The analysis and compensation of errors of precise simple harmonic motion control under high speed and large load conditions based on servo electric cylinder

NASA Astrophysics Data System (ADS)

Ma, Chen-xi; Ding, Guo-qing

2017-10-01

Simple harmonic waves and synthesized simple harmonic waves are widely used in the test of instruments. However, because of the errors caused by clearance of gear and time-delay error of FPGA, it is difficult to control servo electric cylinder in precise simple harmonic motion under high speed, high frequency and large load conditions. To solve the problem, a method of error compensation is proposed in this paper. In the method, a displacement sensor is fitted on the piston rod of the electric cylinder. By using the displacement sensor, the real-time displacement of the piston rod is obtained and fed back to the input of servo motor, then a closed loop control is realized. There is compensation of pulses in the next period of the synthetic waves. This paper uses FPGA as the processing core. The software mainly comprises a waveform generator, an Ethernet module, a memory module, a pulse generator, a pulse selector, a protection module, an error compensation module. A durability of shock absorbers is used as the testing platform. The durability mainly comprises a single electric cylinder, a servo motor for driving the electric cylinder, and the servo motor driver.

The Implementation of Problem-Solving Based Laboratory Activities to Teach the Concept of Simple Harmonic Motion in Senior High School

NASA Astrophysics Data System (ADS)

Iradat, R. D.; Alatas, F.

2017-09-01

Simple harmonic motion is considered as a relatively complex concept to be understood by students. This study attempts to implement laboratory activities that focus on solving contextual problems related to the concept. A group of senior high school students participated in this pre-experimental method from a group’s pretest-posttest research design. Laboratory activities have had a positive impact on improving students’ scientific skills, such as, formulating goals, conducting experiments, applying laboratory tools, and collecting data. Therefore this study has added to the theoretical and practical knowledge that needs to be considered to teach better complicated concepts in physics learning.

Physics Notes

ERIC Educational Resources Information Center

School Science Review, 1972

1972-01-01

Short articles describe a method of introducing the study of simple harmonic motion, and suggest models that are analogues for impedence matching, electrical transformers, and birefringent crystals. (AL)

Continuous Quantitative Measurements on a Linear Air Track

ERIC Educational Resources Information Center

Vogel, Eric

1973-01-01

Describes the construction and operational procedures of a spark-timing apparatus which is designed to record the back and forth motion of one or two carts on linear air tracks. Applications to measurements of velocity, acceleration, simple harmonic motion, and collision problems are illustrated. (CC)

On a Simple Formulation of the Golf Ball Paradox

ERIC Educational Resources Information Center

Pujol, O.; Perez, J. Ph.

2007-01-01

The motion of a ball rolling without slipping on the lateral section inside a fixed vertical cylinder is analysed in the Earth referential frame which is assumed to be Galilean. Equations of motion are rapidly obtained and the golf ball paradox is understood: these equations describe a motion consisting of a vertical harmonic oscillation related…

Free fall and harmonic oscillations: analyzing trampoline jumps

NASA Astrophysics Data System (ADS)

Pendrill, Ann-Marie; Eager, David

2015-01-01

Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is obtained in terms of maximum normalized force from the trampoline and the harmonic frequency. A simple expression is obtained for the ratio between air-time and harmonic period, and the maximum g-factor. The results are compared to experimental results, including accelerometer data showing 7g during bounces on a small trampoline in an amusement park play area. Similar results are obtained on a larger garden trampoline, and even larger accelerations have been measured for gymnastic trampolines.

The Local Stellar Velocity Field via Vector Spherical Harmonics

NASA Technical Reports Server (NTRS)

Makarov, V. V.; Murphy, D. W.

2007-01-01

We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism.We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) = (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) = (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star...

Biomechanical analysis of INFINITY rehabilitation method for treatment of low back pain

PubMed Central

Daniel, Matej; Tomanová, Michaela; Hornová, Jana; Novotná, Iva; Lhotská, Lenka

2017-01-01

[Purpose] Low back pain is a pervasive problem in modern societies. Physical rehabilitation in treatment of low back pain should reduce pain, muscle tension and restore spine stability and balance. The INFINITY® rehabilitation method that is based on a figure of eight movement pattern was proved to be effective in low back pain treatment. The aim of the paper is to estimate the effect of a figure of eight motion on the L5/S1 load and lumbar spine muscle activation in comparison to other motion patterns. [Subjects and Methods] Three-dimensional model of lumbar spine musculoskeletal system is used to simulate effect of various load motion pattern induced by displacement of the center of gravity of the upper body. Four motion patterns were examined: lateral and oblique pendulum-like motion, elliptical motion and figure of eight motion. [Results] The simple pendulum-like and elliptical-like patterns induce harmonic muscle activation and harmonic spinal load. The figure of eight motion pattern creates high-frequency spinal loading that activates remodeling of bones and tendons. The figure of eight pattern also requires muscle activity that differs from harmonic frequency and is more demanding on muscle control and could also improve muscle coordination. [Conclusion] The results of the study indicate that complex motion pattern during INFINITY® rehabilitation might enhance the spine stability by influencing its passive, active and neural components. PMID:28603355

Spreadsheets in Science Teaching.

ERIC Educational Resources Information Center

Elliot, Chris

1988-01-01

Described is the use of a spreadsheet to model dynamic phenomena using numerical iterative methods. Uses the discharge of a capacitor, simple and damped harmonic motion, and the flow of heat along a bar as examples. (Author/CW)

On the aerodynamic characteristics of hovering rigid and flexible hawkmoth-like wings

NASA Astrophysics Data System (ADS)

Lua, K. B.; Lai, K. C.; Lim, T. T.; Yeo, K. S.

2010-12-01

Insect wings are subjected to fluid, inertia and gravitational forces during flapping flight. Owing to their limited rigidity, they bent under the influence of these forces. Numerical study by Hamamoto et al. (Adv Robot 21(1-2):1-21, 2007) showed that a flexible wing is able to generate almost as much lift as a rigid wing during flapping. In this paper, we take a closer look at the relationship between wing flexibility (or stiffness) and aerodynamic force generation in flapping hovering flight. The experimental study was conducted in two stages. The first stage consisted of detailed force measurement and flow visualization of a rigid hawkmoth-like wing undergoing hovering hawkmoth flapping motion and simple harmonic flapping motion, with the aim of establishing a benchmark database for the second stage, which involved hawkmoth-like wing of different flexibility performing the same flapping motions. Hawkmoth motion was conducted at Re = 7,254 and reduced frequency of 0.26, while simple harmonic flapping motion at Re = 7,800 and 11,700, and reduced frequency of 0.25. Results show that aerodynamic force generation on the rigid wing is governed primarily by the combined effect of wing acceleration and leading edge vortex generated on the upper surface of the wing, while the remnants of the wake vortices generated from the previous stroke play only a minor role. Our results from the flexible wing study, while generally supportive of the finding by Hamamoto et al. (Adv Robot 21(1-2):1-21, 2007), also reveal the existence of a critical stiffness constant, below which lift coefficient deteriorates significantly. This finding suggests that although using flexible wing in micro air vehicle application may be beneficial in term of lightweight, too much flexibility can lead to deterioration in flapping performance in terms of aerodynamic force generation. The results further show that wings with stiffness constant above the critical value can deliver mean lift coefficient almost the same as a rigid wing when executing hawkmoth motion, but lower than the rigid wing when performing a simple harmonic motion. In all cases studied (7,800 ≤ Re ≤ 11,700), the Reynolds number does not alter the force generation significantly.

Implied dynamics biases the visual perception of velocity.

PubMed

La Scaleia, Barbara; Zago, Myrka; Moscatelli, Alessandro; Lacquaniti, Francesco; Viviani, Paolo

2014-01-01

We expand the anecdotic report by Johansson that back-and-forth linear harmonic motions appear uniform. Six experiments explore the role of shape and spatial orientation of the trajectory of a point-light target in the perceptual judgment of uniform motion. In Experiment 1, the target oscillated back-and-forth along a circular arc around an invisible pivot. The imaginary segment from the pivot to the midpoint of the trajectory could be oriented vertically downward (consistent with an upright pendulum), horizontally leftward, or vertically upward (upside-down). In Experiments 2 to 5, the target moved uni-directionally. The effect of suppressing the alternation of movement directions was tested with curvilinear (Experiment 2 and 3) or rectilinear (Experiment 4 and 5) paths. Experiment 6 replicated the upright condition of Experiment 1, but participants were asked to hold the gaze on a fixation point. When some features of the trajectory evoked the motion of either a simple pendulum or a mass-spring system, observers identified as uniform the kinematic profiles close to harmonic motion. The bias towards harmonic motion was most consistent in the upright orientation of Experiment 1 and 6. The bias disappeared when the stimuli were incompatible with both pendulum and mass-spring models (Experiments 3 to 5). The results are compatible with the hypothesis that the perception of dynamic stimuli is biased by the laws of motion obeyed by natural events, so that only natural motions appear uniform.

The Quantum Arnold Transformation for the damped harmonic oscillator: from the Caldirola-Kanai model toward the Bateman model

NASA Astrophysics Data System (ADS)

López-Ruiz, F. F.; Guerrero, J.; Aldaya, V.; Cossío, F.

2012-08-01

Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.

Using Recent Planetary Science Data to Develop Advanced Undergraduate Physics and Astronomy Activities

NASA Astrophysics Data System (ADS)

Steckloff, Jordan; Lindell, Rebecca

2016-10-01

Teaching science by having students manipulate real data is a popular trend in astronomy and planetary science education. However, many existing activities simply couple this data with traditional "cookbook" style verification labs. As with most topics within science, this instructional technique does not enhance the average students' understanding of the phenomena being studied. Here we present a methodology for developing "science by doing" activities that incorporate the latest discoveries in planetary science with up-to-date constructivist pedagogy to teach advanced concepts in Physics and Astronomy. In our methodology, students are first guided to understand, analyze, and plot real raw scientific data; develop and test physical and computational models to understand and interpret the data; finally use their models to make predictions about the topic being studied and test it with real data.To date, two activities have been developed according to this methodology: Understanding Asteroids through their Light Curves (hereafter "Asteroid Activity"), and Understanding Exoplanetary Systems through Simple Harmonic Motion (hereafter "Exoplanet Activity"). The Asteroid Activity allows students to explore light curves available on the Asteroid Light Curve Database (ALCDB) to discover general properties of asteroids, including their internal structure, strength, and mechanism of asteroid moon formation. The Exoplanet Activity allows students to investigate the masses and semi-major axes of exoplanets in a system by comparing the radial velocity motion of their host star to that of a coupled simple harmonic oscillator. Students then explore how noncircular orbits lead to deviations from simple harmonic motion. These activities will be field tested during the Fall 2016 semester in an advanced undergraduate mechanics and astronomy courses at a large Midwestern STEM-focused university. We will present the development methodologies for these activities, description of the activities, and results from the pre-tests.

Implied Dynamics Biases the Visual Perception of Velocity

PubMed Central

La Scaleia, Barbara; Zago, Myrka; Moscatelli, Alessandro; Lacquaniti, Francesco; Viviani, Paolo

2014-01-01

We expand the anecdotic report by Johansson that back-and-forth linear harmonic motions appear uniform. Six experiments explore the role of shape and spatial orientation of the trajectory of a point-light target in the perceptual judgment of uniform motion. In Experiment 1, the target oscillated back-and-forth along a circular arc around an invisible pivot. The imaginary segment from the pivot to the midpoint of the trajectory could be oriented vertically downward (consistent with an upright pendulum), horizontally leftward, or vertically upward (upside-down). In Experiments 2 to 5, the target moved uni-directionally. The effect of suppressing the alternation of movement directions was tested with curvilinear (Experiment 2 and 3) or rectilinear (Experiment 4 and 5) paths. Experiment 6 replicated the upright condition of Experiment 1, but participants were asked to hold the gaze on a fixation point. When some features of the trajectory evoked the motion of either a simple pendulum or a mass-spring system, observers identified as uniform the kinematic profiles close to harmonic motion. The bias towards harmonic motion was most consistent in the upright orientation of Experiment 1 and 6. The bias disappeared when the stimuli were incompatible with both pendulum and mass-spring models (Experiments 3 to 5). The results are compatible with the hypothesis that the perception of dynamic stimuli is biased by the laws of motion obeyed by natural events, so that only natural motions appear uniform. PMID:24667578

Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field

NASA Astrophysics Data System (ADS)

Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

2017-10-01

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field.

PubMed

Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

2017-10-28

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

High order harmonic generation in rare gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Budil, Kimberly Susan

1994-05-01

The process of high order harmonic generation in atomic gases has shown great promise as a method of generating extremely short wavelength radiation, extending far into the extreme ultraviolet (XUV). The process is conceptually simple. A very intense laser pulse (I ~10 13-10 14 W/cm 2) is focused into a dense (~10 17 particles/cm 3) atomic medium, causing the atoms to become polarized. These atomic dipoles are then coherently driven by the laser field and begin to radiate at odd harmonics of the laser field. This dissertation is a study of both the physical mechanism of harmonic generation as wellmore » as its development as a source of coherent XUV radiation. Recently, a semiclassical theory has been proposed which provides a simple, intuitive description of harmonic generation. In this picture the process is treated in two steps. The atom ionizes via tunneling after which its classical motion in the laser field is studied. Electron trajectories which return to the vicinity of the nucleus may recombine and emit a harmonic photon, while those which do not return will ionize. An experiment was performed to test the validity of this model wherein the trajectory of the electron as it orbits the nucleus or ion core is perturbed by driving the process with elliptically, rather than linearly, polarized laser radiation. The semiclassical theory predicts a rapid turn-off of harmonic production as the ellipticity of the driving field is increased. This decrease in harmonic production is observed experimentally and a simple quantum mechanical theory is used to model the data. The second major focus of this work was on development of the harmonic "source". A series of experiments were performed examining the spatial profiles of the harmonics. The quality of the spatial profile is crucial if the harmonics are to be used as the source for experiments, particularly if they must be refocused.« less

How Computer-Assisted Teaching in Physics Can Enhance Student Learning

ERIC Educational Resources Information Center

Karamustafaoglu, O.

2012-01-01

Simple harmonic motion (SHM) is an important topic for physics or science students and has wide applications all over the world. Computer simulations are applications of special interest in physics teaching because they support powerful modeling environments involving physics concepts. This article is aimed to compare the effect of…

A Classroom Demonstration of Wireless Energy Transfer

ERIC Educational Resources Information Center

Luczak, Matthew; Baker, Blane

2010-01-01

Resonance is one of the recurring themes in physics and, as such, is important in research applications and in explaining many everyday phenomena. Students often encounter resonance during studies of simple harmonic motion, sound, mechanical waves and AC circuits. Alternatively, or in addition, resonance can be demonstrated in the context of…

Understanding the Damped SHM without ODEs

ERIC Educational Resources Information Center

Ng, Chiu-king

2016-01-01

Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM) is surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph of velocity against displacement. In this way, the condition b ? [square root]4mk for the occurrence of the non-oscillating critical damping and…

Lagrangians and Systems They Describe-How Not to Treat Dissipation in Quantum Mechanics.

ERIC Educational Resources Information Center

Ray, John R.

1979-01-01

The author argues that a Lagrangian that yields equations of motion for a damped simple harmonic oscillator does not describe this system, but a completely different physical system, and constructs a physical system that the Lagrangian describes and derives some of its properties. (Author/GA)

Experiments with a Loudspeaker

ERIC Educational Resources Information Center

Kraftmakher, Yaakov

2009-01-01

A common moving-coil loudspeaker is useful for learning harmonic motion. A simple optical method is used to observe free and forced oscillations of the diaphragm of a loudspeaker. With a lock-in amplifier and data-acquisition system, the frequency response of the loudspeaker and its electrical impedance are automatically recorded versus frequency.…

Standing Waves and Inquiry Using Water Droplets

ERIC Educational Resources Information Center

Sinclair, Dina; Vondracek, Mark

2015-01-01

Most high school and introductory college physics classes study simple harmonic motion and various wave phenomena. With the majority of states adopting the Next Generation Science Standards and pushing students to explore the scientific process for themselves, there is a growing demand for hands-on inquiry activities that involve and develop more…

An Experiment on a Physical Pendulum and Steiner's Theorem

ERIC Educational Resources Information Center

Russeva, G. B.; Tsutsumanova, G. G.; Russev, S. C.

2010-01-01

Introductory physics laboratory curricula usually include experiments on the moment of inertia, the centre of gravity, the harmonic motion of a physical pendulum, and Steiner's theorem. We present a simple experiment using very low cost equipment for investigating these subjects in the general case of an asymmetrical test body. (Contains 3 figures…

Fundamentals of Physics, Part 2 (Chapters 12-20)

NASA Astrophysics Data System (ADS)

Halliday, David; Resnick, Robert; Walker, Jearl

2003-12-01

Chapter 12 Equilibrium and Elasticity. What injury can occur to a rock climber hanging by a crimp hold? 12-1 What Is Physics? 12-2 Equilibrium. 12-3 The Requirements of Equilibrium. 12-4 The Center of Gravity. 12-5 Some Examples of Static Equilibrium. 12-6 Indeterminate Structures. 12-7 Elasticity. Review & Summary Questions Problems. Chapter 13 Gravitation. What lies at the center of our Milky Way galaxy? 13-1 What Is Physics? 13-2 Newton's Law of Gravitation. 13-3 Gravitation and the Principle of Superposition. 13-4 Gravitation Near Earth's Surface. 13-5 Gravitation Inside Earth. 13-6 Gravitational Potential Energy. 13-7 Planets and Satellites: Kepler's Laws. 13-8 Satellites: Orbits and Energy. 13-9 Einstein and Gravitation. Review & Summary Questions Problems. Chapter 14 Fluids. What causes ground effect in race car driving? 14-1 What Is Physics? 14-2 What Is a Fluid? 14-3 Density and Pressure. 14-4 Fluids at Rest. 14-5 Measuring Pressure. 14-6 Pascal's Principle. 14-7 Archimedes' Principle. 14-8 Ideal Fluids in Motion. 14-9 The Equation of Continuity. 14-10 Bernoulli's Equation. Review & SummaryQuestionsProblems. Chapter 15 Oscillations. What is the "secret" of a skilled diver's high catapult in springboard diving? 15-1 What Is Physics? 15-2 Simple Harmonic Motion. 15-3 The Force Law for Simple Harmonic Motion. 15-4 Energy in Simple Harmonic Motion. 15-5 An Angular Simple Harmonic Oscillator. 15-6 Pendulums. 15-7 Simple Harmonic Motion and Uniform Circular Motion. 15-8 Damped Simple Harmonic Motion. 15-9 Forced Oscillations and Resonance. Review & Summary Questions Problems. Chapter 16 Waves--I. How can a submarine wreck be located by distant seismic stations? 16-1 What Is Physics? 16-2 Types of Waves. 16-3 Transverse and Longitudinal Waves. 16-4 Wavelength and Frequency. 16-5 The Speed of a Traveling Wave. 16-6 Wave Speed on a Stretched String. 16-7 Energy and Power of a Wave Traveling Along a String. 16-8 The Wave Equation. 16-9 The Principle of Superposition for Waves. 16-10 Interference of Waves. 16-11 Phasors. 16-12 Standing Waves. 16-13 Standing Waves and Resonance. Review & Summary Questions Problems. Chapter 17 Waves--II. How can an emperor penguin .nd its mate among thousands of huddled penguins? 17-1 What Is Physics? 17-2 Sound Waves. 17-3 The Speed of Sound. 17-4 Traveling Sound Waves. 17-5 Interference. 17-6 Intensity and Sound Level. 17-7 Sources of Musical Sound. 17-8 Beats. 17-9 The Doppler Effect. 17-10 Supersonic Speeds, Shock Waves. Review & Summary Questions Problems. Chapter 18 Temperature, Heat, and the First Law of Thermodynamics. How can a dead rattlesnake detect and strike a reaching hand? 18-1 What Is Physics?. 18-2 Temperature. 18-3 The Zeroth Law of Thermodynamics. 18-4 Measuring Temperature. 18-5 The Celsius and Fahrenheit Scales. 18-6 Thermal Expansion. 18-7 Temperature and Heat. 18-8 The Absorption of Heat by Solids and Liquids. 18-9 A Closer Look at Heat and Work. 18-10 The First Law of Thermodynamics. 18-11 Some Special Cases of the First Law of Thermodynamics. 18-12 Heat Transfer Mechanisms. Review & Summary Questions Problems. Chapter 19 The Kinetic Theory of Gases. How can cooling steam inside a railroad tank car cause the car to be crushed? 19-1 What Is Physics? 19-2 Avogadro's Number. 19-3 Ideal Gases. 19-4 Pressure, Temperature, and RMS Speed. 19-5 Translational Kinetic Energy. 19-6 Mean Free Path. 19-7 The Distribution of Molecular Speeds. 19-8 The Molar Speci.c Heats of an Ideal Gas. 19-9 Degrees of Freedom and Molar Speci.c Heats. 19-10 A Hint of Quantum Theory. 19-11 The Adiabatic Expansion of an Ideal Gas. Review & Summary Questions Problems. Chapter 20 Entropy and the Second Law of Thermodynamics. Why is the popping of popcorn irreversible? 20-1 What Is Physics? 20-2 Irreversible Processes and Entropy. 20-3 Change in Entropy. 20-4 The Second Law of Thermodynamics. 20-5 Entropy in the Real World: Engines. 20-6 Entropy in the Real World: Refrigerators. 20-7 The Ef.ciencies of Real Engines. 20-8 A Statistical View of Entropy. Review & Summary Questions Problems. Appendices. A The International System of Units (SI). B Some Fundamental Constants of Physics. C Some Astronomical Data. D Conversion Factors. E Mathematical Formulas. F Properties of the Elements. G Periodic Table of the Elements. Answers to Checkpoints and Odd-Numbered Questions and Problems. Index.

Analysing harmonic motions with an iPhone’s magnetometer

NASA Astrophysics Data System (ADS)

Yavuz, Ahmet; Kağan Temiz, Burak

2016-05-01

In this paper, we propose an experiment for analysing harmonic motion using an iPhone’s (or iPad’s) magnetometer. This experiment consists of the detection of magnetic field variations obtained from an iPhone’s magnetometer sensor. A graph of harmonic motion is directly displayed on the iPhone’s screen using the Sensor Kinetics application. Data from this application was analysed with Eureqa software to establish the equation of the harmonic motion. Analyses show that the use of an iPhone’s magnetometer to analyse harmonic motion is a practical and effective method for small oscillations and frequencies less than 15-20 Hz.

Evaluation of geopotential and luni-solar perturbations by a recursive algorithm

NASA Technical Reports Server (NTRS)

Giacaglia, G. E. O.

1975-01-01

The disturbing functions due to the geopotential and Luni-solar attractions are linear and bilinear forms in spherical harmonics. Making use of recurrence relations for the solid spherical harmonics and their derivatives, recurrence formulas are obtained for high degree terms as function of lower degree for any term of those disturbing functions and their derivative with respect to any element. The equations obtained are effective when a numerical integration of the equations of motion is appropriate. In analytical theories, they provide a fast way of obtaining high degree terms starting from initial very simple functions.

The Local Stellar Velocity Field via Vector Spherical Harmonics

NASA Technical Reports Server (NTRS)

Markarov, V. V.; Murphy, D. W.

2007-01-01

We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism. We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not corrected for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star. The Oort parameters determined by a straightforward least-squares adjustment in vector spherical harmonics are A=14.0 +/- 1.4, B=13.1 +/- 1.2, K=1.1 +/- 1.8, and C=2.9 +/- 1.4 km s(exp -1) kpc(exp -1). The physical meaning and the implications of these parameters are discussed in the framework of a general linear model of the velocity field. We find a few statistically significant higher degree harmonic terms that do not correspond to any parameters in the classical linear model. One of them, a third-degree electric harmonic, is tentatively explained as the response to a negative linear gradient of rotation velocity with distance from the Galactic plane, which we estimate at approximately -20 km s(exp -1) kpc(exp -1). A similar vertical gradient of rotation velocity has been detected for more distant stars representing the thick disk (z greater than 1 kpc), but here we surmise its existence in the thin disk at z less than 200 pc. The most unexpected and unexplained term within the Ogorodnikov-Milne model is the first-degree magnetic harmonic, representing a rigid rotation of the stellar field about the axis -Y pointing opposite to the direction of rotation. This harmonic comes out with a statistically robust coefficient of 6.2 +/- 0.9 km s(exp -1) kpc(exp -1) and is also present in the velocity field of more distant stars. The ensuing upward vertical motion of stars in the general direction of the Galactic center and the downward motion in the anticenter direction are opposite to the vector field expected from the stationary Galactic warp model.

The harmonic oscillator and nuclear physics

NASA Technical Reports Server (NTRS)

Rowe, D. J.

1993-01-01

The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.

An Arduino Investigation of Simple Harmonic Motion

ERIC Educational Resources Information Center

Galeriu, Calin; Edwards, Scott; Esper, Geoffrey

2014-01-01

We cannot hope for a new generation of scientists and engineers if we don't let our young students take ownership of their scientific and engineering explorations, if we don't let them enjoy the hands-on cycle of design and production, and if we don't let them implant their creativity into a technologically friendly environment.…

A simple derivation for amplitude and time period of charged particles in an electrostatic bathtub potential

NASA Astrophysics Data System (ADS)

Prathap Reddy, K.

2016-11-01

An ‘electrostatic bathtub potential’ is defined and analytical expressions for the time period and amplitude of charged particles in this potential are obtained and compared with simulations. These kinds of potentials are encountered in linear electrostatic ion traps, where the potential along the axis appears like a bathtub. Ion traps are used in basic physics research and mass spectrometry to store ions; these stored ions make oscillatory motion within the confined volume of the trap. Usually these traps are designed and studied using ion optical software, but in this work the bathtub potential is reproduced by making two simple modifications to the harmonic oscillator potential. The addition of a linear ‘k 1|x|’ potential makes the simple harmonic potential curve steeper with a sharper turn at the origin, while the introduction of a finite-length zero potential region at the centre reproduces the flat region of the bathtub curve. This whole exercise of modelling a practical experimental situation in terms of a well-known simple physics problem may generate interest among readers.

Global behavior of a vibro-impact system with asymmetric clearances

NASA Astrophysics Data System (ADS)

Li, Guofang; Ding, Wangcai

2018-06-01

A simple dynamic model of a vibro-impact system subjected to harmonic excitation with two asymmetric clearances is considered. The Semi-Analytical Method for getting periodic solutions of the vibro-impact system is proposed. Diversity and evolution of the fundamental periodic impact motions are analyzed. The formation mechanism of the complete chatting-impact periodic motion with sticking motion by the influence of gazing bifurcation is analyzed. The transitional law of periodic motions in the periodical inclusions area is presented. The coexistence of periodic motions and the extreme sensitivity of the initial value within the high frequency region are studied. The global distribution of the periodic and chaos motions of the system is obtained by the state-parameter space co-simulation method which very few have considered before. The distribution of the attractor and the corresponding attracting domain corresponding to different periodic motions are also studied.

Improved Shear Wave Motion Detection Using Pulse-Inversion Harmonic Imaging with a Phased Array Transducer

PubMed Central

Song, Pengfei; Zhao, Heng; Urban, Matthew W.; Manduca, Armando; Pislaru, Sorin V.; Kinnick, Randall R.; Pislaru, Cristina; Greenleaf, James F.; Chen, Shigao

2013-01-01

Ultrasound tissue harmonic imaging is widely used to improve ultrasound B-mode imaging quality thanks to its effectiveness in suppressing imaging artifacts associated with ultrasound reverberation, phase aberration, and clutter noise. In ultrasound shear wave elastography (SWE), because the shear wave motion signal is extracted from the ultrasound signal, these noise sources can significantly deteriorate the shear wave motion tracking process and consequently result in noisy and biased shear wave motion detection. This situation is exacerbated in in vivo SWE applications such as heart, liver, and kidney. This paper, therefore, investigated the possibility of implementing harmonic imaging, specifically pulse-inversion harmonic imaging, in shear wave tracking, with the hypothesis that harmonic imaging can improve shear wave motion detection based on the same principles that apply to general harmonic B-mode imaging. We first designed an experiment with a gelatin phantom covered by an excised piece of pork belly and show that harmonic imaging can significantly improve shear wave motion detection by producing less underestimated shear wave motion and more consistent shear wave speed measurements than fundamental imaging. Then, a transthoracic heart experiment on a freshly sacrificed pig showed that harmonic imaging could robustly track the shear wave motion and give consistent shear wave speed measurements while fundamental imaging could not. Finally, an in vivo transthoracic study of seven healthy volunteers showed that the proposed harmonic imaging tracking sequence could provide consistent estimates of the left ventricular myocardium stiffness in end-diastole with a general success rate of 80% and a success rate of 93.3% when excluding the subject with Body Mass Index (BMI) higher than 25. These promising results indicate that pulse-inversion harmonic imaging can significantly improve shear wave motion tracking and thus potentially facilitate more robust assessment of tissue elasticity by SWE. PMID:24021638

Analysing Harmonic Motions with an iPhone's Magnetometer

ERIC Educational Resources Information Center

Yavuz, Ahmet; Temiz, Burak Kagan

2016-01-01

In this paper, we propose an experiment for analysing harmonic motion using an iPhone's (or iPad's) magnetometer. This experiment consists of the detection of magnetic field variations obtained from an iPhone's magnetometer sensor. A graph of harmonic motion is directly displayed on the iPhone's screen using the "Sensor Kinetics"…

Finding the Effective Mass and Spring Constant of a Force Probe from Simple Harmonic Motion

ERIC Educational Resources Information Center

Greene, Nathaniel R.; Gill, Tom; Eyerly, Stephen

2016-01-01

Force probes are versatile tools in the physics lab, but their internal workings can introduce artifacts when measuring rapidly changing forces. The Dual-Range Force Sensor by Vernier uses strain gage technology to measure force, based on the bending of a beam. Strain gages along the length of the beam change resistance as the beam bends. The…

Retrogressive harmonic motion as structural and stylistic characteristic of pop-rock music

NASA Astrophysics Data System (ADS)

Carter, Paul S.

The central issue addressed in this dissertation is that of progressive and retrogressive harmonic motion as it is utilized in the repertoire of pop-rock music. I believe that analysis in these terms may prove to be a valuable tool for the understanding of the structure, style and perception of this music. Throughout my study of this music, various patterns of progressive and retrogressive harmonic motions within a piece reveal a kind of musical character about it, a character on which much of a work's style, organization and extramusical nature often depends. Several influential theorists, especially Jean-Phillipe Rameau, Hugo Riemann, and Arnold Schoenberg, have addressed the issues of functional harmony and the nature of the motion between chords of a tonal harmonic space. After assessing these views, I have found that it is possible to differentiate between two fundamental types of harmonic motions. This difference, one that I believe is instrumental in characterizing pop-rock music, is the basis for the analytical perspective I wish to embrace. After establishing a method of evaluating tonal harmonic root motions in these terms, I wish to examine a corpus of this music in order to discover what a characterization of its harmonic motion may reveal about each piece. Determining this harmonic character may help to establish structural and stylistic traits for that piece, its genre, composer, period, or even its sociological purpose. Conclusions may then be drawn regarding the role these patterns play in defining musical style traits of pop-rock. Partly as a tool for serving the study mentioned above I develop a graphical method of accounting for root motion I name the tonal "Space-Plot"; This apparatus allows the analyst to measure several facets about the harmonic motion of the music, and to see a wide scope of relations in and around a diatonic key.

Energy in a String Wave

NASA Astrophysics Data System (ADS)

Ng, Chiu-king

2010-01-01

When one end of a taut horizontal elastic string is shaken repeatedly up and down, a transverse wave (assume sine waveform) will be produced and travel along it. College students know this type of wave motion well. They know when the wave passes by, each element of the string will perform an oscillating up-down motion, which in mechanics is termed simple harmonic2. They also know elements of the string at the highest and the lowest positions—the crests and the troughs—are momentarily at rest, while those at the centerline (zero displacement) have the greatest speed, as shown in Fig. 1. Irrespective of this, they are less familiar with the energy associated with the wave. They may fail to answer a question such as, "In a traveling string wave, which elements have respectively the greatest kinetic energy (KE) and the greatest potential energy (PE)?" The answer to the former is not difficult; elements at zero position have the fastest speed and hence their KE, being proportional to the square of speed, is the greatest. To the PE, what immediately comes to their mind may be the simple harmonic motion (SHM), in which the PE is the greatest and the KE is zero at the two turning points. It may thus lead them to think elements at crests or troughs have the greatest PE. Unfortunately, this association is wrong. Thinking that the crests or troughs have the greatest PE is a misconception.3

Localized, Non-Harmonic Active Flap Motions for Low Frequency In-Plane Rotor Noise Reduction

NASA Technical Reports Server (NTRS)

Sim, Ben W.; Potsdam, Mark; Kitaplioglu, Cahit; LeMasurier, Philip; Lorber, Peter; Andrews, Joseph

2012-01-01

A first-of-its-kind demonstration of the use of localized, non-harmonic active flap motions, for suppressing low frequency, in-plane rotor noise, is reported in this paper. Operational feasibility is verified via testing of the full-scale AATD/Sikorsky/UTRC active flap demonstration rotor in the NFAC's 40- by 80-Foot anechoic wind tunnel. Effectiveness of using localized, non-harmonic active flap motions are compared to conventional four-per-rev harmonic flap motions, and also active flap motions derived from closed-loop acoustics implementations. All three approaches resulted in approximately the same noise reductions over an in-plane three-by-three microphone array installed forward and near in-plane of the rotor in the nearfield. It is also reported that using an active flap in this localized, non-harmonic manner, resulted in no more that 2% rotor performance penalty, but had the tendency to incur higher hub vibration levels.

Fourier functional analysis for unsteady aerodynamic modeling

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Chin, Suei

1991-01-01

A method based on Fourier analysis is developed to analyze the force and moment data obtained in large amplitude forced oscillation tests at high angles of attack. The aerodynamic models for normal force, lift, drag, and pitching moment coefficients are built up from a set of aerodynamic responses to harmonic motions at different frequencies. Based on the aerodynamic models of harmonic data, the indicial responses are formed. The final expressions for the models involve time integrals of the indicial type advocated by Tobak and Schiff. Results from linear two- and three-dimensional unsteady aerodynamic theories as well as test data for a 70-degree delta wing are used to verify the models. It is shown that the present modeling method is accurate in producing the aerodynamic responses to harmonic motions and the ramp type motions. The model also produces correct trend for a 70-degree delta wing in harmonic motion with different mean angles-of-attack. However, the current model cannot be used to extrapolate data to higher angles-of-attack than that of the harmonic motions which form the aerodynamic model. For linear ramp motions, a special method is used to calculate the corresponding frequency and phase angle at a given time. The calculated results from modeling show a higher lift peak for linear ramp motion than for harmonic ramp motion. The current model also shows reasonably good results for the lift responses at different angles of attack.

Relation of squeezed states between damped harmonic and simple harmonic oscillators

NASA Technical Reports Server (NTRS)

Um, Chung-In; Yeon, Kyu-Hwang; George, Thomas F.; Pandey, Lakshmi N.

1993-01-01

The minimum uncertainty and other relations are evaluated in the framework of the coherent states of the damped harmonic oscillator. It is shown that the coherent states of the damped harmonic oscillator are the squeezed coherent states of the simple harmonic oscillator. The unitary operator is also constructed, and this connects coherent states with damped harmonic and simple harmonic oscillators.

Single-Particle Quantum Dynamics in a Magnetic Lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Venturini, Marco

2001-02-01

We study the quantum dynamics of a spinless charged-particle propagating through a magnetic lattice in a transport line or storage ring. Starting from the Klein-Gordon equation and by applying the paraxial approximation, we derive a Schroedinger-like equation for the betatron motion. A suitable unitary transformation reduces the problem to that of a simple harmonic oscillator. As a result we are able to find an explicit expression for the particle wavefunction.

Detection of cyclic-fold bifurcation in electrostatic MEMS transducers by motion-induced current

NASA Astrophysics Data System (ADS)

Park, Sangtak; Khater, Mahmoud; Effa, David; Abdel-Rahman, Eihab; Yavuz, Mustafa

2017-08-01

This paper presents a new detection method of cyclic-fold bifurcations in electrostatic MEMS transducers based on a variant of the harmonic detection of resonance method. The electrostatic transducer is driven by an unbiased harmonic signal at half its natural frequency, ω a   =  1/2 ω o . The response of the transducer consists of static displacement and a series of harmonics at 2 ω a , 4 ω a , and so on. Its motion-induced current is shifted by the excitation frequency, ω a , to appear at 3 ω a , 5 ω a , and higher odd harmonics, providing higher sensitivity to the measurement of harmonic motions. With this method, we successfully detected the variation in the location of the cyclic-fold bifurcation of an encapsulated electrostatic MEMS transducer. We also detected a regime of tapping mode motions subsequent to the bifurcation.

Social forces for team coordination in ball possession game

NASA Astrophysics Data System (ADS)

Yokoyama, Keiko; Shima, Hiroyuki; Fujii, Keisuke; Tabuchi, Noriyuki; Yamamoto, Yuji

2018-02-01

Team coordination is a basic human behavioral trait observed in many real-life communities. To promote teamwork, it is important to cultivate social skills that elicit team coordination. In the present work, we consider which social skills are indispensable for individuals performing a ball possession game in soccer. We develop a simple social force model that describes the synchronized motion of offensive players. Comparing the simulation results with experimental observations, we uncovered that the cooperative social force, a measure of perception skill, has the most important role in reproducing the harmonized collective motion of experienced players in the task. We further developed an experimental tool that facilitates real players' perceptions of interpersonal distance, revealing that the tool improves novice players' motions as if the cooperative social force were imposed.

Analytic Reflected Lightcurves for Exoplanets

NASA Astrophysics Data System (ADS)

Haggard, Hal M.; Cowan, Nicolas B.

2018-04-01

The disk-integrated reflected brightness of an exoplanet changes as a function of time due to orbital and rotational motion coupled with an inhomogeneous albedo map. We have previously derived analytic reflected lightcurves for spherical harmonic albedo maps in the special case of a synchronously-rotating planet on an edge-on orbit (Cowan, Fuentes & Haggard 2013). In this letter, we present analytic reflected lightcurves for the general case of a planet on an inclined orbit, with arbitrary spin period and non-zero obliquity. We do so for two different albedo basis maps: bright points (δ-maps), and spherical harmonics (Y_l^m-maps). In particular, we use Wigner D-matrices to express an harmonic lightcurve for an arbitrary viewing geometry as a non-linear combination of harmonic lightcurves for the simpler edge-on, synchronously rotating geometry. These solutions will enable future exploration of the degeneracies and information content of reflected lightcurves, as well as fast calculation of lightcurves for mapping exoplanets based on time-resolved photometry. To these ends we make available Exoplanet Analytic Reflected Lightcurves (EARL), a simple open-source code that allows rapid computation of reflected lightcurves.

Some anticipated contributions to core fluid dynamics from the GRM

NASA Technical Reports Server (NTRS)

Vanvorhies, C.

1985-01-01

It is broadly maintained that the secular variation (SV) of the large scale geomagnetic field contains information on the fluid dynamics of Earth's electrically conducting outer core. The electromagnetic theory appropriate to a simple Earth model has recently been combined with reduced geomagnetic data in order to extract some of this information and ascertain its significance. The simple Earth model consists of a rigid, electrically insulating mantle surrounding a spherical, inviscid, and perfectly conducting liquid outer core. This model was tested against seismology by using truncated spherical harmonic models of the observed geomagnetic field to locate Earth's core-mantle boundary, CMB. Further electromagnetic theory has been developed and applied to the problem of estimating the horizontal fluid motion just beneath CMB. Of particular geophysical interest are the hypotheses that these motions: (1) include appreciable surface divergence indicative of vertical motion at depth, and (2) are steady for time intervals of a decade or more. In addition to the extended testing of the basic Earth model, the proposed GRM provides a unique opportunity to test these dynamical hypotheses.

Configurational entropy: an improvement of the quasiharmonic approximation using configurational temperature.

PubMed

Nguyen, Phuong H; Derreumaux, Philippe

2012-01-14

One challenge in computational biophysics and biology is to develop methodologies able to estimate accurately the configurational entropy of macromolecules. Among many methods, the quasiharmonic approximation (QH) is most widely used as it is simple in both theory and implementation. However, it has been shown that this method becomes inaccurate by overestimating entropy for systems with rugged free energy landscapes. Here, we propose a simple method to improve the QH approximation, i.e., to reduce QH entropy. We approximate the potential energy landscape of the system by an effective harmonic potential, and request that this potential must produce exactly the configurational temperature of the system. Due to this constraint, the force constants associated with the effective harmonic potential are increased, or equivalently, entropy of motion governed by this effective harmonic potential is reduced. We also introduce the effective configurational temperature concept which can be used as an indicator to check the anharmonicity of the free energy landscape. To validate the new method we compare it with the recently developed expansion approximate method by calculating entropy of one simple model system and two peptides with 3 and 16 amino acids either in gas phase or in explicit solvent. We show that the new method appears to be a good choice in practice as it is a compromise between accuracy and computational speed. A modification of the expansion approximate method is also introduced and advantages are discussed in some detail.

Finding the Effective Mass and Spring Constant of a Force Probe from Simple Harmonic Motion

NASA Astrophysics Data System (ADS)

Greene, Nathaniel R.; Gill, Tom; Eyerly, Stephen

2016-03-01

Force probes are versatile tools in the physics lab, but their internal workings can introduce artifacts when measuring rapidly changing forces. The Dual-Range Force Sensor by Vernier (Fig. 1) uses strain gage technology to measure force, based on the bending of a beam. Strain gages along the length of the beam change resistance as the beam bends (Fig. 2). The elasticity of the beam leads to oscillations that persist after being excited by an impulsive force. How quickly the force probe freely returns to zero is thus related to the rigidity of the beam and the total mass attached to it. By varying the added mass and measuring the resulting frequency of the probe's internal free oscillations, the effective mass and spring constant of the probe's moveable parts can be found. Weighing of the probe parts and conducting a Hooke's law experiment provide static verification of these parameters. Study of the force sensor's behavior helps students to learn about damped harmonic motion, mathematical modeling, and the limitations of measuring devices.

Two- and three-cluster decays of light nuclei within a hyperspherical harmonics approach

NASA Astrophysics Data System (ADS)

Vasilevsky, V. S.; Lashko, Yu. A.; Filippov, G. F.

2018-06-01

We consider a set of three-cluster systems (4He, 7Li, 7Be, 8Be, 10Be) within a microscopic model which involves hyperspherical harmonics to represent intercluster motion. We selected three-cluster systems which have at least one binary channel. Our aim is to study whether hyperspherical harmonics are able, and under what conditions, to describe two-body channel(s) (nondemocratic motion) or if they are suitable for describing the three-cluster continuum only (democratic motion). It is demonstrated that a rather restricted number of hyperspherical harmonics allows us to describe bound states and scattering states in the two-body continuum for a three-cluster system.

High Harmonic Radiation Generation and Attosecond pulse generation from Intense Laser-Solid Interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thomas, Alexander Roy; Krushelnick, Karl

2016-09-08

We have studied ion motion effects in high harmonic generation, including shifts to the harmonics which result in degradation of the attosecond pulse train, and how to mitigate them. We have examined the scaling with intensity of harmonic emission. We have also switched the geometry of the interaction to measure, for the first time, harmonics from a normal incidence interaction. This was performed by using a special parabolic reflector with an on axis hole and is to allow measurements of the attosecond pulses using standard techniques. Here is a summary of the findings: First high harmonic generation in laser-solid interactionsmore » at 10 21 Wcm -2, demonstration of harmonic focusing, study of ion motion effects in high harmonic generation in laser-solid interactions, and demonstration of harmonic amplification.« less

Physics experiments with Nintendo Wii controllers

NASA Astrophysics Data System (ADS)

Wheeler, Martyn D.

2011-01-01

This article provides a detailed description of the use of Nintendo Wii game controllers in physics demonstrations. The main features of the controller relevant to physics are outlined and the procedure for communicating with a PC is described. A piece of software written by the author is applied to gathering data from a controller suspended from a spring undergoing simple harmonic motion, a pair of controllers mounted on colliding gliders on a linear air track, and a person jumping from a balance board.

