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Impingement of Droplets in 60 Degree Elbows with Potential Flow

Description: Trajectories were determined for water droplets or other aerosol particles in air flowing through 600 elbows especially designed for two-dimensional potential motion. The elbows were established by selecting as walls of each elbow two streamlines of a flow field produced by a complex potential function that establishes a two-dimensional flow around. a 600 bend. An unlimited number of elbows with slightly different shapes can be established by selecting different pairs of streamlines as walls. Some of these have a pocket on the outside wall. The elbows produced by the complex potential function are suitable for use in aircraft air-inlet ducts and have the following characteristics: (1) The resultant velocity at any point inside the elbow is always greater than zero but never exceeds the velocity at the entrance. (2) The air flow field at the entrance and exit is almost uniform and rectilinear. (3) The elbows are symmetrical with respect to the bisector of the angle of bend. These elbows should have lower pressure losses than bends of constant cross-sectional area.
Date: October 1956
Creator: Hacker, Paul T.; Saper, Paul G. & Kadow, Charles F.
Partner: UNT Libraries Government Documents Department

Particle Trajectories in Homogeneous Magnetic Field with Linear Time Dependence

Description: Abstract: "Formulas are derived for the trajectory of a charged particle in a magnetic field which is a linear function of time. Graphs of certain functions are presented, by means of which a trajectory with given initial position and velocity may be plotted."
Date: August 9, 1955
Creator: Gardner, Clifford S.
Partner: UNT Libraries Government Documents Department

Comparison and Evaluation of Two Model Techniques Used in Predicting Bomb-Release Motions

Description: "For the purpose of calculating bomb trajectories, forces and moments have been measured on bombs of three fineness ratio sin the presence of a swept-wing fighter bomber configuration at a Mach number of 1.61. Trajectories thus obtained have been compared with those from dynamic model tests and an analysis has been made to determine the source of errors and to suggest improvements in both techniques." (p. 1).
Date: December 27, 1957
Creator: Carlson, Harry W.; Geier, Douglas J. & Lee, John B.
Partner: UNT Libraries Government Documents Department

Bomb Trajectories

Description: The report is a mathematical treatise dealing with the trajectories of bombs of high terminal velocity, dropped from a great altitude.
Date: 1920
Creator: Wilson, Edwin Bidwell
Partner: UNT Libraries Government Documents Department

How Small Can a Launch Vehicle Be?

Description: Trajectory simulations from Earth to orbit indicate comparative velocity requirements depending on vehicle size, for several propellant options. Smaller vehicles are more affected by drag, resulting in steeper trajectories that require more total velocity. Although they are technically challenging, launch vehicles smaller than 1 ton are not ruled out by the nature of ascent trajectories.
Date: June 23, 2005
Creator: Whitehead, J C
Partner: UNT Libraries Government Documents Department

A study of the motion and aerodynamic heating of ballistic missiles entering the earth's atmosphere at high supersonic speeds

Description: From Summary: "A simplified analysis of the velocity and deceleration history of ballistic missiles entering the earth's atmosphere at high supersonic speeds is presented. The results of this motion analysis are employed to indicate means available to the designer for minimizing aerodynamic heating. The heating problem considered involves not only the total heat transferred to a missile by convection, but also the maximum average and local time rates of convective heat transfer."
Date: April 28, 1953
Creator: Allen, H. Julian & Eggers, A. J., Jr.
Partner: UNT Libraries Government Documents Department

A method for numerically calculating the area and distribution of water impingement on the leading edge of an airfoil in a cloud

Description: Report presenting a method for determining, by step-by-step integration, the trajectories of water drops around any body in two-dimensional flow for which the streamline velocity components are known or can be computed. The equations are presented in general form and then water-drop trajectories are calculated about a 12-percent-thick symmetric Joukowski profile.
Date: August 1947
Creator: Bergrun, Norman R.
Partner: UNT Libraries Government Documents Department

The Paths of Quintessence

Description: The structure of the dark energy equation of state phase plane holds important information on the nature of the physics. We explain the bounds of the freezing and thawing models of scalar field dark energy in terms of the tension between the steepness of the potential vs. the Hubble drag. Additionally, we extend the phase plane structure to modified gravity theories, examine trajectories of models with certain properties, and categorize regions in terms of scalar field hierarchical parameters, showing that dark energy is generically not a slow roll phenomenon.
Date: March 13, 2006
Creator: Linder, Eric V.
Partner: UNT Libraries Government Documents Department

Comparison and Evaluation of Two Model Techniques Used in Predicting Bomb-Release Motions

