effect was observed in numerical simulations. This effect is explained by a change in the shape of the cathode plasma during the current pulse, which, according to calculations, leads to a change in the beam parameters, such as the electron pitch angle and the spread over the longitudinal electron momentum. These parameters are hard to measure experimentally; however, the time evolution of the radial profile of the beam current density, which can be measured reliably, coincides with the simulation results. This allows one to expect that the behavior of the other beam parameters also agrees with numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

ON IMPROVING ANALYTICAL MODELS OF COSMIC REIONIZATION FOR MATCHING NUMERICAL SIMULATION

The methods for studying the epoch of cosmic reionization vary from full radiative transfer simulations to purely analytical models. While numerical approaches are computationally expensive and are not suitable for generating many mock catalogs, analytical methods are based on assumptions and approximations. We explore the interconnection between both methods. First, we ask how the analytical framework of excursion set formalism can be used for statistical analysis of numerical simulations and visual representation of the morphology of ionization fronts. Second, we explore the methods of training the analytical model on a given numerical simulation. We present a new code which emerged from this study. Its main application is to match the analytical model with a numerical simulation. Then, it allows one to generate mock reionization catalogs with volumes exceeding the original simulation quickly and computationally inexpensively, meanwhile reproducing large-scale statistical properties. These mock catalogs are particularly useful for cosmic microwave background polarization and 21 cm experiments, where large volumes are required to simulate the observed signal.

79 ASTRONOMY AND ASTROPHYSICS↗

Closed-form solutions of Lucas–Uzawa model with externalities via partial Hamiltonian approach

In this paper, we establish multiple closed-form solutions for all the variables in the Lucas–Uzawa model with externalities for the case with no parameter restrictions as well as for cases with specific parameter restrictions. These multiple solutions are derived with the help of the results derived in Naz et al. (Commun Nonlinear Sci Numer Simul 30(1):299–306, 2016) and Naz and Chaudhry (Math Modell Anal 22(4):464–483, 2017). This multiplicity of solutions is new to the economic growth literature on Lucas–Uzawa model with externalities. After finding solutions for the Lucas–Uzawa model with externalities, we use these solutions to derive the growth rates of all the variables in the system which enables us to fully describe the dynamics of the model. The multiple solutions can potentially explain why some countries economically overtake other countries even though they start from the same initial conditions. We have provided results of the numerical simulations procedure for σ=β.

97 MATHEMATICS AND COMPUTING↗