Sines and Cosines. Part 3 of 3

NASA Technical Reports Server (NTRS)

Apostol, Tom M. (Editor)

1994-01-01

In this 'Project Mathematics' series video, the addition formulas of sines and cosines are explained and their real life applications are demonstrated. Both film footage and computer animation is used. Several mathematical concepts are discussed and include: Ptolemy's theorem concerned with quadrilaterals; the difference between a central angle and an inscribed angle; sines and chord lengths; special angles; subtraction formulas; and a application to simple harmonic motion. A brief history of the city Alexandria, its mathematicians, and their contribution to the field of mathematics is shown.

The application of the sinusoidal model to lung cancer patient respiratory motion

DOE Office of Scientific and Technical Information (OSTI.GOV)

George, R.; Vedam, S.S.; Chung, T.D.

2005-09-15

Accurate modeling of the respiratory cycle is important to account for the effect of organ motion on dose calculation for lung cancer patients. The aim of this study is to evaluate the accuracy of a respiratory model for lung cancer patients. Lujan et al. [Med. Phys. 26(5), 715-720 (1999)] proposed a model, which became widely used, to describe organ motion due to respiration. This model assumes that the parameters do not vary between and within breathing cycles. In this study, first, the correlation of respiratory motion traces with the model f(t) as a function of the parameter n(n=1,2,3) was undertakenmore » for each breathing cycle from 331 four-minute respiratory traces acquired from 24 lung cancer patients using three breathing types: free breathing, audio instruction, and audio-visual biofeedback. Because cos{sup 2} and cos{sup 4} had similar correlation coefficients, and cos{sup 2} and cos{sup 1} have a trigonometric relationship, for simplicity, the cos{sup 1} value was consequently used for further analysis in which the variations in mean position (z{sub 0}), amplitude of motion (b) and period ({tau}) with and without biofeedback or instructions were investigated. For all breathing types, the parameter values, mean position (z{sub 0}), amplitude of motion (b), and period ({tau}) exhibited significant cycle-to-cycle variations. Audio-visual biofeedback showed the least variations for all three parameters (z{sub 0}, b, and {tau}). It was found that mean position (z{sub 0}) could be approximated with a normal distribution, and the amplitude of motion (b) and period ({tau}) could be approximated with log normal distributions. The overall probability density function (pdf) of f(t) for each of the three breathing types was fitted with three models: normal, bimodal, and the pdf of a simple harmonic oscillator. It was found that the normal and the bimodal models represented the overall respiratory motion pdfs with correlation values from 0.95 to 0.99, whereas the range of the simple harmonic oscillator pdf correlation values was 0.71 to 0.81. This study demonstrates that the pdfs of mean position (z{sub 0}), amplitude of motion (b), and period ({tau}) can be used for sampling to obtain more realistic respiratory traces. The overall standard deviations of respiratory motion were 0.48, 0.57, and 0.55 cm for free breathing, audio instruction, and audio-visual biofeedback, respectively.« less

XTRAN2L - A PROGRAM FOR SOLVING THE GENERAL-FREQUENCY UNSTEADY TWO-DIMENSIONAL TRANSONIC SMALL-DISTURBANCE EQUATIONS

NASA Technical Reports Server (NTRS)

Seidel, D. A.

1994-01-01

The Program for Solving the General-Frequency Unsteady Two-Dimensional Transonic Small-Disturbance Equation, XTRAN2L, is used to calculate time-accurate, finite-difference solutions of the nonlinear, small-disturbance potential equation for two- dimensional transonic flow about airfoils. The code can treat forced harmonic, pulse, or aeroelastic transient type motions. XTRAN2L uses a transonic small-disturbance equation that incorporates a time accurate finite-difference scheme. Airfoil flow tangency boundary conditions are defined to include airfoil contour, chord deformation, nondimensional plunge displacement, pitch, and trailing edge control surface deflection. Forced harmonic motion can be based on: 1) coefficients of harmonics based on information from each quarter period of the last cycle of harmonic motion; or 2) Fourier analyses of the last cycle of motion. Pulse motion (an alternate to forced harmonic motion) in which the airfoil is given a small prescribed pulse in a given mode of motion, and the aerodynamic transients are calculated. An aeroelastic transient capability is available within XTRAN2L, wherein the structural equations of motion are coupled with the aerodynamic solution procedure for simultaneous time-integration. The wake is represented as a slit downstream of the airfoil trailing edge. XTRAN2L includes nonreflecting farfield boundary conditions. XTRAN2L was developed on a CDC CYBER mainframe running under NOS 2.4. It is written in FORTRAN 5 and uses overlays to minimize storage requirements. The program requires 120K of memory in overlayed form. XTRAN2L was developed in 1987.

Human motion retrieval from hand-drawn sketch.

PubMed

Chao, Min-Wen; Lin, Chao-Hung; Assa, Jackie; Lee, Tong-Yee

2012-05-01

The rapid growth of motion capture data increases the importance of motion retrieval. The majority of the existing motion retrieval approaches are based on a labor-intensive step in which the user browses and selects a desired query motion clip from the large motion clip database. In this work, a novel sketching interface for defining the query is presented. This simple approach allows users to define the required motion by sketching several motion strokes over a drawn character, which requires less effort and extends the users’ expressiveness. To support the real-time interface, a specialized encoding of the motions and the hand-drawn query is required. Here, we introduce a novel hierarchical encoding scheme based on a set of orthonormal spherical harmonic (SH) basis functions, which provides a compact representation, and avoids the CPU/processing intensive stage of temporal alignment used by previous solutions. Experimental results show that the proposed approach can well retrieve the motions, and is capable of retrieve logically and numerically similar motions, which is superior to previous approaches. The user study shows that the proposed system can be a useful tool to input motion query if the users are familiar with it. Finally, an application of generating a 3D animation from a hand-drawn comics strip is demonstrated.

Tumor characterization and treatment monitoring of postsurgical human breast specimens using harmonic motion imaging (HMI).

PubMed

Han, Yang; Wang, Shutao; Hibshoosh, Hanina; Taback, Bret; Konofagou, Elisa

2016-05-09

High-intensity focused ultrasound (HIFU) is a noninvasive technique used in the treatment of early-stage breast cancer and benign tumors. To facilitate its translation to the clinic, there is a need for a simple, cost-effective device that can reliably monitor HIFU treatment. We have developed harmonic motion imaging (HMI), which can be used seamlessly in conjunction with HIFU for tumor ablation monitoring, namely harmonic motion imaging for focused ultrasound (HMIFU). The overall objective of this study was to develop an all ultrasound-based system for real-time imaging and ablation monitoring in the human breast in vivo. HMI was performed in 36 specimens (19 normal, 15 invasive ductal carcinomas, and 2 fibroadenomas) immediately after surgical removal. The specimens were securely embedded in a tissue-mimicking agar gel matrix and submerged in degassed phosphate-buffered saline to mimic in vivo environment. The HMI setup consisted of a HIFU transducer confocally aligned with an imaging transducer to induce an oscillatory radiation force and estimate the resulting displacement. 3D HMI displacement maps were reconstructed to represent the relative tissue stiffness in 3D. The average peak-to-peak displacement was found to be significantly different (p = 0.003) between normal breast tissue and invasive ductal carcinoma. There were also significant differences before and after HMIFU ablation in both the normal (53.84 % decrease) and invasive ductal carcinoma (44.69 % decrease) specimens. HMI can be used to map and differentiate relative stiffness in postsurgical normal and pathological breast tissues. HMIFU can also successfully monitor thermal ablations in normal and pathological human breast specimens. This HMI technique may lead to a new clinical tool for breast tumor imaging and HIFU treatment monitoring.

Analytic reflected light curves for exoplanets

NASA Astrophysics Data System (ADS)

Haggard, Hal M.; Cowan, Nicolas B.

2018-07-01

The disc-integrated reflected brightness of an exoplanet changes as a function of time due to orbital and rotational motions coupled with an inhomogeneous albedo map. We have previously derived analytic reflected light curves for spherical harmonic albedo maps in the special case of a synchronously rotating planet on an edge-on orbit (Cowan, Fuentes & Haggard). In this paper, we present analytic reflected light curves for the general case of a planet on an inclined orbit, with arbitrary spin period and non-zero obliquity. We do so for two different albedo basis maps: bright points (δ-maps), and spherical harmonics (Y_ l^m-maps). In particular, we use Wigner D-matrices to express an harmonic light curve for an arbitrary viewing geometry as a non-linear combination of harmonic light curves for the simpler edge-on, synchronously rotating geometry. These solutions will enable future exploration of the degeneracies and information content of reflected light curves, as well as fast calculation of light curves for mapping exoplanets based on time-resolved photometry. To these ends, we make available Exoplanet Analytic Reflected Lightcurves, a simple open-source code that allows rapid computation of reflected light curves.

A new paradigm for human stick balancing: a suspended not an inverted pendulum.

PubMed

Lee, Kwee-Yum; O'Dwyer, Nicholas; Halaki, Mark; Smith, Richard

2012-09-01

We studied 14 skilled subjects balancing a stick (a television antenna, 52 cm, 34 g) on their middle fingertip. Comprehensive three-dimensional analyses revealed that the movement of the finger was 1.75 times that of the stick tip, such that the balanced stick behaved more like a normal noninverted pendulum than the inverted pendulum common to engineering models for stick balancing using motors. The average relation between the torque applied to the stick and its angle of deviation from the vertical was highly linear, consistent with simple harmonic motion. We observed clearly greater rotational movement of the stick in the anteroposterior plane than the mediolateral plane. Despite this magnitude difference, the duration of stick oscillatory cycles was very similar in both planes, again consistent with simple harmonic motion. The control parameter in balancing was the ratio of active torque applied to the stick relative to gravitational torque. It determined both the pivot point and oscillatory cycle period of the pendulum. The pivot point was located at the radius of gyration (about the centre of mass) of the stick from its centre of mass, showing that the subjects attuned to the gravitational dynamics and mass distribution of the stick. Hence, the key to controlling instability here was mastery of the physics of the unstable object. The radius of gyration may--similar to centre of mass--contribute to the kinesthesis of rotating limb segments and control of their gravitational dynamics.

An Arduino Investigation of Simple Harmonic Motion

NASA Astrophysics Data System (ADS)

Galeriu, Calin; Edwards, Scott; Esper, Geoffrey

2014-03-01

We cannot hope for a new generation of scientists and engineers if we don't let our young students take ownership of their scientific and engineering explorations, if we don't let them enjoy the hands-on cycle of design and production, and if we don't let them implant their creativity into a technologically friendly environment. With this educational philosophy in mind, Massimo Banzi and his team have developed and popularized the open source Arduino microcontroller board. The Arduino board has helped countless people in their science, electronics, robotics, or engineering projects, allowing them to build things that we have not even dreamed of. Physics instructors have also realized the advantages of using Arduino boards for lab experiments. The schools are saving money because the homemade experimental equipment is much cheaper than the commercial alternatives. The students are thankful for an educational experience that is more interesting, more loaded with STEM content, and more fun. As further proof of this new trend in physics education, Vernier5 is now documenting the use of their probes with Arduino boards. This is why we have developed an Arduino-based physics investigation of the simple harmonic motion (SHM) of a mass on a spring. The experimental data are collected with the help of an ultrasonic distance sensor and an Arduino Uno board. The data are then graphed and analyzed using Origin 9. This rich cross-curricular STEM activity integrates electronics, computer programming, physics, and mathematics in a way that is both experimentally exciting and intellectually rewarding.

On the local well-posedness of Lovelock and Horndeski theories

NASA Astrophysics Data System (ADS)

Papallo, Giuseppe; Reall, Harvey S.

2017-08-01

We investigate local well-posedness of the initial value problem for Lovelock and Horndeski theories of gravity. A necessary condition for local well-posedness is strong hyperbolicity of the equations of motion. Even weak hyperbolicity can fail for strong fields so we restrict to weak fields. The Einstein equation is known to be strongly hyperbolic in harmonic gauge so we study Lovelock theories in harmonic gauge. We show that the equation of motion is always weakly hyperbolic for weak fields but, in a generic weak-field background, it is not strongly hyperbolic. For Horndeski theories, we prove that, for weak fields, the equation of motion is always weakly hyperbolic in any generalized harmonic gauge. For some Horndeski theories there exists a generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a weak-field background. This includes "k-essence" like theories. However, for more general Horndeski theories, there is no generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a generic weak-field background. Our results show that the standard method used to establish local well-posedness of the Einstein equation does not extend to Lovelock or general Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields.

Modeling of aircraft unsteady aerodynamic characteristics. Part 1: Postulated models

NASA Technical Reports Server (NTRS)

Klein, Vladislav; Noderer, Keith D.

1994-01-01

A short theoretical study of aircraft aerodynamic model equations with unsteady effects is presented. The aerodynamic forces and moments are expressed in terms of indicial functions or internal state variables. The first representation leads to aircraft integro-differential equations of motion; the second preserves the state-space form of the model equations. The formulations of unsteady aerodynamics is applied in two examples. The first example deals with a one-degree-of-freedom harmonic motion about one of the aircraft body axes. In the second example, the equations for longitudinal short-period motion are developed. In these examples, only linear aerodynamic terms are considered. The indicial functions are postulated as simple exponentials and the internal state variables are governed by linear, time-invariant, first-order differential equations. It is shown that both approaches to the modeling of unsteady aerodynamics lead to identical models.

Introductory Physics Experiments Using the Wiimote

NASA Astrophysics Data System (ADS)

Somers, William; Rooney, Frank; Ochoa, Romulo

2009-03-01

The Wii, a video game console, is a very popular device with millions of units sold worldwide over the past two years. Although computationally it is not a powerful machine, to a physics educator its most important components can be its controllers. The Wiimote (or remote) controller contains three accelerometers, an infrared detector, and Bluetooth connectivity at a relatively low price. Thanks to available open source code, any PC with Bluetooth capability can detect the information sent out by the Wiimote. We have designed several experiments for introductory physics courses that make use of the accelerometers and Bluetooth connectivity. We have adapted the Wiimote to measure the: variable acceleration in simple harmonic motion, centripetal and tangential accelerations in circular motion, and the accelerations generated when students lift weights. We present the results of our experiments and compare them with those obtained when using motion and/or force sensors.

Coherent Optomechanical Switch for Motion Transduction Based on Dynamically Localized Mechanical Modes

NASA Astrophysics Data System (ADS)

Fu, Hao; Gong, Zhi-cheng; Yang, Li-ping; Mao, Tian-hua; Sun, Chang-pu; Yi, Su; Li, Yong; Cao, Geng-yu

2018-05-01

We present a coherent switch for motion transduction based on dynamically localized mechanical modes in an optomechanical system consisting of two coupled cantilevers. By placing one of the cantilevers inside a harmonically oscillating optical trap, the effective coupling strength between the degenerate cantilevers can be tuned experimentally. In particular, when the coupling is turned off, we show that mechanical motion becomes tightly bounded to the isolated cantilevers rather than propagating away as a result of destructive Landau-Zener-Stückelberg-like interference. The effect of dynamical localization is adopted to implement a coherent switch, through which the tunneling oscillation is turned on and off with well-preserved phase coherence. We provide a simple yet efficient approach for full control of the coupling between mechanical resonators, which is highly desirable for coherent control of transport phenomena in a coupled-mechanical-resonator array.

NMR signals within the generalized Langevin model for fractional Brownian motion

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2018-03-01

The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spin-bearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.

Quantum mechanics in rotating-radio-frequency traps and Penning traps with a quadrupole rotating field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abe, K.; Hasegawa, T.

2010-03-15

Quantum-mechanical analysis of ion motion in a rotating-radio-frequency (rrf) trap or in a Penning trap with a quadrupole rotating field is carried out. Rrf traps were introduced by Hasegawa and Bollinger [Phys. Rev. A 72, 043404 (2005)]. The classical motion of a single ion in this trap is described by only trigonometric functions, whereas in the conventional linear radio-frequency (rf) traps it is by the Mathieu functions. Because of the simple classical motion in the rrf trap, it is expected that the quantum-mechanical analysis of the rrf traps is also simple compared to that of the linear rf traps. Themore » analysis of Penning traps with a quadrupole rotating field is also possible in a way similar to the rrf traps. As a result, the Hamiltonian in these traps is the same as the two-dimensional harmonic oscillator, and energy levels and wave functions are derived as exact results. In these traps, it is found that one of the vibrational modes in the rotating frame can have negative energy levels, which means that the zero-quantum-number state (''ground'' state) is the highest energy state.« less

FINITE ELEMENT MODEL FOR TIDAL AND RESIDUAL CIRCULATION.

USGS Publications Warehouse

Walters, Roy A.

1986-01-01

Harmonic decomposition is applied to the shallow water equations, thereby creating a system of equations for the amplitude of the various tidal constituents and for the residual motions. The resulting equations are elliptic in nature, are well posed and in practice are shown to be numerically well-behaved. There are a number of strategies for choosing elements: the two extremes are to use a few high-order elements with continuous derivatives, or to use a large number of simpler linear elements. In this paper simple linear elements are used and prove effective.

Implementing Computer Based Laboratories

NASA Astrophysics Data System (ADS)

Peterson, David

2001-11-01

Physics students at Francis Marion University will complete several required laboratory exercises utilizing computer-based Vernier probes. The simple pendulum, the acceleration due to gravity, simple harmonic motion, radioactive half lives, and radiation inverse square law experiments will be incorporated into calculus-based and algebra-based physics courses. Assessment of student learning and faculty satisfaction will be carried out by surveys and test results. Cost effectiveness and time effectiveness assessments will be presented. Majors in Computational Physics, Health Physics, Engineering, Chemistry, Mathematics and Biology take these courses, and assessments will be categorized by major. To enhance the computer skills of students enrolled in the courses, MAPLE will be used for further analysis of the data acquired during the experiments. Assessment of these enhancement exercises will also be presented.

The harmonic oscillator and the position dependent mass Schroedinger equation: isospectral partners and factorization operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morales, J.; Ovando, G.; Pena, J. J.

2010-12-23

One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potentialmore » as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.« less

Harmonic motion detection in a vibrating scattering medium.

PubMed

Urban, Matthew W; Chen, Shigao; Greenleaf, James

2008-09-01

Elasticity imaging is an emerging medical imaging modality that seeks to map the spatial distribution of tissue stiffness. Ultrasound radiation force excitation and motion tracking using pulse-echo ultrasound have been used in numerous methods. Dynamic radiation force is used in vibrometry to cause an object or tissue to vibrate, and the vibration amplitude and phase can be measured with exceptional accuracy. This paper presents a model that simulates harmonic motion detection in a vibrating scattering medium incorporating 3-D beam shapes for radiation force excitation and motion tracking. A parameterized analysis using this model provides a platform to optimize motion detection for vibrometry applications in tissue. An experimental method that produces a multifrequency radiation force is also presented. Experimental harmonic motion detection of simultaneous multifrequency vibration is demonstrated using a single transducer. This method can accurately detect motion with displacement amplitude as low as 100 to 200 nm in bovine muscle. Vibration phase can be measured within 10 degrees or less. The experimental results validate the conclusions observed from the model and show multifrequency vibration induction and measurements can be performed simultaneously.

Harmonic Motion Detection in a Vibrating Scattering Medium

PubMed Central

Urban, Matthew W.; Chen, Shigao; Greenleaf, James F.

2008-01-01

Elasticity imaging is an emerging medical imaging modality that seeks to map the spatial distribution of tissue stiffness. Ultrasound radiation force excitation and motion tracking using pulse-echo ultrasound have been used in numerous methods. Dynamic radiation force is used in vibrometry to cause an object or tissue to vibrate, and the vibration amplitude and phase can be measured with exceptional accuracy. This paper presents a model that simulates harmonic motion detection in a vibrating scattering medium incorporating 3-D beam shapes for radiation force excitation and motion tracking. A parameterized analysis using this model provides a platform to optimize motion detection for vibrometry applications in tissue. An experimental method that produces a multifrequency radiation force is also presented. Experimental harmonic motion detection of simultaneous multifrequency vibration is demonstrated using a single transducer. This method can accurately detect motion with displacement amplitude as low as 100 to 200 nm in bovine muscle. Vibration phase can be measured within 10° or less. The experimental results validate the conclusions observed from the model and show multifrequency vibration induction and measurements can be performed simultaneously. PMID:18986892

The effects of motion artifact on mechanomyography: A comparative study of microphones and accelerometers.

PubMed

Posatskiy, A O; Chau, T

2012-04-01

Mechanomyography (MMG) is an important kinesiological tool and potential communication pathway for individuals with disabilities. However, MMG is highly susceptible to contamination by motion artifact due to limb movement. A better understanding of the nature of this contamination and its effects on different sensing methods is required to inform robust MMG sensor design. Therefore, in this study, we recorded MMG from the extensor carpi ulnaris of six able-bodied participants using three different co-located condenser microphone and accelerometer pairings. Contractions at 30% MVC were recorded with and without a shaker-induced single-frequency forearm motion artifact delivered via a custom test rig. Using a signal-to-signal-plus-noise-ratio and the adaptive Neyman curve-based statistic, we found that microphone-derived MMG spectra were significantly less influenced by motion artifact than corresponding accelerometer-derived spectra (p⩽0.05). However, non-vanishing motion artifact harmonics were present in both spectra, suggesting that simple bandpass filtering may not remove artifact influences permeating into typical MMG bands of interest. Our results suggest that condenser microphones are preferred for MMG recordings when the mitigation of motion artifact effects is important. Copyright © 2011. Published by Elsevier Ltd.

Mechanics

NASA Astrophysics Data System (ADS)

Cox, John

2014-05-01

Part 1. The Winning of the Principles: 1. Introduction; 2. The beginnings of statics. Archimedes. Problem of the lever and of the centre of gravity; 2. Experimental verification and applications of the principle of the lever; 3. The centre of gravity; 4. The balance; 5. Stevinus of Bruges. The principle of the inclined plane; 6. The parallelogram of forces; 7. The principle of virtual work; 8. Review of the principles of statics; 9. The beginnings of dynamics. Galileo. The problem of falling bodies; 10. Huyghens. The problem of uniform motion in a circle. 'Centrifugal force'; 11. Final statement of the principles of dynamics. Extension to the motions of the heavenly bodies. The law of universal gravitation. Newton; Part II. Mathematical Statement of the Principles: Introduction; 12. Kinematics; 13. Kinetics of a particle moving in a straight line. The laws of motion; 14. Experimental verification of the laws of motion. Atwood's machine; 15. Work and energy; 16. The parallelogram law; 17. The composition and resolution of forces. Resultant. Component. Equilibrium; 18. Forces in one plane; 19. Friction; Part III. Application to Various Problems: 20. Motion on an inclined plane. Brachistochrones; 21. Projectiles; 22. Simple harmonic motion; 23. The simple pendulum; 24. Central forces. The law of gravitation; 25. Impact and impulsive forces; Part IV. The Elements of Rigid Dynamics: 26. The compound pendulum. Huyghens' solution; 27. D'alembert's principle; 28. Moment of inertia; 29. Experimental determination of moments of inertia; 30. Determination of the value of gravity by Kater's pendulum; 31. The constant of gravitation, or weighing the Earth. The Cavendish experiment; Answers to the examples; Index.

Identification of aerodynamic models for maneuvering aircraft

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Hu, C. C.

1992-01-01

A Fourier analysis method was developed to analyze harmonic forced-oscillation data at high angles of attack as functions of the angle of attack and its time rate of change. The resulting aerodynamic responses at different frequencies are used to build up the aerodynamic models involving time integrals of the indicial type. An efficient numerical method was also developed to evaluate these time integrals for arbitrary motions based on a concept of equivalent harmonic motion. The method was verified by first using results from two-dimensional and three-dimensional linear theories. The developed models for C sub L, C sub D, and C sub M based on high-alpha data for a 70 deg delta wing in harmonic motions showed accurate results in reproducing hysteresis. The aerodynamic models are further verified by comparing with test data using ramp-type motions.

Development of student performance assessment based on scientific approach for a basic physics practicum in simple harmonic motion materials

NASA Astrophysics Data System (ADS)

Serevina, V.; Muliyati, D.

2018-05-01

This research aims to develop students’ performance assessment instrument based on scientific approach is valid and reliable in assessing the performance of students on basic physics lab of Simple Harmonic Motion (SHM). This study uses the ADDIE consisting of stages: Analyze, Design, Development, Implementation, and Evaluation. The student performance assessment developed can be used to measure students’ skills in observing, asking, conducting experiments, associating and communicate experimental results that are the ‘5M’ stages in a scientific approach. Each grain of assessment in the instrument is validated by the instrument expert and the evaluation with the result of all points of assessment shall be eligible to be used with a 100% eligibility percentage. The instrument is then tested for the quality of construction, material, and language by panel (lecturer) with the result: 85% or very good instrument construction aspect, material aspect 87.5% or very good, and language aspect 83% or very good. For small group trial obtained instrument reliability level of 0.878 or is in the high category, where r-table is 0.707. For large group trial obtained instrument reliability level of 0.889 or is in the high category, where r-table is 0.320. Instruments declared valid and reliable for 5% significance level. Based on the result of this research, it can be concluded that the student performance appraisal instrument based on the developed scientific approach is declared valid and reliable to be used in assessing student skill in SHM experimental activity.

Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps

ERIC Educational Resources Information Center

Pendrill, Ann-Marie; Eager, David

2015-01-01

Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…

Helicopter vibration suppression using simple pendulum absorbers on the rotor blade

NASA Technical Reports Server (NTRS)

Hamouda, M.-N. H.; Pierce, G. A.

1981-01-01

A design procedure is presented for the installation of simple pendulums on the blades of a helicopter rotor to suppress the root reactions. The procedure consists of a frequency response analysis for a hingeless rotor blade excited by a harmonic variation of spanwise airload distributions during forward flight, as well as a concentrated load at the tip. The structural modeling of the blade provides for elastic degrees of freedom in flap and lead-lag bending plus torsion. Simple flap and lead-lag pendulums are considered individually. Using a rational order scheme, the general nonlinear equations of motion are linearized. A quasi-steady aerodynamic representation is used in the formation of the airloads. The solution of the system equations derives from their representation as a transfer matrix. The results include the effect of pendulum tuning on the minimization of the hub reactions.

A harmonic analysis method for unsteady transonic flow and its application to the flutter of airfoils

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Weatherill, W. H.

1982-01-01

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. A study is presented of the shock motion associated with an oscillating airfoil and its representation by the harmonic procedure. The effects of the shock motion and the resulting pressure pulse are shown to be included in the harmonic pressure distributions and the corresponding generalized forces. Analytical and experimental pressure distributions for the NACA 64A010 airfoil are compared for Mach numbers of 0.75, 0.80 and 0.842. A typical section, two-degree-of-freedom flutter analysis of a NACA 64A010 airfoil is performed. The results show a sharp transonic bucket in one case and abrupt changes in instability modes.

Time-Perception Network and Default Mode Network Are Associated with Temporal Prediction in a Periodic Motion Task

PubMed Central

Carvalho, Fabiana M.; Chaim, Khallil T.; Sanchez, Tiago A.; de Araujo, Draulio B.

2016-01-01

The updating of prospective internal models is necessary to accurately predict future observations. Uncertainty-driven internal model updating has been studied using a variety of perceptual paradigms, and have revealed engagement of frontal and parietal areas. In a distinct literature, studies on temporal expectations have also characterized a time-perception network, which relies on temporal orienting of attention. However, the updating of prospective internal models is highly dependent on temporal attention, since temporal attention must be reoriented according to the current environmental demands. In this study, we used functional magnetic resonance imaging (fMRI) to evaluate to what extend the continuous manipulation of temporal prediction would recruit update-related areas and the time-perception network areas. We developed an exogenous temporal task that combines rhythm cueing and time-to-contact principles to generate implicit temporal expectation. Two patterns of motion were created: periodic (simple harmonic oscillation) and non-periodic (harmonic oscillation with variable acceleration). We found that non-periodic motion engaged the exogenous temporal orienting network, which includes the ventral premotor and inferior parietal cortices, and the cerebellum, as well as the presupplementary motor area, which has previously been implicated in internal model updating, and the motion-sensitive area MT+. Interestingly, we found a right-hemisphere preponderance suggesting the engagement of explicit timing mechanisms. We also show that the periodic motion condition, when compared to the non-periodic motion, activated a particular subset of the default-mode network (DMN) midline areas, including the left dorsomedial prefrontal cortex (DMPFC), anterior cingulate cortex (ACC), and bilateral posterior cingulate cortex/precuneus (PCC/PC). It suggests that the DMN plays a role in processing contextually expected information and supports recent evidence that the DMN may reflect the validation of prospective internal models and predictive control. Taken together, our findings suggest that continuous manipulation of temporal predictions engages representations of temporal prediction as well as task-independent updating of internal models. PMID:27313526

Long period nodal motion of sun synchronous orbits

NASA Technical Reports Server (NTRS)

Duck, K. I.

1975-01-01

An approximative model is formulated for assessing these perturbations that significantly affect long term modal motion of sun synchronous orbits. Computer simulations with several independent computer programs consider zonal and tesseral gravitational harmonics, third body gravitational disturbances induced by the sun and the moon, and atmospheric drag. A pendulum model consisting of evenzonal harmonics through order 4 and solar gravity dominated nodal motion approximation. This pendulum motion results from solar gravity inducing an inclination oscillation which couples into the nodal precession induced by the earth's oblateness. The pendulum model correlated well with simulations observed flight data.

Implications of respiratory motion for the quantification of 2D MR spectroscopic imaging data in the abdomen

NASA Astrophysics Data System (ADS)

Schwarz, A. J.; Leach, M. O.

2000-08-01

Magnetic resonance spectroscopic imaging (MRSI) studies in the abdomen or breast are acquired in the presence of respiratory motion. This modifies the point spread function (PSF) and hence the reconstructed spectra. We evaluated the quantitative effects of both periodic and aperiodic motion on spectra localized by MRSI. Artefactual signal changes, both the modification of native to a voxel and spurious signals arising elsewhere, depend primarily upon the motion amplitude relative to the voxel dimension. A similar dependence on motion amplitude was observed for simple harmonic motion (SHM), quasi-periodic motion and random displacements. No systematic dependence upon the period or initial phase of SHM or on the array size was found. There was also no significant variation with motion direction relative to the internal and external phase-encoding directions. In measured excursion ranges of 20 breast and abdominal tumours, 70% moved ≤ 5 mm, while 30% moved 6-23 mm. The diaphragm and fatty tissues in the gut typically moved ~ 15-20 mm. While tumour/organ excursions less than half the voxel dimension do not substantially affect native signals, the bleeding in of strong lipid signals will be problematic in 1H studies. MRSI studies in the abdomen, even of relatively well-anchored tumours, are thus likely to benefit from the addition of respiratory triggering or other motion compensation strategies.

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

PubMed Central

Kang, Chang-kwon; Shyy, Wei

2013-01-01

We report a comprehensive scaling law and novel lift generation mechanisms relevant to the aerodynamic functions of structural flexibility in insect flight. Using a Navier–Stokes equation solver, fully coupled to a structural dynamics solver, we consider the hovering motion of a wing of insect size, in which the dynamics of fluid–structure interaction leads to passive wing rotation. Lift generated on the flexible wing scales with the relative shape deformation parameter, whereas the optimal lift is obtained when the wing deformation synchronizes with the imposed translation, consistent with previously reported observations for fruit flies and honeybees. Systematic comparisons with rigid wings illustrate that the nonlinear response in wing motion results in a greater peak angle compared with a simple harmonic motion, yielding higher lift. Moreover, the compliant wing streamlines its shape via camber deformation to mitigate the nonlinear lift-degrading wing–wake interaction to further enhance lift. These bioinspired aeroelastic mechanisms can be used in the development of flapping wing micro-robots. PMID:23760300

Rotational diffusion of a molecular cat

NASA Astrophysics Data System (ADS)

Katz-Saporta, Ori; Efrati, Efi

We show that a simple isolated system can perform rotational random walk on account of internal excitations alone. We consider the classical dynamics of a ''molecular cat'': a triatomic molecule connected by three harmonic springs with non-zero rest lengths, suspended in free space. In this system, much like for falling cats, the angular momentum constraint is non-holonomic allowing for rotations with zero overall angular momentum. The geometric nonlinearities arising from the non-zero rest lengths of the springs suffice to break integrability and lead to chaotic dynamics. The coupling of the non-integrability of the system and its non-holonomic nature results in an angular random walk of the molecule. We study the properties and dynamics of this angular motion analytically and numerically. For low energy excitations the system displays normal-mode-like motion, while for high enough excitation energy we observe regular random-walk. In between, at intermediate energies we observe an angular Lévy-walk type motion associated with a fractional diffusion coefficient interpolating between the two regimes.

Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2018-02-01

Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.

Self-excited multi-scale skin vibrations probed by optical tracking micro-motions of tracers on arms

NASA Astrophysics Data System (ADS)

Chen, Wei-Chia; Chen, Hsiang-Ying; Chen, Yu-Sheng; Tian, Yong; I, Lin

2017-07-01

The self-excited multi-scale mechanical vibrations, their sources and their mutual coupling of different regions on the forearms of supine subjects, are experimentally investigated, using a simple noncontact method, optical video microscopy, which provides 1 μm and 25 ms spatiotemporal resolutions. It is found that, in proximal regions far from the radial artery, the vibrations are the global vibrations of the entire forearm excited by remote sources, propagating through the trunk and the limb. The spectrum is mainly composed of peaks of very low frequency motion (down to 0.05 Hz), low frequency respiration modes, and heartbeat induced modes (about 1 Hz and its harmonics), standing out of the spectrum floor exhibiting power law decay. The nonlinear mode-mode coupling leads to the cascaded modulations of higher frequency modes by lower frequency modes. The nearly identical waveforms without detectable phase delays for a pair of signals along or transverse to the meridian of regions far away from the artery rule out the detectable contribution from the propagation of Qi, some kind of collective excitation which more efficiently propagates along meridians, according to the Chinese medicine theory. Around the radial artery, in addition to the global vibration, the local vibration spectrum shows very slow breathing type vibration around 0.05 Hz, and the artery pulsation induced fundamental and higher harmonics with descending intensities up to the fifth harmonics, standing out of a flat spectrum floor. All the artery pulsation modes are also modulated by respiration and the very slow vibration.

Analysis on the multi-dimensional spectrum of the thrust force for the linear motor feed drive system in machine tools

NASA Astrophysics Data System (ADS)

Yang, Xiaojun; Lu, Dun; Ma, Chengfang; Zhang, Jun; Zhao, Wanhua

2017-01-01

The motor thrust force has lots of harmonic components due to the nonlinearity of drive circuit and motor itself in the linear motor feed drive system. What is more, in the motion process, these thrust force harmonics may vary with the position, velocity, acceleration and load, which affects the displacement fluctuation of the feed drive system. Therefore, in this paper, on the basis of the thrust force spectrum obtained by the Maxwell equation and the electromagnetic energy method, the multi-dimensional variation of each thrust harmonic is analyzed under different motion parameters. Then the model of the servo system is established oriented to the dynamic precision. The influence of the variation of the thrust force spectrum on the displacement fluctuation is discussed. At last the experiments are carried out to verify the theoretical analysis above. It can be found that the thrust harmonics show multi-dimensional spectrum characteristics under different motion parameters and loads, which should be considered to choose the motion parameters and optimize the servo control parameters in the high-speed and high-precision machine tools equipped with the linear motor feed drive system.

Double simple-harmonic-oscillator formulation of the thermal equilibrium of a fluid interacting with a coherent source of phonons

NASA Technical Reports Server (NTRS)

Defacio, B.; Vannevel, Alan; Brander, O.

1993-01-01

A formulation is given for a collection of phonons (sound) in a fluid at a non-zero temperature which uses the simple harmonic oscillator twice; one to give a stochastic thermal 'noise' process and the other which generates a coherent Glauber state of phonons. Simple thermodynamic observables are calculated and the acoustic two point function, 'contrast' is presented. The role of 'coherence' in an equilibrium system is clarified by these results and the simple harmonic oscillator is a key structure in both the formulation and the calculations.

The hybrid mass-spring pendulum model of human leg swinging: stiffness in the control of cycle period.

PubMed

Obusek, J P; Holt, K G; Rosenstein, R M

1995-07-01

Human leg swinging is modeled as the harmonic motion of a hybrid mass-spring pendulum. The cycle period is determined by a gravitational component and an elastic component, which is provided by the attachment of a soft-tissue/muscular spring of variable stiffness. To confirm that the stiffness of the spring changes with alterations in the inertial properties of the oscillator and that stiffness is relevant for the control of cycle period, we conducted this study in which the simple pendulum equivalent length was experimentally manipulated by adding mass to the ankle of a comfortably swinging leg. Twenty-four young, healthy adults were videotaped as they swung their right leg under four conditions: no added mass and with masses of 2.27, 4.55, and 6.82kg added to the ankle. Strong, linear relationships between the acceleration and displacement of the swinging leg within subjects and conditions were found, confirming the motion's harmonic nature. Cycle period significantly increased with the added mass. However, the observed increases were not as large as would be predicted by the induced changes in the gravitational component alone. These differences were interpreted as being due to increases in the active muscular stiffness. Significant linear increases in the elastic component (and hence stiffness) were demonstrated with increases in the simple pendulum equivalent length in 20 of the individual subjects, with r2 values ranging between 0.89 and 0.99. Significant linear relationships were also demonstrated between the elastic and gravitational components in 22 subjects, with individual r2 values between 0.90 and 0.99.(ABSTRACT TRUNCATED AT 250 WORDS)

Fast antibody fragment motion: flexible linkers act as entropic spring

PubMed Central

Stingaciu, Laura R.; Ivanova, Oxana; Ohl, Michael; Biehl, Ralf; Richter, Dieter

2016-01-01

A flexible linker region between three fragments allows antibodies to adjust their binding sites to an antigen or receptor. Using Neutron Spin Echo Spectroscopy we observed fragment motion on a timescale of 7 ns with motional amplitudes of about 1 nm relative to each other. The mechanistic complexity of the linker region can be described by a spring model with Brownian motion of the fragments in a harmonic potential. Displacements, timescale, friction and force constant of the underlying dynamics are accessed. The force constant exhibits a similar strength to an entropic spring, with friction of the fragment matching the unbound state. The observed fast motions are fluctuations in pre-existing equilibrium configurations. The Brownian motion of domains in a harmonic potential is the appropriate model to examine functional hinge motions dependent on the structural topology and highlights the role of internal forces and friction to function. PMID:27020739

Fast antibody fragment motion: flexible linkers act as entropic spring

DOE PAGES

Stingaciu, Laura R.; Ivanova, Oxana; Ohl, Michael; ...

2016-03-29

A flexible linker region between three fragments allows antibodies to adjust their binding sites to an antigen or receptor. Using Neutron Spin Echo Spectroscopy we observed fragment motion on a timescale of 7 ns with motional amplitudes of about 1 nm relative to each other. The mechanistic complexity of the linker region can be described by a spring model with Brownian motion of the fragments in a harmonic potential. Displacements, timescale, friction and force constant of the underlying dynamics are accessed. The force constant exhibits a similar strength to an entropic spring, with friction of the fragment matching the unboundmore » state. The observed fast motions are fluctuations in pre-existing equilibrium configurations. In conclusion, the Brownian motion of domains in a harmonic potential is the appropriate model to examine functional hinge motions dependent on the structural topology and highlights the role of internal forces and friction to function.« less

Fast antibody fragment motion: flexible linkers act as entropic spring.

PubMed

Stingaciu, Laura R; Ivanova, Oxana; Ohl, Michael; Biehl, Ralf; Richter, Dieter

2016-03-29

A flexible linker region between three fragments allows antibodies to adjust their binding sites to an antigen or receptor. Using Neutron Spin Echo Spectroscopy we observed fragment motion on a timescale of 7 ns with motional amplitudes of about 1 nm relative to each other. The mechanistic complexity of the linker region can be described by a spring model with Brownian motion of the fragments in a harmonic potential. Displacements, timescale, friction and force constant of the underlying dynamics are accessed. The force constant exhibits a similar strength to an entropic spring, with friction of the fragment matching the unbound state. The observed fast motions are fluctuations in pre-existing equilibrium configurations. The Brownian motion of domains in a harmonic potential is the appropriate model to examine functional hinge motions dependent on the structural topology and highlights the role of internal forces and friction to function.

Crossover from Super- to Subdiffusive Motion and Memory Effects in Crystalline Organic Semiconductors

NASA Astrophysics Data System (ADS)

De Filippis, G.; Cataudella, V.; Mishchenko, A. S.; Nagaosa, N.; Fierro, A.; de Candia, A.

2015-02-01

The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining an exact diagonalization technique, Monte Carlo approaches, and a maximum entropy method. The temperature-dependent mobility data measured in single crystals of rubrene are successfully reproduced: a crossover from super- to subdiffusive motion occurs in the range 150 ≤T ≤200 K , where the mean free path becomes of the order of the lattice parameter and strong memory effects start to appear. We provide an effective model, which can successfully explain features of the absorption spectra at low frequencies. The observed response to slowly varying electric field is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.

Crossover from super- to subdiffusive motion and memory effects in crystalline organic semiconductors.

PubMed

De Filippis, G; Cataudella, V; Mishchenko, A S; Nagaosa, N; Fierro, A; de Candia, A

2015-02-27

The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining an exact diagonalization technique, Monte Carlo approaches, and a maximum entropy method. The temperature-dependent mobility data measured in single crystals of rubrene are successfully reproduced: a crossover from super- to subdiffusive motion occurs in the range 150≤T≤200  K, where the mean free path becomes of the order of the lattice parameter and strong memory effects start to appear. We provide an effective model, which can successfully explain features of the absorption spectra at low frequencies. The observed response to slowly varying electric field is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.

Contribution to harmonic balance calculations of self-sustained periodic oscillations with focus on single-reed instruments.

PubMed

Farner, Snorre; Vergez, Christophe; Kergomard, Jean; Lizée, Aude

2006-03-01

The harmonic balance method (HBM) was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has been adapted to self-sustained musical instruments. Unlike time-domain methods, this frequency-domain method does not capture transients and so is not adapted for sound synthesis. However, its independence of time makes it very useful for studying any periodic solution, whether stable or unstable, without care of particular initial conditions in time. A computer program for solving general problems involving nonlinearly coupled exciter and resonator, HARMBAL, has been developed based on the HBM. The method as well as convergence improvements and continuation facilities are thoroughly presented and discussed in the present paper. Applications of the method are demonstrated, especially on problems with severe difficulties of convergence: the Helmholtz motion (square signals) of single-reed instruments when no losses are taken into account, the reed being modeled as a simple spring.

A relativistic gravity train

NASA Astrophysics Data System (ADS)

Parker, Edward

2017-08-01

A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can attain speeds arbitrarily close to the speed of light; generalizing the electrostatic and gravitational cases requires special and general relativity, respectively. We find exact closed-form relations between the position, proper time, and coordinate time in both cases, and find that they are no longer harmonic, with oscillation periods that depend on the amplitude. In the highly relativistic limit of both cases, the particle spends almost all of its proper time near the turning points, but almost all of the coordinate time moving through the bulk of the ball. Buchdahl's theorem imposes nontrivial constraints on the general-relativistic case, as a ball of given density can only attain a finite maximum radius before collapsing into a black hole. This article is intended to be pedagogical, and should be accessible to those who have taken an undergraduate course in general relativity.

Bio-inspired piezoelectric linear motor driven by a single-phase harmonic wave with an asymmetric stator.

PubMed

Pan, Qiaosheng; Miao, Enming; Wu, Bingxuan; Chen, Weikang; Lei, Xiujun; He, Liangguo

2017-07-01

A novel, bio-inspired, single-phase driven piezoelectric linear motor (PLM) using an asymmetric stator was designed, fabricated, and tested to avoid mode degeneracy and to simplify the drive mechanism of a piezoelectric motor. A piezoelectric transducer composed of two piezoelectric stacks and a displacement amplifier was used as the driving element of the PLM. Two simple and specially designed claws performed elliptical motion. A numerical simulation was performed to design the stator and determine the feasibility of the design mechanism of the PLM. Moreover, an experimental setup was built to validate the working principles, as well as to evaluate the performance, of the PLM. The prototype motor outputs a no-load speed of 233.7 mm/s at a voltage of 180 V p-p and a maximum thrust force of 2.3 N under a preload of 10 N. This study verified the feasibility of the proposed design and provided a method to simplify the driving harmonic signal and structure of PLMs.