Description: "For the purpose of calculating bomb trajectories, forces and moments have been measured on bombs of three fineness ratios in the presence of a swept-wing fighter-bomber configuration at a Mach number of 1.61. Trajectories thus obtained have been compared with those from dynamic model tests and an analysis has been made to determine the source of errors and to suggest improvements in both techniques."
Date: December 27, 1957
Creator: Carlson, Harry W.; Geier, Douglas J. & Lee, John B.
Partner: UNT Libraries Government Documents Department


Description: The paper discusses the issues, the consequences and the methods for controlling the edge effects caused by particles entering and leaving magnets with trajectories at non-vanishing angles with the edges in FFAG accelerators made of Non-Scaling Lattices.
Date: October 13, 2004
Creator: RUGGIERO, A. G.
Partner: UNT Libraries Government Documents Department

Semiclassical (SC) Description of Electronically Non-AdiabaticDynamics via the Initial Value Representation (IVR)

Description: The initial value representation (IVR) of semiclassical (SC) theory is used in conjunction with the Meyer-Miller/Stock-Thoss description of electronic degrees of freedom in order to treat electronically non-adiabatic processes. It is emphasized that the classical equations of motion for the nuclear and electronic degrees of freedom that emerge in this description are precisely the Ehrenfest equations of motion (the force on the nuclei is the force averaged over the electronic wavefunction), but that the trajectories given by these equations of motion do not have the usual shortcomings of the traditional Ehrenfest model when they are used within the SC-IVR framework. For example, in the traditional Ehrenfest model (a mixed quantum-classical approach) the nuclear motion emerges from a non-adiabatic encounter on an average potential energy surface (a weighted average according to the population in the various electronic states), while the SC-IVR describes the correct correlation between electronic and nuclear dynamics, i.e., the nuclear motion is on one potential energy surface or the other depending on the electronic state. Calculations using forward-backward versions of SC-IVR theory (FB-IVR) are presented to illustrate this behavior. An even more approximate version of the SC-IVR, the linearized approximation (LSC-IVR), is slightly better than the traditional Ehrenfest model, but since it cannot describe quantum coherence effects, the LSC-IVR is also not able to describe the correct correlation between nuclear and electronic dynamics.
Date: June 22, 2007
Creator: Ananth, V.; Venkataraman, C. & Miller, W.H.
Partner: UNT Libraries Government Documents Department

Real time correlation function in a single phase spaceintegral--beyond the linearized semiclassical initial valuerepresentation

Description: It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the 2nd order WD based on 'Winger trajectories', and the full Donoso-Martens dynamics (full DMD) and the 2nd order DMD based on 'Donoso-Martens trajectories'--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of these four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (non-linear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.
Date: July 10, 2007
Creator: Liu, Jian & Miller, William H.
Partner: UNT Libraries Government Documents Department

An infinite branching hierarchy of time-periodic solutions of the Benjamin-Ono equation

Description: We present a new representation of solutions of the Benjamin-Ono equation that are periodic in space and time. Up to an additive constant and a Galilean transformation, each of these solutions is a previously known, multi-periodic solution; however, the new representation unifies the subset of such solutions with a fixed spatial period and a continuously varying temporal period into a single network of smooth manifolds connected together by an infinite hierarchy of bifurcations. Our representation explicitly describes the evolution of the Fourier modes of the solution as well as the particle trajectories in a meromorphic representation of these solutions; therefore, we have also solved the problem of finding periodic solutions of the ordinary differential equation governing these particles, including a description of a bifurcation mechanism for adding or removing particles without destroying periodicity. We illustrate the types of bifurcation that occur with several examples, including degenerate bifurcations not predicted by linearization about traveling waves.
Date: July 1, 2008
Creator: Wilkening, Jon
Partner: UNT Libraries Government Documents Department

Beam losses due to abrupt crab cavity failures in the LHC

Description: A major concern for the implementation of crab crossing in a future High-Luminosity LHC (HL-LHC) is machine protection in an event of a fast crab-cavity failure. Certain types of abrupt crab-cavity amplitude and phase changes are simulated to characterize the effect of failures on the beam and the resulting particle-loss signatures. The time-dependent beam loss distributions around the ring and particle trajectories obtained from the simulations allow for a first assessment of the resulting beam impact on LHC collimators and on sensitive components around the ring. Results for the nominal LHC lattice is presented.
Date: March 28, 2011
Creator: Baer, T.; Barranco, J.; Calaga, R.; Tomas, R.; Wenninger, B.; Yee, B. et al.
Partner: UNT Libraries Government Documents Department