Acceleration and Velocity Sensing from Measured Strain

NASA Technical Reports Server (NTRS)

Pak, Chan-Gi; Truax, Roger

2015-01-01

A simple approach for computing acceleration and velocity of a structure from the strain is proposed in this study. First, deflection and slope of the structure are computed from the strain using a two-step theory. Frequencies of the structure are computed from the time histories of strain using a parameter estimation technique together with an autoregressive moving average model. From deflection, slope, and frequencies of the structure, acceleration and velocity of the structure can be obtained using the proposed approach. Simple harmonic motion is assumed for the acceleration computations, and the central difference equation with a linear autoregressive model is used for the computations of velocity. A cantilevered rectangular wing model is used to validate the simple approach. Quality of the computed deflection, acceleration, and velocity values are independent of the number of fibers. The central difference equation with a linear autoregressive model proposed in this study follows the target response with reasonable accuracy. Therefore, the handicap of the backward difference equation, phase shift, is successfully overcome.

Effects of the oceans on polar motion: Extended investigations

NASA Technical Reports Server (NTRS)

Dickman, Steven R.

1986-01-01

A method was found for expressing the tide current velocities in terms of the tide height (with all variables expanded in spherical harmonics). All time equations were then combined into a single, nondifferential matrix equation involving only the unknown tide height. The pole tide was constrained so that no tidewater flows across continental boundaries. The constraint was derived for the case of turbulent oceans; with the tide velocities expressed in terms of the tide height. The two matrix equations were combined. Simple matrix inversion then yielded the constrained solution. Programs to construct and invert the matrix equations were written. Preliminary results were obtained and are discussed.

Complementarity and Young's interference fringes from two atoms

NASA Astrophysics Data System (ADS)

Itano, W. M.; Bergquist, J. C.; Bollinger, J. J.; Wineland, D. J.; Eichmann, U.; Raizen, M. G.

1998-06-01

The interference pattern of the resonance fluorescence from a J=1/2 to J=1/2 transition of two identical atoms confined in a three-dimensional harmonic potential is calculated. The thermal motion of the atoms is included. Agreement is obtained with experiments [U. Eichmann et al., Phys. Rev. Lett. 70, 2359 (1993)]. Contrary to some theoretical predictions, but in agreement with the present calculations, a fringe visibility greater than 50% can be observed with polarization-selective detection. The dependence of the fringe visibility on polarization has a simple interpretation, based on whether or not it is possible in principle to determine which atom emitted the photon.

Uniform function constants of motion and their first-order perturbation

NASA Astrophysics Data System (ADS)

Prato, Domingo; Hamity, Victor H.

2005-05-01

The main purpose of this work is to present some uniform function constants of motion rather than the well-known quantities arising from spacetime symmetries. These constants are usually associated with the intrinsic characteristics of the trajectories of a particle in a central potential field. We treat two cases. The first is the Lenz vector which sometimes is found in the literature [1, 2]; the other is associated with the isotropic harmonic oscillator, of relative importance in some simple models of the classical molecular interaction. The first example is applied to describe the perturbation of the trajectories in the Rutherford scattering and the precession of the Keplerian orbit of a planet. In the other case the conserved quantity is a symmetric tensor. We find the eigenvectors and eigenvalues of that tensor while at the same time we obtain the solution to the problem of calculating the rotation rate of the orbits in first order of a perturbation parameter in the potential energy, by performing a simple coordinate transformation in the Cartesian plane. We think that the present work addresses many aspects of mechanics with a didactical interest in other physics or mathematics courses.

Methods for Boundary-Value Problems in Free-Surface Flows: The Third David W. Taylor Lecture, 27 August through 19 September 1974,

DTIC Science & Technology

1974-09-01

reduction arnd reflection, the method of Green functions, the method of multipole expansions, and, time permitting,* variational methods. I shall try to...depending upon the circumstances. If the motion is assumed to be harmonic in time with frequency 0, we may write cD(x,y,z,t) 4)1(x,y,z) cos at + • 2 (x,y,z... time , so that transient j motions associated with starting the wavemaker have died out and the fluid motion is also harmonic with frequency c. 1 Let

Current-driven second-harmonic domain wall resonance in ferromagnetic metal/nonmagnetic metal bilayers: A field-free method for spin Hall angle measurements

NASA Astrophysics Data System (ADS)

Hajiali, M. R.; Hamdi, M.; Roozmeh, S. E.; Mohseni, S. M.

2017-10-01

We study the ac current-driven domain wall motion in bilayer ferromagnetic metal (FM)/nonmagnetic metal (NM) nanowires. The solution of the modified Landau-Lifshitz-Gilbert equation including all the spin transfer torques is used to describe motion of the domain wall in the presence of the spin Hall effect. We show that the domain wall center has a second-harmonic frequency response in addition to the known first-harmonic excitation. In contrast to the experimentally observed second-harmonic response in harmonic Hall measurements of spin-orbit torque in magnetic thin films, this second-harmonic response directly originates from spin-orbit torque driven domain wall dynamics. Based on the spin current generated by domain wall dynamics, the longitudinal spin motive force generated voltage across the length of the nanowire is determined. The second-harmonic response introduces additionally a practical field-free and all-electrical method to probe the effective spin Hall angle for FM/NM bilayer structures that could be applied in experiments. Our results also demonstrate the capability of utilizing FM/NM bilayer structures in domain wall based spin-torque signal generators and resonators.

Exact solution of a quantum forced time-dependent harmonic oscillator

NASA Technical Reports Server (NTRS)

Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN

1992-01-01

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.

Coherent Motion of Monolayer Sheets under Confinement and Its Pathological Implications.

PubMed

Soumya, S S; Gupta, Animesh; Cugno, Andrea; Deseri, Luca; Dayal, Kaushik; Das, Dibyendu; Sen, Shamik; Inamdar, Mandar M

2015-12-01

Coherent angular rotation of epithelial cells is thought to contribute to many vital physiological processes including tissue morphogenesis and glandular formation. However, factors regulating this motion, and the implications of this motion if perturbed, remain incompletely understood. In the current study, we address these questions using a cell-center based model in which cells are polarized, motile, and interact with the neighboring cells via harmonic forces. We demonstrate that, a simple evolution rule in which the polarization of any cell tends to orient with its velocity vector can induce coherent motion in geometrically confined environments. In addition to recapitulating coherent rotational motion observed in experiments, our results also show the presence of radial movements and tissue behavior that can vary between solid-like and fluid-like. We show that the pattern of coherent motion is dictated by the combination of different physical parameters including number density, cell motility, system size, bulk cell stiffness and stiffness of cell-cell adhesions. We further observe that perturbations in the form of cell division can induce a reversal in the direction of motion when cell division occurs synchronously. Moreover, when the confinement is removed, we see that the existing coherent motion leads to cell scattering, with bulk cell stiffness and stiffness of cell-cell contacts dictating the invasion pattern. In summary, our study provides an in-depth understanding of the origin of coherent rotation in confined tissues, and extracts useful insights into the influence of various physical parameters on the pattern of such movements.

Coherent Motion of Monolayer Sheets under Confinement and Its Pathological Implications

PubMed Central

Soumya, S S; Gupta, Animesh; Cugno, Andrea; Deseri, Luca; Dayal, Kaushik; Das, Dibyendu; Sen, Shamik; Inamdar, Mandar M.

2015-01-01

Coherent angular rotation of epithelial cells is thought to contribute to many vital physiological processes including tissue morphogenesis and glandular formation. However, factors regulating this motion, and the implications of this motion if perturbed, remain incompletely understood. In the current study, we address these questions using a cell-center based model in which cells are polarized, motile, and interact with the neighboring cells via harmonic forces. We demonstrate that, a simple evolution rule in which the polarization of any cell tends to orient with its velocity vector can induce coherent motion in geometrically confined environments. In addition to recapitulating coherent rotational motion observed in experiments, our results also show the presence of radial movements and tissue behavior that can vary between solid-like and fluid-like. We show that the pattern of coherent motion is dictated by the combination of different physical parameters including number density, cell motility, system size, bulk cell stiffness and stiffness of cell-cell adhesions. We further observe that perturbations in the form of cell division can induce a reversal in the direction of motion when cell division occurs synchronously. Moreover, when the confinement is removed, we see that the existing coherent motion leads to cell scattering, with bulk cell stiffness and stiffness of cell-cell contacts dictating the invasion pattern. In summary, our study provides an in-depth understanding of the origin of coherent rotation in confined tissues, and extracts useful insights into the influence of various physical parameters on the pattern of such movements. PMID:26691341

Ideas for Use of an IPad in Introductory Physics Education

NASA Astrophysics Data System (ADS)

Aurora, Tarlok S.

2014-03-01

Mobile devices such as an IPad, tablet computers and smartphones offer an opportunity to collect information to facilitate physics teaching and learning. The data collected with built-in sensors, such as a video camera, may be analyzed on the mobile device itself or on a desktop computer. In this work, first, the circular motion of a steel ball rolling in a cereal bowl was analyzed to show that it consisted of two simple harmonic motions, in perpendicular directions. Secondly, motion of two balls-one dropped vertically down, and the other one launched as a projectile - was analyzed. Data was analyzed with Logger Pro software, and value of g was determined graphically. Details of the work, its limitations and additional examples will be described. The material so obtained may be used as a demonstration, in a classroom, to clarify physics concepts. In a school, where students are required to have such portable devices, one may assign such activities as homework, to enhance student engagement in learning physics. The author is thankful to USciences for the IPad; and Rich Cosgriff, Phyllis Blumberg and Elia Eschenazi for useful discussions.

User's Guide for ECAP2D: an Euler Unsteady Aerodynamic and Aeroelastic Analysis Program for Two Dimensional Oscillating Cascades, Version 1.0

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.

1995-01-01

This guide describes the input data required for using ECAP2D (Euler Cascade Aeroelastic Program-Two Dimensional). ECAP2D can be used for steady or unsteady aerodynamic and aeroelastic analysis of two dimensional cascades. Euler equations are used to obtain aerodynamic forces. The structural dynamic equations are written for a rigid typical section undergoing pitching (torsion) and plunging (bending) motion. The solution methods include harmonic oscillation method, influence coefficient method, pulse response method, and time integration method. For harmonic oscillation method, example inputs and outputs are provided for pitching motion and plunging motion. For the rest of the methods, input and output for pitching motion only are given.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hailong; Vibration Control Lab, School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042; Zhang, Ning

Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phasemore » trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.« less

Applications of the trilinear Hamiltonian with three trapped ions

NASA Astrophysics Data System (ADS)

Hablutzel Marrero, Roland Esteban; Ding, Shiqian; Maslennikov, Gleb; Gan, Jaren; Nimmrichter, Stefan; Roulet, Alexandre; Dai, Jibo; Scarani, Valerio; Matsukevich, Dzmitry

2017-04-01

The trilinear Hamiltonian a† bc + ab†c† , which describes a nonlinear interaction between harmonic oscillators, can be implemented to study different phenomena ranging from simple quantum models to quantum thermodynamics. We engineer this coupling between three modes of motion of three trapped 171Yb+ ions, where the interaction arises naturally from their mutual (anharmonic) Coulomb repulsion. By tuning our trapping parameters we are able to turn on / off resonant exchange of energy between the modes on demand. We present applications of this Hamiltonian for simulations of the parametric down conversion process in the regime of depleted pump, a simple model of Hawking radiation, and the Tavis-Cummings model. We also discuss the implementation of the quantum absorption refrigerator in such system and experimentally study effects of quantum coherence on its performance. This research is supported by the National Research Foundation, Prime Minister's Office, Singapore and the Ministry of Education, Singapore under the Research Centres of Excellence programme.

Numerical simulation of fluid flow through simplified blade cascade with prescribed harmonic motion using discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Vimmr, Jan; Bublík, Ondřej; Prausová, Helena; Hála, Jindřich; Pešek, Luděk

2018-06-01

This paper deals with a numerical simulation of compressible viscous fluid flow around three flat plates with prescribed harmonic motion. This arrangement presents a simplified blade cascade with forward wave motion. The aim of this simulation is to determine the aerodynamic forces acting on the flat plates. The mathematical model describing this problem is formed by Favre-averaged system of Navier-Stokes equations in arbitrary Lagrangian-Eulerian (ALE) formulation completed by one-equation Spalart-Allmaras turbulence model. The simulation was performed using the developed in-house CFD software based on discontinuous Galerkin method, which offers high order of accuracy.

Improving Power Density of Free-Piston Stirling Engines

NASA Technical Reports Server (NTRS)

Briggs, Maxwell H.; Prahl, Joseph M.; Loparo, Kenneth A.

2016-01-01

Analyses and experiments demonstrate the potential benefits of optimizing piston and displacer motion in a free-piston Stirling Engine. Isothermal analysis shows the theoretical limits of power density improvement due to ideal motion in ideal Stirling engines. More realistic models based on nodal analysis show that ideal piston and displacer waveforms are not optimal, often producing less power than engines that use sinusoidal piston and displacer motion. Constrained optimization using nodal analysis predicts that Stirling engine power density can be increased by as much as 58 percent using optimized higher harmonic piston and displacer motion. An experiment is conducted in which an engine designed for sinusoidal motion is forced to operate with both second and third harmonics, resulting in a piston power increase of as much as 14 percent. Analytical predictions are compared to experimental data and show close agreement with indirect thermodynamic power calculations, but poor agreement with direct electrical power measurements.

Improving Power Density of Free-Piston Stirling Engines

NASA Technical Reports Server (NTRS)

Briggs, Maxwell H.; Prahl, Joseph; Loparo, Kenneth

2016-01-01

Analyses and experiments demonstrate the potential benefits of optimizing piston and displacer motion in a free piston Stirling Engine. Isothermal analysis shows the theoretical limits of power density improvement due to ideal motion in ideal Stirling engines. More realistic models based on nodal analysis show that ideal piston and displacer waveforms are not optimal, often producing less power than engines that use sinusoidal piston and displacer motion. Constrained optimization using nodal analysis predicts that Stirling engine power density can be increased by as much as 58 using optimized higher harmonic piston and displacer motion. An experiment is conducted in which an engine designed for sinusoidal motion is forced to operate with both second and third harmonics, resulting in a maximum piston power increase of 14. Analytical predictions are compared to experimental data showing close agreement with indirect thermodynamic power calculations, but poor agreement with direct electrical power measurements.

Improving Free-Piston Stirling Engine Power Density

NASA Technical Reports Server (NTRS)

Briggs, Maxwell H.

2016-01-01

Analyses and experiments demonstrate the potential benefits of optimizing piston and displacer motion in a free piston Stirling Engine. Isothermal analysis shows the theoretical limits of power density improvement due to ideal motion in ideal Stirling engines. More realistic models based on nodal analysis show that ideal piston and displacer waveforms are not optimal, often producing less power than engines that use sinusoidal piston and displacer motion. Constrained optimization using nodal analysis predicts that Stirling engine power density can be increased by as much as 58% using optimized higher harmonic piston and displacer motion. An experiment is conducted in which an engine designed for sinusoidal motion is forced to operate with both second and third harmonics, resulting in a maximum piston power increase of 14%. Analytical predictions are compared to experimental data showing close agreement with indirect thermodynamic power calculations, but poor agreement with direct electrical power measurements.

On Fitts's and Hooke's laws: simple harmonic movement in upper-limb cyclical aiming.

PubMed

Guiard, Y

1993-03-01

Can discrete, single-shot movements and continuous, cyclical movements be reduced to a single concept? In the classical, computational approach to human motor behaviour, cyclical aimed movement has generally been considered to derive from discrete primitives through a concatenation mechanism. Much importance, accordingly, has been attached to discrete-movement paradigms and to techniques allowing the segmentation of continuous data. An alternative approach, suggested by the nonlinear dynamical systems theory, views discreteness as a limiting case of cyclicity. Although attempts have been made recently to account for discrete movements in dynamical terms, cyclical paradigms have been favoured. The concatenation interpretation of cyclical aimed movement is criticized on the ground that it implies a complete waste of mechanical energy once in every half-cycle. Some kinematic data from a one-dimensional reciprocal (i.e., cyclical) aiming experiment are reported, suggesting that human subjects do save muscular efforts from one movement to the next in upper-limb cyclical aiming. The experiment demonstrated convergence on simple harmonic motion as aiming tolerance was increased, an outcome interpreted with reference to Hooke's law, in terms of the muscles' capability of storing potential, elastic energy across movement reversals. Not only is the concatenation concept problematic for understanding cyclical aimed movements, but the very reality of discrete movements is questionable too. It is pointed out that discrete motor acts of real life are composed of complete cycles, rather than half-cycles.

Fluid powered linear piston motor with harmonic coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raymond, David W.

2016-09-20

A motor is disclosed that includes a module assembly including a piston that is axially cycled. The piston axial motion is coupled to torque couplers that convert the axial motion into rotary motion. The torque couplers are coupled to a rotor to rotate the rotor.

Hamilton-Jacobi modelling of relative motion for formation flying.

PubMed

Kolemen, Egemen; Kasdin, N Jeremy; Gurfil, Pini

2005-12-01

A precise analytic model for the relative motion of a group of satellites in slightly elliptic orbits is introduced. With this aim, we describe the relative motion of an object relative to a circular or slightly elliptic reference orbit in the rotating Hill frame via a low-order Hamiltonian, and solve the Hamilton-Jacobi equation. This results in a first-order solution to the relative motion identical to the Clohessy-Wiltshire approach; here, however, rather than using initial conditions as our constants of the motion, we utilize the canonical momenta and coordinates. This allows us to treat perturbations in an identical manner, as in the classical Delaunay formulation of the two-body problem. A precise analytical model for the base orbit is chosen with the included effect of zonal harmonics (J(2), J(3), J(4)). A Hamiltonian describing the real relative motion is formed and by differing this from the nominal Hamiltonian, the perturbing Hamiltonian is obtained. Using the Hamilton equations, the variational equations for the new constants are found. In a manner analogous to the center manifold reduction procedure, the non-periodic part of the motion is canceled through a magnitude analysis leading to simple boundedness conditions that cancel the drift terms due to the higher order perturbations. Using this condition, the variational equations are integrated to give periodic solutions that closely approximate the results from numerical integration (1 mm/per orbit for higher order and eccentricity perturbations and 30 cm/per orbit for zonal perturbations). This procedure provides a compact and insightful analytic description of the resulting relative motion.

Spectral Analysis of Vibrational Harmonic Motion by use of a Continuous-Wave CO2 Doppler Lidar

NASA Technical Reports Server (NTRS)

Jarzembski, Maurice A.; Srivastava, Vandana

1999-01-01

Vibrational motion of a harmonic oscillator was investigated using a focused continuous wave CO2 Doppler lidar at 9.1 microns wavelength. A continuum of frequencies along with many discrete, equally spaced, resonant frequency modes was observed. The frequency modes are similar in structure to the oscillatory longitudinal modes of a laser cavity and arise because of interference of the natural resonant frequency of the oscillator with specific frequencies within the continuum. The spectra revealed departures from linear motion for vigorous vibrations of the oscillator. Each consecutive resonant frequency mode occurred for a movement of the oscillator much less than the wavelength of incident lidar radiation.

A Simple Mechanical Model for the Isotropic Harmonic Oscillator

ERIC Educational Resources Information Center

Nita, Gelu M.

2010-01-01

A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)

Mathematical Development and Computational Analysis of Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) Based on Bloch Nuclear Magnetic Resonance (NMR) Diffusion Model for Myocardial Motion.

PubMed

Dada, Michael O; Jayeoba, Babatunde; Awojoyogbe, Bamidele O; Uno, Uno E; Awe, Oluseyi E

2017-09-13

Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) is a tagged image analysis method that can measure myocardial motion and strain in near real-time and is considered a potential candidate to make magnetic resonance tagging clinically viable. However, analytical expressions of radially tagged transverse magnetization in polar coordinates (which is required to appropriately describe the shape of the heart) have not been explored because the physics required to directly connect myocardial deformation of tagged Nuclear Magnetic Resonance (NMR) transverse magnetization in polar geometry and the appropriate harmonic phase parameters are not yet available. The analytical solution of Bloch NMR diffusion equation in spherical geometry with appropriate spherical wave tagging function is important for proper analysis and monitoring of heart systolic and diastolic deformation with relevant boundary conditions. In this study, we applied Harmonic Phase MRI method to compute the difference between tagged and untagged NMR transverse magnetization based on the Bloch NMR diffusion equation and obtained radial wave tagging function for analysis of myocardial motion. The analytical solution of the Bloch NMR equations and the computational simulation of myocardial motion as developed in this study are intended to significantly improve healthcare for accurate diagnosis, prognosis and treatment of cardiovascular related deceases at the lowest cost because MRI scan is still one of the most expensive anywhere. The analysis is fundamental and significant because all Magnetic Resonance Imaging techniques are based on the Bloch NMR flow equations.

Unlocking higher harmonics in atomic force microscopy with gentle interactions.

PubMed

Santos, Sergio; Barcons, Victor; Font, Josep; Verdaguer, Albert

2014-01-01

In dynamic atomic force microscopy, nanoscale properties are encoded in the higher harmonics. Nevertheless, when gentle interactions and minimal invasiveness are required, these harmonics are typically undetectable. Here, we propose to externally drive an arbitrary number of exact higher harmonics above the noise level. In this way, multiple contrast channels that are sensitive to compositional variations are made accessible. Numerical integration of the equation of motion shows that the external introduction of exact harmonic frequencies does not compromise the fundamental frequency. Thermal fluctuations are also considered within the detection bandwidth of interest and discussed in terms of higher-harmonic phase contrast in the presence and absence of an external excitation of higher harmonics. Higher harmonic phase shifts further provide the means to directly decouple the true topography from that induced by compositional heterogeneity.

Testing a simple control law to reduce broadband frequency harmonic vibrations using semi-active tuned mass dampers

NASA Astrophysics Data System (ADS)

Moutinho, Carlos

2015-05-01

This paper is focused on the control problems related to semi-active tuned mass dampers (TMDs) used to reduce harmonic vibrations, specially involving civil structures. A simplified version of the phase control law is derived and its effectiveness is investigated and evaluated. The objective is to improve the functioning of control systems of this type by simplifying the measurement process and reducing the number of variables involved, making the control system more feasible and reliable. Because the control law is of ON/OFF type, combined with appropriate trigger conditions, the activity of the actuation system may be significantly reduced, which may be of few seconds a day in many practical cases, increasing the durability of the device and reducing its maintenance. Moreover, due to the ability of the control system to command the motion of the inertial mass, the semi-active TMD is relatively insensitive to its initial tuning, resulting in the capability of self-tuning and in the possibility of controlling several vibration modes of a structure over a significant broadband frequency.

Linking Quantum Mechanics to Freshman Physics

NASA Astrophysics Data System (ADS)

Vandegrift, Guy

1998-10-01

First-year quantum mechanics can be linked to introductory physics. One example is the Mossbauer effect, which is explained using a simple solution to Schrodinger's equation involving the Dirac delta function. Generalization to N coupled harmonic oscillators shows that the equality of the forces exerted by winner and loser in the game of "tug-of-war" is only an approximation because Newton's third law of motion is not valid (unless phonon momentum is considered). Another example is a treatment of the Gaussian wavepacket which involves less algebra than found in standard textbooks, yet shows that the peak moves according to the familiar equation of motion x = vt + (1/2)at^2 when the applied force is uniform. Finally, a rendition of "Turkey in the Straw" on the viola illustrates Heisenberg's uncertainty principle, which can be written in the less mysterious form, f=(N+-.1)/T , where N cycles are counted in T seconds. Students experience this uncertainty as they try to measure the frequency of a stretched slinky.

Characterizing Aeroelastic Systems Using Eigenanalysis, Explicitly Retaining The Aerodynamic Degrees of Freedom

NASA Technical Reports Server (NTRS)

Heeg, Jennifer; Dowell, Earl H.

2001-01-01

Discrete time aeroelastic models with explicitly retained aerodynamic modes have been generated employing a time marching vortex lattice aerodynamic model. This paper presents analytical results from eigenanalysis of these models. The potential of these models to calculate the behavior of modes that represent damped system motion (noncritical modes) in addition to the simple harmonic modes is explored. A typical section with only structural freedom in pitch is examined. The eigenvalues are examined and compared to experimental data. Issues regarding the convergence of the solution with regard to refining the aerodynamic discretization are investigated. Eigenvector behavior is examined; the eigenvector associated with a particular eigenvalue can be viewed as the set of modal participation factors for that particular mode. For the present formulation of the equations of motion, the vorticity for each aerodynamic element appears explicitly as an element of each eigenvector in addition to the structural dynamic generalized coordinates. Thus, modal participation of the aerodynamic degrees of freedom can be assessed in M addition to participation of structural degrees of freedom.

Nonlinear Ion Harmonics in the Paul Trap with Added Octopole Field: Theoretical Characterization and New Insight into Nonlinear Resonance Effect.

PubMed

Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu

2016-02-01

The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.

Long-term motion of resonant satellites with arbitrary eccentricity and inclination

NASA Technical Reports Server (NTRS)

Nacozy, P. E.; Diehl, R. E.

1982-01-01

A first-order, semi-analytical method for the long-term motion of resonant satellites is introduced. The method provides long-term solutions, valid for nearly all eccentricities and inclinations, and for all commensurability ratios. The method allows the inclusion of all zonal and tesseral harmonics of a nonspherical planet. We present here an application of the method to a synchronous satellite including J2 and J22 harmonics. Global, long-term solutions for this problem are given for arbitrary values of eccentricity, argument of perigee and inclination.

Solutions of the motion of synchronous satellites with arbitrary eccentricity and inclination

NASA Technical Reports Server (NTRS)

Nacozy, P. E.; Diehl, R. E.

1975-01-01

A first order, semianalytical theory for the long term motion of resonant satellites is presented. The theory is valid for all eccentricities and inclinations and for all commensurability ratios. The method allows the inclusion of all the zonal and tesseral harmonics as well as luni solar perturbations and radiation pressure. The method is applied to a synchronous satellite including only the J sub 2 and J sub 22 harmonics. Global, long term solutions for this problem, eccentricity, argument of perigee, and inclination are obtained.

Harmonic and Anharmonic Behaviour of a Simple Oscillator

ERIC Educational Resources Information Center

O'Shea, Michael J.

2009-01-01

We consider a simple oscillator that exhibits harmonic and anharmonic regimes and analyse its behaviour over the complete range of possible amplitudes. The oscillator consists of a mass "m" fixed at the midpoint of a horizontal rope. For zero initial rope tension and small amplitude the period of oscillation, tau, varies as tau is approximately…

Extended aeroelastic analysis for helicopter rotors with prescribed hub motion and blade appended penduluum vibration absorbers

NASA Technical Reports Server (NTRS)

Bielawa, R. L.

1984-01-01

The mathematical development for the expanded capabilities of the G400 rotor aeroelastic analysis was examined. The G400PA expanded analysis simulates the dynamics of all conventional rotors, blade pendulum vibration absorbers, and the higher harmonic excitations resulting from prescribed vibratory hub motions and higher harmonic blade pitch control. The methodology for modeling the unsteady stalled airloads of two dimensional airfoils is discussed. Formulations for calculating the rotor impedance matrix appropriate to the higher harmonic blade excitations are outlined. This impedance matrix, and the associated vibratory hub loads, are the rotor dynamic characteristic elements for use in the simplified coupled rotor/fuselage vibration analysis (SIMVIB). Updates to the development of the original G400 theory, program documentation, user instructions and information are presented.

Production of High Harmonic X-ray Radiation from Non-linear Thomson Scattering at LLNL PLEIADES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lim, J; Doyuran, A; Frigola, P

2005-05-17

We describe an experiment for production of high harmonic x-ray radiation from Thomson backscattering of an ultra-short high power density laser by a relativistic electron beam at the PLEIADES facility at LLNL. In this scenario, electrons execute a ''figure-8'' motion under the influence of the high-intensity laser field, where the constant characterizing the field strength is expected to exceed unity: a{sub L} = eE{sub L}/m{sub e}cw{sub L} {ge} 1. With large a{sub L} this motion produces high harmonic x-ray radiation and significant broadening of the spectral peaks. This paper is intended to give a layout of the PLEIADES experiment, alongmore » with progress towards experimental goals.« less

Quantum harmonic oscillator in a thermal bath

NASA Technical Reports Server (NTRS)

Zhang, Yuhong

1993-01-01

The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.

Late Quaternary variations in relative sea level due to glacial cycle polar wander

USGS Publications Warehouse

Bills, B.G.; James, T.S.

1996-01-01

Growth and decay of continental ice sheets can excite significant motion of the Earth's rotation pole and cause a complex spatio-temporal pattern of changes in relative sea level. These two effects have generally been considered separately, but may interact in important ways. In particular, a simple model of the melting of the Laurentide ice sheet causes a uniform eustatic sea level rise of 55 m, and also induces a motion of the rotation pole by 0.1 to 1 degree, depending on viscosity structure in the mantle. This motion produces a secular pole tide, which is a spherical harmonic degree 2, order 1 component of the relative sea level pattern, with peak-to-peak amplitude of 20 to 40 m. The maximum effect is along the great circle passing through the path of the pole and at latitudes of ??45??. This secular pole tide has been ignored in most previous attempts to estimate ice sheet loading history and mantle viscosity from global patterns of relative sea level change. It has a large influence along the East coast of North America and the West coast of South America, and significantly contributes to present day rates of relative sea level change.

Rates of change of the earth's magnetic field measured by recent analyses

NASA Technical Reports Server (NTRS)

Harrison, C. G. A.; Huang, Qilin

1990-01-01

Typical rates of change of the earth's magnetic field are presented as a function of the earth's spherical harmonics. Harmonics up to the eight degree are analyzed. With the increase in the degree of the harmonics an increase in the relative rate of change can be observed. For higher degrees, the rate of change can be predicted. This enables a differentiation between harmonics originating in the core and harmonics caused by crustal magnetization. The westward drift of the magnetic field depends on the longitudinal gradient of the field. In order to determine the longitudinal motions, harmonics up to degree 20 can be utilized. The average rate of secular acceleration increases with the degree of harmonics from 0.001 deg/sq yr for a dipole term to an average of 0.05 deg/sq yr for degree eight harmonics.

The Fermi-Pasta-Ulam System as a Model for Glasses

NASA Astrophysics Data System (ADS)

Carati, A.; Maiocchi, A.; Galgani, L.; Amati, G.

2015-12-01

We show that the standard Fermi-Pasta-Ulam system, with a suitable choice for the interparticle potential, constitutes a model for glasses, and indeed an extremely simple and manageable one. Indeed, it allows one to describe the landscape of the minima of the potential energy and to deal concretely with any one of them, determining the spectrum of frequencies and the normal modes. A relevant role is played by the harmonic energy {E} relative to a given minimum, i.e., the expansion of the Hamiltonian about the minimum up to second order. Indeed we find that there exists an energy threshold in {E} such that below it the harmonic energy {E} appears to be an approximate integral of motion for the whole observation time. Consequently, the system remains trapped near the minimum, in what may be called a vitreous or glassy state. Instead, for larger values of {E} the system rather quickly relaxes to a final equilibrium state. Moreover we find that the vitreous states present peculiar statistical behaviors, still involving the harmonic energy {E}. Indeed, the vitreous states are described by a Gibbs distribution with an effective Hamiltonian close to {E} and with a suitable effective inverse temperature. The final equilibrium state presents instead statistical properties which are in very good agreement with the Gibbs distribution relative to the full Hamiltonian of the system.

Experimental Aerodynamic Derivatives of a Sinusoidally Oscillating Airfoil in Two-Dimensional Flow

NASA Technical Reports Server (NTRS)

Halfman, Robert L

1952-01-01

Experimental measurements of the aerodynamic reactions on a symmetrical airfoil oscillating harmonically in a two-dimensional flow are presented and analyzed. Harmonic motions include pure pitch and pure translation, for several amplitudes and superimposed on an initial angle of attack, as well as combined pitch and translation. The apparatus and testing program are described briefly and the necessary theoretical background is presented. In general, the experimental results agree remarkably well with the theory, especially in the case of the pure motions. The net work per cycle for a motion corresponding to flutter is experimentally determined to be zero. Considerable consistent data for pure pitch were obtained from a search of available reference material, and several definite Reynolds number effects are evident.

Fundamentals of Physics, Volume 1, (Chapters 1 - 21)

NASA Astrophysics Data System (ADS)

Walker, Jearl

2004-01-01

Chapter 1. Measurement 1. How does the appearance of a new type of cloud signal changes in Earth's atmosphere? 1-1 What Is Physics? 1-2 Measuring Things. 1-3 The International System of Units. 1-4 Changing Units. 1-5 Length. 1-6 Time. 1-7 Mass. Review & Summary. Problems. Chapter 2. Motion Along a Straight Line. What causes whiplash injury in rear-end collisions of cars? 2-1 What Is Physics? 2-2 Motion. 2-3 Position and Displacement. 2-4 Average Velocity and Average Speed. 2-5 Instantaneous Velocity and Speed. 2-6 Acceleration. 2-7 Constant Acceleration: A Special Case. 2-8 Another Look at Constant Acceleration. 2-9 Free-Fall Acceleration. 2-10 Graphical Integration in Motion Analysis. 2 Review & Summary. Questions. Problems. Chapter 3. Vectors. How does an ant know the way home with no guiding clues on the desert plains? 3-1 What Is Physics? 3-2 Vectors and Scalars. 3-3 Adding Vectors Geometrically. 3-4 Components of Vectors. 3-5 Unit Vectors. 3-6 Adding Vectors by Components. 3-7 Vectors and the Laws of Physics. 3-8 Multiplying Vectors. Review & Summary. Questions. Problems. Chapter 4. Motion in Two and Three Dimensions. In a motorcycle jump for record distance, where does the jumper put the second ramp? 4-1 What Is Physics? 4-2 Position and Displacement. 4-3 Average Velocity and Instantaneous Velocity. 4-4 Average Acceleration and Instantaneous Acceleration. 4-5 Projectile Motion. 4-6 Projectile Motion Analyzed. 4-7 Uniform Circular Motion. 4-8 Relative Motion in One Dimension. 4-9 Relative Motion in Two Dimensions. Review & Summary. Questions. Problems. Chapter 5. Force and Motion--I. When a pilot takes off from an aircraft carrier, what causes the compulsion to .y the plane into the ocean? 5-1 What Is Physics? 5-2 Newtonian Mechanics. 5-3 Newton's First Law. 5-4 Force. 5-5 Mass. 5-6 Newton's Second Law. 5-7 Some Particular Forces. 5-8 Newton's Third Law. 5-9 Applying Newton's Laws. Review & Summary. Questions. Problems. Chapter 6. Force and Motion--II. Can a Grand Prix race car be driven upside down on a ceiling? 6-1 What Is Physics? 6-2 Friction. 6-3 Properties of Friction. 6-4 The Drag Force and Terminal Speed. 6-5 Uniform Circular Motion. Review & Summary. Questions. Problems. Chapter 7. Kinetic Energy and Work. In an epidural procedure, what sensations clue a surgeon that the needle has reached the spinal canal? 7-1 What Is Physics? 7-2 What Is Energy? 7-3 Kinetic Energy. 7-4 Work. 7-5 Work and Kinetic Energy. 7-6 Work Done by the Gravitational Force. 7-7 Work Done by a Spring Force. 7-8 Work Done by a General Variable Force. 7-9 Power. Review & Summary. Questions. Problems. Chapter 8. Potential Energy and Conservation of Energy. In rock climbing, what subtle factor determines if a falling climber will snap the rope? 8-1 What Is Physics? 8-2 Work and Potential Energy. 8-3 Path Independence of Conservative Forces. 8-4 Determining Potential Energy Values. 8-5 Conservation of Mechanical Energy. 8-6 Reading a Potential Energy Curve. 8-7 Work Done on a System by an External Force. 8-8 Conservation of Energy. Review & Summary. Questions. Problems. Chapter 9. Center of Mass and Linear Momentum. Does the presence of a passenger reduce the fatality risk in head-on car collisions? 9-1 What Is Physics? 9-2 The Center of Mass. 9-3 Newton's Second Law for a System of Particles. 9-4 Linear Momentum. 9-5 The Linear Momentum of a System of Particles. 9-6 Collision and Impulse. 9-7 Conservation of Linear Momentum. 9-8 Momentum and Kinetic Energy in Collisions. 9-9 Inelastic Collisions in One Dimension. 9-10 Elastic Collisions in One Dimension. 9-11 Collisions in Two Dimensions. 9-12 Systems with Varying Mass: A Rocket. Review & Summary. Questions. Problems. Chapter 10. Rotation. What causes roller-coaster headache? 10-1 What Is Physics? 10-2 The Rotational Variables. 10-3 Are Angular Quantities Vectors? 10-4 Rotation with Constant Angular Acceleration. 10-5 Relating the Linear and Angular Variables. 10-6 Kinetic Energy of Rotation. 10-7 Calculating the Rotational Inertia. 10-8 Torque. 10-9 Newton's Second Law for Rotation. 10-10 Work and Rotational Kinetic Energy. Review & Summary. Questions. Problems. Chapter 11. Rolling, Torque, and Angular Momentum. When a jet-powered car became supersonic in setting the land-speed record, what was the danger to the wheels? 11-1 What Is Physics? 11-2 Rolling as Translation and Rotation Combined. 11-3 The Kinetic Energy of Rolling. 11-4 The Forces of Rolling. 11-5 The Yo-Yo. 11-6 Torque Revisited. 11-7 Angular Momentum. 11-8 Newton's Second Law in Angular Form. 11-9 The Angular Momentum of a System of Particles. 11-10 The Angular Momentum of a Rigid Body Rotating About a Fixed Axis. 11-11 Conservation of Angular Momentum. 11-12 Precession of a Gyroscope. Review & Summary. Questions. Problems. Chapter 12. Equilibrium and Elasticity. What injury can occur to a rock climber hanging by a crimp hold? 12-1 What Is Physics? 12-2 Equilibrium. 12-3 The Requirements of Equilibrium. 12-4 The Center of Gravity. 12-5 Some Examples of Static Equilibrium. 12-6 Indeterminate Structures. 12-7 Elasticity. Review & Summary. Questions. Problems. Chapter 13. Gravitation. What lies at the center of our Milky Way galaxy? 13-1 What Is Physics? 13-2 Newton's Law of Gravitation. 13-3 Gravitation and the Principle of Superposition. 13-4 Gravitation Near Earth's Surface. 13-5 Gravitation Inside Earth. 13-6 Gravitational Potential Energy. 13-7 Planets and Satellites: Kepler's Laws. 13-8 Satellites: Orbits and Energy. 13-9 Einstein and Gravitation. Review & Summary. Questions. Problems. Chapter 14. Fluids. What causes ground effect in race car driving? 14-1 What Is Physics? 14-2 What Is a Fluid? 14-3 Density and Pressure. 14-4 Fluids at Rest. 14-5 Measuring Pressure. 14-6 Pascal's Principle. 14-7 Archimedes' Principle. 14-8 Ideal Fluids in Motion. 14-9 The Equation of Continuity. 14-10 Bernoulli's Equation. Review & Summary. Questions. Problems. Chapter 15. Oscillations. What is the "secret" of a skilled diver's high catapult in springboard diving? 15-1 What Is Physics? 15-2 Simple Harmonic Motion. 15-3 The Force Law for Simple Harmonic Motion. 15-4 Energy in Simple Harmonic Motion. 15-5 An Angular Simple Harmonic Oscillator. 15-6 Pendulums. 15-7 Simple Harmonic Motion and Uniform Circular Motion. 15-8 Damped Simple Harmonic Motion. 15-9 Forced Oscillations and Resonance. Review & Summary. Questions. Problems. Chapter 16. Waves--I. How can a submarine wreck be located by distant seismic stations? 16-1 What Is Physics? 16-2 Types of Waves. 16-3 Transverse and Longitudinal Waves. 16-4 Wavelength and Frequency. 16-5 The Speed of a Traveling Wave. 16-6 Wave Speed on a Stretched String. 16-7 Energy and Power of a Wave Traveling Along a String. 16-8 The Wave Equation. 16-9 The Principle of Superposition for Waves. 16-10 Interference of Waves. 16-11 Phasors. 16-12 Standing Waves. 16-13 Standing Waves and Resonance. Review & Summary. Questions. Problems. Chapter 17. Waves--II. How can an emperor penguin .nd its mate among thousands of huddled penguins? 17-1 What Is Physics? 17-2 Sound Waves. 17-3 The Speed of Sound. 17-4 Traveling Sound Waves. 17-5 Interference. 17-6 Intensity and Sound Level. 17-7 Sources of Musical Sound. 17-8 Beats. 17-9 The Doppler Effect. 17-10 Supersonic Speeds, Shock Waves. Review & Summary. Questions. Problems. Chapter 18. Temperature, Heat, and the First Law of Thermodynamics. How can a dead rattlesnake detect and strike a reaching hand? 18-1 What Is Physics? 18-2 Temperature. 18-3 The Zeroth Law of Thermodynamics. 18-4 Measuring Temperature. 18-5 The Celsius and Fahrenheit Scales. 18-6 Thermal Expansion. 18-7 Temperature and Heat. 18-8 The Absorption of Heat by Solids and Liquids. 18-9 A Closer Look at Heat and Work. 18-10 The First Law of Thermodynamics. 18-11 Some Special Cases of the First Law of Thermodynamics. 18-12 Heat Transfer Mechanisms. Review & Summary. Questions. Problems. Chapter 19. The Kinetic Theory of Gases. How can cooling steam inside a railroad tank car cause the car to be crushed? 19-1 What Is Physics? 19-2 Avogadro's Number. 19-3 Ideal Gases. 19-4 Pressure, Temperature, and RMS Speed. 19-5 Translational Kinetic Energy. 19-6 Mean Free Path. 19-7 The Distribution of Molecular Speeds. 19-8 The Molar Speci.c Heats of an Ideal Gas. 19-9 Degrees of Freedom and Molar Speci.c Heats. 19-10 A Hint of Quantum Theory. 19-11 The Adiabatic Expansion of an Ideal Gas. Review & Summary. Questions. Problems. Chapter 20. Entropy and the Second Law of Thermodynamics. Why is the popping of popcorn irreversible? 20-1 What Is Physics? 20-2 Irreversible Processes and Entropy. 20-3 Change in Entropy. 20-4 The Second Law of Thermodynamics. 20-5 Entropy in the Real World: Engines. 20-6 Entropy in the Real World: Refrigerators. 20-7 The Ef.ciencies of Real Engines. 20-8 A Statistical View of Entropy. Review & Summary. Questions. Problems. Appendices. A The International System of Units (SI). B Some Fundamental Constants of Physics. C Some Astronomical Data. D Conversion Factors. E Mathematical Formulas. F Properties of the Elements. G Periodic Table of the Elements. Answers to Checkpoints and Odd-Numbered Questions and Problems. Index.

A Method for Harmonic Sources Detection based on Harmonic Distortion Power Rate

NASA Astrophysics Data System (ADS)

Lin, Ruixing; Xu, Lin; Zheng, Xian

2018-03-01

Harmonic sources detection at the point of common coupling is an essential step for harmonic contribution determination and harmonic mitigation. The harmonic distortion power rate index is proposed for harmonic source location based on IEEE Std 1459-2010 in the paper. The method only based on harmonic distortion power is not suitable when the background harmonic is large. To solve this problem, a threshold is determined by the prior information, when the harmonic distortion power is larger than the threshold, the customer side is considered as the main harmonic source, otherwise, the utility side is. A simple model of public power system was built in MATLAB/Simulink and field test results of typical harmonic loads verified the effectiveness of proposed method.

Perturbations of non-resonant satellite orbits due to a rotating earth. [tesseral harmonics and the Von Ziepel method

NASA Technical Reports Server (NTRS)

Mueller, A.

1978-01-01

The dominant perturbations of the motion of a satellite near the earth are due to atmospheric drag and the non-symmetrical gravitational field. Atmospheric drag perturbation continually pulls the satellite in and out of the different long period resonant frequencies. The result is that the resonances never become apparent and may be neglected. The tesseral harmonics have no true secular perturbation but the periodicities in the mean motion induce a secular perturbation in the mean anomaly. This secular perturbation may be determined by simply using the average mean motion instead of the osculating mean motion. The Von Ziepel method is used to determine tesseral perturbations. The solution is found first in the singular DS phi elements and then rewritten in the PS phi elements to remove singularities. The notation used in the development is described in the appendix.

Chaotic motion of a harmonically bound charged particle in a magnetic field, in the presence of a half-plane barrier

NASA Astrophysics Data System (ADS)

Geurts, Bernard J.; Wiegel, Frederik W.; Creswick, Richard J.

1990-05-01

The motion in the plane of an harmonically bound charged particle interacting with a magnetic field and a half-plane barrier along the positive x-axis is studied. The magnetic field is perpendicular to the plane in which the particle moves. This motion is integrable in between collisions of the particle with the barrier. However, the overall motion of the particle is very complicated. Chaotic regions in phase space exist next to island structures associated with linearly stable periodic orbits. We study in detail periodic orbits of low period and in particular their bifurcation behavior. Independent sequences of period doubling bifurcations and resonant bifurcations are observed associated with independent fixed points in the Poincaré section. Due to the perpendicular magnetic field an orientation is induced on the plane and time-reversal symmetry is broken.

The Influence of Second Harmonic Phase and Amplitude Variation in Cyclically Pitching Wings

NASA Astrophysics Data System (ADS)

Culler, Ethan; Farnsworth, John

2017-11-01

From wind tunnel testing of a cyber-physical wing model, it has been found that the pitch trajectory for stall flutter is described by an array of higher harmonic frequencies with decaying energy content. These frequencies distort the stall flutter motion from that of a pure sinusoidal oscillation in pitch and can have a significant effect on the resulting force production. In order to understand how these higher harmonic frequencies contribute to the overall pitching moment characteristics of a wing in stall flutter, a rigid finite span wing model, with aspect ratio four, was pitched in the wind tunnel. The prescribed motion of the pitch cycle was varied by changing the amplitude ratio and phase of the second harmonic of the oscillation frequency. The second harmonic represents the second highest energy mode in the pitching cycle spectra. Pitching moment and planar particle image velocimetry data was collected. From these pitching trajectories, a significant dependence of pitching moment on both the phase and amplitude of the prescribed waveforms was found. Specifically, for the same amplitude ratio, variations in the phase produced changes of approximately 30 percent in the phase averaged pitching moment.

Finite state modeling of aeroelastic systems

NASA Technical Reports Server (NTRS)

Vepa, R.

1977-01-01

A general theory of finite state modeling of aerodynamic loads on thin airfoils and lifting surfaces performing completely arbitrary, small, time-dependent motions in an airstream is developed and presented. The nature of the behavior of the unsteady airloads in the frequency domain is explained, using as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. The modeling technique is applied to several two dimensional and three dimensional airfoils. Circular, elliptic, rectangular and tapered planforms are considered as examples. Identical functions are also obtained for control surfaces for two and three dimensional airfoils.

Dynamic image reconstruction: MR movies from motion ghosts.

PubMed

Xiang, Q S; Henkelman, R M

1992-01-01

It has been previously shown that an image with motion ghost artifacts can be decomposed into a ghost mask superimposed over a ghost-free image. The present study demonstrates that the ghost components carry useful dynamic information and should not be discarded. Specifically, ghosts of different orders indicate the intensity and phase of the corresponding harmonics contained in the quasi-periodically varying spin-density distribution. A summation of the ghosts weighted by appropriate temporal phase factors can give a time-dependent dynamic image that is a movie of the object motion. This dynamic image reconstruction technique does not necessarily require monitoring of the motion and thus is easy to implement and operate. It also has a shorter imaging time than point-by-point imaging of temporal variation, because the periodic motion is more efficiently sampled with a limited number of harmonics recorded in the motion ghosts. This technique was tested in both moving phantoms and volunteers. It is believed to be useful for dynamic imaging of time-varying anatomic structures, such as in the cardiovascular system.

Theoretical analysis of chirp excitation of contrast agents

NASA Astrophysics Data System (ADS)

Barlow, Euan; Mulholland, Anthony J.; Nordon, Alison; Gachagan, Anthony

2010-01-01

Analytic expressions are found for the amplitude of the first and second harmonics of the Ultrasound Contrast Agent's (UCA's) dynamics when excited by a chirp. The dependency of the second harmonic amplitude on the system parameters, the UCA shell parameters, and the insonifying signal parameters is then investigated. It is shown that optimal parameter values exist which give rise to a clear increase in the second harmonic component of the UCA's motion.

Autoregressive harmonic analysis of the earth's polar motion using homogeneous International Latitude Service data

NASA Technical Reports Server (NTRS)

Chao, B. F.

1983-01-01

The homogeneous set of 80-year-long (1900-1979) International Latitude Service (ILS) polar motion data is analyzed using the autoregressive method (Chao and Gilbert, 1980), which resolves and produces estimates for the complex frequency (or frequency and Q) and complex amplitude (or amplitude and phase) of each harmonic component in the data. The ILS data support the multiple-component hypothesis of the Chandler wobble. It is found that the Chandler wobble can be adequately modeled as a linear combination of four (coherent) harmonic components, each of which represents a steady, nearly circular, prograde motion. The four-component Chandler wobble model 'explains' the apparent phase reversal during 1920-1940 and the pre-1950 empirical period-amplitude relation. The annual wobble is shown to be rather stationary over the years both in amplitude and in phase, and no evidence is found to support the large variations reported by earlier investigations. The Markowitz wobble is found to be marginally retrograde and appears to have a complicated behavior which cannot be resolved because of the shortness of the data set.

Autoregressive harmonic analysis of the earth's polar motion using homogeneous International Latitude Service data

NASA Astrophysics Data System (ADS)

Chao, B. F.

1983-12-01

The homogeneous set of 80-year-long (1900-1979) International Latitude Service (ILS) polar motion data is analyzed using the autoregressive method (Chao and Gilbert, 1980), which resolves and produces estimates for the complex frequency (or frequency and Q) and complex amplitude (or amplitude and phase) of each harmonic component in the data. The ILS data support the multiple-component hypothesis of the Chandler wobble. It is found that the Chandler wobble can be adequately modeled as a linear combination of four (coherent) harmonic components, each of which represents a steady, nearly circular, prograde motion. The four-component Chandler wobble model 'explains' the apparent phase reversal during 1920-1940 and the pre-1950 empirical period-amplitude relation. The annual wobble is shown to be rather stationary over the years both in amplitude and in phase, and no evidence is found to support the large variations reported by earlier investigations. The Markowitz wobble is found to be marginally retrograde and appears to have a complicated behavior which cannot be resolved because of the shortness of the data set.

A three-dimensional quality-guided phase unwrapping method for MR elastography

NASA Astrophysics Data System (ADS)

Wang, Huifang; Weaver, John B.; Perreard, Irina I.; Doyley, Marvin M.; Paulsen, Keith D.

2011-07-01

Magnetic resonance elastography (MRE) uses accumulated phases that are acquired at multiple, uniformly spaced relative phase offsets, to estimate harmonic motion information. Heavily wrapped phase occurs when the motion is large and unwrapping procedures are necessary to estimate the displacements required by MRE. Two unwrapping methods were developed and compared in this paper. The first method is a sequentially applied approach. The three-dimensional MRE phase image block for each slice was processed by two-dimensional unwrapping followed by a one-dimensional phase unwrapping approach along the phase-offset direction. This unwrapping approach generally works well for low noise data. However, there are still cases where the two-dimensional unwrapping method fails when noise is high. In this case, the baseline of the corrupted regions within an unwrapped image will not be consistent. Instead of separating the two-dimensional and one-dimensional unwrapping in a sequential approach, an interleaved three-dimensional quality-guided unwrapping method was developed to combine both the two-dimensional phase image continuity and one-dimensional harmonic motion information. The quality of one-dimensional harmonic motion unwrapping was used to guide the three-dimensional unwrapping procedures and it resulted in stronger guidance than in the sequential method. In this work, in vivo results generated by the two methods were compared.

Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow

DOE PAGES

Giacomin, A. J.; Gilbert, P. H.; Schmalzer, A. M.

2015-03-19

In our previous work, we explored the dynamics of a dilute suspension of rigid dumbbells as a model for polymeric liquids in large-amplitude oscillatory shear flow, a flow experiment that has gained a significant following in recent years. We chose rigid dumbbells since these are the simplest molecular model to give higher harmonics in the components of the stress response. We derived the expression for the dumbbell orientation distribution, and then we used this function to calculate the shear stress response, and normal stress difference responses in large-amplitude oscillatory shear flow. In this paper, we deepen our understanding of themore » polymer motion underlying large-amplitude oscillatory shear flow by decomposing the orientation distribution function into its first five Fourier components (the zeroth, first, second, third, and fourth harmonics). We use three-dimensional images to explore each harmonic of the polymer motion. Our analysis includes the three most important cases: (i) nonlinear steady shear flow (where the Deborah number λω is zero and the Weissenberg number λγ 0 is above unity), (ii) nonlinear viscoelasticity (where both λω and λγ 0 exceed unity), and (iii) linear viscoelasticity (where λω exceeds unity and where λγ 0 approaches zero). We learn that the polymer orientation distribution is spherical in the linear viscoelastic regime, and otherwise tilted and peanut-shaped. We find that the peanut-shaping is mainly caused by the zeroth harmonic, and the tilting, by the second. The first, third, and fourth harmonics of the orientation distribution make only slight contributions to the overall polymer motion.« less

Non-planar vibrations of slightly curved pipes conveying fluid in simple and combination parametric resonances

NASA Astrophysics Data System (ADS)

Czerwiński, Andrzej; Łuczko, Jan

2018-01-01

The paper summarises the experimental investigations and numerical simulations of non-planar parametric vibrations of a statically deformed pipe. Underpinning the theoretical analysis is a 3D dynamic model of curved pipe. The pipe motion is governed by four non-linear partial differential equations with periodically varying coefficients. The Galerkin method was applied, the shape function being that governing the beam's natural vibrations. Experiments were conducted in the range of simple and combination parametric resonances, evidencing the possibility of in-plane and out-of-plane vibrations as well as fully non-planar vibrations in the combination resonance range. It is demonstrated that sub-harmonic and quasi-periodic vibrations are likely to be excited. The method suggested allows the spatial modes to be determined basing on results registered at selected points in the pipe. Results are summarised in the form of time histories, phase trajectory plots and spectral diagrams. Dedicated video materials give us a better insight into the investigated phenomena.

REVIEWS OF TOPICAL PROBLEMS: Periodic weather and climate variations

NASA Astrophysics Data System (ADS)

Ivanov, Vladimir V.

2002-07-01

Variations in meteorological parameters are largely due to periodic processes and can be forecast for several years. Many such processes are related to astronomical factors such as the gravitational influences of the Moon and the Sun, and the modulation of solar irradiance by lunar and planetary motion. The Moon, Jupiter, and Venus have the strongest effect. These influences produce lines in the spectra of meteorological variations, which are combinations of the harmonics of the frequencies of revolution of the planets, the Earth, and the Moon around the Sun with the harmonics of the lunar revolution around the Earth. Due to frequency differences between the orbital and radial motions, fine spectral features of three types appear: line splitting, line-profile complications due to radial oscillations, and additional lines due to the combination of radial-oscillation frequencies with perturbation harmonics.

Chaos, ergodic convergence, and fractal instability for a thermostated canonical harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.; Isbister, Dennis J.

2001-02-01

The authors thermostat a qp harmonic oscillator using the two additional control variables ζ and ξ to simulate Gibbs' canonical distribution. In contrast to the motion of purely Hamiltonian systems, the thermostated oscillator motion is completely ergodic, covering the full four-dimensional \\{q,p,ζ,ξ\\} phase space. The local Lyapunov spectrum (instantaneous growth rates of a comoving corotating phase-space hypersphere) exhibits singularities like those found earlier for Hamiltonian chaos, reinforcing the notion that chaos requires kinetic-as opposed to statistical-study, both at and away from equilibrium. The exponent singularities appear to have a fractal character.

Localized Harmonic Motion Imaging for Focused Ultrasound Surgery Targeting

PubMed Central

Curiel, Laura; Hynynen, Kullervo

2011-01-01

Recently, an in vivo real-time ultrasound-based monitoring technique that uses localized harmonic motion (LHM) to detect changes in tissues during focused ultrasound surgery (FUS) has been proposed to control the exposure. This technique can potentially be used as well for targeting imaging. In the present study we evaluated the potential of using LHM to detect changes in stiffness and the feasibility of using it for imaging purposes in phantoms and in vivo tumor detection. A single-element FUS transducer (80 mm focal length, 100 mm diameter, 1.485 MHz) was used for inducing a localized harmonic motion and a separate ultrasound diagnostic transducer excited by a pulser/receiver (5 kHz PRF, 5 MHz) was used to track motion. The motion was estimated using cross-correlation techniques on the acquired RF signal. Silicon phantom studies were performed in order to determine the size of inclusion that was possible to detect using this technique. Inclusions were discerned from the surroundings as a reduction on LHM amplitude and it was possible to depict inclusions as small as 4 mm. The amplitude of the induced LHM was always lower at the inclusions as compared with the one obtained at the surroundings. Ten New Zealand rabbits had VX2 tumors implanted on their thighs and LHM was induced and measured at the tumor region. Tumors (as small as 10 mm in length and 4 mm in width) were discerned from the surroundings as a reduction on LHM amplitude. PMID:21683514

Nonlinear dynamic modeling of a simple flexible rotor system subjected to time-variable base motions

NASA Astrophysics Data System (ADS)

Chen, Liqiang; Wang, Jianjun; Han, Qinkai; Chu, Fulei

2017-09-01

Rotor systems carried in transportation system or under seismic excitations are considered to have a moving base. To study the dynamic behavior of flexible rotor systems subjected to time-variable base motions, a general model is developed based on finite element method and Lagrange's equation. Two groups of Euler angles are defined to describe the rotation of the rotor with respect to the base and that of the base with respect to the ground. It is found that the base rotations would cause nonlinearities in the model. To verify the proposed model, a novel test rig which could simulate the base angular-movement is designed. Dynamic experiments on a flexible rotor-bearing system with base angular motions are carried out. Based upon these, numerical simulations are conducted to further study the dynamic response of the flexible rotor under harmonic angular base motions. The effects of base angular amplitude, rotating speed and base frequency on response behaviors are discussed by means of FFT, waterfall, frequency response curve and orbits of the rotor. The FFT and waterfall plots of the disk horizontal and vertical vibrations are marked with multiplications of the base frequency and sum and difference tones of the rotating frequency and the base frequency. Their amplitudes will increase remarkably when they meet the whirling frequencies of the rotor system.

Analysis of variability in the burst oscillations of the accreting millisecond pulsar XTE J1814-338

NASA Technical Reports Server (NTRS)

Watts, Anna L.; Strohmayer, Tod E.; Markwardt, Craig B.

2005-01-01

The accreting millisecond pulsar XTE J1814-338 exhibits oscillations at the known spin frequency during Type I X-ray bursts. The properties of the burst oscillations reflect the nature of the thermal asymmetry on the stellar surface. We present an analysis of the variability of the burst oscillations of this source, focusing on three characteristics: fractional amplitude, harmonic content and frequency. Fractional amplitude and harmonic content constrain the size, shape and position of the emitting region, whilst variations in frequency indicate motion of the emitting region on the neutron star surface. We examine both long-term variability over the course of the outburst, and short-term variability during the bursts. For most of the bursts, fractional amplitude is consistent with that of the accretion pulsations, implying a low degree of fuel spread. There is however a population of bursts whose fractional amplitudes are substantially lower, implying a higher degree of fuel spread, possibly forced by the explosive burning front of a precursor burst. For the first harmonic, substantial differences between the burst and accretion pulsations suggest that hotspot geometry is not the only mechanism giving rise to harmonic content in the latter. Fractional amplitude variability during the bursts is low; we can only rule out the hypothesis that the fractional amplitude remains constant at the l(sigma) level for bursts that do not exhibit photospheric radius expansion (PRE). There are no significant variations in frequency in any of the bursts except for the one burst that exhibits PRE. This burst exhibits a highly significant but small (= 0.1Hz) drop in frequency in the burst rise. The timescale of the frequency shift is slower than simple burning layer expansion models predict, suggesting that other mechanisms may be at work.

Solvable Quantum Macroscopic Motions and Decoherence Mechanisms in Quantum Mechanics on Nonstandard Space

NASA Technical Reports Server (NTRS)

Kobayashi, Tsunehiro

1996-01-01

Quantum macroscopic motions are investigated in the scheme consisting of N-number of harmonic oscillators in terms of ultra-power representations of nonstandard analysis. Decoherence is derived from the large internal degrees of freedom of macroscopic matters.

Exploiting bistable oscillator subharmonics for magnified broadband vibration energy harvesting

NASA Astrophysics Data System (ADS)

Huguet, Thomas; Badel, Adrien; Lallart, Mickaël

2017-10-01

Recent research on primary battery alternatives for supplying autonomous wireless devices has recently highlighted the advantages of nonlinear oscillators' dynamics and more particularly bistable oscillators' behavior for ambient vibration harvesting. The key property of bistable oscillators compared to linear ones is their enhanced operational frequency bandwidth under harmonic excitation, potentially leading to a better adaptation to the environment. However, the classical frequency response characterization of such devices does not reveal all the possible dynamic behaviors offered by bistable oscillators. Thus, subharmonic motions are experimentally investigated in this letter, and their energy harvesting potential as well as their ability to enhance the bistable generator bandwidth is evaluated. The results obtained with a generator integrating buckled beams for the bistability feature show that, in addition to the commonly considered harmonic behavior, subharmonics allow widening of the useful operating frequency band of the bistable microgenerator by 180% compared to the sole exploitation of the first harmonic motion.

Can even-order laser harmonics exhibited by Bohmian trajectories in symmetric potentials be observed?

PubMed

Peatross, J; Johansen, J

2014-01-13

Strong-field laser-atom interactions provide extreme conditions that may be useful for investigating the de Broglie-Bohm quantum interpretation. Bohmian trajectories representing bound electrons in individual atoms exhibit both even and odd harmonic motion when subjected to a strong external laser field. The phases of the even harmonics depend on the random initial positions of the trajectories within the wave function, making the even harmonics incoherent. In contrast, the phases of odd harmonics remain for the most part coherent regardless of initial position. Under the conjecture that a Bohmian point particle plays the role of emitter, this suggests an experiment to determine whether both even and odd harmonics are produced at the atomic level. Estimates suggest that incoherent emission of even harmonics may be detectable out the side of an intense laser focus interacting with a large number of atoms.

Observation of redshifting and harmonic radiation in inverse Compton scattering

DOE PAGES

Sakai, Y.; Pogorelsky, I.; Williams, O.; ...

2015-06-17

Inverse Compton scattering of laser photons by ultrarelativistic electron beam provides polarized x- to γ-ray pulses due to the Doppler blueshifting. Nonlinear electrodynamics in the relativistically intense linearly polarized laser field changes the radiation kinetics established during the Compton interaction. These are due to the induced figure-8 motion, which introduces an overall redshift in the radiation spectrum, with the concomitant emission of higher order harmonics. To experimentally analyze the strong field physics associated with the nonlinear electron-laser interaction, clear modifications to the angular and wavelength distributions of x rays are observed. The relativistic photon wave field is provided by themore » ps CO 2 laser of peak normalized vector potential of 0.5L<0.7, which due to the quadratic dependence of the strength of nonlinear phenomena on aL permits sufficient effects not observed in past 2 nd harmonic study with a L ≈ 0.3 laser [M. Babzien et al., Phys. Rev. Lett. 96, 054802 (2006)]. The angular spectral characteristics are revealed using K-, L-edge, and high energy attenuation filters. The observation indicates existence of the electrons’ longitudinal motion through frequency redshifting understood as the mass shift effect. The 3 rd harmonic radiation has been observed containing on-axis x-ray component that is directly associated with the induced figure-8 motion. These are further supported by an initial evidence of off-axis 2 nd harmonic radiation produced in a circularly polarized laser wave field. Total x-ray photon number per pulse, scattered by 65 MeV electron beam of 0.3 nC, at the interaction point is measured to be approximately 10 9.« less

On the Retrieval of Geocenter Motion from Gravity Data

NASA Astrophysics Data System (ADS)

Rosat, S.; Mémin, A.; Boy, J. P.; Rogister, Y. J. G.

2017-12-01

The center of mass of the whole Earth, the so-called geocenter, is moving with respect to the Center of Mass of the solid Earth because of the loading exerted by the Earth's fluid layers on the solid crust. Space geodetic techniques tying satellites and ground stations (e.g. GNSS, SLR and DORIS) have been widely employed to estimate the geocenter motion. Harmonic degree-1 variations of the gravity field are associated to the geocenter displacement. We show that ground records of time-varying gravity from Superconducting Gravimeters (SGs) can be used to constrain the geocenter motion. Two major difficulties have to be tackled: (1) the sensitivity of surface gravimetric measurements to local mass changes, and in particular hydrological and atmospheric variabilities; (2) the spatial aliasing (spectral leakage) of spherical harmonic degrees higher than 1 induced by the under-sampling of station distribution. The largest gravity variations can be removed from the SG data by subtracting solid and oceanic tides as well as atmospheric and hydrologic effects using global models. However some hydrological signal may still remain. Since surface water content is well-modelled using GRACE observations, we investigate how the spatial aliasing in SG data can be reduced by employing GRACE solutions when retrieving geocenter motion. We show synthetic simulations using complete surface loading models together with GRACE solutions computed at SG stations. In order to retrieve the degree-one gravity variations that are associated with the geocenter motion, we use a multi-station stacking method that performs better than a classical spherical harmonic stacking when the station distribution is inhomogeneous. We also test the influence of the network configuration on the estimate of the geocenter motion. An inversion using SG and GRACE observations is finally presented and the results are compared with previous geocenter estimates.

An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.

1979-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.

Harmonics analysis of the ITER poloidal field converter based on a piecewise method

NASA Astrophysics Data System (ADS)

Xudong, WANG; Liuwei, XU; Peng, FU; Ji, LI; Yanan, WU

2017-12-01

Poloidal field (PF) converters provide controlled DC voltage and current to PF coils. The many harmonics generated by the PF converter flow into the power grid and seriously affect power systems and electric equipment. Due to the complexity of the system, the traditional integral operation in Fourier analysis is complicated and inaccurate. This paper presents a piecewise method to calculate the harmonics of the ITER PF converter. The relationship between the grid input current and the DC output current of the ITER PF converter is deduced. The grid current is decomposed into the sum of some simple functions. By calculating simple function harmonics based on the piecewise method, the harmonics of the PF converter under different operation modes are obtained. In order to examine the validity of the method, a simulation model is established based on Matlab/Simulink and a relevant experiment is implemented in the ITER PF integration test platform. Comparative results are given. The calculated results are found to be consistent with simulation and experiment. The piecewise method is proved correct and valid for calculating the system harmonics.

The `Miracle' of Applicability? The Curious Case of the Simple Harmonic Oscillator

NASA Astrophysics Data System (ADS)

Bangu, Sorin; Moir, Robert H. C.

2018-05-01

The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner's famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of the Wigner problem.

The `Miracle' of Applicability? The Curious Case of the Simple Harmonic Oscillator

NASA Astrophysics Data System (ADS)

Bangu, Sorin; Moir, Robert H. C.

2018-03-01

The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner's famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of the Wigner problem.

Investigation of optimal method for inducing harmonic motion in tissue using a linear ultrasound phased array--a simulation study.

PubMed

Heikkilä, Janne; Hynynen, Kullervo

2006-04-01

Many noninvasive ultrasound techniques have been developed to explore mechanical properties of soft tissues. One of these methods, Localized Harmonic Motion Imaging (LHMI), has been proposed to be used for ultrasound surgery monitoring. In LHMI, dynamic ultrasound radiation-force stimulation induces displacements in a target that can be measured using pulse-echo imaging and used to estimate the elastic properties of the target. In this initial, simulation study, the use of a one-dimensional phased array is explored for the induction of the tissue motion. The study compares three different dual-frequency and amplitude-modulated single-frequency methods for the inducing tissue motion. Simulations were computed in a homogeneous soft-tissue volume. The Rayleigh integral was used in the simulations of the ultrasound fields and the tissue displacements were computed using a finite-element method (FEM). The simulations showed that amplitude-modulated sonication using a single frequency produced the largest vibration amplitude of the target tissue. These simulations demonstrate that the properties of the tissue motion are highly dependent on the sonication method and that it is important to consider the full three-dimensional distribution of the ultrasound field for controlling the induction of tissue motion.

Pump-dump iterative squeezing of vibrational wave packets.

PubMed

Chang, Bo Y; Sola, Ignacio R

2005-12-22

The free motion of a nonstationary vibrational wave packet in an electronic potential is a source of interesting quantum properties. In this work we propose an iterative scheme that allows continuous stretching and squeezing of a wave packet in the ground or in an excited electronic state, by switching the wave function between both potentials with pi pulses at certain times. Using a simple model of displaced harmonic oscillators and delta pulses, we derive the analytical solution and the conditions for its possible implementation and optimization in different molecules and electronic states. We show that the main constraining parameter is the pulse bandwidth. Although in principle the degree of squeezing (or stretching) is not bounded, the physical resources increase quadratically with the number of iterations, while the achieved squeezing only increases linearly.

Method for targetless tracking subpixel in-plane movements.

PubMed

Espinosa, Julian; Perez, Jorge; Ferrer, Belen; Mas, David

2015-09-01

We present a targetless motion tracking method for detecting planar movements with subpixel accuracy. This method is based on the computation and tracking of the intersection of two nonparallel straight-line segments in the image of a moving object in a scene. The method is simple and easy to implement because no complex structures have to be detected. It has been tested and validated using a lab experiment consisting of a vibrating object that was recorded with a high-speed camera working at 1000 fps. We managed to track displacements with an accuracy of hundredths of pixel or even of thousandths of pixel in the case of tracking harmonic vibrations. The method is widely applicable because it can be used for distance measuring amplitude and frequency of vibrations with a vision system.

Equations of motion for a spectrum-generating algebra: Lipkin Meshkov Glick model

NASA Astrophysics Data System (ADS)

Rosensteel, G.; Rowe, D. J.; Ho, S. Y.

2008-01-01

For a spectrum-generating Lie algebra, a generalized equations-of-motion scheme determines numerical values of excitation energies and algebra matrix elements. In the approach to the infinite particle number limit or, more generally, whenever the dimension of the quantum state space is very large, the equations-of-motion method may achieve results that are impractical to obtain by diagonalization of the Hamiltonian matrix. To test the method's effectiveness, we apply it to the well-known Lipkin-Meshkov-Glick (LMG) model to find its low-energy spectrum and associated generator matrix elements in the eigenenergy basis. When the dimension of the LMG representation space is 106, computation time on a notebook computer is a few minutes. For a large particle number in the LMG model, the low-energy spectrum makes a quantum phase transition from a nondegenerate harmonic vibrator to a twofold degenerate harmonic oscillator. The equations-of-motion method computes critical exponents at the transition point.

Wave function for time-dependent harmonically confined electrons in a time-dependent electric field.

PubMed

Li, Yu-Qi; Pan, Xiao-Yin; Sahni, Viraht

2013-09-21

The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the Harmonic Potential Theorem wave function for the case of the time-independent harmonic confining potential.

The Study of Two-Dimensional Oscillations Using a Smartphone Acceleration Sensor: Example of Lissajous Curves

ERIC Educational Resources Information Center

Tuset-Sanchis, Luis; Castro-Palacio, Juan C.; Gómez-Tejedor, José A.; Manjón, Francisco J.; Monsoriu, Juan A.

2015-01-01

A smartphone acceleration sensor is used to study two-dimensional harmonic oscillations. The data recorded by the free android application, Accelerometer Toy, is used to determine the periods of oscillation by graphical analysis. Different patterns of the Lissajous curves resulting from the superposition of harmonic motions are illustrated for…

High-Speed Video Analysis of Damped Harmonic Motion

ERIC Educational Resources Information Center

Poonyawatpornkul, J.; Wattanakasiwich, P.

2013-01-01

In this paper, we acquire and analyse high-speed videos of a spring-mass system oscillating in glycerin at different temperatures. Three cases of damped harmonic oscillation are investigated and analysed by using high-speed video at a rate of 120 frames s[superscript -1] and Tracker Video Analysis (Tracker) software. We present empirical data for…

Separation of High Order Harmonics with Fluoride Windows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allison, Tom; van Tilborg, Jeroen; Wright, Travis

2010-08-02

The lower orders produced in high order harmonic generation can be effciently temporally separated into monochromatic pulses by propagation in a Fluoride window while still preserving their femtosecond pulse duration. We present calculations for MgF2, CaF2, and LiF windows for the third, fifth, and seventh harmonics of 800 nm. We demonstrate the use of this simple and inexpensive technique in a femtosecond pump/probe experiment using the fifth harmonic.

Equity prices as a simple harmonic oscillator with noise

NASA Astrophysics Data System (ADS)

Ataullah, Ali; Tippett, Mark

2007-08-01

The centred return on the London Stock Exchange's FTSE All Share Index is modelled as a simple harmonic oscillator with noise over the period from 1 January, 1994 until 30 June 2006. Our empirical results are compatible with the hypothesis that there is a period in the FTSE All Share Index of between two and two and one half years. This means the centred return will on average continue to increase for about a year after reaching the minimum in its oscillatory cycle; alternatively, it will continue on average to decline for about a year after reaching a maximum. Our analysis also shows that there is potential to exploit the harmonic nature of the returns process to earn abnormal profits. Extending our analysis to the low energy states of a quantum harmonic oscillator is also suggested.

Hearing the Transformation of Conical to Closed-Pipe Resonances

ERIC Educational Resources Information Center

Ruiz, Michael J.

2017-01-01

The harmonics for an open cone with slant length "L" are the same as the harmonics for an open pipe with length "L." When the cone is transformed through phases of closed-open conical frusta into a cylinder of length "L" closed at one end, the fundamental halves and only odd harmonics remain. A simple approach using…

The Harmonic Series Diverges Again and Again

ERIC Educational Resources Information Center

Kifowit, Steven J.; Stamps, Terra A.

2006-01-01

The harmonic series is one of the most celebrated infinite series of mathematics. A quick glance at a variety of modern calculus textbooks reveals that there are two very popular proofs of the divergence of the harmonic series. In this article, the authors survey these popular proofs along with many other proofs that are equally simple and…

Characterization of simple wireless neurostimulators and sensors.

PubMed

Gulick, Daniel W; Towe, Bruce C

2014-01-01

A single diode with a wireless power source and electrodes can act as an implantable stimulator or sensor. We have built such devices using RF and ultrasound power coupling. These simple devices could drastically reduce the size, weight, and cost of implants for applications where efficiency is not critical. However, a shortcoming has been a lack of control: any movement of the external power source would change the power coupling, thereby changing the stimulation current or modulating the sensor response. To correct for changes in power and signal coupling, we propose to use harmonic signals from the device. The diode acts as a frequency multiplier, and the harmonics it emits contain information about the drive level and bias. A simplified model suggests that estimation of power, electrode bias, and electrode resistance is possible from information contained in radiated harmonics even in the presence of significant noise. We also built a simple RF-powered stimulator with an onboard voltage limiter.

Towards harmonized seismic analysis across Europe using supervised machine learning approaches

NASA Astrophysics Data System (ADS)

Zaccarelli, Riccardo; Bindi, Dino; Cotton, Fabrice; Strollo, Angelo

2017-04-01

In the framework of the Thematic Core Services for Seismology of EPOS-IP (European Plate Observing System-Implementation Phase), a service for disseminating a regionalized logic-tree of ground motions models for Europe is under development. While for the Mediterranean area the large availability of strong motion data qualified and disseminated through the Engineering Strong Motion database (ESM-EPOS), supports the development of both selection criteria and ground motion models, for the low-to-moderate seismic regions of continental Europe the development of ad-hoc models using weak motion recordings of moderate earthquakes is unavoidable. Aim of this work is to present a platform for creating application-oriented earthquake databases by retrieving information from EIDA (European Integrated Data Archive) and applying supervised learning models for earthquake records selection and processing suitable for any specific application of interest. Supervised learning models, i.e. the task of inferring a function from labelled training data, have been extensively used in several fields such as spam detection, speech and image recognition and in general pattern recognition. Their suitability to detect anomalies and perform a semi- to fully- automated filtering on large waveform data set easing the effort of (or replacing) human expertise is therefore straightforward. Being supervised learning algorithms capable of learning from a relatively small training set to predict and categorize unseen data, its advantage when processing large amount of data is crucial. Moreover, their intrinsic ability to make data driven predictions makes them suitable (and preferable) in those cases where explicit algorithms for detection might be unfeasible or too heuristic. In this study, we consider relatively simple statistical classifiers (e.g., Naive Bayes, Logistic Regression, Random Forest, SVMs) where label are assigned to waveform data based on "recognized classes" needed for our use case. These classes might be a simply binary case (e.g., "good for analysis" vs "bad") or more complex one (e.g., "good for analysis" vs "low SNR", "multi-event", "bad coda envelope"). It is important to stress the fact that our approach can be generalized to any use case providing, as in any supervised approach, an adequate training set of labelled data, a feature-set, a statistical classifier, and finally model validation and evaluation. Examples of use cases considered to develop the system prototype are the characterization of the ground motion in low seismic areas; harmonized spectral analysis across Europe for source and attenuation studies; magnitude calibration; coda analysis for attenuation studies.

Ship Detection and Measurement of Ship Motion by Multi-Aperture Synthetic Aperture Radar

DTIC Science & Technology

2014-06-01

Reconstructed periodic components of the Doppler histories shown in Fig. 27, (b) splined harmonic component amplitudes as a function of range...78 Figure 42: (a) Reconstructed periodic components of the Doppler histories shown in Figure 30, (b) Splined amplitudes of the...Figure 29 (b) Splined amplitudes of the harmonic components. ............................................ 79 Figure 44: Ship focusing by standard

Doppler-based motion compensation algorithm for focusing the signature of a rotorcraft.

PubMed

Goldman, Geoffrey H

2013-02-01

A computationally efficient algorithm was developed and tested to compensate for the effects of motion on the acoustic signature of a rotorcraft. For target signatures with large spectral peaks that vary slowly in amplitude and have near constant frequency, the time-varying Doppler shift can be tracked and then removed from the data. The algorithm can be used to preprocess data for classification, tracking, and nulling algorithms. The algorithm was tested on rotorcraft data. The average instantaneous frequency of the first harmonic of a rotorcraft was tracked with a fixed-lag smoother. Then, state space estimates of the frequency were used to calculate a time warping that removed the effect of a time-varying Doppler shift from the data. The algorithm was evaluated by analyzing the increase in the amplitude of the harmonics in the spectrum of a rotorcraft. The results depended upon the frequency of the harmonics and the processing interval duration. Under good conditions, the results for the fundamental frequency of the target (~11 Hz) almost achieved an estimated upper bound. The results for higher frequency harmonics had larger increases in the amplitude of the peaks, but significantly lower than the estimated upper bounds.

Numerical verification of bounce-harmonic resonances in neoclassical toroidal viscosity for tokamaks.

PubMed

Kim, Kimin; Park, Jong-Kyu; Boozer, Allen H

2013-05-03

This Letter presents the first numerical verification for the bounce-harmonic (BH) resonance phenomena of the neoclassical transport in a tokamak perturbed by nonaxisymmetric magnetic fields. The BH resonances were predicted by analytic theories of neoclassical toroidal viscosity (NTV), as the parallel and perpendicular drift motions can be resonant and result in a great enhancement of the radial momentum transport. A new drift-kinetic δf guiding-center particle code, POCA, clearly verified that the perpendicular drift motions can reduce the transport by phase-mixing, but in the BH resonances the motions can form closed orbits and particles radially drift out fast. The POCA calculations on resulting NTV torque are largely consistent with analytic calculations, and show that the BH resonances can easily dominate the NTV torque when a plasma rotates in the perturbed tokamak and therefore, is a critical physics for predicting the rotation and stability in the International Thermonuclear Experimental Reactor.

Focused Ultrasound Steering for Harmonic Motion Imaging.

PubMed

Han, Yang; Payen, Thomas; Wang, Shutao; Konofagou, Elisa

2018-02-01

Harmonic motion imaging (HMI) is a radiation-force-based ultrasound elasticity imaging technique, which is designed for both tissue relative stiffness imaging and reliable high-intensity focused ultrasound treatment monitoring. The objective of this letter is to develop and demonstrate the feasibility of 2-D focused ultrasound (FUS) beam steering for HMI using a 93-element, FUS phased array. HMI with steered FUS beam was acquired in tissue-mimicking phantoms. The HMI displacement was imaged within the steering range of ±1.7 mm laterally and ±2 mm axially. Using the steered FUS beam, HMI can be used to image a larger tissue volume with higher efficiency and without requiring mechanical movement of the transducer.

Computerized series solution of relativistic equations of motion.

NASA Technical Reports Server (NTRS)

Broucke, R.

1971-01-01

A method of solution of the equations of planetary motion is described. It consists of the use of numerical general perturbations in orbital elements and in rectangular coordinates. The solution is expanded in Fourier series in the mean anomaly with the aid of harmonic analysis and computerized series manipulation techniques. A detailed application to the relativistic motion of the planet Mercury is described both for Schwarzschild and isotropic coordinates.

Swarms with canonical active Brownian motion.

PubMed

Glück, Alexander; Hüffel, Helmuth; Ilijić, Saša

2011-05-01

We present a swarm model of Brownian particles with harmonic interactions, where the individuals undergo canonical active Brownian motion, i.e., each Brownian particle can convert internal energy to mechanical energy of motion. We assume the existence of a single global internal energy of the system. Numerical simulations show amorphous swarming behavior as well as static configurations. Analytic understanding of the system is provided by studying stability properties of equilibria.

Motion-artifact-robust, polarization-resolved second-harmonic-generation microscopy based on rapid polarization switching with electro-optic Pockells cell and its application to in vivo visualization of collagen fiber orientation in human facial skin

PubMed Central

Tanaka, Yuji; Hase, Eiji; Fukushima, Shuichiro; Ogura, Yuki; Yamashita, Toyonobu; Hirao, Tetsuji; Araki, Tsutomu; Yasui, Takeshi

2014-01-01

Polarization-resolved second-harmonic-generation (PR-SHG) microscopy is a powerful tool for investigating collagen fiber orientation quantitatively with low invasiveness. However, the waiting time for the mechanical polarization rotation makes it too sensitive to motion artifacts and hence has hampered its use in various applications in vivo. In the work described in this article, we constructed a motion-artifact-robust, PR-SHG microscope based on rapid polarization switching at every pixel with an electro-optic Pockells cell (PC) in synchronization with step-wise raster scanning of the focus spot and alternate data acquisition of a vertical-polarization-resolved SHG signal and a horizontal-polarization-resolved one. The constructed PC-based PR-SHG microscope enabled us to visualize orientation mapping of dermal collagen fiber in human facial skin in vivo without the influence of motion artifacts. Furthermore, it implied the location and/or age dependence of the collagen fiber orientation in human facial skin. The robustness to motion artifacts in the collagen orientation measurement will expand the application scope of SHG microscopy in dermatology and collagen-related fields. PMID:24761292

An analogue of the Berry phase for simple harmonic oscillators

NASA Astrophysics Data System (ADS)

Suslov, S. K.

2013-03-01

We evaluate a variant of Berry's phase for a ‘missing’ family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found here by integration with the help of a computer algebra system.

Quantization and instability of the damped harmonic oscillator subject to a time-dependent force

NASA Astrophysics Data System (ADS)

Majima, H.; Suzuki, A.

2011-12-01

We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity ( -γẋ) and a time-dependent external force ( K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman's system, which is described by the Lagrangian: ℒ=mẋẏ-U(x+{1}/{2}y)+U(x-{1}/{2}y)+{γ}/{2}(xẏ-yẋ)-xK(t)+yK(t), which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting U(x±y/2)={1}/{2}k( specifically for a dual extended damped-amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman's Hamiltonian ℋ. The Heisenberg equations of motion utilizing the quantized Hamiltonian ℋ̂ surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped-amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force.

Distilling free-form natural laws from experimental data.

PubMed

Schmidt, Michael; Lipson, Hod

2009-04-03

For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. We propose a principle for the identification of nontriviality. We demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the "alphabet" used to describe those systems.

Path integral analysis of Jarzynski's equality: Analytical results

NASA Astrophysics Data System (ADS)

Minh, David D. L.; Adib, Artur B.

2009-02-01

We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time-dependent natural frequency, we find such trajectories, evaluate the work-weighted propagators, and validate Jarzynski’s equality.

78 FR 73858 - Harmon, Steven A.; Notice of Filing

Federal Register 2010, 2011, 2012, 2013, 2014

2013-12-09

....211, 385.214). Protests will be considered by the Commission in determining the appropriate action to... become a party must file a notice of intervention or motion to intervene, as appropriate. Such notices, motions, or protests must be filed on or before the comment date. On or before the comment date, it is not...

Split-Waveguide Mounts For Submillimeter-Wave Multipliers And Harmonic Mixers

NASA Technical Reports Server (NTRS)

Raisanen, Antti; Choudhury, Debabani; Dengler, Robert J.; Oswald, John E.; Siegel, Peter H.

1996-01-01

Novel variation of split-waveguide mount for millimeter-and submillimeter-wavelength frequency multipliers and harmonic mixers developed. Designed to offer wide range of available matching impedances, while maintaining relatively simple fabrication sequence. Wide tuning range achieved with separate series and parallel elements, consisting of two pairs of noncontacting sliding backshorts, at fundamental and harmonic frequencies. Advantages include ease of fabrication, reliability, and tunability.

An algebraic cluster model based on the harmonic oscillator basis

NASA Technical Reports Server (NTRS)

Levai, Geza; Cseh, J.

1995-01-01

We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.

Wireless System and Method for Collecting Motion and Non-Motion Related Data of a Rotating System

NASA Technical Reports Server (NTRS)

Woodard, Stanley E. (Inventor); Taylor, Bryant D. (Inventor)

2011-01-01

A wireless system for collecting data indicative of a tire's characteristics uses at least one open-circuit electrical conductor in a tire. The conductor is shaped such that it can store electrical and magnetic energy. In the presence of a time-varying magnetic field, the conductor resonates to generate a harmonic response having a frequency, amplitude and bandwidth. A magnetic field response recorder is used to (i) wirelessly transmit the time-varying magnetic field to the conductor, and (ii) wirelessly detect the harmonic response and the frequency, amplitude and bandwidth, associated therewith. The recorder is adapted to be positioned in a location that is fixed with respect to the tire as the tire rotates.

Particles trajectories in magnetic filaments

NASA Astrophysics Data System (ADS)

Bret, A.

2015-07-01

The motion of a particle in a spatially harmonic magnetic field is a basic problem involved, for example, in the mechanism of formation of a collisionless shock. In such settings, it is generally reasoned that particles entering a Weibel generated turbulence are trapped inside it, provided their Larmor radius in the peak field is smaller than the field coherence length. The goal of this work is to put this heuristic conclusion on firm ground by studying, both analytically and numerically, such motion. A toy model is analyzed, consisting of a relativistic particle entering a region of space occupied by a spatially harmonic field. The particle penetrates the magnetic structure in a direction aligned with the magnetic filaments. Although the conclusions are not trivial, the main result is confirmed.

On the Tesseral-Harmonics Resonance Problem in Artificial-Satellite Theory, Part 2

NASA Technical Reports Server (NTRS)

Romanowicz, B. A.

1976-01-01

Equations were derived for the perturbations on an artificial satellite when the motion of the satellite is commensurable with that of the earth. This was done by first selecting the tesseral harmonics that contribute the most to the perturbations and then by applying Hori's method by use of Lie series. Here, are introduced some modifications to the perturbations, which now result in better agreement with numerical integration.

Tripartite correlations over two octaves from cascaded harmonic generation

NASA Astrophysics Data System (ADS)

Olsen, M. K.