Reference Undulator Measurement Results

Description: The LCLS reference undulator has been measured 22 times during the course of undulator tuning. These measurements provide estimates of various statistical errors. This note gives a summary of the reference undulator measurements and it provides estimates of the undulator tuning errors. We measured the reference undulator many times during the tuning of the LCLS undulators. These data sets give estimates of the random errors in the tuned undulators. The measured trajectories in the reference undulator are stable and straight to within {+-}2 {micro}m. Changes in the phase errors are less than {+-}2 deg between data sets. The phase advance in the cell varies by less than {+-}2 deg between data sets. The rms variation between data sets of the first integral of B{sub x} is 9.98 {micro}Tm, and the rms variation of the second integral of B{sub x} is 17.4 {micro}Tm{sup 2}. The rms variation of the first integral of B{sub y} is 6.65 {micro}Tm, and the rms variation of the second integral of B{sub y} is 12.3 {micro}Tm{sup 2}. The rms variation of the x-position of the fiducialized beam axis is 35 {micro}m in the final production run This corresponds to an rms uncertainty in the K value of {Delta}K/K = 2.7 x 10{sup -5}. The rms variation of the y-position of the fiducialized beam axis is 4 {micro}m in the final production run.
Date: August 18, 2011
Creator: Wolf, Zachary; Levashov, Yurii; /SLAC & ,
Partner: UNT Libraries Government Documents Department

Sampling diffusive transition paths

Description: We address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the well-known stiffness problem associated with sampling infinitesimal Brownian increments of the path, as well as a different type of stiffness associated with sampling the coarse features of long paths. The fine-features sampling stiffness is eliminated with the use of the fast sampling algorithm (FSA), and the coarse-feature sampling stiffness is avoided by introducing the sliding and sampling (S&S) algorithm. A key feature of the S&S algorithm is that it enables massively parallel computers to sample diffusive trajectories that are long in time. We use the algorithm to sample the transition path ensemble for the structural interconversion of the 38-atom Lennard-Jones cluster at low temperature.
Date: October 12, 2006
Creator: F. Miller III, Thomas & Predescu, Cristian
Partner: UNT Libraries Government Documents Department

Electronically Nonadiabatic Dynamics via Semiclassical Initial Value Methods

Description: In the late 1970's Meyer and Miller (MM) [J. Chem. Phys. 70, 3214 (1979)] presented a classical Hamiltonian corresponding to a finite set of electronic states of a molecular system (i.e., the various potential energy surfaces and their couplings), so that classical trajectory simulations could be carried out treating the nuclear and electronic degrees of freedom (DOF) in an equivalent dynamical framework (i.e., by classical mechanics), thereby describing non-adiabatic dynamics in a more unified manner. Much later Stock and Thoss (ST) [Phys. Rev. Lett. 78, 578 (1997)] showed that the MM model is actually not a 'model', but rather a 'representation' of the nuclear-electronic system; i.e., were the MMST nuclear-electronic Hamiltonian taken as a Hamiltonian operator and used in the Schroedinger equation, the exact (quantum) nuclear-electronic dynamics would be obtained. In recent years various initial value representations (IVRs) of semiclassical (SC) theory have been used with the MMST Hamiltonian to describe electronically non-adiabatic processes. Of special interest is the fact that though the classical trajectories generated by the MMST Hamiltonian (and which are the 'input' for an SC-IVR treatment) are 'Ehrenfest trajectories', when they are used within the SC-IVR framework the nuclear motion emerges from regions of non-adiabaticity on one potential energy surface (PES) or another, and not on an average PES as in the traditional Ehrenfest model. Examples are presented to illustrate and (hopefully) illuminate this behavior.
Date: December 11, 2008
Creator: Miller, William H.
Partner: UNT Libraries Government Documents Department

Orbit Correction Techniques for a Multipass Linac

Description: The CEBAF accelerator includes a linac section which accelerates multiple beams with different energies. Problems arise when performing orbit correction, due to the fact that correction of higher energy passes disturb lower energy trajectories. Therefore, a perfect orbit correction cannot be obtained for all energy beams at the same time.\nWe present methods and performance (using simulation results) for performing orbit corrections in such a system. Limitations to the correction methods are also addressed.\n
Date: September 1, 1990
Creator: Barry, Andrea; Bowling, Bruce & Kewisch, Jorg
Partner: UNT Libraries Government Documents Department

Three-dimensional Reconstruction of Dust Particle Trajectories in the NSTX

Description: Highly mobile incandescent dust particles are routinely observed on NSTX using two fast cameras operating in the visible region. An analysis method to reconstruct dust particle trajectories in space using two fast cameras is presented in this paper. Position accuracies of a few millimeters depending on the particle's location have been achieved and particle velocities between 10 and 200 m/s have been observed. 2008 American Institute of Physics. __________________________________________________
Date: March 6, 2009
Creator: Boeglin, W. U.; Roquemore, A. L. & Maqueda, R.
Partner: UNT Libraries Government Documents Department