2018-03-01

We analyse the output quantum tripartite correlations from an intracavity nonlinear optical system which uses cascaded nonlinearities to produce both second and fourth harmonic outputs from an input field at the fundamental frequency. Using fully quantum equations of motion, we investigate two parameter regimes and show that the system produces tripartite inseparability, entanglement and EPR steering, with the detection of these depending on the correlations being considered.

Real Time Digital Control of a Magnetostrictive Actuator

NASA Technical Reports Server (NTRS)

Zrostlik, Rick L.; Hall, David L.; Flatau, Alison B.

1996-01-01

The use of the magnetostrictive material Terfenol-D as a motion source in active vibration control (AVC) systems are being studied. Currently it is of limited use due to the nonlinear nature of the strain versus magnetization curve and the magnetic hysteresis in the Terfenol-D. One manifestation of these nonlinearities is waveform distortion in the output velocity of the transducer. For Terfenol-D to be used in ever greater numbers of AVC systems, these nonlinearities must be addressed. In this study the nonlinearities are treated as disturbances to a linear system. The acceleration output is used in simple analog and digital feedback control schemes to improve linearity of the transducer. In addition, the use of a Terfenol-D actuator in an AVC system is verified. Both analog and digital controllers are implemented and results compared. A cantilever beam system is considered for AVC applications. The second thrust of this presentation is the reduction of harmonic distortions. Two conclusions can be reached from this work. One, the linearization of Terfenol-D transducers is possible with the use of feedback controllers, both digital and analog. Second, Terfenol-D is a viable motion source in active vibration control systems utilizing either analog or digital controllers.

A time-correlation function approach to nuclear dynamical effects in X-ray spectroscopy

NASA Astrophysics Data System (ADS)

Karsten, Sven; Bokarev, Sergey I.; Aziz, Saadullah G.; Ivanov, Sergei D.; Kühn, Oliver

2017-06-01

Modern X-ray spectroscopy has proven itself as a robust tool for probing the electronic structure of atoms in complex environments. Despite working on energy scales that are much larger than those corresponding to nuclear motions, taking nuclear dynamics and the associated nuclear correlations into account may be of importance for X-ray spectroscopy. Recently, we have developed an efficient protocol to account for nuclear dynamics in X-ray absorption and resonant inelastic X-ray scattering spectra [Karsten et al., J. Phys. Chem. Lett. 8, 992 (2017)], based on ground state molecular dynamics accompanied with state-of-the-art calculations of electronic excitation energies and transition dipoles. Here, we present an alternative derivation of the formalism and elaborate on the developed simulation protocol using gas phase and bulk water as examples. The specific spectroscopic features stemming from the nuclear motions are analyzed and traced down to the dynamics of electronic energy gaps and transition dipole correlation functions. The observed tendencies are explained on the basis of a simple harmonic model, and the involved approximations are discussed. The method represents a step forward over the conventional approaches that treat the system in full complexity and provides a reasonable starting point for further improvements.

Extended analytical formulas for the perturbed Keplerian motion under a constant control acceleration

NASA Astrophysics Data System (ADS)

Zuiani, Federico; Vasile, Massimiliano

2015-03-01

This paper presents a set of analytical formulae for the perturbed Keplerian motion of a spacecraft under the effect of a constant control acceleration. The proposed set of formulae can treat control accelerations that are fixed in either a rotating or inertial reference frame. Moreover, the contribution of the zonal harmonic is included in the analytical formulae. It will be shown that the proposed analytical theory allows for the fast computation of long, multi-revolution spirals while maintaining good accuracy. The combined effect of different perturbations and of the shadow regions due to solar eclipse is also included. Furthermore, a simplified control parameterisation is introduced to optimise thrusting patterns with two thrust arcs and two cost arcs per revolution. This simple parameterisation is shown to ensure enough flexibility to describe complex low thrust spirals. The accuracy and speed of the proposed analytical formulae are compared against a full numerical integration with different integration schemes. An averaging technique is then proposed as an application of the analytical formulae. Finally, the paper presents an example of design of an optimal low-thrust spiral to transfer a spacecraft from an elliptical to a circular orbit around the Earth.

Illustrating dynamical symmetries in classical mechanics: The Laplace-Runge-Lenz vector revisited

NASA Astrophysics Data System (ADS)

O'Connell, Ross C.; Jagannathan, Kannan

2003-03-01

The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and degeneracy associated with this vector and with analogous dynamical symmetries. We define a conserved dynamical variable α that characterizes the orientation of the orbit in two-dimensional configuration space for the Kepler problem and an analogous variable β for the isotropic harmonic oscillator. This orbit orientation variable is canonically conjugate to the angular momentum component normal to the plane of motion. We explore the canonical one-parameter group of transformations generated by α(β). Because we have an obvious pair of conserved canonically conjugate variables, it is desirable to use them as a coordinate-momentum pair. In terms of these phase space coordinates, the form of the Hamiltonian is nearly trivial because neither member of the pair can occur explicitly in the Hamiltonian. From these considerations we gain a simple picture of dynamics in phase space. The procedure we use is in the spirit of the Hamilton-Jacobi method.

A time-correlation function approach to nuclear dynamical effects in X-ray spectroscopy.

PubMed

Karsten, Sven; Bokarev, Sergey I; Aziz, Saadullah G; Ivanov, Sergei D; Kühn, Oliver

2017-06-14

Modern X-ray spectroscopy has proven itself as a robust tool for probing the electronic structure of atoms in complex environments. Despite working on energy scales that are much larger than those corresponding to nuclear motions, taking nuclear dynamics and the associated nuclear correlations into account may be of importance for X-ray spectroscopy. Recently, we have developed an efficient protocol to account for nuclear dynamics in X-ray absorption and resonant inelastic X-ray scattering spectra [Karsten et al., J. Phys. Chem. Lett. 8, 992 (2017)], based on ground state molecular dynamics accompanied with state-of-the-art calculations of electronic excitation energies and transition dipoles. Here, we present an alternative derivation of the formalism and elaborate on the developed simulation protocol using gas phase and bulk water as examples. The specific spectroscopic features stemming from the nuclear motions are analyzed and traced down to the dynamics of electronic energy gaps and transition dipole correlation functions. The observed tendencies are explained on the basis of a simple harmonic model, and the involved approximations are discussed. The method represents a step forward over the conventional approaches that treat the system in full complexity and provides a reasonable starting point for further improvements.

Transitions in the vortex wake behind the plunging profile

NASA Astrophysics Data System (ADS)

Kozłowski, Tomasz; Kudela, Henryk

2014-12-01

In this study we investigate numerically the vortex wake formation behind the profile performing simple harmonic motion known in the literature as plunging. This research was inspired by the flapping motion which is appropriate for birds, insects and fishes. We assume the two dimensional model of flow. Depending on the parameters such as plunging amplitude, frequency and the Reynolds number, we demonstrate many different types of vortex street behind the profile. It is well known that the type of vortex wake determines the hydrodynamic forces acting on the profile. Dependences of the plunging amplitude, the Strouhal number and various topology vortices are established by constructing the phase transition diagram. The areas in the diagram related to the drag, thrust, and lift force generation are captured. We notice also the areas where the vorticity field is disordered. The disordered vorticity field does not allow maintenance of the periodic forces on the profile. An increase in the Reynolds number leads to the transition of the vortex wake behind the profile. The transition is caused by the phenomenon of boundary layer eruption. Further increase of the Reynolds number causes the vortex street related to the generation of the lift force to vanish.

Black–white asymmetry in visual perception

PubMed Central

Lu, Zhong-Lin; Sperling, George

2012-01-01

With eleven different types of stimuli that exercise a wide gamut of spatial and temporal visual processes, negative perturbations from mean luminance are found to be typically 25% more effective visually than positive perturbations of the same magnitude (range 8–67%). In Experiment 12, the magnitude of the black–white asymmetry is shown to be a saturating function of stimulus contrast. Experiment 13 shows black–white asymmetry primarily involves a nonlinearity in the visual representation of decrements. Black–white asymmetry in early visual processing produces even-harmonic distortion frequencies in all ordinary stimuli and in illusions such as the perceived asymmetry of optically perfect sine wave gratings. In stimuli intended to stimulate exclusively second-order processing in which motion or shape are defined not by luminance differences but by differences in texture contrast, the black–white asymmetry typically generates artifactual luminance (first-order) motion and shape components. Because black–white asymmetry pervades psychophysical and neurophysiological procedures that utilize spatial or temporal variations of luminance, it frequently needs to be considered in the design and evaluation of experiments that involve visual stimuli. Simple procedures to compensate for black–white asymmetry are proposed. PMID:22984221

VLBI2020: From Reality to Vision

NASA Technical Reports Server (NTRS)

Titov, Oleg

2010-01-01

The individual apparent motions of distant radio sources are believed to be caused by the effect of intrinsic structure variations of the active galactic nuclei (AGN). However, some cosmological models of the expanded Universe predict that systematic astrometric proper motions of distant quasars do not vanish as the radial distance from the observer to the quasar grows. These systematic effects can even increase with the distance, making it possible to measure them with high-precision astrometric techniques like VLBI. The Galactocentric acceleration of the Solar System barycenter may cause a secular aberration drift with a magnitude of 4 uas/yr. The Solar System motion relative to the cosmic microwave background produces an additional dipole effect, proportional to red shift. We analyzed geodetic VLBI data spanning from 1979 until 2009 to estimate the vector spherical harmonics in the expansion of the vector field of the proper motion of 687 radio sources. The dipole and quadrupole vector spherical harmonics were estimated with an accuracy of 1-5 as/yr. We have shown that over the next decade the geodetic VLBI may approach the level of accuracy on which the cosmological models of the Universe could be tested. Hence, it is important to organize a dedicated observational program to increase the number of measured proper motions to 3000.

Bunching phase and constraints on echo enabled harmonic generation

NASA Astrophysics Data System (ADS)

Hemsing, E.

2018-05-01

A simple mathematical description is developed for the bunching spectrum in echo enabled harmonic generation (EEHG) that incorporates the effect of additional electron beam energy modulations. Under common assumptions, they are shown to contribute purely through the phase of the longitudinal bunching factor, which allows the spectral moments of the bunching to be calculated directly from the known energy modulations. In particular, the second moment (spectral bandwidth) serves as simple constraint on the amplitude of the energy modulations to maintain a transform-limited seed. We show that, in general, the impact on the spectrum of energy distortions that develop between the EEHG chicanes scales like the harmonic number compared to distortions that occur upstream. This may limit the parameters that will allow EEHG to reach short wavelengths in high brightness FELs.

A dendrite-autonomous mechanism for direction selectivity in retinal starburst amacrine cells.

PubMed

Hausselt, Susanne E; Euler, Thomas; Detwiler, Peter B; Denk, Winfried

2007-07-01

Detection of image motion direction begins in the retina, with starburst amacrine cells (SACs) playing a major role. SACs generate larger dendritic Ca(2+) signals when motion is from their somata towards their dendritic tips than for motion in the opposite direction. To study the mechanisms underlying the computation of direction selectivity (DS) in SAC dendrites, electrical responses to expanding and contracting circular wave visual stimuli were measured via somatic whole-cell recordings and quantified using Fourier analysis. Fundamental and, especially, harmonic frequency components were larger for expanding stimuli. This DS persists in the presence of GABA and glycine receptor antagonists, suggesting that inhibitory network interactions are not essential. The presence of harmonics indicates nonlinearity, which, as the relationship between harmonic amplitudes and holding potential indicates, is likely due to the activation of voltage-gated channels. [Ca(2+)] changes in SAC dendrites evoked by voltage steps and monitored by two-photon microscopy suggest that the distal dendrite is tonically depolarized relative to the soma, due in part to resting currents mediated by tonic glutamatergic synaptic input, and that high-voltage-activated Ca(2+) channels are active at rest. Supported by compartmental modeling, we conclude that dendritic DS in SACs can be computed by the dendrites themselves, relying on voltage-gated channels and a dendritic voltage gradient, which provides the spatial asymmetry necessary for direction discrimination.

Autoregressive harmonic analysis of the earth's polar motion using homogeneous international latitude service data

NASA Astrophysics Data System (ADS)

Fong Chao, B.

1983-12-01

The homogeneous set of 80-year-long (1900-1979) International Latitude Service (ILS) polar motion data is analyzed using the autoregressive method (Chao and Gilbert, 1980) which resolves and produces estimates for the complex frequency (or frequency and Q) and complex amplitude (or amplitude and phase) of each harmonic component in the data. Principal conclusion of this analysis are that (1) the ILS data support the multiple-component hypothesis of the Chandler wobble (it is found that the Chandler wobble can be adequately modeled as a linear combination of four (coherent) harmonic components, each of which represents a steady, nearly circular, prograte motion, a behavior that is inconsistent with the hypothesis of a single Chandler period excited in a temporally and/or spatially random fashion). (2) the four-component Chandler wobble model ``explains'' the apparent phase reversal during 1920-1940 and the pre-1950 empirical period-amplitude relation, (3) the annual wobble is shown to be rather stationary over the years both in amplitude and in phase and no evidence is found to support the large variations reported by earlier investigations. (4) the Markowitz wobble is found to support the large variations reported by earlier investigations. (4) the Markowitz wobble is found to be marginally retrograde and appears to have a complicated behavior which cannot be resolved because of the shortness of the data set.

Harmonic generation with multiple wiggler schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonifacio, R.; De Salvo, L.; Pierini, P.

1995-02-01

In this paper the authors give a simple theoretical description of the basic physics of the single pass high gain free electron laser (FEL), describing in some detail the FEL bunching properties and the harmonic generation technique with a multiple-wiggler scheme or a high gain optical klystron configuration.

The One-Dimensional Damped Forced Harmonic Oscillator Revisited

ERIC Educational Resources Information Center

Flores-Hidalgo, G.; Barone, F. A.

2011-01-01

In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.

High-harmonic generation in graphene enhanced by elliptically polarized light excitation

NASA Astrophysics Data System (ADS)

Yoshikawa, Naotaka; Tamaya, Tomohiro; Tanaka, Koichiro

2017-05-01

The electronic properties of graphene can give rise to a range of nonlinear optical responses. One of the most desirable nonlinear optical processes is high-harmonic generation (HHG) originating from coherent electron motion induced by an intense light field. Here, we report on the observation of up to ninth-order harmonics in graphene excited by mid-infrared laser pulses at room temperature. The HHG in graphene is enhanced by an elliptically polarized laser excitation, and the resultant harmonic radiation has a particular polarization. The observed ellipticity dependence is reproduced by a fully quantum mechanical treatment of HHG in solids. The zero-gap nature causes the unique properties of HHG in graphene, and our findings open up the possibility of investigating strong-field and ultrafast dynamics and nonlinear behavior of massless Dirac fermions.

A method for the investigation of hyperbolic motions in the gravitational field of a spheroidal planet

NASA Astrophysics Data System (ADS)

Konks, V. Ia.

1981-05-01

Barrar's (1961) method for the analysis of the motion of a satellite of an oblate planet is extended to the case of hyperbolic motion. An analysis is presented of the motion of a material point in the gravitational field of a fixed center, combined with a gravitational dipole located at the point of inertia of a dynamically symmetric planet. Formulas are obtained for the hyperbolic motion of a spacecraft in the gravitational field of a spheroidal planet with an accuracy up to the second zonal harmonic of the expansion of its potential into a Legendre polynomial series in spherical coordinates.

A note about Norbert Wiener and his contribution to Harmonic Analysis and Tauberian Theorems

NASA Astrophysics Data System (ADS)

Almira, J. M.; Romero, A. E.

2009-05-01

In this note we explain the main motivations Norbert Wiener had for the creation of his Generalized Harmonic Analysis [13] and his Tauberian Theorems [14]. Although these papers belong to the most pure mathematical tradition, they were deeply based on some Engineering and Physics Problems and Wiener was able to use them for such diverse areas as Optics, Brownian motion, Filter Theory, Prediction Theory and Cybernetics.

Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1)

NASA Astrophysics Data System (ADS)

Babichenko, Andrei; Creutzig, Thomas

2015-08-01

Takiff superalgebras are a family of non semi-simple Lie superalgebras that are believed to give rise to a rich structure of indecomposable representations of associated conformal field theories. We consider the Takiff superalgebra of gl(1\\vert 1), especially we perform harmonic analysis for the corresponding supergroup. We find that every simple module appears as submodule of an infinite-dimensional indecomposable but reducible module. We lift our results to two free field realizations for the corresponding conformal field theory and construct some modules.

Flapping response characteristics of hingeless rotor blades by a gereralized harmonic balance method

NASA Technical Reports Server (NTRS)

Peters, D. A.; Ormiston, R. A.

1975-01-01

Linearized equations of motion for the flapping response of flexible rotor blades in forward flight are derived in terms of generalized coordinates. The equations are solved using a matrix form of the method of linear harmonic balance, yielding response derivatives for each harmonic of the blade deformations and of the hub forces and moments. Numerical results and approximate closed-form expressions for rotor derivatives are used to illustrate the relationships between rotor parameters, modeling assumptions, and rotor response characteristics. Finally, basic hingeless rotor response derivatives are presented in tabular and graphical form for a wide range of configuration parameters and operating conditions.

Investigation of Student Reasoning about Harmonic Motions

NASA Astrophysics Data System (ADS)

Tongnopparat, N.; Poonyawatpornkul, J.; Wattanakasiwich, P.

This study aimed to investigate student reasoning about harmonic oscillations. We conducted a semi-structured interview based on three situations of harmonic motions—(1) a mass attaching to spring and horizontally oscillating without damping, (2) the same situation but vertically oscillating and (3) a mass attaching to spring and oscillating in viscous liquid. Forty-five second-year students taking a vibrations and wave course at Chiang Mai University, Thailand participated in a fifteen-minute interview, which was video-recorded. The videos were transcribed and analyzed by three physics instructors. As results, we found that most students had misconceptions about angular frequency and energy mostly in the second and third situations.

A new Euler scheme based on harmonic-polygon approach for solving first order ordinary differential equation

NASA Astrophysics Data System (ADS)

Yusop, Nurhafizah Moziyana Mohd; Hasan, Mohammad Khatim; Wook, Muslihah; Amran, Mohd Fahmi Mohamad; Ahmad, Siti Rohaidah

2017-10-01

There are many benefits to improve Euler scheme for solving the Ordinary Differential Equation Problems. Among the benefits are simple implementation and low-cost computational. However, the problem of accuracy in Euler scheme persuade scholar to use complex method. Therefore, the main purpose of this research are show the construction a new modified Euler scheme that improve accuracy of Polygon scheme in various step size. The implementing of new scheme are used Polygon scheme and Harmonic mean concept that called as Harmonic-Polygon scheme. This Harmonic-Polygon can provide new advantages that Euler scheme could offer by solving Ordinary Differential Equation problem. Four set of problems are solved via Harmonic-Polygon. Findings show that new scheme or Harmonic-Polygon scheme can produce much better accuracy result.

Using Performance Assessment Model in Physics Laboratory to Increase Students’ Critical Thinking Disposition

NASA Astrophysics Data System (ADS)

Emiliannur, E.; Hamidah, I.; Zainul, A.; Wulan, A. R.

2017-09-01

Performance Assessment Model (PAM) has been developed to represent the physics concepts which able to be devided into five experiments: 1) acceleration due to gravity; 2) Hooke’s law; 3) simple harmonic motion; 4) work-energy concepts; and 5) the law of momentum conservation. The aim of this study was to determine the contribution of PAM in physics laboratory to increase students’ Critical Thinking Disposition (CTD) at senior high school. Subject of the study were 11th grade consist 32 students of a senior high school in Lubuk Sikaping, West Sumatera. The research used one group pretest-postest design. Data was collected through essay test and questionnaire about CTD. Data was analyzed using quantitative way with N-gain value. This study concluded that performance assessmet model effectively increases the N-gain at medium category. It means students’ critical thinking disposition significant increase after implementation of performance assessment model in physics laboratory.

On-the-Fly Control of High-Harmonic Generation Using a Structured Pump Beam

NASA Astrophysics Data System (ADS)

Hareli, Liran; Lobachinsky, Lilya; Shoulga, Georgiy; Eliezer, Yaniv; Michaeli, Linor; Bahabad, Alon

2018-05-01

We demonstrate experimentally a relatively simple yet powerful all-optical enhancement and control technique for high harmonic generation. This is achieved by using as a pump beam two different spatial optical modes interfering together to realize tunable periodic quasi-phase matching of the interaction. With this technique, we demonstrate on-the-fly quasi-phase matching of harmonic orders 29-41 at ambient gas pressure levels of 50 and 100 Torr, where an up to 100-fold enhancement of the emission is observed. The technique is scalable to different harmonic orders and ambient pressure conditions.

On-the-Fly Control of High-Harmonic Generation Using a Structured Pump Beam.

PubMed

Hareli, Liran; Lobachinsky, Lilya; Shoulga, Georgiy; Eliezer, Yaniv; Michaeli, Linor; Bahabad, Alon

2018-05-04

We demonstrate experimentally a relatively simple yet powerful all-optical enhancement and control technique for high harmonic generation. This is achieved by using as a pump beam two different spatial optical modes interfering together to realize tunable periodic quasi-phase matching of the interaction. With this technique, we demonstrate on-the-fly quasi-phase matching of harmonic orders 29-41 at ambient gas pressure levels of 50 and 100 Torr, where an up to 100-fold enhancement of the emission is observed. The technique is scalable to different harmonic orders and ambient pressure conditions.

Quantum Brownian motion under generalized position measurements: a converse Zeno scenario

NASA Astrophysics Data System (ADS)

Magazzù, Luca; Talkner, Peter; Hänggi, Peter

2018-03-01

We study the quantum Brownian motion of a harmonic oscillator undergoing a sequence of generalized position measurements. Our exact analytical results capture the interplay of the measurement backaction and dissipation. Here we demonstrate that no freeze-in Zeno effect occurs upon increasing the monitoring frequency. A similar behavior is also found in the presence of generalized momentum measurements.

Particles trajectories in magnetic filaments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bret, A.; Instituto de Investigaciones Energéticas y Aplicaciones Industriales, Campus Universitario de Ciudad Real, 13071 Ciudad Real

2015-07-15

The motion of a particle in a spatially harmonic magnetic field is a basic problem involved, for example, in the mechanism of formation of a collisionless shock. In such settings, it is generally reasoned that particles entering a Weibel generated turbulence are trapped inside it, provided their Larmor radius in the peak field is smaller than the field coherence length. The goal of this work is to put this heuristic conclusion on firm ground by studying, both analytically and numerically, such motion. A toy model is analyzed, consisting of a relativistic particle entering a region of space occupied by amore » spatially harmonic field. The particle penetrates the magnetic structure in a direction aligned with the magnetic filaments. Although the conclusions are not trivial, the main result is confirmed.« less

Digital resolver for helicopter model blade motion analysis

NASA Technical Reports Server (NTRS)

Daniels, T. S.; Berry, J. D.; Park, S.

1992-01-01

The paper reports the development and initial testing of a digital resolver to replace existing analog signal processing instrumentation. Radiometers, mounted directly on one of the fully articulated blades, are electrically connected through a slip ring to analog signal processing circuitry. The measured signals are periodic with azimuth angle and are resolved into harmonic components, with 0 deg over the tail. The periodic nature of the helicopter blade motion restricts the frequency content of each flapping and yaw signal to the fundamental and harmonics of the rotor rotational frequency. A minicomputer is employed to collect these data and then plot them graphically in real time. With this and other information generated by the instrumentation, a helicopter test pilot can then adjust the helicopter model's controls to achieve the desired aerodynamic test conditions.

Frequency modulation of high-order harmonic generation in an orthogonally polarized two-color laser field.

PubMed

Li, Guicun; Zheng, Yinghui; Ge, Xiaochun; Zeng, Zhinan; Li, Ruxin

2016-08-08

We have experimentally investigated the frequency modulation of high-order harmonics in an orthogonally polarized two-color laser field consisting of a mid-infrared 1800nm fundamental pulse and its second harmonic pulse. It is demonstrated that the high harmonic spectra can be fine-tuned as we slightly change the relative delay of the two-color laser pulses. By analyzing the relative frequency shift of each harmonic at different two-color delays, the nonadiabatic spectral shift induced by the rapid variation of the intensity-dependent intrinsic dipole phase can be distinguished from the blueshift induced by the change of the refractive index during self-phase modulation (SPM). Our comprehensive analysis shows that the frequency modulation pattern is a reflection of the average emission time of high-order harmonic generation (HHG), thus offering a simple method to fine-tune the spectra of the harmonics on a sub-cycle time scale.

The study of two-dimensional oscillations using a smartphone acceleration sensor: example of Lissajous curves

NASA Astrophysics Data System (ADS)

Tuset-Sanchis, Luis; Castro-Palacio, Juan C.; Gómez-Tejedor, José A.; Manjón, Francisco J.; Monsoriu, Juan A.

2015-08-01

A smartphone acceleration sensor is used to study two-dimensional harmonic oscillations. The data recorded by the free android application, Accelerometer Toy, is used to determine the periods of oscillation by graphical analysis. Different patterns of the Lissajous curves resulting from the superposition of harmonic motions are illustrated for three experiments. This work introduces an example of how two-dimensional oscillations can be easily studied with a smartphone acceleration sensor.

Introduction to Radar Polarimetry

DTIC Science & Technology

1991-04-23

Coulomb force 11 1,2 Static etectric fields 13 1.3 Summary 15 2 ELECTROMAGNETIC WAVES 16 2.1 Harmonic plane waves 16 2.2 The average intensity of a...harmonic plane wave 17 2.3 Spherical harmonic waves 18 2.4 Summary 19 3 THE POLARIZATION OF AN ELECTROMAGNETIC WAVE 20 3.1 The polarization ellipse 20 3.2...CHANGE OF POLARIZATION 31 4.1 Simple examples 31 4.2 Scattering at a plane interface 33 4.3 Summary 36 5 THE SCATTERING MATRIX 37 5.1 Transmission

Nonlinear surge motions of a ship in bi-chromatic following waves

NASA Astrophysics Data System (ADS)

Spyrou, Kostas J.; Themelis, Nikos; Kontolefas, Ioannis

2018-03-01

Unintended motions of a ship operating in steep and long following waves are investigated. A well-known such case is ;surf-riding; where a ship is carried forward by a single wave, an event invoking sometimes lateral instability and even capsize. The dynamics underlying this behavior has been clarified earlier for monochromatic waves. However, the unsteadiness of the phase space associated with ship behavior in a multichromatic sea, combined with the intrinsically strong system nonlinearity, pose new challenges. Here, current theory is extended to cover surging and surf-riding behavior in unidirectional bi-chromatic waves encountering a ship from the stern. Excitation is provided by two unidirectional harmonic wave components having their lengths comparable to the ship length and their frequencies in rational ratio. The techniques applied include (a) continuation analysis; (b) tracking of Lagrangian coherent structures in phase space, approximated through a finite-time Lyapunov exponents' calculation; and (c) large scale simulation. A profound feature of surf-riding in bi-chromatic waves is that it is turned oscillatory. Initially it appears as a frequency-locked motion, ruled by the harmonic wave component dominating the excitation. Transformations of oscillatory surf-riding are realized as the waves become steeper. In particular, heteroclinic tanglings are identified, governing abrupt transitions between qualitatively different motions. Chaotic transients, as well as long-term chaotic motions, exist near to these events. Some extraordinary patterns of ship motion are discovered. These include a counterintuitive low speed motion at very high wave excitation level; and a hybrid motion characterized by a wildly fluctuating velocity. Due to the quite generic nature of the core mathematical model of our investigation, the current results are believed to offer clues about the behavior of a class of nonlinear dynamical systems having in their modeling some analogy with a perturbed pendulum with bias.

Predicting charmonium and bottomonium spectra with a quark harmonic oscillator.

PubMed

Norbury, J W; Badavi, F F; Townsend, L W

1986-11-01

We present a simple application of the three-dimensional harmonic oscillator which should provide a very nice particle physics example to be presented in introductory undergraduate quantum mechanics course. The idea is to use the nonrelativistic quark model to calculate the spin-averaged mass levels of the charmonium and bottomonium spectra.

The Study of Damped Harmonic Oscillations Using an Electronic Counter

ERIC Educational Resources Information Center

Wadhwa, Ajay

2009-01-01

We study damped harmonic oscillations in mechanical systems like the loaded spring and simple pendulum with the help of an oscillation measuring electronic counter. The experimental data are used in a software program that solves the differential equation for damped vibrations of any system and determines its position, velocity and acceleration as…

High harmonic generation in underdense plasmas by intense laser pulses with orbital angular momentum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mendonça, J. T., E-mail: josetitomend@gmail.com; Vieira, J., E-mail: jorge.vieira@ist.utl.pt

We study high harmonic generation produced by twisted laser pulses, with orbital angular momentum in the relativistic regime, for pulse propagation in underdense plasma. We consider fast time scale processes associated with an ultra-short pulse, where the ion motion can be neglected. We use both analytical models and numerical simulations using a relativistic particle-in-cell code. The present description is valid for relativistic laser intensities, when the normalized field amplitude is much larger than one, a ≫ 1. We also discuss two distinct processes associated with linear and circular polarization. Using both analytical solutions and particle-in-cell simulations, we are able tomore » show that, for laser pulses in a well defined Laguerre-Gauss mode, angular momentum conservation is observed during the process of harmonic generation. Intensity modulation of the harmonic spectrum is also verified, as imposed by the nonlinear time-scale for energy transfer between different harmonics.« less

Hyperbolic Harmonic Mapping for Surface Registration

PubMed Central

Shi, Rui; Zeng, Wei; Su, Zhengyu; Jiang, Jian; Damasio, Hanna; Lu, Zhonglin; Wang, Yalin; Yau, Shing-Tung; Gu, Xianfeng

2016-01-01

Automatic computation of surface correspondence via harmonic map is an active research field in computer vision, computer graphics and computational geometry. It may help document and understand physical and biological phenomena and also has broad applications in biometrics, medical imaging and motion capture inducstries. Although numerous studies have been devoted to harmonic map research, limited progress has been made to compute a diffeomorphic harmonic map on general topology surfaces with landmark constraints. This work conquers this problem by changing the Riemannian metric on the target surface to a hyperbolic metric so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints. The computational algorithms are based on Ricci flow and nonlinear heat diffusion methods. The approach is general and robust. We employ our algorithm to study the constrained surface registration problem which applies to both computer vision and medical imaging applications. Experimental results demonstrate that, by changing the Riemannian metric, the registrations are always diffeomorphic and achieve relatively high performance when evaluated with some popular surface registration evaluation standards. PMID:27187948

Strong-field control and enhancement of chiral response in bi-elliptical high-order harmonic generation: an analytical model

NASA Astrophysics Data System (ADS)

Ayuso, David; Decleva, Piero; Patchkovskii, Serguei; Smirnova, Olga

2018-06-01

The generation of high-order harmonics in a medium of chiral molecules driven by intense bi-elliptical laser fields can lead to strong chiroptical response in a broad range of harmonic numbers and ellipticities (Ayuso et al 2018 J. Phys. B: At. Mol. Opt. Phys. 51 06LT01). Here we present a comprehensive analytical model that can describe the most relevant features arising in the high-order harmonic spectra of chiral molecules driven by strong bi-elliptical fields. Our model recovers the physical picture underlying chiral high-order harmonic generation (HHG) based on ultrafast chiral hole motion and identifies the rotationally invariant molecular pseudoscalars responsible for chiral dynamics. Using the chiral molecule propylene oxide as an example, we show that one can control and enhance the chiral response in bi-elliptical HHG by tailoring the driving field, in particular by tuning its frequency, intensity and ellipticity, exploiting a suppression mechanism of achiral background based on the linear Stark effect.

EDITORIAL: Attosecond and x-ray free-electron laser physics Attosecond and x-ray free-electron laser physics

NASA Astrophysics Data System (ADS)

Moshammer, R.; Ullrich, J.

2009-07-01

Currently, we are witnessing a revolution in photon science, driven by the vision to time-resolve ultra-fast electronic motion in atoms, molecules, and solids as well as by the quest for the characterization of time-dependent structural changes in large molecules and solids. Quantum jumps in the development of light sources are the key technologies for this emerging field of research. Thus, high harmonic radiation bursts now penetrate the attosecond (10-18 s) regime and free-electron lasers (FELs) deliver ultra-brilliant femtosecond, coherent VUV and x-ray pulses. This special issue presents a snapshot of this ongoing revolution and brings together, for the first time, pioneering results in both of these fields that are expected to evolve synergetically in the future. The volume is based on the spirit of the International Conference on Multi-Photon Processes, ICOMP08, which was held at the Max Planck Institute for Nuclear Physics in Heidelberg in summer 2008. The first contributions include articles that envision tracing electronic motion on an attosecond time scale and its relation to nuclear motion. After more technical papers on the generation of attosecond pulses via high harmonic generation (HHG), molecular and two-electron atomic dynamics in strong optical fields at a typical wavelength of 800 nm are presented pointing to sub-cycle, attosecond features. Making the transition to shorter wavelengths, nonlinear dynamics in atoms and molecules is explored via experimental and theoretical methods, where the present measurements are nearly exclusively performed at FEL sources. A substantial number of articles focus on the investigation of the most simple many- (few-) photon two-electron processes in double ionization of helium at optical and VUV wavelengths, with the goal of characterizing this fundamental reaction, not yet consistently solved theoretically, in spite of huge efforts. Finally, the behaviour of more complex nanoscaled systems, i.e. clusters, is investigated bridging the gap from atoms and molecules to solids introduced to intense FEL radiation. Beyond the basic interest in many-particle dynamics in finite systems, these studies are of enormous practical relevance for upcoming research at X-ray FELs. Here, realizing the dream of coherent imaging of the structure of single bio-molecules in the gas phase with atomic resolution is critically dependent on ultra-fast dynamics initiated by the pulse. In other words, it is reduced to the simple question of whether the molecule is first imaged and then destroyed or vice versa! During the preparation of this Editorial, the first lasing at the Stanford Linac Coherent Light Source (LCLS) was achieved at a photon energy of about 8 keV - a further milestone in this exciting revolution in the science related to light.

A theoretical study of the application of jet flap circulation control for reduction of rotor vibratory forces

NASA Technical Reports Server (NTRS)

Piziali, R. A.; Trenka, A. R.

1974-01-01

The results of a study to investigate the theoretical potential of a jet-flap control system for reducing the vertical and horizontal non-cancelling helicopter rotor blade root shears are presented. A computer simulation describing the jet-flap control rotor system was developed to examine the reduction of each harmonic of the transmitted shears as a function of various rotor and jet parameters, rotor operating conditions and rotor configurations. The computer simulation of the air-loads included the influences of nonuniform inflow and blade elastic motions. (no hub motions were allowed.) The rotor trim and total rotor power (including jet compressor power) were also determined. It was found that all harmonics of the transmitted horizontal and vertical shears could be suppressed simultaneously using a single jet control.

Dynamic analysis of a magnetic bearing system with flux control

NASA Technical Reports Server (NTRS)

Knight, Josiah; Walsh, Thomas; Virgin, Lawrence

1994-01-01

Using measured values of two-dimensional forces in a magnetic actuator, equations of motion for an active magnetic bearing are presented. The presence of geometric coupling between coordinate directions causes the equations of motion to be nonlinear. Two methods are used to examine the unbalance response of the system: simulation by direct integration in time; and determination of approximate steady state solutions by harmonic balance. For relatively large values of the derivative control coefficient, the system behaves in an essentially linear manner, but for lower values of this parameter, or for higher values of the coupling coefficient, the response shows a split of amplitudes in the two principal directions. This bifurcation is sensitive to initial conditions. The harmonic balance solution shows that the separation of amplitudes actually corresponds to a change in stability of multiple coexisting solutions.

Comparison between spin-orbit torques measured by domain-wall motions and harmonic measurements

NASA Astrophysics Data System (ADS)

Kim, Joo-Sung; Nam, Yune-Seok; Kim, Dae-Yun; Park, Yong-Keun; Park, Min-Ho; Choe, Sug-Bong

2018-05-01

Here we report the comparison of the spin torque efficiencies measured by three different experimental schemes for Pt/Co/X stacks with material X (= Pt, Ta, Ti, Al, Au, Pd, and Ru. 7 materials). The first two spin torque efficiencies ɛDW (1 ) and ɛDW (2 ) are quantified by the measurement of spin-torque-induced effective field for domain-wall depinning and creeping motions, respectively. The last one—longitudinal spin torque efficiency ɛL—is measured by harmonic signal measurement of the magnetization rotation with uniform magnetization configuration. The results confirm that, for all measured Pt/Co/X stacks, ɛDW (1 ) and ɛDW (2 ) are exactly consistent to each other and these two efficiencies are roughly proportional to ɛL with proportionality constant π/2, which comes from the integration over the domain-wall configuration.

The forced vibration of one-dimensional multi-coupled periodic structures: An application to finite element analysis

NASA Astrophysics Data System (ADS)

Mead, Denys J.

2009-01-01

A general theory for the forced vibration of multi-coupled one-dimensional periodic structures is presented as a sequel to a much earlier general theory for free vibration. Starting from the dynamic stiffness matrix of a single multi-coupled periodic element, it derives matrix equations for the magnitudes of the characteristic free waves excited in the whole structure by prescribed harmonic forces and/or displacements acting at a single periodic junction. The semi-infinite periodic system excited at its end is first analysed to provide the basis for analysing doubly infinite and finite periodic systems. In each case, total responses are found by considering just one periodic element. An already-known method of reducing the size of the computational problem is reexamined, expanded and extended in detail, involving reduction of the dynamic stiffness matrix of the periodic element through a wave-coordinate transformation. Use of the theory is illustrated in a combined periodic structure+finite element analysis of the forced harmonic in-plane motion of a uniform flat plate. Excellent agreement between the computed low-frequency responses and those predicted by simple engineering theories validates the detailed formulations of the paper. The primary purpose of the paper is not towards a specific application but to present a systematic and coherent forced vibration theory, carefully linked with the existing free-wave theory.

Numerical simulation of the Earth satellites motion using parallel computing. accounting of weak disturbances. (Russian Title: Прогнозирование движения ИСЗ с использованием параллельных вычислений. учет слабых возмущений)

NASA Astrophysics Data System (ADS)

Chuvashov, I. N.

2010-12-01

The features of high-precision numerical simulation of the Earth satellite motion using parallel computing are discussed on example the implementation of the cluster "Skiff Cyberia" software complex "Numerical model of the motion of system satellites". It is shown that the use of 128 bit word length allows considering weak perturbations from the high-order harmonics in the expansion of the geopotential and the effect of strain geopotential harmonics arising due to the combination of tidal perturbations associated with exposure to the moon and sun on the solid Earth and its oceans.

Beating motion of a circular cylinder in vortex-induced vibrations

NASA Astrophysics Data System (ADS)

Shen, Linwei; Chan, Eng-Soon; Wei, Yan

2018-04-01

In this paper, beating phenomenon of a circular cylinder in vortex-induced vibration is studied by numerical simulations in a systematic manner. The cylinder mass coefficients of 2 and 10 are considered, and the Reynolds number is 150. Two distinctive frequencies, namely cylinder oscillation and vortex shedding frequencies, are obtained from the harmonic analysis of the cylinder displacement. The result is consistent with that observed in laboratory experiments. It is found that the cylinder oscillation frequency changes with the natural frequency of the cylinder while the reduced velocity is varied. The added-mass coefficient of the cylinder in beating motion is therefore estimated. Meanwhile, the vortex shedding frequency does not change dramatically in the beating situations. In fact, it is very close to 0.2. Accordingly, the lift force coefficient has two main components associated with these two frequencies. Besides, higher harmonics of the cylinder oscillation frequency appear in the spectrum of the lift coefficient. Moreover, the vortex shedding timing is studied in the beating motion by examining the instantaneous flow fields in the wake, and two scenarios of the vortex formation are observed.

Sampled-data-based consensus and containment control of multiple harmonic oscillators: A motion-planning approach

NASA Astrophysics Data System (ADS)

Liu, Yongfang; Zhao, Yu; Chen, Guanrong

2016-11-01

This paper studies the distributed consensus and containment problems for a group of harmonic oscillators with a directed communication topology. First, for consensus without a leader, a class of distributed consensus protocols is designed by using motion planning and Pontryagin's principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchange over the sampled interval. By using stability theory and the properties of stochastic matrices, it is proved that the distributed consensus problem can be solved in the motion planning framework. Second, for the case with multiple leaders, a class of distributed containment protocols is developed for followers such that their positions and velocities can ultimately converge to the convex hull formed by those of the leaders. Compared with the existing consensus algorithms, a remarkable advantage of the proposed sampled-data-based protocols is that the sampling periods, communication topologies and control gains are all decoupled and can be separately designed, which relaxes many restrictions in controllers design. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.

Computing multiple periodic solutions of nonlinear vibration problems using the harmonic balance method and Groebner bases

NASA Astrophysics Data System (ADS)

Grolet, Aurelien; Thouverez, Fabrice

2015-02-01

This paper is devoted to the study of vibration of mechanical systems with geometric nonlinearities. The harmonic balance method is used to derive systems of polynomial equations whose solutions give the frequency component of the possible steady states. Groebner basis methods are used for computing all solutions of polynomial systems. This approach allows to reduce the complete system to an unique polynomial equation in one variable driving all solutions of the problem. In addition, in order to decrease the number of variables, we propose to first work on the undamped system, and recover solution of the damped system using a continuation on the damping parameter. The search for multiple solutions is illustrated on a simple system, where the influence of the retained number of harmonic is studied. Finally, the procedure is applied on a simple cyclic system and we give a representation of the multiple states versus frequency.

On the stability of motion of several types of heavy symmetric gyroscopes with damping torques

NASA Astrophysics Data System (ADS)

Ge, Z.-M.; Wu, M.-H.

Sufficient conditions for the stability of motion of several gyroscopes are obtained using Liapunov's direct method. The stability of a 'temporarily' sleeping top with damping torque is considered for the cases of the support being fixed, being in vertical harmonic motion, and being in vertical periodic motion. Sufficient conditions are also obtained for the stability of a heavy symmetric gyroscope with damping torque and motor torque for the cases of regular precession, vertical axis permanent rotation with and without the axis of the outer gimbal being inclined, and the gyroscope being in a Newtonian central gravitational field.

Reduced quantum dynamics with arbitrary bath spectral densities: hierarchical equations of motion based on several different bath decomposition schemes.

PubMed

Liu, Hao; Zhu, Lili; Bai, Shuming; Shi, Qiang

2014-04-07

We investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly in the HEOM formalism. Methods to extract system-bath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spin-Boson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.

Multi-oriented windowed harmonic phase reconstruction for robust cardiac strain imaging.

PubMed

Cordero-Grande, Lucilio; Royuela-del-Val, Javier; Sanz-Estébanez, Santiago; Martín-Fernández, Marcos; Alberola-López, Carlos

2016-04-01

The purpose of this paper is to develop a method for direct estimation of the cardiac strain tensor by extending the harmonic phase reconstruction on tagged magnetic resonance images to obtain more precise and robust measurements. The extension relies on the reconstruction of the local phase of the image by means of the windowed Fourier transform and the acquisition of an overdetermined set of stripe orientations in order to avoid the phase interferences from structures outside the myocardium and the instabilities arising from the application of a gradient operator. Results have shown that increasing the number of acquired orientations provides a significant improvement in the reproducibility of the strain measurements and that the acquisition of an extended set of orientations also improves the reproducibility when compared with acquiring repeated samples from a smaller set of orientations. Additionally, biases in local phase estimation when using the original harmonic phase formulation are greatly diminished by the one here proposed. The ideas here presented allow the design of new methods for motion sensitive magnetic resonance imaging, which could simultaneously improve the resolution, robustness and accuracy of motion estimates. Copyright © 2015 Elsevier B.V. All rights reserved.

Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Hao; Zhu, Lili; Bai, Shuming

2014-04-07

We investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly inmore » the HEOM formalism. Methods to extract system-bath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spin-Boson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.« less

Final Report for Department of Energy Project DE-SC0012198

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lucchese, Robert; Poliakoff, Erwin; Trallero-Herrero, Carlos

The study of the motion of atoms in molecules is important to understanding many areas of physical and life sciences. Such motion occurs on many different times scales, with electronic motion occurring on a sub-femtosecond time scale, and simple vibrational motion in tens to hundreds of femtoseconds. One way to follow such processes in real time is by the use of short-pulsed lasers, and in particular by studying time-resolved photoionization and the related process of high-harmonic generation (HHG). Thus there has been much effort to develop the tools necessary to probe molecular systems using short pulse lasers and understanding themore » sensitivity of the different possible probes to the time dependent geometric structure as well as the electronic structure of molecules. Our research has particularly focused on the connection between high-field processes and the more traditional weak field photoionization processes. Strong field and weak field processes can be connected through models that involve the same matrix elements. We have demonstrated in our study of HHG from SF6 that the spectrum is sensitive to the interplay between the angular dependence of the ionization step and recombination step. In our study of rescattering spectroscopy, we have shown that with a combination of experiment and theory, we can use this high-field spectroscopy to determine molecular structure in molecules such as C2H4. We have also developed new computational tools based on overset grids to enable studies on larger molecular systems which use much more robust numerical approaches so that the resulting code can be a tool that non-specialists can use to study related systems.« less

Harmonic cavities and the transverse mode-coupling instability driven by a resistive wall

DOE Office of Scientific and Technical Information (OSTI.GOV)

Venturini, M.

The effect of rf harmonic cavities on the transverse mode-coupling instability (TMCI) is still not very well understood. We offer a fresh perspective on the problem by proposing a new numerical method for mode analysis and investigating a regime of potential interest to the new generation of light sources where resistive wall is the dominant source of transverse impedance. When the harmonic cavities are tuned for maximum flattening of the bunch profile we demonstrate that at vanishing chromaticities the transverse single-bunch motion is unstable at any current, with growth rate that in the relevant range scales as the 6th powermore » of the current. With these assumptions and radiation damping included, we find that for machine parameters typical of 4th-generation light sources the presence of harmonic cavities could reduce the instability current threshold by more than a factor two.« less

Harmonic cavities and the transverse mode-coupling instability driven by a resistive wall

DOE PAGES

Venturini, M.

2018-02-01

The effect of rf harmonic cavities on the transverse mode-coupling instability (TMCI) is still not very well understood. We offer a fresh perspective on the problem by proposing a new numerical method for mode analysis and investigating a regime of potential interest to the new generation of light sources where resistive wall is the dominant source of transverse impedance. When the harmonic cavities are tuned for maximum flattening of the bunch profile we demonstrate that at vanishing chromaticities the transverse single-bunch motion is unstable at any current, with growth rate that in the relevant range scales as the 6th powermore » of the current. With these assumptions and radiation damping included, we find that for machine parameters typical of 4th-generation light sources the presence of harmonic cavities could reduce the instability current threshold by more than a factor two.« less

Harmonic cavities and the transverse mode-coupling instability driven by a resistive wall

NASA Astrophysics Data System (ADS)

Venturini, M.

2018-02-01

The effect of rf harmonic cavities on the transverse mode-coupling instability (TMCI) is still not very well understood. We offer a fresh perspective on the problem by proposing a new numerical method for mode analysis and investigating a regime of potential interest to the new generation of light sources where resistive wall is the dominant source of transverse impedance. When the harmonic cavities are tuned for maximum flattening of the bunch profile we demonstrate that at vanishing chromaticities the transverse single-bunch motion is unstable at any current, with growth rate that in the relevant range scales as the 6th power of the current. With these assumptions and radiation damping included, we find that for machine parameters typical of 4th-generation light sources the presence of harmonic cavities could reduce the instability current threshold by more than a factor two.

Motion estimation in the frequency domain using fuzzy c-planes clustering.

PubMed

Erdem, C E; Karabulut, G Z; Yanmaz, E; Anarim, E

2001-01-01

A recent work explicitly models the discontinuous motion estimation problem in the frequency domain where the motion parameters are estimated using a harmonic retrieval approach. The vertical and horizontal components of the motion are independently estimated from the locations of the peaks of respective periodogram analyses and they are paired to obtain the motion vectors using a procedure proposed. In this paper, we present a more efficient method that replaces the motion component pairing task and hence eliminates the problems of the pairing method described. The method described in this paper uses the fuzzy c-planes (FCP) clustering approach to fit planes to three-dimensional (3-D) frequency domain data obtained from the peaks of the periodograms. Experimental results are provided to demonstrate the effectiveness of the proposed method.

Moving boundary problems for a rarefied gas: Spatially one-dimensional case

NASA Astrophysics Data System (ADS)

Tsuji, Tetsuro; Aoki, Kazuo

2013-10-01

Unsteady flows of a rarefied gas in a full space caused by an oscillation of an infinitely wide plate in its normal direction are investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation. The paper aims at showing properties and difficulties inherent to moving boundary problems in kinetic theory of gases using a simple one-dimensional setting. More specifically, the following two problems are considered: (Problem I) the plate starts a forced harmonic oscillation (forced motion); (Problem II) the plate, which is subject to an external restoring force obeying Hooke’s law, is displaced from its equilibrium position and released (free motion). The physical interest in Problem I lies in the propagation of nonlinear acoustic waves in a rarefied gas, whereas that in Problem II in the decay rate of the oscillation of the plate. An accurate numerical method, which is capable of describing singularities caused by the oscillating plate, is developed on the basis of the method of characteristics and is applied to the two problems mentioned above. As a result, the unsteady behavior of the solution, such as the propagation of discontinuities and some weaker singularities in the molecular velocity distribution function, are clarified. Some results are also compared with those based on the existing method.

A high resolution pneumatic stepping actuator for harsh reactor environments

NASA Astrophysics Data System (ADS)

Tippetts, Thomas B.; Evans, Paul S.; Riffle, George K.

1993-01-01

A reactivity control actuator for a high-power density nuclear propulsion reactor must be installed in close proximity to the reactor core. The energy input from radiation to the actuator structure could exceed hundreds of W/cc unless low-cross section, low-absorptivity materials are chosen. Also, for post-test handling and subsequent storage, materials should not be used that are activated into long half-life isotopes. Pneumatic actuators can be constructed from various reactor-compatible materials, but conventional pneumatic piston actuators generally lack the stiffness required for high resolution reactivity control unless electrical position sensors and compensated electronic control systems are used. To overcome these limitations, a pneumatic actuator is under development that positions an output shaft in response to a series of pneumatic pulses, comprising a pneumatic analog of an electrical stepping motor. The pneumatic pulses are generated remotely, beyond the strong radiation environment, and transmitted to the actuator through tubing. The mechanically simple actuator uses a nutating gear harmonic drive to convert motion of small pistons directly to high-resolution angular motion of the output shaft. The digital nature of this actuator is suitable for various reactor control algorithms but is especially compatible with the three bean salad algorithm discussed by Ball et al. (1991).

KINEMATIC ANALYSIS OF NUCLEAR SPIRALS: FEEDING THE BLACK HOLE IN NGC 1097

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van de Ven, Glenn; Fathi, Kambiz, E-mail: glenn@mpia.d, E-mail: kambiz@astro.su.s

2010-11-01

We present a harmonic expansion of the observed line-of-sight velocity field as a method to recover and investigate spiral structures in the nuclear regions of galaxies. We apply it to the emission-line velocity field within the circumnuclear star-forming ring of NGC 1097, obtained with the GMOS-IFU spectrograph. The radial variation of the third harmonic terms is well described by a logarithmic spiral, from which we interpret that the gravitational potential is weakly perturbed by a two-arm spiral density wave with an inferred pitch angle of 52{sup 0} {+-} 4{sup 0}. This interpretation predicts a two-arm spiral distortion in the surfacemore » brightness, as hinted by the dust structures in central images of NGC 1097, and predicts a combined one-arm and three-arm spiral structure in the velocity field, as revealed in the non-circular motions of the ionized gas. Next, we use a simple spiral perturbation model to constrain the fraction of the measured non-circular motions that is due to radial inflow. We combine the resulting inflow velocity with the gas density in the spiral arms, inferred from emission-line ratios, to estimate the mass inflow rate as a function of radius, which reaches about 0.011 M{sub sun} yr{sup -1} at a distance of 70 pc from the center. This value corresponds to a fraction of about 4.2 x 10{sup -3} of the Eddington mass accretion rate onto the central black hole in this LINER/Seyfert1 galaxy. We conclude that the line-of-sight velocity can not only provide a cleaner view of nuclear spirals than the associated dust, but that the presented method also allows the quantitative study of these possibly important links in fueling the centers of galaxies, including providing a constraint on the mass inflow rate as a function of radius.« less

Estimating the effects of harmonic voltage fluctuations on the temperature rise of squirrel-cage motors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emanuel, A.E.

1991-03-01

This article presents a preliminary analysis of the effect of randomly varying harmonic voltages on the temperature rise of squirrel-cage motors. The stochastic process of random variations of harmonic voltages is defined by means of simple statistics (mean, standard deviation, type of distribution). Computational models based on a first-order approximation of the motor losses and on the Monte Carlo method yield results which prove that equipment with large thermal time-constant is capable of withstanding for a short period of time larger distortions than THD = 5%.

General Criterion for Harmonicity

NASA Astrophysics Data System (ADS)

Proesmans, Karel; Vandebroek, Hans; Van den Broeck, Christian

2017-10-01

Inspired by Kubo-Anderson Markov processes, we introduce a new class of transfer matrices whose largest eigenvalue is determined by a simple explicit algebraic equation. Applications include the free energy calculation for various equilibrium systems and a general criterion for perfect harmonicity, i.e., a free energy that is exactly quadratic in the external field. As an illustration, we construct a "perfect spring," namely, a polymer with non-Gaussian, exponentially distributed subunits which, nevertheless, remains harmonic until it is fully stretched. This surprising discovery is confirmed by Monte Carlo and Langevin simulations.

Corrected formula for the polarization of second harmonic plasma emission

NASA Technical Reports Server (NTRS)

Melrose, D. B.; Dulk, G. A.; Gary, D. E.

1980-01-01

Corrections for the theory of polarization of second harmonic plasma emission are proposed. The nontransversality of the magnetoionic waves was not taken into account correctly and is here corrected. The corrected and uncorrected results are compared for two simple cases of parallel and isotropic distributions of Langmuir waves. It is found that whereas with the uncorrected formula plausible values of the coronal magnetic fields were obtained from the observed polarization of the second harmonic, the present results imply fields which are stronger by a factor of three to four.

Hearing the transformation of conical to closed-pipe resonances

NASA Astrophysics Data System (ADS)

Ruiz, Michael J.

2017-05-01

The harmonics for an open cone with slant length L are the same as the harmonics for an open pipe with length L . When the cone is transformed through phases of closed-open conical frusta into a cylinder of length L closed at one end, the fundamental halves and only odd harmonics remain. A simple approach using boundary conditions is presented in order to understand this remarkable fact. A new free interactive HMTL5 application is provided which enables the user to hear the resonances of a complete cone transform into the pitches of a conical frustum closed at the small end, and eventually into the odd harmonics of a closed cylindrical pipe.

Conical Euler solution for a highly-swept delta wing undergoing wing-rock motion

NASA Technical Reports Server (NTRS)

Lee, Elizabeth M.; Batina, John T.

1990-01-01

Modifications to an unsteady conical Euler code for the free-to-roll analysis of highly-swept delta wings are described. The modifications involve the addition of the rolling rigid-body equation of motion for its simultaneous time-integration with the governing flow equations. The flow solver utilized in the Euler code includes a multistage Runge-Kutta time-stepping scheme which uses a finite-volume spatial discretization on an unstructured mesh made up of triangles. Steady and unsteady results are presented for a 75 deg swept delta wing at a freestream Mach number of 1.2 and an angle of attack of 30 deg. The unsteady results consist of forced harmonic and free-to-roll calculations. The free-to-roll case exhibits a wing rock response produced by unsteady aerodynamics consistent with the aerodynamics of the forced harmonic results. Similarities are shown with a wing-rock time history from a low-speed wind tunnel test.

Coupled 2-dimensional cascade theory for noise and unsteady aerodynamics of blade row interaction in turbofans. Volume 1: Theory development and parametric studies

NASA Technical Reports Server (NTRS)

Hanson, Donald B.

1994-01-01

Typical analytical models for interaction between rotor and stator in a turbofan analyze the effect of wakes from the rotor impinging on the stator, producing unsteady loading, and thereby generating noise. Reflection/transmission characteristics of the rotor are sometimes added in a separate calculation. In those models, there is a one-to-one relationship between wake harmonics and noise harmonics; that is, the BPF (blade passing frequency) wake harmonic causes only the BPF noise harmonic, etc. This report presents a more complete model in which flow tangency boundary conditions are satisfied on two cascades in relative motion for several harmonics simultaneously. By an extension of S.N. Smith's code for two dimensional flat plate cascades, the noise generation/frequency scattering/blade row reflection problem is solved in a single matrix inversion. It is found that the BPF harmonic excitation of the stator scatters considerable energy in the higher BPF harmonics due to relative motion between the blade rows. Furthermore, when swirl between the rotor and stator is modeled, a 'mode trapping' effect occurs which explains observations on fans operating at rotational speeds below BFP cuton: the BPF mode amplifies between blade rows by multiple reflections but cannot escape to the inlet and exit ducts. However, energy scattered into higher harmonics does propagate and dominates the spectrum at two and three times BPF. This report presents the complete derivation of the theory, comparison with a previous (more limited) coupled rotor/stator interaction theory due to Kaji and Okazaki, exploration of the mode trapping phenomenon, and parametric studies showing the effects of vane/blade ratio and rotor/stator interaction. For generality, the analysis applies to stages where the rotor is either upstream or downstream of the stator and to counter rotation stages. The theory has been coded in a FORTRAN program called CUP2D, documented in Volume 2 of this report. It is concluded that the new features of this analysis - unsteady coupling, frequency scattering, and flow turning between rotor and stator - have a profound effect on noise generation caused by rotor/stator interaction. Treating rotors and stators as isolated cascades is not adequate for noise analysis and prediction.

Method and apparatus for reducing spacecraft instrument induced jitter via multifrequency cancellation

NASA Technical Reports Server (NTRS)

Liu, Ketao (Inventor); Uetrecht, David S. (Inventor)

2002-01-01

A method, apparatus, article of manufacture, and a memory structure for compensating for instrument induced spacecraft jitter is disclosed. The apparatus comprises a spacecraft control processor for producing an actuator command signal, a signal generator, for producing a cancellation signal having at least one harmonic having a frequency and an amplitude substantially equal to that of a disturbance harmonic interacting with a spacecraft structural resonance and a phase substantially out of phase with the disturbance harmonic interacting with the spacecraft structural resonance, and at least one spacecraft control actuator, communicatively coupled to the spacecraft control processor and the signal generator for inducing satellite motion according to the actuator command signal and the cancellation signal. The method comprises the steps of generating a cancellation signal having at least one harmonic having a frequency and an amplitude substantially equal to that of a disturbance harmonic interacting with a spacecraft structural resonance and a phase substantially out of phase with the disturbance harmonic interacting with the spacecraft structural resonance, and providing the cancellation signal to a spacecraft control actuator. The apparatus comprises a storage device tangibly embodying the method steps described above.

Flying Through Polytropes

NASA Technical Reports Server (NTRS)

Pesnell, W. Dean

2016-01-01

Dropping objects into a tunnel bored through Earth has been used to visualize simple harmonic motion for many years, and even imagined for use as rapid transport systems. Unlike previous studies that assumed a constant density Earth, here we calculate the fall-through time of polytropes, models of Earth's interior where the pressure varies as a power of the density. This means the fall-through time can be calculated as the central condensation varies from one to large within the family of polytropes. Having a family of models, rather than a single model, helps to explore the properties of planets and stars. Comparing the family of phase space solutions shows that the fall-through time and velocity approach the limit of radial free-fall onto a point mass as the central condensation increases. More condensed models give higher maximum velocities but do not have the right global properties for Earth. The angular distance one can travel along the surface is calculated as a brachistochrone (path of least time) tunnel that is a function of the depth to which the tunnel is bored. We also show that completely degenerate objects, simple models of white dwarf stars supported by completely degenerate electrons, have sizes similar to Earth but their much higher masses mean a much larger gravitational strength and a shorter fall-through time. Numerical integrations of the equations describing polytropes and completely degenerate objects are used to generate the initial models. Analytic solutions and numerical integration of the equations of motion are used to calculate the fall-through time for each model, and numerical integrations with analytic approximations at the boundaries are used to calculate the brachistochrones in the polytropes. Scaling relationships are provided to help use these results in other planets and stars.

The enhanced nodal equilibrium ocean tide and polar motion

NASA Technical Reports Server (NTRS)

Sanchez, B. V.

1979-01-01

The tidal response of the ocean to long period forcing functions was investigated. The results indicate the possibility of excitation of a wobble component with the amplitude and frequency indicated by the data. An enhancement function for the equilibrium tide was postulated in the form of an expansion in zonal harmonics and the coefficients of such an expansion were estimated so as to obtain polar motion components of the required magnitude.

A short note on the mean exit time of the Brownian motion

NASA Astrophysics Data System (ADS)

Cadeddu, Lucio; Farina, Maria Antonietta

We investigate the functional Ω↦ℰ(Ω) where Ω runs through the set of compact domains of fixed volume v in any Riemannian manifold (M,g) and where ℰ(Ω) is the mean exit time from Ω of the Brownian motion. We give an alternative analytical proof of a well-known fact on its critical points proved by McDonald: the critical points of ℰ(Ω) are harmonic domains.

Solid-state reversible quadratic nonlinear optical molecular switch with an exceptionally large contrast.

PubMed

Sun, Zhihua; Luo, Junhua; Zhang, Shuquan; Ji, Chengmin; Zhou, Lei; Li, Shenhui; Deng, Feng; Hong, Maochun

2013-08-14

Exceptional nonlinear optical (NLO) switching behavior, including an extremely large contrast (on/off) of ∼35 and high NLO coefficients, is displayed by a solid-state reversible quadratic NLO switch. The favorable results, induced by very fast molecular motion and anionic ordering, provides impetus for the design of a novel second-harmonic-generation switch involving molecular motion. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A simple method for calculating the characteristics of the Dutch roll motion of an airplane

NASA Technical Reports Server (NTRS)

Klawans, Bernard B

1956-01-01

A simple method for calculating the characteristics of the Dutch roll motion of an airplane is obtained by arranging the lateral equations of motion in such form and order that an iterative process is quickly convergent.

Fast lesion mapping during HIFU treatment using harmonic motion imaging guided focused ultrasound (HMIgFUS) in vitro and in vivo

NASA Astrophysics Data System (ADS)

Han, Yang; Wang, Shutao; Payen, Thomas; Konofagou, Elisa

2017-04-01

The successful clinical application of high intensity focused ultrasound (HIFU) ablation depends on reliable monitoring of the lesion formation. Harmonic motion imaging guided focused ultrasound (HMIgFUS) is an ultrasound-based elasticity imaging technique, which monitors HIFU ablation based on the stiffness change of the tissue instead of the echo intensity change in conventional B-mode monitoring, rendering it potentially more sensitive to lesion development. Our group has shown that predicting the lesion location based on the radiation force-excited region is feasible during HMIgFUS. In this study, the feasibility of a fast lesion mapping method is explored to directly monitor the lesion map during HIFU. The harmonic motion imaging (HMI) lesion map was generated by subtracting the reference HMI image from the present HMI peak-to-peak displacement map, as streamed on the computer display. The dimensions of the HMIgFUS lesions were compared against gross pathology. Excellent agreement was found between the lesion depth (r 2  =  0.81, slope  =  0.90), width (r 2  =  0.85, slope  =  1.12) and area (r 2  =  0.58, slope  =  0.75). In vivo feasibility was assessed in a mouse with a pancreatic tumor. These findings demonstrate that HMIgFUS can successfully map thermal lesions and monitor lesion development in real time in vitro and in vivo. The HMIgFUS technique may therefore constitute a novel clinical tool for HIFU treatment monitoring.

Fast lesion mapping during HIFU treatment using harmonic motion imaging guided focused ultrasound (HMIgFUS) in vitro and in vivo.

PubMed

Han, Yang; Wang, Shutao; Payen, Thomas; Konofagou, Elisa

2017-04-21

The successful clinical application of high intensity focused ultrasound (HIFU) ablation depends on reliable monitoring of the lesion formation. Harmonic motion imaging guided focused ultrasound (HMIgFUS) is an ultrasound-based elasticity imaging technique, which monitors HIFU ablation based on the stiffness change of the tissue instead of the echo intensity change in conventional B-mode monitoring, rendering it potentially more sensitive to lesion development. Our group has shown that predicting the lesion location based on the radiation force-excited region is feasible during HMIgFUS. In this study, the feasibility of a fast lesion mapping method is explored to directly monitor the lesion map during HIFU. The harmonic motion imaging (HMI) lesion map was generated by subtracting the reference HMI image from the present HMI peak-to-peak displacement map, as streamed on the computer display. The dimensions of the HMIgFUS lesions were compared against gross pathology. Excellent agreement was found between the lesion depth (r 2   =  0.81, slope  =  0.90), width (r 2   =  0.85, slope  =  1.12) and area (r 2   =  0.58, slope  =  0.75). In vivo feasibility was assessed in a mouse with a pancreatic tumor. These findings demonstrate that HMIgFUS can successfully map thermal lesions and monitor lesion development in real time in vitro and in vivo. The HMIgFUS technique may therefore constitute a novel clinical tool for HIFU treatment monitoring.

Higher-order harmonics coupling in different free-electron laser codes

NASA Astrophysics Data System (ADS)

Giannessi, L.; Freund, H. P.; Musumeci, P.; Reiche, S.

2008-08-01

The capability for simulation of the dynamics of a free-electron laser including the higher-order harmonics in linear undulators exists in several existing codes as MEDUSA [H.P. Freund, S.G. Biedron, and S.V. Milton, IEEE J. Quantum Electron. 27 (2000) 243; H.P. Freund, Phys. Rev. ST-AB 8 (2005) 110701] and PERSEO [L. Giannessi, Overview of Perseo, a system for simulating FEL dynamics in Mathcad, < http://www.jacow.org>, in: Proceedings of FEL 2006 Conference, BESSY, Berlin, Germany, 2006, p. 91], and has been recently implemented in GENESIS 1.3 [See < http://www.perseo.enea.it>]. MEDUSA and GENESIS also include the dynamics of even harmonics induced by the coupling through the betatron motion. In addition MEDUSA, which is based on a non-wiggler averaged model, is capable of simulating the generation of even harmonics in the transversally cold beam regime, i.e. when the even harmonic coupling arises from non-linear effects associated with longitudinal particle dynamics and not to a finite beam emittance. In this paper a comparison between the predictions of the codes in different conditions is given.

Sampled-data synchronisation of coupled harmonic oscillators with communication and input delays subject to controller failure

NASA Astrophysics Data System (ADS)

Zhao, Liyun; Zhou, Jin; Wu, Quanjun

2016-01-01

This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.

Three-Dimensional Lissajous Figures.

ERIC Educational Resources Information Center

D'Mura, John M.

1989-01-01

Described is a mechanically driven device for generating three-dimensional harmonic space figures with different frequencies and phase angles on the X, Y, and Z axes. Discussed are apparatus, viewing stereo pairs, equations of motion, and using space figures in classroom. (YP)

Unraveling the origins of electromechanical response in mixed-phase Bismuth Ferrite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasudevan, Rama K; Okatan, M. B.; Liu, Y. Y.

The origin of giant electromechanical response in a mixed-phase rhombohedral-tetragonal BiFeO3 thin film is probed using sub-coercive scanning probe microscopy based multiple-harmonic measurements. Significant contributions to the strain arise from a second-order harmonic response localized at the phase boundaries. Strain and dissipation data, backed by thermodynamic calculations suggest that the source of the enhanced electromechanical response is the motion of phase boundaries. These findings elucidate the key role of labile phase boundaries, both natural and artificial, in achieving thin films with giant electromechanical properties.

Expansion of the gravitational potential with computerized Poisson series

NASA Technical Reports Server (NTRS)

Broucke, R.

1976-01-01

The paper describes a recursive formulation for the expansion of the gravitational potential valid for both the tesseral and zonal harmonics. The expansion is primarily in rectangular coordinates, but the classical orbit elements or equinoctial orbit elements can be easily substituted. The equations of motion for the zonal harmonics in both classical and equinoctial orbital elements are described in a form which will result in closed-form expressions for the first-order perturbations. In order to achieve this result, the true longitude or true anomaly have to be used as independent variables.

Geometry and dynamics in the fractional discrete Fourier transform.

PubMed

Wolf, Kurt Bernardo; Krötzsch, Guillermo

2007-03-01

The N x N Fourier matrix is one distinguished element within the group U(N) of all N x N unitary matrices. It has the geometric property of being a fourth root of unity and is close to the dynamics of harmonic oscillators. The dynamical correspondence is exact only in the N-->infinity contraction limit for the integral Fourier transform and its fractional powers. In the finite-N case, several options have been considered in the literature. We compare their fidelity in reproducing the classical harmonic motion of discrete coherent states.

Ab initio molecular dynamics with enhanced sampling for surface reaction kinetics at finite temperatures: CH2 ⇌ CH + H on Ni(111) as a case study

NASA Astrophysics Data System (ADS)

Sun, Geng; Jiang, Hong

2015-12-01

A comprehensive understanding of surface thermodynamics and kinetics based on first-principles approaches is crucial for rational design of novel heterogeneous catalysts, and requires combining accurate electronic structure theory and statistical mechanics modeling. In this work, ab initio molecular dynamics (AIMD) combined with the integrated tempering sampling (ITS) method has been explored to study thermodynamic and kinetic properties of elementary processes on surfaces, using a simple reaction CH 2 ⇌ CH + H on the Ni(111) surface as an example. By a careful comparison between the results from ITS-AIMD simulation and those evaluated in terms of the harmonic oscillator (HO) approximation, it is found that the reaction free energy and entropy from the HO approximation are qualitatively consistent with the results from ITS-AIMD simulation, but there are also quantitatively significant discrepancies. In particular, the HO model misses the entropy effects related to the existence of multiple adsorption configurations arising from the frustrated translation and rotation motion of adsorbed species, which are different in the reactant and product states. The rate constants are evaluated from two ITS-enhanced approaches, one using the transition state theory (TST) formulated in terms of the potential of mean force (PMF) and the other one combining ITS with the transition path sampling (TPS) technique, and are further compared to those based on harmonic TST. It is found that the rate constants from the PMF-based TST are significantly smaller than those from the harmonic TST, and that the results from PMF-TST and ITS-TPS are in a surprisingly good agreement. These findings indicate that the basic assumptions of transition state theory are valid in such elementary surface reactions, but the consideration of statistical averaging of all important adsorption configurations and reaction pathways, which are missing in the harmonic TST, are critical for accurate description of thermodynamic and kinetic properties of surface processes. This work clearly demonstrates the importance of considering temperature effects beyond the HO model, for which the AIMD simulation in combination with enhanced sampling techniques like ITS provides a feasible and general approach.

Sensitivity of echo enabled harmonic generation to sinusoidal electron beam energy structure

DOE PAGES

Hemsing, E.; Garcia, B.; Huang, Z.; ...

2017-06-19

Here, we analytically examine the bunching factor spectrum of a relativistic electron beam with sinusoidal energy structure that then undergoes an echo-enabled harmonic generation (EEHG) transformation to produce high harmonics. The performance is found to be described primarily by a simple scaling parameter. The dependence of the bunching amplitude on fluctuations of critical parameters is derived analytically, and compared with simulations. Where applicable, EEHG is also compared with high gain harmonic generation (HGHG) and we find that EEHG is generally less sensitive to several types of energy structure. In the presence of intermediate frequency modulations like those produced by themore » microbunching instability, EEHG has a substantially narrower intrinsic bunching pedestal.« less

Selection rules for harmonic generation in solids

NASA Astrophysics Data System (ADS)

Moiseyev, Nimrod

2015-05-01

High-order harmonic generation (HHG) in a bulk crystal was first observed in 2011 [S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, Nat. Phys. 7, 138 (2011), 10.1038/nphys1847]. Only odd-order harmonics were observed as expected on the basis of the selection rules in solids, which were derived when only the interband currents were taken into consideration. Here we study HHG in solids when the intraband currents are taken into consideration as well. We show that the dynamical selection rules are broken in solids and the possibility of generation of even-order harmonics cannot be excluded on the basis of the dynamical symmetry analysis. However, a simple analysis of the expression we obtained for the amplitude of the emitted high-order harmonics shows, without the need to carry out numerical calculations, that the even-order harmonics are suppressed due to the localization of the field-free one-electron density probability on the atoms in the solids.

Angular and Intensity Dependent Spectral Modulations in High Harmonics from N2

NASA Astrophysics Data System (ADS)

McFarland, Brian; Farrell, Joseph; Bucksbaum, Philip; Guehr, Markus

2009-05-01

The spectral amplitude and phase modulation of high harmonics (HHG) in molecules provides important clues to molecular structure and dynamics in strong laser fields. We have studied these effects in aligned N2. Earlier results of HHG experiments claimed that the spectral amplitude modulation was predominantly due to geometrical interference between the recombining electron and the highest occupied molecular orbital (HOMO) [1]. We report evidence that contradicts this simple view. We observe a phase jump accompanied by a spectral minimum for HHG in aligned N2. The minimum shifts to lower harmonics as the angle between the molecular axis and harmonic generation polarization increases, and shifts to higher harmonics with increasing harmonic generation intensity. The features observed cannot be fully explained by a geometrical model. We discuss alternative explanations involving multi orbital effects [2]. [0pt] [1] Lein et al., Phys. Rev. A, 66, 023805 (2002) [2] B. K. McFarland, J. P. Farrell, P. H. Bucksbaum and M. Gühr, Science 322, 1232 (2008)

On the optimization of discrete structures with aeroelastic constraints

NASA Technical Reports Server (NTRS)

Mcintosh, S. C., Jr.; Ashley, H.

1978-01-01

The paper deals with the problem of dynamic structural optimization where constraints relating to flutter of a wing (or other dynamic aeroelastic performance) are imposed along with conditions of a more conventional nature such as those relating to stress under load, deflection, minimum dimensions of structural elements, etc. The discussion is limited to a flutter problem for a linear system with a finite number of degrees of freedom and a single constraint involving aeroelastic stability, and the structure motion is assumed to be a simple harmonic time function. Three search schemes are applied to the minimum-weight redesign of a particular wing: the first scheme relies on the method of feasible directions, while the other two are derived from necessary conditions for a local optimum so that they can be referred to as optimality-criteria schemes. The results suggest that a heuristic redesign algorithm involving an optimality criterion may be best suited for treating multiple constraints with large numbers of design variables.

Validation of Analytical Damping Ratio by Fatigue Stress Limit

NASA Astrophysics Data System (ADS)

Foong, Faruq Muhammad; Chung Ket, Thein; Beng Lee, Ooi; Aziz, Abdul Rashid Abdul

2018-03-01

The optimisation process of a vibration energy harvester is usually restricted to experimental approaches due to the lack of an analytical equation to describe the damping of a system. This study derives an analytical equation, which describes the first mode damping ratio of a clamp-free cantilever beam under harmonic base excitation by combining the transverse equation of motion of the beam with the damping-stress equation. This equation, as opposed to other common damping determination methods, is independent of experimental inputs or finite element simulations and can be solved using a simple iterative convergence method. The derived equation was determined to be correct for cases when the maximum bending stress in the beam is below the fatigue limit stress of the beam. However, an increasing trend in the error between the experiment and the analytical results were observed at high stress levels. Hence, the fatigue limit stress was used as a parameter to define the validity of the analytical equation.

Simulations of magnetic nanoparticle Brownian motion

PubMed Central

Reeves, Daniel B.; Weaver, John B.

2012-01-01

Magnetic nanoparticles are useful in many medical applications because they interact with biology on a cellular level thus allowing microenvironmental investigation. An enhanced understanding of the dynamics of magnetic particles may lead to advances in imaging directly in magnetic particle imaging or through enhanced MRI contrast and is essential for nanoparticle sensing as in magnetic spectroscopy of Brownian motion. Moreover, therapeutic techniques like hyperthermia require information about particle dynamics for effective, safe, and reliable use in the clinic. To that end, we have developed and validated a stochastic dynamical model of rotating Brownian nanoparticles from a Langevin equation approach. With no field, the relaxation time toward equilibrium matches Einstein's model of Brownian motion. In a static field, the equilibrium magnetization agrees with the Langevin function. For high frequency or low amplitude driving fields, behavior characteristic of the linearized Debye approximation is reproduced. In a higher field regime where magnetic saturation occurs, the magnetization and its harmonics compare well with the effective field model. On another level, the model has been benchmarked against experimental results, successfully demonstrating that harmonics of the magnetization carry enough information to infer environmental parameters like viscosity and temperature. PMID:23319830

Quantifying cortical surface harmonic deformation with stereovision during open cranial neurosurgery

NASA Astrophysics Data System (ADS)

Ji, Songbai; Fan, Xiaoyao; Roberts, David W.; Paulsen, Keith D.

2012-02-01

Cortical surface harmonic motion during open cranial neurosurgery is well observed in image-guided neurosurgery. Recently, we quantified cortical surface deformation noninvasively with synchronized blood pressure pulsation (BPP) from a sequence of stereo image pairs using optical flow motion tracking. With three subjects, we found the average cortical surface displacement can reach more than 1 mm and in-plane principal strains of up to 7% relative to the first image pair. In addition, the temporal changes in deformation and strain were in concert with BPP and patient respiration [1]. However, because deformation was essentially computed relative to an arbitrary reference, comparing cortical surface deformation at different times was not possible. In this study, we extend the technique developed earlier by establishing a more reliable reference profile of the cortical surface for each sequence of stereo image acquisitions. Specifically, fast Fourier transform (FFT) was applied to the dynamic cortical surface deformation, and the fundamental frequencies corresponding to patient respiration and BPP were identified, which were used to determine the number of image acquisitions for use in averaging cortical surface images. This technique is important because it potentially allows in vivo characterization of soft tissue biomechanical properties using intraoperative stereovision and motion tracking.

High-harmonic generation by two-color mixing of circularly polarized laser fields

NASA Astrophysics Data System (ADS)

Milošević, D. B.; Becker, W.; Kopold, R.

2000-06-01

Dipole selection rules prevent harmonic generation by an atom in a circularly polarized laser field. However, this is not the case for a superposition of several circularly polarized fields, such as two circularly polarized fields with frequencies ω and 2ω that corotate or counter-rotate in the same plane. Harmonic generation in this environment has been observed and, in fact, found to be very intense in the counter-rotating case [1]. In a certain frequency region, the harmonics may be stronger than those radiated in a linearly polarized field of either frequency. The selection rules dictate that the harmonics are circularly polarized with a helicity that alternates from one harmonic to the next. Besides their practical interest, these harmonics are also intriguing from a fundamental point of view: the standard simple-man picture does not apply since orbits that start with zero velocity in this field almost never return to their point of departure. In terms of quantum trajectories, we discuss the mechanism that generates these harmonics. In several interesting ways, it is complementary to the case of linear polarization. [1] H. Eichmann et al., Phys. Rev. A 51, R3414 (1995)

Predicting charmonium and bottomonium spectra with a quark harmonic oscillator

NASA Technical Reports Server (NTRS)

Norbury, J. W.; Badavi, F. F.; Townsend, L. W.

1986-01-01

The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.

Angle-Resolved Second-Harmonic Light Scattering from Colloidal Particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, N.; Angerer, W. E.; Yodh, A. G.

2001-09-03

We report angle-resolved second-harmonic generation (SHG) measurements from suspensions of centrosymmetric micron-size polystyrene spheres with surface-adsorbed dye (malachite green). The second-harmonic scattering profiles differ qualitatively from linear light scattering profiles of the same particles. We investigated these radiation patterns using several polarization configurations and particle diameters. We introduce a simple Rayleigh-Gans-Debye model to account for the SHG scattering anisotropy. The model compares favorably with our experimental data. Our measurements suggest scattering anisotropy may be used to isolate particle nonlinear optics from other bulk nonlinear optical effects in suspension.

A simple, remote, video based breathing monitor.

PubMed

Regev, Nir; Wulich, Dov

2017-07-01

Breathing monitors have become the all-important cornerstone of a wide variety of commercial and personal safety applications, ranging from elderly care to baby monitoring. Many such monitors exist in the market, some, with vital signs monitoring capabilities, but none remote. This paper presents a simple, yet efficient, real time method of extracting the subject's breathing sinus rhythm. Points of interest are detected on the subject's body, and the corresponding optical flow is estimated and tracked using the well known Lucas-Kanade algorithm on a frame by frame basis. A generalized likelihood ratio test is then utilized on each of the many interest points to detect which is moving in harmonic fashion. Finally, a spectral estimation algorithm based on Pisarenko harmonic decomposition tracks the harmonic frequency in real time, and a fusion maximum likelihood algorithm optimally estimates the breathing rate using all points considered. The results show a maximal error of 1 BPM between the true breathing rate and the algorithm's calculated rate, based on experiments on two babies and three adults.

Localized, Non-Harmonic Active Flap Motions for Low Frequency In-Plane Rotor Noise Reduction

DTIC Science & Technology

2012-05-01

rotating -frame cyclic variations, of two- per-rev or greater, to augment blade motions and blade airloads. Recent studies (Refs. 5, 6) have...Advancing tip Mach number MH Rotational (Hover) tip Mach number NM Noise metric, peak-to-peak value R Blade radius α...from a full-scale, 2,900 lb. gross weight, four-bladed S-434TM helicopter. The rotor head, blade cuffs , and swash-plate were production S

Causal implications of viscous damping in compressible fluid flows

PubMed

Jordan; Meyer; Puri

2000-12-01

Classically, a compressible, isothermal, viscous fluid is regarded as a mathematical continuum and its motion is governed by the linearized continuity, Navier-Stokes, and state equations. Unfortunately, solutions of this system are of a diffusive nature and hence do not satisfy causality. However, in the case of a half-space of fluid set to motion by a harmonically vibrating plate the classical equation of motion can, under suitable conditions, be approximated by the damped wave equation. Since this equation is hyperbolic, the resulting solutions satisfy causal requirements. In this work the Laplace transform and other analytical and numerical tools are used to investigate this apparent contradiction. To this end the exact solutions, as well as their special and limiting cases, are found and compared for the two models. The effects of the physical parameters on the solutions and associated quantities are also studied. It is shown that propagating wave fronts are only possible under the hyperbolic model and that the concept of phase speed has different meanings in the two formulations. In addition, discontinuities and shock waves are noted and a physical system is modeled under both formulations. Overall, it is shown that the hyperbolic form gives a more realistic description of the physical problem than does the classical theory. Lastly, a simple mechanical analog is given and connections to viscoelastic fluids are noted. In particular, the research presented here supports the notion that linear compressible, isothermal, viscous fluids can, at least in terms of causality, be better characterized as a type of viscoelastic fluid.

On Simple Science.

ERIC Educational Resources Information Center

Cole, K.C.

1982-01-01

Discusses San Francisco's Exploratorium, a science teaching center with 500 exhibits focusing on human perception, but extending to everything from the mechanics of voice to the art of illusion, from holograms to harmonics. The Exploratorium emphasizes "simple science" (refractions/resonances, sounds/shadows) to tune in the senses and turn on the…

Computers in the General Physics Laboratory.

ERIC Educational Resources Information Center

Preston, Daryl W.; Good, R. H.

1996-01-01

Provides ideas and outcomes for nine computer laboratory experiments using a commercial eight-bit analog to digital (ADC) interface. Experiments cover statistics; rotation; harmonic motion; voltage, current, and resistance; ADC conversions; temperature measurement; single slit diffraction; and radioactive decay. Includes necessary schematics. (MVL)

The Physics of Marine Biology.

ERIC Educational Resources Information Center

Conn, Kathleen

1992-01-01

Discusses ways in which marine biology can be integrated into the physics classroom. Topics suggested for incorporation include the harmonic motion of ocean waves, ocean currents, the interaction of visible light with ocean water, pressure, light absorption, and sound transfer in water. (MDH)

The anisosphere as a new tool for interpreting Foucault pendulum experiments. Part I: harmonic oscillators

NASA Astrophysics Data System (ADS)

Verreault, René

2017-08-01

In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes' dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2-3 orders of magnitude is achieved.

Statistical mechanics of monatomic liquids

NASA Astrophysics Data System (ADS)

Wallace, Duane C.

1997-10-01

Two key experimental properties of elemental liquids, together with an analysis of the condensed-system potential-energy surface, lead us logically to the dynamical theory of monatomic liquids. Experimentally, the ion motional specific heat is approximately 3Nk for N ions, implying the normal modes of motion are approximately 3N independent harmonic oscillators. This implies the potential surface contains nearly harmonic valleys. The equilibrium configuration at the bottom of each valley is a ``structure.'' Structures are crystalline or amorphous, and amorphous structures can have a remnant of local crystal symmetry, or can be random. The random structures are by far the most numerous, and hence dominate the statistical mechanics of the liquid state, and their macroscopic properties are uniform over the structure class, for large-N systems. The Hamiltonian for any structural valley is the static structure potential, a sum of harmonic normal modes, and an anharmonic correction. Again from experiment, the constant-density entropy of melting contains a universal disordering contribution of NkΔ, suggesting the random structural valleys are of universal number wN, where lnw=Δ. Our experimental estimate for Δ is 0.80. In quasiharmonic approximation, the liquid theory for entropy agrees with experiment, for all currently analyzable experimental data at elevated temperatures, to within 1-2% of the total entropy. Further testable predictions of the theory are mentioned.

Locomotion of C. elegans: A Piecewise-Harmonic Curvature Representation of Nematode Behavior

PubMed Central

Padmanabhan, Venkat; Khan, Zeina S.; Solomon, Deepak E.; Armstrong, Andrew; Rumbaugh, Kendra P.; Vanapalli, Siva A.; Blawzdziewicz, Jerzy

2012-01-01

Caenorhabditis elegans, a free-living soil nematode, displays a rich variety of body shapes and trajectories during its undulatory locomotion in complex environments. Here we show that the individual body postures and entire trails of C. elegans have a simple analytical description in curvature representation. Our model is based on the assumption that the curvature wave is generated in the head segment of the worm body and propagates backwards. We have found that a simple harmonic function for the curvature can capture multiple worm shapes during the undulatory movement. The worm body trajectories can be well represented in terms of piecewise sinusoidal curvature with abrupt changes in amplitude, wavevector, and phase. PMID:22792224

Assessment of terrestrial water contributions to polar motion from GRACE and hydrological models

NASA Astrophysics Data System (ADS)

Jin, S. G.; Hassan, A. A.; Feng, G. P.

2012-12-01

The hydrological contribution to polar motion is a major challenge in explaining the observed geodetic residual of non-atmospheric and non-oceanic excitations since hydrological models have limited input of comprehensive global direct observations. Although global terrestrial water storage (TWS) estimated from the Gravity Recovery and Climate Experiment (GRACE) provides a new opportunity to study the hydrological excitation of polar motion, the GRACE gridded data are subject to the post-processing de-striping algorithm, spatial gridded mapping and filter smoothing effects as well as aliasing errors. In this paper, the hydrological contributions to polar motion are investigated and evaluated at seasonal and intra-seasonal time scales using the recovered degree-2 harmonic coefficients from all GRACE spherical harmonic coefficients and hydrological models data with the same filter smoothing and recovering methods, including the Global Land Data Assimilation Systems (GLDAS) model, Climate Prediction Center (CPC) model, the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis products and European Center for Medium-Range Weather Forecasts (ECMWF) operational model (opECMWF). It is shown that GRACE is better in explaining the geodetic residual of non-atmospheric and non-oceanic polar motion excitations at the annual period, while the models give worse estimates with a larger phase shift or amplitude bias. At the semi-annual period, the GRACE estimates are also generally closer to the geodetic residual, but with some biases in phase or amplitude due mainly to some aliasing errors at near semi-annual period from geophysical models. For periods less than 1-year, the hydrological models and GRACE are generally worse in explaining the intraseasonal polar motion excitations.