Description: Using data on 22 'precise bolides' with up to 882 individual points on their trajectories and using data on 29 'bright bolides' and on 10 artificial meteors, we tried to derive dependence of ablation and shape-density coefficients, and of luminous efficiency on various time dependent parameters. The only significant dependence we found was that on v{sub {infinity}} - v (on difference of initial and instantaneous velocities). We present the results as Eq. 3, 4 and 8, with coefficients a{sub 1}, a{sub 2}, a{sub 3}, a{sub 4}, b{sub 1}, b{sub 2}, a{sub 3}, c{sub 1}, c{sub 2}, computed for different bolide types. Also average values of ablation, and shape-density coefficients as well as average luminous efficiencies for individual bolide types are given.
Date: January 1, 2001
Creator: ReVelle, D. O. (Douglas O.)
Partner: UNT Libraries Government Documents Department

Undulator Changes Due to Temperature Excursions

Description: The temperature of the LCLS undulators has not been controlled during storage. The effects of the temperature excursions are documented in this note. After a number of LCLS undulators were tuned, fiducialized, and placed in storage anticipating their use, a test was made to ensure that their properties had not changed. The test revealed, however, that indeed the undulators had changed. Detailed study of this problem followed. We now believe that the gap of the undulators changes permanently when the undulators go through temperature excursions. We have tested the other possible cause, transportation, and do not see gap changes. In this note, we document how the undulators have changed since they were originally tuned. The undulators were tuned and fiducialized in the Magnetic Measurement Facility (MMF). Afterward, many of them (approximately 18) were taken to building 750 for storage during summer and fall 2007. Building 750 had no temperature control. The undulator temperatures went from 20 C, used for tuning, down to approximately 11 C during the winter. In January 2008, three of the undulators were brought back to the MMF for a check. All three undulators showed similar changes. Trajectories, phases, and most undulator properties stayed the same, but the fiducialization (beam axis position relative to tooling balls on the undulator) had changed. Further investigation showed that the undulator gap was altered in a periodic way along the magnetic axis with a net average gap change causing the fiducialization change. A new storage location in building 33 was found and future undulators were placed there. A failure in the temperature control, however, caused the undulators to get too hot. Again the gap changed, but with a different periodic pattern. This note documents the measured changes in the undulators. In particular, it shows the detailed history of undulator 39 which ...
Date: November 17, 2010
Creator: Wolf, Zachary; Levashov, Yurii & Reese, Ed
Partner: UNT Libraries Government Documents Department

Quantum Irreversibility and Chaos

Description: This article establishes a relation between quantum irreversibility and the chaotic semi-classical solutions for a spin-boson Hamiltonian system.
Date: February 1, 1997
Creator: West, Bruce J.; Grigolini, Paolo; Bonci, Luca & Roncaglia, Roberto
Partner: UNT College of Arts and Sciences

Modeling broadband poroelastic propagation using an asymptotic approach

Description: An asymptotic method, valid in the presence of smoothly-varying heterogeneity, is used to derive a semi-analytic solution to the equations for fluid and solid displacements in a poroelastic medium. The solution is defined along trajectories through the porous medium model, in the manner of ray theory. The lowest order expression in the asymptotic expansion provides an eikonal equation for the phase. There are three modes of propagation, two modes of longitudinal displacement and a single mode of transverse displacement. The two longitudinal modes define the Biot fast and slow waves which have very different propagation characteristics. In the limit of low frequency, the Biot slow wave propagates as a diffusive disturbance, in essence a transient pressure pulse. Conversely, at low frequencies the Biot fast wave and the transverse mode are modified elastic waves. At intermediate frequencies the wave characteristics of the longitudinal modes are mixed. A comparison of the asymptotic solution with analytic and numerical solutions shows reasonably good agreement for both homogeneous and heterogeneous Earth models.
Date: May 1, 2009
Creator: Vasco, Donald W.
Partner: UNT Libraries Government Documents Department

Estimating permeability from quasi-static deformation: Temporal variations and arrival time inversion

Description: Transient pressure variations within a reservoir can be treated as a propagating front and analyzed using an asymptotic formulation. From this perspective one can define a pressure 'arrival time' and formulate solutions along trajectories, in the manner of ray theory. We combine this methodology and a technique for mapping overburden deformation into reservoir volume change as a means to estimate reservoir flow properties, such as permeability. Given the entire 'travel time' or phase field, obtained from the deformation data, we can construct the trajectories directly, there-by linearizing the inverse problem. A numerical study indicates that, using this approach, we can infer large-scale variations in flow properties. In an application to Interferometric Synthetic Aperture (InSAR) observations associated with a CO{sub 2} injection at the Krechba field, Algeria, we image pressure propagation to the northwest. An inversion for flow properties indicates a linear trend of high permeability. The high permeability correlates with a northwest trending fault on the flank of the anticline which defines the field.
Date: May 1, 2008
Creator: Vasco, D.W.; Ferretti, Alessandro & Novali, Fabrizio
Partner: UNT Libraries Government Documents Department