SIFT-based dense pixel tracking on 0.35 T cine-MR images acquired during image-guided radiation therapy with application to gating optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mazur, Thomas R., E-mail: tmazur@radonc.wustl.edu, E-mail: hli@radonc.wustl.edu; Fischer-Valuck, Benjamin W.; Wang, Yuhe

Purpose: To first demonstrate the viability of applying an image processing technique for tracking regions on low-contrast cine-MR images acquired during image-guided radiation therapy, and then outline a scheme that uses tracking data for optimizing gating results in a patient-specific manner. Methods: A first-generation MR-IGRT system—treating patients since January 2014—integrates a 0.35 T MR scanner into an annular gantry consisting of three independent Co-60 sources. Obtaining adequate frame rates for capturing relevant patient motion across large fields-of-view currently requires coarse in-plane spatial resolution. This study initially (1) investigate the feasibility of rapidly tracking dense pixel correspondences across single, sagittal planemore » images (with both moderate signal-to-noise and spatial resolution) using a matching objective for highly descriptive vectors called scale-invariant feature transform (SIFT) descriptors associated to all pixels that describe intensity gradients in local regions around each pixel. To more accurately track features, (2) harmonic analysis was then applied to all pixel trajectories within a region-of-interest across a short training period. In particular, the procedure adjusts the motion of outlying trajectories whose relative spectral power within a frequency bandwidth consistent with respiration (or another form of periodic motion) does not exceed a threshold value that is manually specified following the training period. To evaluate the tracking reliability after applying this correction, conventional metrics—including Dice similarity coefficients (DSCs), mean tracking errors (MTEs), and Hausdorff distances (HD)—were used to compare target segmentations obtained via tracking to manually delineated segmentations. Upon confirming the viability of this descriptor-based procedure for reliably tracking features, the study (3) outlines a scheme for optimizing gating parameters—including relative target position and a tolerable margin about this position—derived from a probability density function that is constructed using tracking results obtained just prior to treatment. Results: The feasibility of applying the matching objective for SIFT descriptors toward pixel-by-pixel tracking on cine-MR acquisitions was first retrospectively demonstrated for 19 treatments (spanning various sites). Both with and without motion correction based on harmonic analysis, sub-pixel MTEs were obtained. A mean DSC value spanning all patients of 0.916 ± 0.001 was obtained without motion correction, with DSC values exceeding 0.85 for all patients considered. While most patients show accurate tracking without motion correction, harmonic analysis does yield substantial gain in accuracy (defined using HDs) for three particularly challenging subjects. An application of tracking toward a gating optimization procedure was then demonstrated that should allow a physician to balance beam-on time and tissue sparing in a patient-specific manner by tuning several intuitive parameters. Conclusions: Tracking results show high fidelity in assessing intrafractional motion observed on cine-MR acquisitions. Incorporating harmonic analysis during a training period improves the robustness of the tracking for challenging targets. The concomitant gating optimization procedure should allow for physicians to quantitatively assess gating effectiveness quickly just prior to treatment in a patient-specific manner.« less

Contrast and harmonic imaging improves accuracy and efficiency of novice readers for dobutamine stress echocardiography

NASA Technical Reports Server (NTRS)

Vlassak, Irmien; Rubin, David N.; Odabashian, Jill A.; Garcia, Mario J.; King, Lisa M.; Lin, Steve S.; Drinko, Jeanne K.; Morehead, Annitta J.; Prior, David L.; Asher, Craig R.;

Simulation of ground motion using the stochastic method

USGS Publications Warehouse

Boore, D.M.

2003-01-01

A simple and powerful method for simulating ground motions is to combine parametric or functional descriptions of the ground motion's amplitude spectrum with a random phase spectrum modified such that the motion is distributed over a duration related to the earthquake magnitude and to the distance from the source. This method of simulating ground motions often goes by the name "the stochastic method." It is particularly useful for simulating the higher-frequency ground motions of most interest to engineers (generally, f>0.1 Hz), and it is widely used to predict ground motions for regions of the world in which recordings of motion from potentially damaging earthquakes are not available. This simple method has been successful in matching a variety of ground-motion measures for earthquakes with seismic moments spanning more than 12 orders of magnitude and in diverse tectonic environments. One of the essential characteristics of the method is that it distills what is known about the various factors affecting ground motions (source, path, and site) into simple functional forms. This provides a means by which the results of the rigorous studies reported in other papers in this volume can be incorporated into practical predictions of ground motion.

Nonlinear collisionless electron cyclotron interaction in the pre-ionisation stage

NASA Astrophysics Data System (ADS)

Farina, D.

2018-06-01

Electron cyclotron (EC) wave-particle interaction is theoretically investigated in the pre-ionisation phase, much before collisions and other mechanisms can play a role. In the very first phase of a plasma discharge with EC-assisted breakdown, the motion of an electron at room temperature in a static magnetic field under the action of a localised microwave beam is nonlinear, and transition to states of larger energy can occur via wave trapping. Within a Hamiltonian adiabatic formalism, the conditions at which the particles gain energy in single beam crossing are derived in a rigorous way, and the energy variation is characterized quantitatively as a function of the wave frequency, harmonic number, polarisation and EC power and beam width. Estimates of interest for applications to tokamak start-up are obtained for the first, second and third cyclotron harmonic. The investigation confirms that electrons can easily gain energies well above the ionisation energy in most conditions at the first two harmonics, while not at the third harmonic, as observed in experiments.

Improvement of Shear Wave Motion Detection Using Harmonic Imaging in Healthy Human Liver.

PubMed

Amador, Carolina; Song, Pengfei; Meixner, Duane D; Chen, Shigao; Urban, Matthew W

2016-05-01

Quantification of liver elasticity is a major application of shear wave elasticity imaging (SWEI) to non-invasive assessment of liver fibrosis stages. SWEI measurements can be highly affected by ultrasound image quality. Ultrasound harmonic imaging has exhibited a significant improvement in ultrasound image quality as well as for SWEI measurements. This was previously illustrated in cardiac SWEI. The purpose of this study was to evaluate liver shear wave particle displacement detection and shear wave velocity (SWV) measurements with fundamental and filter-based harmonic ultrasound imaging. In a cohort of 17 patients with no history of liver disease, a 2.9-fold increase in maximum shear wave displacement, a 0.11 m/s decrease in the overall interquartile range and median SWV and a 17.6% increase in the success rate of SWV measurements were obtained when filter-based harmonic imaging was used instead of fundamental imaging. Copyright © 2016 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Classical versus quantum dynamical chaos: Sensitivity to external perturbations, stability and reversibility

NASA Astrophysics Data System (ADS)

Sokolov, Valentin V.; Zhirov, Oleg V.; Kharkov, Yaroslav A.

The extraordinary complexity of classical trajectories of typical nonlinear systems that manifest stochastic behavior is intimately connected with exponential sensitivity to small variations of initial conditions and/or weak external perturbations. In rigorous terms, such classical systems are characterized by positive algorithmic complexity described by the Lyapunov exponent or, alternatively, by the Kolmogorov-Sinai entropy. The said implies that, in spite of the fact that, formally, any however complex trajectory of a perfectly isolated (closed) system is unique and differentiable for any certain initial conditions and the motion is perfectly reversible, it is impractical to treat that sort of classical systems as closed ones. Inevitably, arbitrary weak influence of an environment crucially impacts the dynamics. This influence, that can be considered as a noise, rapidly effaces the memory of initial conditions and turns the motion into an irreversible random process. In striking contrast, the quantum mechanics of the classically chaotic systems exhibit much weaker sensitivity and strong memory of the initial state. Qualitatively, this crucial difference could be expected in view of a much simpler structure of quantum states as compared to the extraordinary complexity of random and unpredictable classical trajectories. However the very notion of trajectories is absent in quantum mechanics so that the concept of exponential instability seems to be irrelevant in this case. The problem of a quantitative measure of complexity of a quantum state of motion, that is a very important and nontrivial issue of the theory of quantum dynamical chaos, is the one of our concern. With such a measure in hand, we quantitatively analyze the stability and reversibility of quantum dynamics in the presence of external noise. To solve this problem we point out that individual classical trajectories are of minor interest if the motion is chaotic. Properties of all of them are alike in this case and rather the behavior of their manifolds carries really valuable information. Therefore the phase-space methods and, correspondingly, the Liouville form of the classical mechanics become the most adequate. It is very important that, opposite to the classical trajectories, the classical phase space distribution and the Liouville equation have direct quantum analogs. Hence, the analogy and difference of classical and quantum dynamics can be traced by comparing the classical (W(c)(I,θ;t)) and quantum (Wigner function W(I,θ;t)) phase space distributions both expressed in identical phase-space variables but ruled by different(!) linear equations. The paramount property of the classical dynamical chaos is the exponentially fast structuring of the system's phase space on finer and finer scales. On the contrary, degree of structuring of the corresponding Wigner function is restricted by the quantization of the phase space. This makes Wigner function more coarse and relatively "simple" as compared to its classical counterpart. Fourier analysis affords quite suitable ground for analyzing complexity of a phase space distribution, that is equally valid in classical and quantum cases. We demonstrate that the typical number of Fourier harmonics is indeed a relevant measure of complexity of states of motion in both classical as well as quantum cases. This allowed us to investigate in detail and introduce a quantitative measure of sensitivity to an external noisy environment and formulate the conditions under which the quantum motion remains reversible. It turns out that while the mean number of harmonics of the classical phase-space distribution of a non-integrable system grows with time exponentially during the whole time of the motion, the time of exponential upgrowth of this number in the case of the corresponding quantum Wigner function is restricted only to the Ehrenfest interval 0 < t < tE - just the interval within which the Wigner function still satisfies the classical Liouville equation. We showed that the number of harmonics increases beyond this interval algebraically. This fact gains a crucial importance when the Ehrenfest time is so short that the exponential regime has no time to show up. Under this condition the quantum motion turns out to be quite stable and reversible.

Driven damped harmonic oscillator resonance with an Arduino

NASA Astrophysics Data System (ADS)

Goncalves, A. M. B.; Cena, C. R.; Bozano, D. F.

2017-07-01

In this paper we propose a simple experimental apparatus that can be used to show quantitative and qualitative results of resonance in a driven damped harmonic oscillator. The driven oscillation is made by a servo motor, and the oscillation amplitude is measured by an ultrasonic position sensor. Both are controlled by an Arduino board. The frequency of free oscillation measured was campatible with the resonance frequency that was measured.

A simple-harmonic model for depicting the annual cycle of seasonal temperatures of streams

USGS Publications Warehouse

Steele, Timothy Doak

1978-01-01

Due to economic or operational constraints, stream-temperature records cannot always be collected at all sites where information is desired or at frequencies dictated by continuous or near-continuous surveillance requirements. For streams where only periodic measurements are made during the year, and that are not appreciably affected by regulation or by thermal loading , a simple harmonic function may adequately depict the annual seasonal cycle of stream temperature at any given site. Resultant harmonic coefficients obtained from available stream-temperature records may be used in the following ways: (1) To interpolate between discrete measurements by solving the harmonic function at specified times, thereby filling in estimates of stream-temperature values; (2) to characterize areal or regional patterns of natural stream-temperature values; (2) to characterize areal or regional patterns of natural stream-temperature conditions; and (3) to detect and to assess any significant at a site brought about by streamflow regulation or basin development. Moreover, less-than-daily or sampling frequencies at a given site may give estimates of annual variation of stream temperatures that are statistically comparable to estimates obtained from a daily or continuous sampling scheme. The latter procedure may result in potential savings of resources in network operations, with negligible loss in information on annual stream-temperature variations. (Woodard -USGS)

4D Hyperspherical Harmonic (HyperSPHARM) Representation of Multiple Disconnected Brain Subcortical Structures

PubMed Central

Hosseinbor, A. Pasha; Chung, Moo K.; Schaefer, Stacey M.; van Reekum, Carien M.; Peschke-Schmitz, Lara; Sutterer, Matt; Alexander, Andrew L.; Davidson, Richard J.

2014-01-01

We present a novel surface parameterization technique using hyperspherical harmonics (HSH) in representing compact, multiple, disconnected brain subcortical structures as a single analytic function. The proposed hyperspherical harmonic representation (HyperSPHARM) has many advantages over the widely used spherical harmonic (SPHARM) parameterization technique. SPHARM requires flattening 3D surfaces to 3D sphere which can be time consuming for large surface meshes, and can’t represent multiple disconnected objects with single parameterization. On the other hand, HyperSPHARM treats 3D object, via simple stereographic projection, as a surface of 4D hypersphere with extremely large radius, hence avoiding the computationally demanding flattening process. HyperSPHARM is shown to achieve a better reconstruction with only 5 basis compared to SPHARM that requires more than 441. PMID:24505716

Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation.

PubMed

Sels, Dries; Brosens, Fons

2013-10-01

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.

Comparison of the hydrological excitation functions HAM of polar motion for the period 1980.0-2007.0

NASA Astrophysics Data System (ADS)

Nastula, J.; Pasnicka, M.; Kolaczek, B.

2011-10-01

In this study we compared contributions of polar motion excitation determined from hydrological models and harmonic coefficients of the Earth gravity field obtained from Gravity Recovery and Climate Experiment (GRACE). Hydrological excitation function (hydrological angular momentum - HAM) has been estimated from models of global hydrology, based on the observed distribution of surface water, snow, ice and soil moisture. All of them were compared with observed Geodetic Angular Momentum (GAM), excitations of polar motion. The spectra of these excitation functions of polar motion and residual geodetic excitation function G-A-O obtained from GAM by elimination of atmospheric and oceanic excitation functions were computed too. Phasor diagrams of the seasonal components of the polar motion excitation functions of all HAM excitation functions as well as of two GRACE solutions: CSR, CNES were determined and discussed.

Real-Time Monitoring Of Regional Tissue Elasticity During FUS Focused Ultrasound Therapy Using Harmonic Motion Imaging

NASA Astrophysics Data System (ADS)

Maleke, Caroline; Pernot, Mathieu; Konofagou, Elisa

2006-05-01

The feasibility of the Harmonic Motion Imaging (HMI) technique for simultaneous monitoring and generation of focused ultrasound therapy using two separate focused ultrasound transducer elements has previously been shown. In this study, a new HMI technique is described that images tissue displacement induced by a harmonic radiation force induced using a single focused ultrasound element. First, wave propagation simulation models were used to compare the use of a single Amplitude-Modulated (AM) focused beam versus two overlapping focused beams as previously implemented for HMI. Simulation results indicated that, unlike in the two-beam configuration, the AM beam produced a consistent, stable focus for the applied harmonic radiation force. The AM beam thus offered the unique advantage of sustaining the application of the spatially-invariant radiation force. Experiments were then performed on gelatin gel phantoms and tissue in vitro bovine liver. The radiation force was generated by a 4.68 MHz focused transducer using a low-frequency Amplitude-Modulated (AM) RF-signal. RF data were acquired at 7.5 MHz with a PRF of 6.5 kHz and displacements were estimated using a 1D cross-correlation algorithm on successive RF signals. Furthermore, taking advantage of the real-time capability of our method, the change in the elastic properties was monitored during focused ultrasound (FUS) ablation of tissue in vitro bovine liver. Based on the harmonic displacements, their temperature-dependence, and the calculated acoustic radiation force, the change in the relative, regional stiffness could be monitored during heating and ablation, both using the displacement amplitude and the resulting phase shift change of the displacement relative to the radiation force temporal profile. In conclusion, the feasibility of using an AM radiation force for HMI for simultaneous monitoring and treatment during ultrasound therapy was demonstrated in phantoms and tissues in vitro. Further study of this method will include, ex vivo and in vivo, stiffness and temperature.

Ergodicity of a singly-thermostated harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, William Graham; Sprott, Julien Clinton; Hoover, Carol Griswold

2016-03-01

Although Nosé's thermostated mechanics is formally consistent with Gibbs' canonical ensemble, the thermostated Nosé-Hoover (harmonic) oscillator, with its mean kinetic temperature controlled, is far from ergodic. Much of its phase space is occupied by regular conservative tori. Oscillator ergodicity has previously been achieved by controlling two oscillator moments with two thermostat variables. Here we use computerized searches in conjunction with visualization to find singly-thermostated motion equations for the oscillator which are consistent with Gibbs' canonical distribution. Such models are the simplest able to bridge the gap between Gibbs' statistical ensembles and Newtonian single-particle dynamics.

Exact Harmonic Metric for a Uniformly Moving Schwarzschild Black Hole

NASA Astrophysics Data System (ADS)

He, Guan-Sheng; Lin, Wen-Bin

2014-02-01

The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.

Type III bursts in interplanetary space - Fundamental or harmonic?

NASA Technical Reports Server (NTRS)

Dulk, G. A.; Steinberg, J. L.; Hoang, S.

1984-01-01

ISEE-3 spacecraft observation of 120 relatively simple, isolated bursts in the 30-1980 kHz range are the basis of the present study of Type III bursts in the solar wind. Several characteristics are identified for many of these bursts which imply that the mode of emission changes from predominantly fundamental plasma radiation during the rise phase to predominantly second harmonic during decay. The fundamental emission begins in time coincidence with the start of Langmuir waves, confirming the conventional belief in these waves' causation of Type III bursts. Attention is given to the characteristics of fundamental components, by comparison to harmonics, at km-wavelengths.

Scaling Law of High Harmonic Generation in the Framework of Photon Channels

NASA Astrophysics Data System (ADS)

Li, Liang; Lan, Pengfei; He, Lixin; Zhu, Xiaosong; Chen, Jing; Lu, Peixiang

2018-06-01

A photon channel perspective on high harmonic generation (HHG) is proposed by quantizing both the driving laser and high harmonics. It is shown that the HHG yield can be expressed as a sum of the contribution of all the photon channels. From this perspective, the contribution of a specific photon channel follows a simple scaling law and the competition between the channels is well interpreted. Our prediction is shown to be in good agreement with the simulations by solving the time-dependent Schrödinger equation. It also can explain well the experimental results of the HHG in the noncollinear two-color field and bicicular laser field.

Scaling Law of High Harmonic Generation in the Framework of Photon Channels.

PubMed

Li, Liang; Lan, Pengfei; He, Lixin; Zhu, Xiaosong; Chen, Jing; Lu, Peixiang

2018-06-01

A photon channel perspective on high harmonic generation (HHG) is proposed by quantizing both the driving laser and high harmonics. It is shown that the HHG yield can be expressed as a sum of the contribution of all the photon channels. From this perspective, the contribution of a specific photon channel follows a simple scaling law and the competition between the channels is well interpreted. Our prediction is shown to be in good agreement with the simulations by solving the time-dependent Schrödinger equation. It also can explain well the experimental results of the HHG in the noncollinear two-color field and bicicular laser field.

Simulation study of amplitude-modulated (AM) harmonic motion imaging (HMI) for stiffness contrast quantification with experimental validation.

PubMed

Maleke, Caroline; Luo, Jianwen; Gamarnik, Viktor; Lu, Xin L; Konofagou, Elisa E

2010-07-01

The objective of this study is to show that Harmonic Motion Imaging (HMI) can be used as a reliable tumor-mapping technique based on the tumor's distinct stiffness at the early onset of disease. HMI is a radiation-force-based imaging method that generates a localized vibration deep inside the tissue to estimate the relative tissue stiffness based on the resulting displacement amplitude. In this paper, a finite-element model (FEM) study is presented, followed by an experimental validation in tissue-mimicking polyacrylamide gels and excised human breast tumors ex vivo. This study compares the resulting tissue motion in simulations and experiments at four different gel stiffnesses and three distinct spherical inclusion diameters. The elastic moduli of the gels were separately measured using mechanical testing. Identical transducer parameters were used in both the FEM and experimental studies, i.e., a 4.5-MHz single-element focused ultrasound (FUS) and a 7.5-MHz diagnostic (pulse-echo) transducer. In the simulation, an acoustic pressure field was used as the input stimulus to generate a localized vibration inside the target. Radiofrequency (rf) signals were then simulated using a 2D convolution model. A one-dimensional cross-correlation technique was performed on the simulated and experimental rf signals to estimate the axial displacement resulting from the harmonic radiation force. In order to measure the reliability of the displacement profiles in estimating the tissue stiffness distribution, the contrast-transfer efficiency (CTE) was calculated. For tumor mapping ex vivo, a harmonic radiation force was applied using a 2D raster-scan technique. The 2D HMI images of the breast tumor ex vivo could detect a malignant tumor (20 x 10 mm2) surrounded by glandular and fat tissues. The FEM and experimental results from both gels and breast tumors ex vivo demonstrated that HMI was capable of detecting and mapping the tumor or stiff inclusion with various diameters or stiffnesses. HMI may thus constitute a promising technique in tumor detection (>3 mm in diameter) and mapping based on its distinct stiffness.

Instability of surface electron cyclotron TM-modes influenced by non-monochromatic alternating electric field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Girka, I. O., E-mail: igorgirka@karazin.ua; Girka, V. O.; Sydora, R. D.

2016-06-15

The influence of non-monochromaticity of an external alternating electric field on excitation of TM eigenmodes at harmonics of the electron cyclotron frequency is considered here. These TM-modes propagate along the plasma interface in a metal waveguide. An external static constant magnetic field is oriented perpendicularly to the plasma interface. The problem is solved theoretically using the kinetic Vlasov-Boltzmann equation for description of plasma particles motion and the Maxwell equations for description of the electromagnetic mode fields. The external alternating electric field is supposed to be a superposition of two waves, whose amplitudes are different and their frequencies correlate as 2:1.more » An infinite set of equations for electric field harmonics of these modes is derived with the aid of nonlinear boundary conditions. This set is solved using the wave packet approach consisting of the main harmonic frequency and two nearest satellite temporal harmonics. Analytical studies of the obtained set of equations allow one to find two different regimes of parametric instability, namely, enhancement and suppression of the instability. Numerical analysis of the instability is carried out for the three first electron cyclotron harmonics.« less

Mapping quadrupole collectivity in the Cd isotopes: The breakdown of harmonic vibrational motion

NASA Astrophysics Data System (ADS)

Garrett, P. E.; Green, K. L.; Bangay, J.; Varela, A. Diaz; Sumithrarachchi, C. S.; Austin, R. A. E.; Ball, G. C.; Bandyopadhyay, D. S.; Bianco, L.; Colosimo, S.; Cross, D. S.; Demand, G. A.; Finlay, P.; Garnsworthy, A. B.; Grinyer, G. F.; Hackman, G.; Kulp, W. D.; Leach, K. G.; Morton, A. C.; Orce, J. N.; Pearson, C. J.; Phillips, A. A.; Schumaker, M. A.; Svensson, C. E.; Triambak, S.; Wong, J.; Wood, J. L.; Yates, S. W.

2011-10-01

The stable Cd isotopes have long been used as paradigms for spherical vibrational motion. Extensive investigations with in-beam γ spectroscopy have resulted in very-well-established level schemes, including many lifetimes or lifetime limits. A programme has been initiated to complement these studies with very-high-statistics β decay using the 8π spectrometer at the TRIUMF radioactive beam facility. The decays of 112In and 112Ag have been studied with an emphasis on the observation of, or the placement of stringent limits on, low-energy branches between potential multi-phonon levels. A lack of suitable 0+ or 2+ three-phonon candidates has been revealed. Further, the sum of the B(E2) strength from spin 0+ and 2+ states up to 3 MeV in excitation energy to the assigned two-phonon levels falls far short of the harmonic-vibrational expectations. This lack of strength points to the failing of collective models based on vibrational phonon structures.

Experimental observation of attosecond control over relativistic electron bunches with two-colour fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yeung, M.; Rykovanov, S.; Bierbach, J.

2016-12-05

Energy coupling during relativistically intense laser–matter interactions is encoded in the attosecond motion of strongly driven electrons at the pre-formed plasma–vacuum boundary. Studying and controlling this motion can reveal details about the microscopic processes that govern a vast array of light–matter interaction phenomena, including those at the forefront of extreme laser–plasma science such as laser-driven ion acceleration, bright attosecond pulse generation and efficient energy coupling for the generation and study of warm dense matter. Here in this paper, we experimentally demonstrate that by precisely adjusting the relative phase of an additional laser beam operating at the second harmonic of themore » driving laser it is possible to control the trajectories of relativistic electron bunches formed during the interaction with a solid target at the attosecond scale. Finally, we observe significant enhancements in the resulting high-harmonic yield, suggesting potential applications for sources of ultra-bright, extreme ultraviolet attosecond radiation to be used in atomic and molecular pump–probe experiments« less

Electrode surface profile and the performance of condenser microphones.

PubMed

Fletcher, N H; Thwaites, S

2002-12-01

Condenser microphones of all types are traditionally made with a planar electrode parallel to an electrically conducting diaphragm, additional diaphragm stiffness at acoustic frequencies being provided by the air enclosed in a cavity behind the diaphragm. In all designs, the motion of the diaphragm in response to an acoustic signal is greatest near its center and reduces to zero at its edges. Analysis shows that this construction leads to less than optimal sensitivity and to harmonic distortion at high sound levels when the diaphragm motion is appreciable compared with its spacing from the electrode. Microphones of this design are also subject to acoustic collapse of the diaphragm under the influence of pressure pulses such as might be produced by wind. A new design is proposed in which the electrode is shaped as a shallow dish, and it is shown that this construction increases the sensitivity by about 4.5 dB, and also completely eliminates harmonic distortion originating in the cartridge.

Quantum Brownian motion and its conflict with the second law

NASA Astrophysics Data System (ADS)

Nieuwenhuizen, Theo M.; Allahverdyan, Armen E.

2002-11-01

The Brownian motion of a harmonically bound quantum particle and coupled to a harmonic quantum bath is exactly solvable. At low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. This happens when a cloud of bath modes around the particle is formed. Equilibrium thermodynamics for particle plus bath together, does not imply standard thermodynamics for the particle itself at low T. Various formulations of the second law are then invalid. First, the Clausius inequality can be violated. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the rate of entropy production is partly negative. Third, for non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobile of the second kind, having several work extraction cycles, enter the realm of condensed matter physics.

Non-Linear Steady State Vibrations of Beams Excited by Vortex Shedding

NASA Astrophysics Data System (ADS)

LEWANDOWSKI, R.

2002-05-01

In this paper the non-linear vibrations of beams excited by vortex-shedding are considered. In particular, the steady state responses of beams near the synchronization region are taken into account. The main aerodynamic properties of wind are described by using the semi-empirical model proposed by Hartlen and Currie. The finite element method and the strip method are used to formulate the equation of motion of the system treated. The harmonic balance method is adopted to derive the amplitude equations. These equations are solved with the help of the continuation method which is very convenient to perform the parametric studies of the problem and to determine the response curve in the synchronization region. Moreover, the equations of motion are also integrated using the Newmark method. The results of calculations of several example problems are also shown to confirm the efficiency and accuracy of the presented method. The results obtained by the harmonic balance method and by the Newmark methods are in good agreement with each other.

Aeroacoustic Codes for Rotor Harmonic and BVI Noise. CAMRAD.Mod1/HIRES: Methodology and Users' Manual

NASA Technical Reports Server (NTRS)

Boyd, D. Douglas, Jr.; Brooks, Thomas F.; Burley, Casey L.; Jolly, J. Ralph, Jr.

1998-01-01

This document details the methodology and use of the CAMRAD.Mod1/HIRES codes, which were developed at NASA Langley Research Center for the prediction of helicopter harmonic and Blade-Vortex Interaction (BVI) noise. CANMAD.Mod1 is a substantially modified version of the performance/trim/wake code CANMAD. High resolution blade loading is determined in post-processing by HIRES and an associated indicial aerodynamics code. Extensive capabilities of importance to noise prediction accuracy are documented, including a new multi-core tip vortex roll-up wake model, higher harmonic and individual blade control, tunnel and fuselage correction input, diagnostic blade motion input, and interfaces for acoustic and CFD aerodynamics codes. Modifications and new code capabilities are documented with examples. A users' job preparation guide and listings of variables and namelists are given.

Electron path control of high-order harmonic generation by a spatially inhomogeneous field

NASA Astrophysics Data System (ADS)

Mohebbi, Masoud; Nazarpoor Malaei, Sakineh

2016-04-01

We theoretically investigate the control of high-order harmonics cut-off and as-pulse generation by a chirped laser field using a metallic bow tie-shaped nanostructure. The numerical results show that the trajectories of the electron wave packet are strongly modified, the short quantum path is enhanced, the long quantum path is suppressed and the low modulated spectrum of the harmonics can be remarkably extended. Our calculated results also show that, by confining electron motion, a broadband supercontinuum with the width of 1670 eV can be produced which directly generates an isolated 34 as-pulse without phase compensation. To explore the underlying mechanism responsible for the cut-off extension and the quantum path selection, we perform time-frequency analysis and a classical simulation based on the three-step model.

Rotationally invariant clustering of diffusion MRI data using spherical harmonics

NASA Astrophysics Data System (ADS)

Liptrot, Matthew; Lauze, François

2016-03-01

We present a simple approach to the voxelwise classification of brain tissue acquired with diffusion weighted MRI (DWI). The approach leverages the power of spherical harmonics to summarise the diffusion information, sampled at many points over a sphere, using only a handful of coefficients. We use simple features that are invariant to the rotation of the highly orientational diffusion data. This provides a way to directly classify voxels whose diffusion characteristics are similar yet whose primary diffusion orientations differ. Subsequent application of machine-learning to the spherical harmonic coefficients therefore may permit classification of DWI voxels according to their inferred underlying fibre properties, whilst ignoring the specifics of orientation. After smoothing apparent diffusion coefficients volumes, we apply a spherical harmonic transform, which models the multi-directional diffusion data as a collection of spherical basis functions. We use the derived coefficients as voxelwise feature vectors for classification. Using a simple Gaussian mixture model, we examined the classification performance for a range of sub-classes (3-20). The results were compared against existing alternatives for tissue classification e.g. fractional anisotropy (FA) or the standard model used by Camino.1 The approach was implemented on both two publicly-available datasets: an ex-vivo pig brain and in-vivo human brain from the Human Connectome Project (HCP). We have demonstrated how a robust classification of DWI data can be performed without the need for a model reconstruction step. This avoids the potential confounds and uncertainty that such models may impose, and has the benefit of being computable directly from the DWI volumes. As such, the method could prove useful in subsequent pre-processing stages, such as model fitting, where it could inform about individual voxel complexities and improve model parameter choice.

Notes on Experiments.

ERIC Educational Resources Information Center

Physics Education, 1984

1984-01-01

Describes (1) use of VELA (a stand-alone programmable instrument); (2) forced harmonic motion of galvanometers; (3) holographic interferometry and measurement of small angular displacement; and (4) an analogy useful on teaching capacitors at A-level. Also describes a comparison of fuses and circuit breakers using a microcomputer as a storage…

Properties of AT Quartz Resonators on Wedgy Plates,

DTIC Science & Technology

assuming a small linear thickness variation ( wedginess ) across the plate. The model predicts that the standing waves corresponding to the different an... wedginess that will lower order an harmonics. The observed consequence of this behavior is that the motional capacitance of the lowest mode (the desired

A simple model for strong ground motions and response spectra

USGS Publications Warehouse

Safak, Erdal; Mueller, Charles; Boatwright, John

1988-01-01

A simple model for the description of strong ground motions is introduced. The model shows that response spectra can be estimated by using only four parameters of the ground motion, the RMS acceleration, effective duration and two corner frequencies that characterize the effective frequency band of the motion. The model is windowed band-limited white noise, and is developed by studying the properties of two functions, cumulative squared acceleration in the time domain, and cumulative squared amplitude spectrum in the frequency domain. Applying the methods of random vibration theory, the model leads to a simple analytical expression for the response spectra. The accuracy of the model is checked by using the ground motion recordings from the aftershock sequences of two different earthquakes and simulated accelerograms. The results show that the model gives a satisfactory estimate of the response spectra.

Saturn Ring Mass and Zonal Gravitational Harmonics Estimate at the End of the Cassini "Grand Finale"

NASA Astrophysics Data System (ADS)

Brozovic, M.; Jacobson, R. A.; Roth, D. C.

2015-12-01

"Solstice" mission is the 7-year extension of the Cassini-Huygens spacecraft exploration of the Saturn system that will culminate with the "Grand Finale". Beginning in mid-2017, the spacecraft is scheduled to execute 22 orbits that have their periapses between the innermost D-ring and the upper layers of Saturn's atmosphere. These orbits will be perturbed by the gravitational field of Saturn as well as by the rings. We present an analysis of simulated "Grand Finale" radiometric data, and we investigate their sensitivity to the ring mass and higher zonal gravitational harmonics of the planet. We model the data quantity with respect to the available coverage of the tracking stations on Earth, and we account for the times when the spacecraft is occulted either by Saturn or the rings. We also use different data weights to simulate changes in the data quality. The dynamical model of the spacecraft motion includes both gravitational and non-gravitational forces, such as the daily momentum management due to Reaction Wheel Assembly and radioisotope thermo-electric generator accelerations. We solve the equations of motion and use a weighted-least squares fit to obtain spacecraft's state vector, mass(es) of the ring or the individual rings, zonal harmonics, and non-gravitational accelerations. We also investigate some a-priori values of the A- and B-ring masses from Tiscareno et al. (2007) and Hedman et al. (2015) analyses. The preliminary results suggest that the "Grand Finale" orbits should remain sensitive to the ring mass even for GMring<2 km3/s2 and that they will also provide high accuracy estimates of the zonal harmonics J8, J10, and J12.

Strong second harmonic generation in two-dimensional ferroelectric IV-monochalcogenides

NASA Astrophysics Data System (ADS)

Panday, Suman Raj; Fregoso, Benjamin M.

2017-11-01

The two-dimensional ferroelectrics GeS, GeSe, SnS and SnSe are expected to have large spontaneous in-plane electric polarization and enhanced shift-current response. Using density functional methods, we show that these materials also exhibit the largest effective second harmonic generation reported so far. It can reach magnitudes up to 10~nm~V-1 which is about an order of magnitude larger than that of prototypical GaAs. To rationalize this result we model the optical response with a simple one-dimensional two-band model along the spontaneous polarization direction. Within this model the second-harmonic generation tensor is proportional to the shift-current response tensor. The large shift current and second harmonic responses of GeS, GeSe, SnS and SnSe make them promising non-linear materials for optoelectronic applications.

The Impact of Complex Forcing on the Viscous Torsional Vibration Damper's Work in the Crankshaft of the Rotating Combustion Engine

NASA Astrophysics Data System (ADS)

Jagiełowicz-Ryznar, C.

2016-12-01

The numerical calculations results of torsional vibration of the multi-cylinder crankshaft in the serial combustion engine (MC), including a viscous damper (VD), at complex forcing, were shown. In fact, in the MC case the crankshaft rotation forcings spectrum is the sum of harmonic forcing whose amplitude can be compared with the amplitude of the 1st harmonic. A significant impact, in the engine operational velocity, on the vibration damping process of MC, may be the amplitude of the 2nd harmonic of a forcing moment. The calculations results of MC vibration, depending on the amplitude of the 2nd harmonic of the forcing moment, for the first form of the torsional vibration, were shown. Higher forms of torsional vibrations have no practical significance. The calculations assume the optimum damping coefficient VD, when the simple harmonic forcing is equal to the base critical velocity of the MC crankshaft.

Wide-range narrowband multilayer mirror for selecting a single-order harmonic in the photon energy range of 40-70 eV.

PubMed

Hatayama, Masatoshi; Ichimaru, Satoshi; Ohcni, Tadayuki; Takahashi, Eiji J; Midorikawa, Katsumi; Oku, Satoshi

2016-06-27

An experimental demonstration of a wide-range narrowband multilayer mirror for selecting a single-order high-harmonic (HH) beam from multiple-order harmonics in the photon energy range between 40 eV and 70 eV was carried out. This extreme ultraviolet (XUV) mirror, based on a pair of Zr and Al_0.7Si_0.3 multilayers, has a reflectivity of 20-35% and contrast of more than 7 with respect to neighboring HHs at angles of incidence from 10 to 56.9 degrees, assuming HHs pumped at 1.55 eV. Thus, specific single-order harmonic beams can be arbitrarily selected from multiple-order harmonics in this photo energy range. In addition, the dispersion for input pulses of the order of 1 fs is negligible. This simple-to-align optical component is useful for the many various applications in physics, chemistry and biology that use ultrafast monochromatic HH beams.

Compensation of high order harmonic long quantum-path attosecond chirp

NASA Astrophysics Data System (ADS)

Guichard, R.; Caillat, J.; Lévêque, C.; Risoud, F.; Maquet, A.; Taïeb, R.; Zaïr, A.

2017-12-01

We propose a method to compensate for the extreme ultra violet (XUV) attosecond chirp associated with the long quantum-path in the high harmonic generation process. Our method employs an isolated attosecond pulse (IAP) issued from the short trajectory contribution in a primary target to assist the infrared driving field to produce high harmonics from the long trajectory in a secondary target. In our simulations based on the resolution of the time-dependent Schrödinger equation, the resulting high harmornics present a clear phase compensation of the long quantum-path contribution, near to Fourier transform limited attosecond XUV pulse. Employing time-frequency analysis of the high harmonic dipole, we found that the compensation is not a simple far-field photonic interference between the IAP and the long-path harmonic emission, but a coherent phase transfer from the weak IAP to the long quantum-path electronic wavepacket. Our approach opens the route to utilizing the long quantum-path for the production and applications of attosecond pulses.

Tomographic reconstruction of circularly polarized high-harmonic fields: 3D attosecond metrology

PubMed Central

Chen, Cong; Tao, Zhensheng; Hernández-García, Carlos; Matyba, Piotr; Carr, Adra; Knut, Ronny; Kfir, Ofer; Zusin, Dimitry; Gentry, Christian; Grychtol, Patrik; Cohen, Oren; Plaja, Luis; Becker, Andreas; Jaron-Becker, Agnieszka; Kapteyn, Henry; Murnane, Margaret

2016-01-01

Bright, circularly polarized, extreme ultraviolet (EUV) and soft x-ray high-harmonic beams can now be produced using counter-rotating circularly polarized driving laser fields. Although the resulting circularly polarized harmonics consist of relatively simple pairs of peaks in the spectral domain, in the time domain, the field is predicted to emerge as a complex series of rotating linearly polarized bursts, varying rapidly in amplitude, frequency, and polarization. We extend attosecond metrology techniques to circularly polarized light by simultaneously irradiating a copper surface with circularly polarized high-harmonic and linearly polarized infrared laser fields. The resulting temporal modulation of the photoelectron spectra carries essential phase information about the EUV field. Utilizing the polarization selectivity of the solid surface and by rotating the circularly polarized EUV field in space, we fully retrieve the amplitude and phase of the circularly polarized harmonics, allowing us to reconstruct one of the most complex coherent light fields produced to date. PMID:26989782

The dynamics and control of large flexible space structures. Part B: Development of continuum model and computer simulation

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Kumar, V. K.; James, P. K.

1978-01-01

The equations of motion of an arbitrary flexible body in orbit were derived. The model includes the effects of gravity with all its higher harmonics. As a specific example, the motion of a long, slender, uniform beam in circular orbit was modelled. The example considers both the inplane and three dimensional motion of the beam in orbit. In the case of planar motion with only flexible vibrations, the pitch motion is not influenced by the elastic motion of the beam. For large values of the square of the ratio of the structural modal frequency to the orbital angular rate the elastic motion was decoupled from the pitch motion. However, for small values of the ratio and small amplitude pitch motion, the elastic motion was governed by a Hill's 3 term equation. Numerical simulation of the equation indicates the possibilities of instability for very low values of the square of the ratio of the modal frequency to the orbit angular rate. Also numerical simulations of the first order nonlinear equations of motion for a long flexible beam in orbit were performed. The effect of varying the initial conditions and the number of modes was demonstrated.

Ferroelectric Zinc Oxide Nanowire Embedded Flexible Sensor for Motion and Temperature Sensing.

PubMed

Shin, Sung-Ho; Park, Dae Hoon; Jung, Joo-Yun; Lee, Min Hyung; Nah, Junghyo

2017-03-22

We report a simple method to realize multifunctional flexible motion sensor using ferroelectric lithium-doped ZnO-PDMS. The ferroelectric layer enables piezoelectric dynamic sensing and provides additional motion information to more precisely discriminate different motions. The PEDOT:PSS-functionalized AgNWs, working as electrode layers for the piezoelectric sensing layer, resistively detect a change of both movement or temperature. Thus, through the optimal integration of both elements, the sensing limit, accuracy, and functionality can be further expanded. The method introduced here is a simple and effective route to realize a high-performance flexible motion sensor with integrated multifunctionalities.

Single-crystal diffuse scattering studies on polymorphs of molecular crystals. I. The room-temperature polymorphs of the drug benzocaine.

PubMed

Chan, E J; Welberry, T R; Goossens, D J; Heerdegen, A P; Beasley, A G; Chupas, P J

2009-06-01

The drug benzocaine (ethyl 4-aminobenzoate), commonly used as a local anaesthetic, is a bimorphic solid at room temperature. Form (I) is monoclinic P2(1)/c, while the metastable form (II) is orthorhombic P2(1)2(1)2(1). Three-dimensional diffuse X-ray scattering data have been collected for the two forms on the 11-ID-B beamline at the Advanced Photon Source (APS). Both forms show strong and highly structured diffuse scattering. The data have been interpreted and analysed using Monte Carlo (MC) modelling on the basis that the scattering is purely thermal in origin and indicates the presence of highly correlated molecular motions. In both forms (I) and (II) broad diffuse streaks are observed in the 0kl section which indicate strong longitudinal displacement correlations between molecules in the 031 directions, extending over distances of up to 50 A. Streaks extending between Bragg peaks in the hk0 section normal to [100] correspond to correlated motions of chains of molecules extending along a that are linked by N-H...O=C hydrogen bonds and which occur together as coplanar ribbon pairs. The main difference between the two forms is in the dynamical behaviour of the ribbon pairs and in particular how they are able to slide relative to each other. While for form (I) a model involving harmonic springs is able to describe the motion satisfactorily, as simple excursions away from the average structure, there is evidence in form (II) of anharmonic effects that are precursors of a phase transition to a new low-temperature phase, form (III), that was subsequently found.

A novel sandwich-type traveling wave piezoelectric tracked mobile system.

PubMed

Wang, Liang; Shu, Chengyou; Zhang, Quan; Jin, Jiamei

2017-03-01

In this paper, a novel sandwich-type traveling wave piezoelectric tracked mobile system was proposed, designed, fabricated and experimentally investigated. The proposed system exhibits the advantages of simple structure, high mechanical integration, lack of electromagnetic interference, and lack of lubrication requirement, and hence shows potential application to robotic rovers for planetary exploration. The tracked mobile system is comprised of a sandwich actuating mechanism and a metal track. The actuating mechanism includes a sandwich piezoelectric transducer and two annular parts symmetrically placed at either end of the transducer, while the metal track is tensioned along the outer surfaces of the annular parts. Traveling waves with the same rotational direction are generated in the two annular parts, producing the microscopic elliptical motions of the surface particles on the annular parts. In this situation, if the pre-load is applied properly, the metal track can be driven by friction force to achieve bidirectional movement. At first, the finite element method was adopted to conduct the modal analysis and harmonic response analysis of the actuating mechanism, and the vibration characteristics were measured to confirm the operating principle. Then the optimal driving frequency of the system prototype, namely 35.1kHz, was measured by frequency sensitivity experiments. At last, the mechanical motion characteristics of the prototype were investigated experimentally. The results show that the average motion speeds of the prototype in dual directions were as 72mm/s and 61.5mm/s under the excitation voltage of 500V RMS , respectively. The optimal loading weights of the prototype in bi-directions were 0.32kg and 0.24kg with a maximum speed of 59.5mm/s and 61.67mm/s at the driving voltage of 300V RMS , respectively. Copyright © 2016 Elsevier B.V. All rights reserved.

A comparison of Lorentz, planetary gravitational, and satellite gravitational resonances

NASA Technical Reports Server (NTRS)

Hamilton, Douglas P.

1994-01-01

We consider a charged dust grain whose orbital motion is dominated by a planet's point-source gravity, but perturbed by higher-order terms in the planet's gravity field as well as by the Lorentz force arising from an asymmetric planetary magnetic field. Perturbations to Keplerian orbits due to a nonspherical gravity field are expressed in the traditional way: in terms of a disturbing function which can be expanded in a series of spherical harmonics (W. M. Kaula, 1966). In order to calculate the electromagnetic perturbation, we first write the Lorentz force in terms of the orbital elements and then substitute it into Gauss' perturbation equations. We use our result to derive strengths of Lorentz resonances and elucidate their properties. In particular, we compare Lorentz resonances to two types of gravitational resonances: those arising from periodic tugs of a satellite and those due to the attraction of an arbitrarily shaped planet. We find that Lorentz resonances share numerous properties with their gravitational counterparts and show, using simple physical arguments, that several of these patterns are fundamental, applying not only to our expansions, but to all quantities expressed in terms of orbital elements. Some of these patterns have been previously called 'd'Alembert rules' for satellite resonances. Other similarities arise because, to first-order in the perturbing force, the three problems share an integral of the motion. Yet there are also differences; for example, first-order inclination resonances exist for perturbations arising from planetary gravity and from the Lorentz force, but not for those due to an orbiting satellite. Finally, we provide a heuristic treatment of a particle's orbital evolution under the influence of drag and resonant forces. Particles brought into mean-motion resonances experience either trapping or resonant 'jumps,' depending on the direction from which the resonance is approached. We show that this behavior does not depend on the details of the perturbing force but rather is fundamental to all mean-motion resonances.

The lucky image-motion prediction for simple scene observation based soft-sensor technology

NASA Astrophysics Data System (ADS)

Li, Yan; Su, Yun; Hu, Bin

2015-08-01

High resolution is important to earth remote sensors, while the vibration of the platforms of the remote sensors is a major factor restricting high resolution imaging. The image-motion prediction and real-time compensation are key technologies to solve this problem. For the reason that the traditional autocorrelation image algorithm cannot meet the demand for the simple scene image stabilization, this paper proposes to utilize soft-sensor technology in image-motion prediction, and focus on the research of algorithm optimization in imaging image-motion prediction. Simulations results indicate that the improving lucky image-motion stabilization algorithm combining the Back Propagation Network (BP NN) and support vector machine (SVM) is the most suitable for the simple scene image stabilization. The relative error of the image-motion prediction based the soft-sensor technology is below 5%, the training computing speed of the mathematical predication model is as fast as the real-time image stabilization in aerial photography.

Experimenting with Inexpensive Plastic Springs

ERIC Educational Resources Information Center

Perez, Leander; Marques, Adriana; Sánchez, Iván

2014-01-01

Acommon undergraduate laboratory experience is the determination of the elastic constant of a spring, whether studying the elongation under a static load or studying the damped harmonic motion of the spring with a suspended mass. An alternative approach to this laboratory experience has been suggested by Menezes et al., aimed at studying the…

Making chaotic behavior in a damped linear harmonic oscillator

NASA Astrophysics Data System (ADS)

Konishi, Keiji

2001-06-01

The present Letter proposes a simple control method which makes chaotic behavior in a damped linear harmonic oscillator. This method is a modified scheme proposed in paper by Wang and Chen (IEEE CAS-I 47 (2000) 410) which presents an anti-control method for making chaotic behavior in discrete-time linear systems. We provide a systematic procedure to design parameters and sampling period of a feedback controller. Furthermore, we show that our method works well on numerical simulations.

Discrete retardance second harmonic generation ellipsometry.

PubMed

Dehen, Christopher J; Everly, R Michael; Plocinik, Ryan M; Hedderich, Hartmut G; Simpson, Garth J

2007-01-01

A new instrument was constructed to perform discrete retardance nonlinear optical ellipsometry (DR-NOE). The focus of the design was to perform second harmonic generation NOE while maximizing sample and application flexibility and minimizing data acquisition time. The discrete retardance configuration results in relatively simple computational algorithms for performing nonlinear optical ellipsometric analysis. NOE analysis of a disperse red 19 monolayer yielded results that were consistent with previously reported values for the same surface system, but with significantly reduced acquisition times.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pirozhkov, A.S.; Kando, M.; Esirkepov, T.Zh.

We propose a new mechanism of high-order harmonic generation during an interaction of a high-intensity laser pulse with underdense plasma. A tightly focused laser pulse creates a cavity in plasma pushing electrons aside and exciting the wake wave and the bow wave. At the joint of the cavity wall and the bow wave boundary, an annular spike of electron density is formed. This spike surrounds the cavity and moves together with the laser pulse. Collective motion of electrons in the spike driven by the laser field generates high-order harmonics. A strong localization of the electron spike, its robustness to oscillationsmore » imposed by the laser field and, consequently, its ability to produce high-order harmonics is explained by catastrophe theory. The proposed mechanism explains the experimental observations of high-order harmonics with the 9 TW J-KAREN laser (JAEA, Japan) and the 120 TW Astra Gemini laser (CLF RAL, UK) [A. S. Pirozhkov, et al., arXiv:1004.4514 (2010); A. S. Pirozhkov et al, AIP Proceedings, this volume]. The theory is corroborated by high-resolution two-and three-dimensional particle-in-cell simulations.« less

The equations of motion of an artificial satellite in nonsingular variables

NASA Technical Reports Server (NTRS)

Giacaglia, G. E. O.

1975-01-01

The equations of motion of an artificial satellite are given in nonsingular variables. Any term in the geopotential is considered as well as luni-solar perturbations up to an arbitrary power of r/r prime; r prime being the geocentric distance of the disturbing body. Resonances with tesseral harmonics and with the moon or sun are also considered. By neglecting the shadow effect, the disturbing function for solar radiation is also developed in nonsingular variables for the long periodic perturbations. Formulas are developed for implementation of the theory in actual computations.

OSA Proceedings of the Topical Meeting (5th) on Short-Wave Length Coherent Radiation: Generation and Applications Held in Monterey, California on 8-10 April 1991. Volume 11

DTIC Science & Technology

1992-05-22

PIC simulation code to study several of the constraints imposed by plasma phenomena on the propagation of ultrashort high intensity laser pulses in...and radiation spectrum of free electrons in the focus of an ultrashort high intensity laser pulse is solved. Motion and radiation of electrons in a...higher harmonics. These studies are intended as a prelude to experiments with high intensity ultrashort laser pulses . To investigate the motion of

Generation of coherent terahertz radiation in ultrafast laser-gas interactionsa)

NASA Astrophysics Data System (ADS)

Kim, Ki-Yong

2009-05-01

The generation of intense terahertz radiation in ultrafast laser-gas interactions is studied on a basis of transient electron current model. When an ultrashort pulse laser's fundamental and its second harmonic fields are mixed to ionize a gas, a nonvanishing, directional photoelectron current can be produced, which simultaneously emits terahertz radiation in the far field. Here, the generation mechanism is examined with an analytic derivation and numerical simulations, in which tunneling ionization and subsequent electron motion in the combined laser field play a key role. In the simulations, three types of laser-gas interactions are considered: (i) mixing the fundamental and its second harmonic fields, (ii) mixing nonharmonic, two-color fields, and (iii) focusing single-color, few-cycle pulses. In these interactions, terahertz generation and other nonlinear effects driven by the transient current are investigated. In particular, anticorrelation between terahertz and second (or third) harmonic generation is observed and analyzed.

Advanced Gouy phase high harmonics interferometer

NASA Astrophysics Data System (ADS)

Mustary, M. H.; Laban, D. E.; Wood, J. B. O.; Palmer, A. J.; Holdsworth, J.; Litvinyuk, I. V.; Sang, R. T.

2018-05-01

We describe an extreme ultraviolet (XUV) interferometric technique that can resolve ∼100 zeptoseconds (10‑21 s) delay between high harmonic emissions from two successive sources separated spatially along the laser propagation in a single Gaussian beam focus. Several improvements on our earlier work have been implemented in the advanced interferometer. In this paper, we report on the design, characterization and optimization of the advanced Gouy phase interferometer. Temporal coherence for both atomic argon and molecular hydrogen gases has been observed for several harmonic orders. It has been shown that phase shift of XUV pulses mainly originates from the emission time delay due to the Gouy phase in the laser focus and the observed interference is independent of the generating medium. This interferometer can be a useful tool for measuring the relative phase shift between any two gas species and for studying ultrafast dynamics of their electronic and nuclear motion.

Non-unique monopole oscillations of harmonically confined Yukawa systems

NASA Astrophysics Data System (ADS)

Ducatman, Samuel; Henning, Christian; Kaehlert, Hanno; Bonitz, Michael

2008-11-01

Recently it was shown that the Breathing Mode (BM), the mode of uniform radial expansion and contraction, which is well known from harmonically confined Coulomb systems [1], does not exist in general for other systems [2]. As a consequence the monopole oscillation (MO), the radial collective excitation, is not unique, but there are several MO with different frequencies. Within this work we show simulation results of those monopole oscillations of 2-dimensional harmonically confined Yukawa systems, which are known from, e.g., dusty plasma crystals [3,4]. We present the corresponding spectrum of the particle motion, including analysis of the frequencies found, and compare with theoretical investigations.[1] D.H.E. Dubin and J.P. Schiffer, Phys. Rev. E 53, 5249 (1996)[2] C. Henning at al., accepted for publication in Phys. Rev. Lett. (2008)[3] A. Melzer et al., Phys. Rev. Lett. 87, 115002 (2001)[4] M. Bonitz et al., Phys. Rev. Lett. 96, 075001 (2006)

Modeling methods for high-fidelity rotorcraft flight mechanics simulation

NASA Technical Reports Server (NTRS)

Mansur, M. Hossein; Tischler, Mark B.; Chaimovich, Menahem; Rosen, Aviv; Rand, Omri

1992-01-01

The cooperative effort being carried out under the agreements of the United States-Israel Memorandum of Understanding is discussed. Two different models of the AH-64 Apache Helicopter, which may differ in their approach to modeling the main rotor, are presented. The first model, the Blade Element Model for the Apache (BEMAP), was developed at Ames Research Center, and is the only model of the Apache to employ a direct blade element approach to calculating the coupled flap-lag motion of the blades and the rotor force and moment. The second model was developed at the Technion-Israel Institute of Technology and uses an harmonic approach to analyze the rotor. The approach allows two different levels of approximation, ranging from the 'first harmonic' (similar to a tip-path-plane model) to 'complete high harmonics' (comparable to a blade element approach). The development of the two models is outlined and the two are compared using available flight test data.

High-order-harmonic generation from solids: The contributions of the Bloch wave packets moving at the group and phase velocities

NASA Astrophysics Data System (ADS)

Du, Tao-Yuan; Huang, Xiao-Huan; Bian, Xue-Bin

2018-01-01

We study numerically the Bloch electron wave-packet dynamics in periodic potentials to simulate laser-solid interactions. We introduce an alternative perspective in the coordinate space combined with the motion of the Bloch electron wave packets moving at group and phase velocities under the laser fields. This model interprets the origins of the two contributions (intra- and interband transitions) in the high-order harmonic generation (HHG) processes by investigating the local and global behaviours of the wave packets. It also elucidates the underlying physical picture of the HHG intensity enhancement by means of carrier-envelope phase, chirp, and inhomogeneous fields. It provides a deep insight into the emission of high-order harmonics from solids. This model is instructive for experimental measurements and provides an alternative avenue to distinguish mechanisms of the HHG from solids in different laser fields.

Correlation of the earth's rotation rate and the secular change of the geomagnetic field. [power spectra/harmonic analysis

NASA Technical Reports Server (NTRS)

Jin, R. S.

1975-01-01

Power spectral density analysis using Burg's maximum entropy method was applied to the geomagnetic dipole field and its rate of change for the years 1901 to 1969. Both spectra indicate relative maxima at 0.015 cycles/year and its harmonics. These maxima correspond approximately to 66, 33, 22, 17, 13, 11, and 9-year spectral lines. The application of the same analysis techniques to the length-of-day (l.o.d) fluctuations for the period 1865 to 1961 reveal similar spectral characteristics. Although peaks were observed at higher harmonics of the fundamental frequency, the 22-year and 11-year lines are not attributed unambiguously to the solar magnetic cycle and the solar cycle. It is suggested that the similarity in the l.o.d fluctuations and the dipole field variations is related to the motion within the earth's fluid core during the past one hundred years.

Second-harmonic diffraction from holographic volume grating.

PubMed

Nee, Tsu-Wei

2006-10-01

The full polarization property of holographic volume-grating enhanced second-harmonic diffraction (SHD) is investigated theoretically. The nonlinear coefficient is derived from a simple atomic model of the material. By using a simple volume-grating model, the SHD fields and Mueller matrices are first derived. The SHD phase-mismatching effect for a thick sample is analytically investigated. This theory is justified by fitting with published experimental SHD data of thin-film samples. The SHD of an existing polymethyl methacrylate (PMMA) holographic 2-mm-thick volume-grating sample is investigated. This sample has two strong coupling linear diffraction peaks and five SHD peaks. The splitting of SHD peaks is due to the phase-mismatching effect. The detector sensitivity and laser power needed to measure these peak signals are quantitatively estimated.

Unusual Volcanic Tremor Observations in Fogo Island, Cape Verde

NASA Astrophysics Data System (ADS)

Custodio, S. I.; Heleno, S. I.

2004-12-01

Volcanic tremor is a ground motion characterized by well-defined frequencies, and has traditionally been explained by the movement of fluids, namely magma, in conduits or cracks (Chouet, 1996). Thus tremor has the potential to reveal key aspects of volcanic structure and dynamics. Two types of previously unreported seismic signals have been observed in Fogo volcano: a) tide-modulated seismic noise and volcanic tremor, and b) high-frequency low-attenuation harmonic tremor. Amplitude modulation of seismic noise can be detected by simple eye-inspection of raw data in some stations of the VIGIL Network, Fogo Volcano. A more detailed analysis shows that certain frequency bands which we interpret as volcanic tremor, mainly in the range 2.0-3.0Hz, are preferentially modulated. The main frequency of modulation is 1.93 c.p.d., which corresponds to M2, the semi-diurnal lunar harmonic. Air pressure and temperature, which are continuously monitored in Fogo Island, have been analyzed and cannot explain the observed periodicity. Thus we conclude that seismic noise and tremor amplitudes are controlled by tides (Custodio et al., 2003). A relation between the tidal modulation and hydrothermal systems activity is suspected and under investigation. High-frequency (HF) tremor (5-20 Hz) has been recorded simultaneously in several stations in Fogo Island and even in different islands of the Cape Verde archipelago (up to distances of 120 km). In volcanic environments high-frequency motions are normally recorded in a small area close to the source, due to the strong attenuation of seismic waves. Non-volcanic origins for HF tremor were examined: cultural noise, whale vocalizations, ship noise, electronic/processing artifacts and path and/or site effects were all considered and dismissed. Emergent arrivals and strong site effects render source location a difficult task, but the analysis of wave polarizations and amplitude distributions seems to point to an offshore source. Two alternative mechanisms are presently being considered: a) propagation in the ocean sound channel of T-waves generated by resonance in a shallow conduit/chamber, and b) existence of a deep strong source, such as a large fluid-filled crack, capable of producing tremor with a complex pattern that propagates to large distances.

CORRELATED AND ZONAL ERRORS OF GLOBAL ASTROMETRIC MISSIONS: A SPHERICAL HARMONIC SOLUTION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makarov, V. V.; Dorland, B. N.; Gaume, R. A.

We propose a computer-efficient and accurate method of estimating spatially correlated errors in astrometric positions, parallaxes, and proper motions obtained by space- and ground-based astrometry missions. In our method, the simulated observational equations are set up and solved for the coefficients of scalar and vector spherical harmonics representing the output errors rather than for individual objects in the output catalog. Both accidental and systematic correlated errors of astrometric parameters can be accurately estimated. The method is demonstrated on the example of the JMAPS mission, but can be used for other projects in space astrometry, such as SIM or JASMINE.

Correlated and Zonal Errors of Global Astrometric Missions: A Spherical Harmonic Solution

NASA Astrophysics Data System (ADS)

Makarov, V. V.; Dorland, B. N.; Gaume, R. A.; Hennessy, G. S.; Berghea, C. T.; Dudik, R. P.; Schmitt, H. R.

2012-07-01

We propose a computer-efficient and accurate method of estimating spatially correlated errors in astrometric positions, parallaxes, and proper motions obtained by space- and ground-based astrometry missions. In our method, the simulated observational equations are set up and solved for the coefficients of scalar and vector spherical harmonics representing the output errors rather than for individual objects in the output catalog. Both accidental and systematic correlated errors of astrometric parameters can be accurately estimated. The method is demonstrated on the example of the JMAPS mission, but can be used for other projects in space astrometry, such as SIM or JASMINE.

Propagation of relativistic surface harmonics radiation in free space

NASA Astrophysics Data System (ADS)

an der Brügge, Daniel; Pukhov, Alexander

2007-09-01

Relativistic high-harmonics generation from overdense plasma surfaces is studied using three-dimensional particle-in-cell simulations. It is shown that the simple vacuum propagation in the real three-dimensional geometry strongly affects the harmonics spectrum on the optical axis. It may even lead to the formation of attosecond pulses without any special optical filters. To make good use of these effects it is necessary to shape either the laser pulse focal spot, or the surface material in such a way that the S-number of the interaction [see Gordienko and Pukhov, Phys. Plasmas 12, 043109 (2005)] is preserved over the largest possible area. The three-dimensional simulations are carefully compared with the one-dimensional ones. It is shown that the one-dimensional models work well even in cases where the laser is focused to a quite small spot on the harmonics generating surface (σ≈λ).

Near-threshold harmonics from a femtosecond enhancement cavity-based EUV source: effects of multiple quantum pathways on spatial profile and yield.

PubMed

Hammond, T J; Mills, Arthur K; Jones, David J

2011-12-05

We investigate the photon flux and far-field spatial profiles for near-threshold harmonics produced with a 66 MHz femtosecond enhancement cavity-based EUV source operating in the tight-focus regime. The effects of multiple quantum pathways in the far-field spatial profile and harmonic yield show a strong dependence on gas jet dynamics, particularly nozzle diameter and position. This simple system, consisting of only a 700 mW Ti:Sapphire oscillator and an enhancement cavity produces harmonics up to 20 eV with an estimated 30-100 μW of power (intracavity) and > 1μW (measured) of power spectrally-resolved and out-coupled from the cavity. While this power is already suitable for applications, a quantum mechanical model of the system indicates substantial improvements should be possible with technical upgrades.

The response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric resonance

NASA Astrophysics Data System (ADS)

Nayfeh, A. H.

1983-09-01

An analysis is presented of the response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric excitation in the presence of an internal resonance of the combination type ω3 ≈ ω2 + ω1, where the ωn are the linear natural frequencies of the systems. In the case of a fundamental resonance of the third mode (i.e., Ω ≈ω 3, where Ω is the frequency of the excitation), one can identify two critical values ζ 1 and ζ 2, where ζ 2 ⩾ ζ 1, of the amplitude F of the excitation. The value F = ζ2 corresponds to the transition from stable to unstable solutions. When F < ζ1, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but the non-linearity limits the motion to a finite amplitude steady state. The amplitude of the third mode, which is directly excited, is independent of F, whereas the amplitudes of the first and second modes, which are indirectly excited through the internal resonance, are functions of F. When ζ1 ⩽ F ⩽ ζ2, the motion decays or achieves a finite amplitude steady state depending on the initial conditions according to the non-linear theory, whereas it decays to zero according to the linear theory. This is an example of subcritical instability. In the case of a fundamental resonance of either the first or second mode, the trivial response is the only possible steady state. When F ⩽ ζ2, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but it is aperiodic according to the non-linear theory. Experiments are being planned to check these theoretical results.

Nonlinear gyrotropic motion of skyrmion in a magnetic nanodisk

NASA Astrophysics Data System (ADS)

Chen, Yi-fu; Li, Zhi-xiong; Zhou, Zhen-wei; Xia, Qing-lin; Nie, Yao-zhuang; Guo, Guang-hua

2018-07-01

We study the nonlinear gyrotropic motion of a magnetic skyrmion in a nanodisk by means of micromagnetic simulations. The skyrmion is driven by a linearly polarized harmonic field with the frequency of counterclockwise gyrotropic mode. It is found that the motion of the skyrmion displays different patterns with increasing field amplitude. In the linear regime of weak driving field, the skyrmion performs a single counterclockwise gyrotropic motion. The guiding center of the skyrmion moves along a helical line from the centre of the nanodisk to a stable circular orbit. The stable orbital radius increases linearly with the field amplitude. When the driving field is larger than a critical value, the skyrmion exhibits complex nonlinear motion. With the advance of time, the motion trajectory of the skyrmion goes through a series of evolution process, from a single circular motion to a bird nest-like and a flower-like trajectory and finally, to a gear-like steady-state motion. The frequency spectra show that except the counterclockwise gyrotropic mode, the clockwise gyrotropic mode is also nonlinearly excited and its amplitude increases with time. The complex motion trajectory of the skyrmion is the result of superposition of the two gyrotropic motions with changing amplitude. Both the linear and nonlinear gyrotropic motions of the skyrmion can be well described by a generalized Thiele's equation of motion.

Wiggler magnetic field assisted third harmonic generation in expanding clusters

NASA Astrophysics Data System (ADS)

Vij, Shivani

2018-04-01

A simple theoretical model is constructed to study the wiggler magnetic field assisted third harmonic generation of intense short pulse laser in a cluster in its expanding phase. The ponderomotive force of laser causes density perturbations in cluster electron density which couples with wiggler magnetic field to produce a nonlinear current that generates transverse third harmonic. An intense short pulse laser propagating through a gas embedded with atomic clusters, converts it into hot plasma balls via tunnel ionization. Initially, the electron plasma frequency inside the clusters ω pe > \\sqrt{3}{ω }1 (with ω 1 being the frequency of the laser). As the cluster expands under Coulomb force and hydrodynamic pressure, ω pe decreases to \\sqrt{3}{ω }1. At this time, there is resonant enhancement in the efficiency of the third harmonic generation. The efficiency of third harmonic generation is enhanced due to cluster plasmon resonance and by phase matching due to wiggler magnetic field. The effect of cluster size on the expansion rate is studied to observe that the clusters of different radii would expand differently. The impact of laser intensity and wiggler magnetic field on the efficiency of third harmonic generation is also explored.

Difference of Horizontal-to-Vertical (H/V) Spectral Ratios of Microtremors and Earthquake Motions: Theory and Observation

NASA Astrophysics Data System (ADS)

Kawase, H.; Nagashima, F.; Matsushima, S.; Sanchez-Sesma, F. J.

2013-05-01

Horizontal-to-vertical spectral ratios (HVRs) of microtremors have been traditionally interpreted theoretically as representing the Rayleigh wave ellipticity or just utilized a convenient tool to extract predominant periods of ground. However, based on the diffuse field theory (Sánchez-Sesma et al., 2011) the microtremor H/V spectral ratios (MHVRs) correspond to the square root of the ratio of the imaginary part of horizontal displacement for a horizontally applied unit harmonic load and the imaginary part of vertical displacement for a vertically applied unit load. The same diffuse field concept leads us to derive a simple formula for earthquake HVRs (EHVRs), that is, the ratio of the horizontal motion on the surface for a vertical incidence of S wave divided by the vertical motion on the surface for a vertical incidence of P wave with a fixed coefficient (Kawase et al., 2011). The difference for EHVRs comes from the fact that primary contribution of earthquake motions would be of plane body waves. Traditionally EHVRs are interpreted as the responses of inclined SV wave incidence only for their S wave portions. Without these compact theoretical solutions, EHVRs and MHVRs are either considered to be very similar/equivalent, or totally different in the previous studies. With these theoretical solutions we need to re-focus our attention on the difference of HVRs. Thus we have compared here HVRs at several dozens of strong motion stations in Japan. When we compared observed HVRs we found that EHVRs tend to be higher in general than the MHVRs, especially around their peaks. As previously reported, their general shapes share the common features. Especially their fundamental peak and trough frequencies show quite a good match to each other. However, peaks in EHVRs in the higher frequency range would not show up in MHVRs. When we calculated theoretical HVRs separately at these target sites, their basic characteristics correspond to these observed differences. At this stage of research we found that the underground structures that are optimized for EHVRs would not explain perfectly MHVRs. This strongly suggests that we need to optimize underground structures to explain both EHVRs and MHVRs at the same time.

Motional studies of one and two laser-cooled trapped ions for electric-field sensing applications

NASA Astrophysics Data System (ADS)

Domínguez, F.; Gutiérrez, M. J.; Arrazola, I.; Berrocal, J.; Cornejo, J. M.; Del Pozo, J. J.; Rica, R. A.; Schmidt, S.; Solano, E.; Rodríguez, D.

2018-03-01

We have studied the dynamics of one and two laser-cooled trapped ?Ca? ions by applying electric fields of different nature along the axial direction of the trap, namely, driving the motion with a harmonic dipolar field, or with white noise. These two types of driving induce distinct motional states of the axial modes: a coherent oscillation with the dipolar field, or an enhanced Brownian motion due to an additional contribution to the heating rate from the electric noise. In both scenarios, the sensitivity of an isolated ion and a laser-cooled two-ion crystal has been evaluated and compared. The analysis and understanding of this dynamics is important towards the implementation of a novel Penning trap mass-spectroscopy technique based on optical detection, aiming at improving precision and sensitivity.

Development of instrument for assessing students’ critical and creative thinking ability

NASA Astrophysics Data System (ADS)

Herpiana, R.; Rosidin, U.

2018-01-01

The purpose of this study was to develop instruments to measure critical thinking ability and creative students in the topics of physics simple harmonic motion. The research method used was research development with application of procedures including research and data collection, planning, and initial product development. The participants of the study were thirty-four tenth grade students and five physics teachers of physics who were selected randomly from schools in the province of Lampung. The data collected by using test and analyzed in quantitative descriptive. Initial data showed that students’ critical and creative thinking ability were still low and instruments to assess students’ critical thinking skills and creative students was not yet available. Most of assessment conducted focused on memorization. Thus, the researchers developed a draft of instrument in the form of the test description based on criteria that encouraged students’ activity in understanding the concepts, strategies and decision/solution in dealing with problems. The development of the instrument was conducted considering real-world phenomena in the form of pictures and stories, description of the situation, and verbal presentation.

A modal aeroelastic analysis scheme for turbomachinery blading. M.S. Thesis - Case Western Reserve Univ. Final Report

NASA Technical Reports Server (NTRS)

Smith, Todd E.

1991-01-01

An aeroelastic analysis is developed which has general application to all types of axial-flow turbomachinery blades. The approach is based on linear modal analysis, where the blade's dynamic response is represented as a linear combination of contributions from each of its in-vacuum free vibrational modes. A compressible linearized unsteady potential theory is used to model the flow over the oscillating blades. The two-dimensional unsteady flow is evaluated along several stacked axisymmetric strips along the span of the airfoil. The unsteady pressures at the blade surface are integrated to result in the generalized force acting on the blade due to simple harmonic motions. The unsteady aerodynamic forces are coupled to the blade normal modes in the frequency domain using modal analysis. An iterative eigenvalue problem is solved to determine the stability of the blade when the unsteady aerodynamic forces are included in the analysis. The approach is demonstrated by applying it to a high-energy subsonic turbine blade from a rocket engine turbopump power turbine. The results indicate that this turbine could undergo flutter in an edgewise mode of vibration.

Cyclic fluctuations of water level as a basis for determining aquifer transmissibility

USGS Publications Warehouse

Ferris, John G.

1952-01-01

In coastal areas, wells near bodies of tidal water frequently exhibit sinusoidal fluctuations of water level, in response to periodic changes of tidewater stage.  Inland, the regulation of a surface reservoir often produces correlative changes of ground-water stage in wells adjacent either to the reservoir or to its attendant stream.  As the stage of the surface water rises, the head upon the subaqueous outcrop of the aquifer increases and thereby either increases the rate of inflow to the aquifer or reduces the rate of outflow therefrom.  The increase in recharge or reduction in discharge results in a general recovery of water level in the aquifer. On the subsequent falling stage this pattern is reversed.  When the stage of the surface body fluctuates as a simple harmonic motion a train of sinusoidal waves is propagated shoreward through the sub-outcrop of the aquifer.  With increasing distance from the sub-outcrop, the amplitude of the transmitted wave decreases and the time lag of a given maximum or minimum increases.

An unsteady lifting surface method for single rotation propellers

NASA Technical Reports Server (NTRS)

Williams, Marc H.

1990-01-01

The mathematical formulation of a lifting surface method for evaluating the steady and unsteady loads induced on single rotation propellers by blade vibration and inflow distortion is described. The scheme is based on 3-D linearized compressible aerodynamics and presumes that all disturbances are simple harmonic in time. This approximation leads to a direct linear integral relation between the normal velocity on the blade (which is determined from the blade geometry and motion) and the distribution of pressure difference across the blade. This linear relation is discretized by breaking the blade up into subareas (panels) on which the pressure difference is treated as approximately constant, and constraining the normal velocity at one (control) point on each panel. The piece-wise constant loads can then be determined by Gaussian elimination. The resulting blade loads can be used in performance, stability and forced response predictions for the rotor. Mathematical and numerical aspects of the method are examined. A selection of results obtained from the method is presented. The appendices include various details of the derivation that were felt to be secondary to the main development in Section 1.

Quantum dynamical framework for Brownian heat engines

NASA Astrophysics Data System (ADS)

Agarwal, G. S.; Chaturvedi, S.

2013-07-01

We present a self-contained formalism modeled after the Brownian motion of a quantum harmonic oscillator for describing the performance of microscopic Brownian heat engines such as Carnot, Stirling, and Otto engines. Our theory, besides reproducing the standard thermodynamics results in the steady state, enables us to study the role dissipation plays in determining the efficiency of Brownian heat engines under actual laboratory conditions. In particular, we analyze in detail the dynamics associated with decoupling a system in equilibrium with one bath and recoupling it to another bath and obtain exact analytical results, which are shown to have significant ramifications on the efficiencies of engines involving such a step. We also develop a simple yet powerful technique for computing corrections to the steady state results arising from finite operation time and use it to arrive at the thermodynamic complementarity relations for various operating conditions and also to compute the efficiencies of the three engines cited above at maximum power. Some of the methods and exactly solvable models presented here are interesting in their own right and could find useful applications in other contexts as well.

Theory of diatomic molecules in an external electromagnetic field from first quantum mechanical principles.

PubMed

Sindelka, Milan; Moiseyev, Nimrod

2006-04-27

We study a general problem of the translational/rotational/vibrational/electronic dynamics of a diatomic molecule exposed to an interaction with an arbitrary external electromagnetic field. The theory developed in this paper is relevant to a variety of specific applications, such as alignment or orientation of molecules by lasers, trapping of ultracold molecules in optical traps, molecular optics and interferometry, rovibrational spectroscopy of molecules in the presence of intense laser light, or generation of high order harmonics from molecules. Starting from the first quantum mechanical principles, we derive an appropriate molecular Hamiltonian suitable for description of the center of mass, rotational, vibrational, and electronic molecular motions driven by the field within the electric dipole approximation. Consequently, the concept of the Born-Oppenheimer separation between the electronic and the nuclear degrees of freedom in the presence of an electromagnetic field is introduced. Special cases of the dc/ac-field limits are then discussed separately. Finally, we consider a perturbative regime of a weak dc/ac field, and obtain simple analytic formulas for the associated Born-Oppenheimer translational/rotational/vibrational molecular Hamiltonian.

Excitation of a buried magmatic pipe: A seismic source model for volcanic tremor

NASA Astrophysics Data System (ADS)

Chouet, Bernard

1985-02-01

Recent observations of seismic events at various volcanoes suggest that harmonic tremor results from the sustained occurrence of so-called long-period or low-frequency events. Accordingly, we can view the long-period volcanic event as the elementary process of tremor and interpret it as the impulse response of the tremor-generating system. We present a seismic model in which the source of tremor is the acoustic resonance of a fluid-filled volcanic pipe triggered by excess gas pressure. The model consists of three elements, namely, a triggering mechanism, a resonator, and a radiator. For simplicity, we assume a hemispherical trigger, cylindrial resonator, and circular radiator set in a vertical configuration with the trigger capping the top of the pipe and the disk-shaped radiator shutting off its bottom. Considering the simple case of a source buried in a homogeneous half space, we then apply the discrete wave number method to obtain a complete representation of the ground motion response at near and intermediate distances. The results demonstrate that the displacement attributed to the pipe dominates the near-field motion, while that due to the disk is representative of the intermediate and far fields. The trigger itself has a smaller contribution, mainly limited to the field in the proximity of the source. The characteristics displayed by the free surface response evolve from a strong impulsive signature in the immediate vicinity of the epicenter to a well-developed harmonic wave train dominated by Rayleigh waves at larger distances. No clear shear arrival can be detected in the synthetic seismograms. The displacement spectrum reflects the organ-pipe modes of the conduit, and the bandwidth associated with the dominant spectral peak of motion is controlled by the combined losses due to viscous attenuation in the fluid and elastic radiation into the solid. In the case of the cylindrical magma column considered, the radiation loss is proportional to the square of the pipe radius, while the loss related to viscous damping is inversely proportional to the same factor, indicating that the relative importance of the two loss mechanisms is critically dependent on the geometry of the magma reservoir. The relative importance of the pipe and disk elements, likewise, is a function of the conduit cross section. This suggests the possibility of determining the geometry of the source as well as the radiation loss and in situ magma viscosity from a comparison of near- and far-field observations.

Simple One-Dimensional Quantum-Mechanical Model for a Particle Attached to a Surface

ERIC Educational Resources Information Center

Fernandez, Francisco M.

2010-01-01

We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships…

Teaching Harmonic Motion in Trigonometry: Inductive Inquiry Supported by Physics Simulations

ERIC Educational Resources Information Center

Sokolowski, Andrzej; Rackley, Robin

2011-01-01

In this article, the authors present a lesson whose goal is to utilise a scientific environment to immerse a trigonometry student in the process of mathematical modelling. The scientific environment utilised during this activity is a physics simulation called "Wave on a String" created by the PhET Interactive Simulations Project at…

Evaluation of Rotor Structural and Aerodynamic Loads using Measured Blade Properties

NASA Technical Reports Server (NTRS)

Jung, Sung N.; You, Young-Hyun; Lau, Benton H.; Johnson, Wayne; Lim, Joon W.

2012-01-01

The structural properties of Higher harmonic Aeroacoustic Rotor Test (HART I) blades have been measured using the original set of blades tested in the wind tunnel in 1994. A comprehensive rotor dynamics analysis is performed to address the effect of the measured blade properties on airloads, blade motions, and structural loads of the rotor. The measurements include bending and torsion stiffness, geometric offsets, and mass and inertia properties of the blade. The measured properties are correlated against the estimated values obtained initially by the manufacturer of the blades. The previously estimated blade properties showed consistently higher stiffnesses, up to 30% for the flap bending in the blade inboard root section. The measured offset between the center of gravity and the elastic axis is larger by about 5% chord length, as compared with the estimated value. The comprehensive rotor dynamics analysis was carried out using the measured blade property set for HART I rotor with and without HHC (Higher Harmonic Control) pitch inputs. A significant improvement on blade motions and structural loads is obtained with the measured blade properties.

Quantum dynamics of a plane pendulum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leibscher, Monika; Schmidt, Burkhard

A semianalytical approach to the quantum dynamics of a plane pendulum is developed, based on Mathieu functions which appear as stationary wave functions. The time-dependent Schroedinger equation is solved for pendular analogs of coherent and squeezed states of a harmonic oscillator, induced by instantaneous changes of the periodic potential energy function. Coherent pendular states are discussed between the harmonic limit for small displacements and the inverted pendulum limit, while squeezed pendular states are shown to interpolate between vibrational and free rotational motion. In the latter case, full and fractional revivals as well as spatiotemporal structures in the time evolution ofmore » the probability densities (quantum carpets) are quantitatively analyzed. Corresponding expressions for the mean orientation are derived in terms of Mathieu functions in time. For periodic double well potentials, different revival schemes, and different quantum carpets are found for the even and odd initial states forming the ground tunneling doublet. Time evolution of the mean alignment allows the separation of states with different parity. Implications for external (rotational) and internal (torsional) motion of molecules induced by intense laser fields are discussed.« less

Motion of vortices in inhomogeneous Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Groszek, Andrew J.; Paganin, David M.; Helmerson, Kristian; Simula, Tapio P.

2018-02-01

We derive a general and exact equation of motion for a quantized vortex in an inhomogeneous two-dimensional Bose-Einstein condensate. This equation expresses the velocity of a vortex as a sum of local ambient density and phase gradients in the vicinity of the vortex. We perform Gross-Pitaevskii simulations of single-vortex dynamics in both harmonic and hard-walled disk-shaped traps, and find excellent agreement in both cases with our analytical prediction. The simulations reveal that, in a harmonic trap, the main contribution to the vortex velocity is an induced ambient phase gradient, a finding that contradicts the commonly quoted result that the local density gradient is the only relevant effect in this scenario. We use our analytical vortex velocity formula to derive a point-vortex model that accounts for both density and phase contributions to the vortex velocity, suitable for use in inhomogeneous condensates. Although good agreement is obtained between Gross-Pitaevskii and point-vortex simulations for specific few-vortex configurations, the effects of nonuniform condensate density are in general highly nontrivial, and are thus difficult to efficiently and accurately model using a simplified point-vortex description.

Anderson localization of shear waves observed by magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Papazoglou, S.; Klatt, D.; Braun, J.; Sack, I.

2010-07-01

In this letter we present for the first time an experimental investigation of shear wave localization using motion-sensitive magnetic resonance imaging (MRI). Shear wave localization was studied in gel phantoms containing arrays of randomly positioned parallel glass rods. The phantoms were exposed to continuous harmonic vibrations in a frequency range from 25 to 175 Hz, yielding wavelengths on the order of the elastic mean free path, i.e. the Ioffe-Regel criterion of Anderson localization was satisfied. The experimental setup was further chosen such that purely shear horizontal waves were induced to avoid effects due to mode conversion and pressure waves. Analysis of the distribution of shear wave intensity in experiments and simulations revealed a significant deviation from Rayleigh statistics indicating that shear wave energy is localized. This observation is further supported by experiments on weakly scattering samples exhibiting Rayleigh statistics and an analysis of the multifractality of wave functions. Our results suggest that motion-sensitive MRI is a promising tool for studying Anderson localization of time-harmonic shear waves, which are increasingly used in dynamic elastography.

Ultrafast creation of large Schrödinger cat states of an atom.

PubMed

Johnson, K G; Wong-Campos, J D; Neyenhuis, B; Mizrahi, J; Monroe, C

2017-09-26

Mesoscopic quantum superpositions, or Schrödinger cat states, are widely studied for fundamental investigations of quantum measurement and decoherence as well as applications in sensing and quantum information science. The generation and maintenance of such states relies upon a balance between efficient external coherent control of the system and sufficient isolation from the environment. Here we create a variety of cat states of a single trapped atom's motion in a harmonic oscillator using ultrafast laser pulses. These pulses produce high fidelity impulsive forces that separate the atom into widely separated positions, without restrictions that typically limit the speed of the interaction or the size and complexity of the resulting motional superposition. This allows us to quickly generate and measure cat states larger than previously achieved in a harmonic oscillator, and create complex multi-component superposition states in atoms.Generation of mesoscopic quantum superpositions requires both reliable coherent control and isolation from the environment. Here, the authors succeed in creating a variety of cat states of a single trapped atom, mapping spin superpositions into spatial superpositions using ultrafast laser pulses.

Analytical solution of the time-dependent Bloch NMR flow equations: a translational mechanical analysis

NASA Astrophysics Data System (ADS)

Awojoyogbe, O. B.

2004-08-01

Various biological and physiological properties of living tissue can be studied by means of nuclear magnetic resonance techniques. Unfortunately, the basic physics of extracting the relevant information from the solution of Bloch nuclear magnetic resource (NMR) equations to accurately monitor the clinical state of biological systems is still not yet fully understood. Presently, there are no simple closed solutions known to the Bloch equations for a general RF excitation. Therefore the translational mechanical analysis of the Bloch NMR equations presented in this study, which can be taken as definitions of new functions to be studied in detail may reveal very important information from which various NMR flow parameters can be derived. Fortunately, many of the most important but hidden applications of blood flow parameters can be revealed without too much difficulty if appropriate mathematical techniques are used to solve the equations. In this study we are concerned with a mathematical study of the laws of NMR physics from the point of view of translational mechanical theory. The important contribution of this study is that solutions to the Bloch NMR flow equations do always exist and can be found as accurately as desired. We shall restrict our attention to cases where the radio frequency field can be treated by simple analytical methods. First we shall derive a time dependant second-order non-homogeneous linear differential equation from the Bloch NMR equation in term of the equilibrium magnetization M0, RF B1( t) field, T1 and T2 relaxation times. Then, we would develop a general method of solving the differential equation for the cases when RF B1( t)=0, and when RF B1( t)≠0. This allows us to obtain the intrinsic or natural behavior of the NMR system as well as the response of the system under investigation to a specific influence of external force to the system. Specifically, we consider the case where the RF B1 varies harmonically with time. Here the complete motion of the system consists of two parts. The first part describes the motion of the transverse magnetization My in the absence of RF B( t) field. The second part of the motion described by the particular integral of the derived differential equation does not decay with time but continues its periodic behavior indefinitely. The complete motion of the NMR flow system is then quantitatively and qualitatively described.

Simultaneous Tracking of Multiple Points Using a Wiimote

NASA Astrophysics Data System (ADS)

Skeffington, Alex; Scully, Kyle

2012-11-01

This paper reviews the construction of an inexpensive motion tracking and data logging system, which can be used for a wide variety of teaching experiments ranging from entry-level physics courses to advanced courses. The system utilizes an affordable infrared camera found in a Nintendo Wiimote to track IR LEDs mounted to the objects to be tracked. Two quick experiments are presented using the motion tracking system to demonstrate the diversity of tasks this system can handle. The first experiment uses the Wiimote to record the harmonic motion of oscillating masses on a near-frictionless surface, while the second experiment uses the Wiimote as part of a feedback mechanism in a rotational system. The construction, capabilities, demonstrations, and suggested improvements of the system are reported here.

High Harmonic Fast Wave Damping on an Ion Beam: NSTX and DIII-D Regimes Compared

NASA Astrophysics Data System (ADS)

Pinsker, R. I.; Choi, C. C.; Petty, C. C.; Porkolab, M.; Wilson, J. R.; Murakami, M.; Harvey, R. W.

2004-11-01

Both NSTX and DIII-D use the combination of fast Alfven waves (FW) and neutral beam injection (NBI) for central electron heating and current drive. Damping of the fast wave on the beam ions at moderate to high harmonics (4th--20th) of the beam ion cyclotron frequency represents a loss process. In DIII-D current drive experiments at low density in which 4th and 8th harmonics were compared, damping at the 8th harmonic damping was much weaker than at the 4th [1]. However, recent simulations have predicted that in higher density and higher beam power regimes (of interest to the Advanced Tokamak program) the beam ion absorption will transition to the unmagnetized ion regime, where the damping is significant and essentially independent of harmonic number. In the present work, the transition from magnetized to unmagnetized ion regimes for the NSTX and DIII-D HHFW experiments is studied theoretically, with a combination of simple semi-analytic models and numerical models. \\vspace0.25 em [1] C.C. Petty, et al., Plasma Phys. and Contr. Fusion 43, 1747 (2001).

Harmonic Allocation of Authorship Credit: Source-Level Correction of Bibliometric Bias Assures Accurate Publication and Citation Analysis

PubMed Central

Hagen, Nils T.

2008-01-01

Authorship credit for multi-authored scientific publications is routinely allocated either by issuing full publication credit repeatedly to all coauthors, or by dividing one credit equally among all coauthors. The ensuing inflationary and equalizing biases distort derived bibliometric measures of merit by systematically benefiting secondary authors at the expense of primary authors. Here I show how harmonic counting, which allocates credit according to authorship rank and the number of coauthors, provides simultaneous source-level correction for both biases as well as accommodating further decoding of byline information. I also demonstrate large and erratic effects of counting bias on the original h-index, and show how the harmonic version of the h-index provides unbiased bibliometric ranking of scientific merit while retaining the original's essential simplicity, transparency and intended fairness. Harmonic decoding of byline information resolves the conundrum of authorship credit allocation by providing a simple recipe for source-level correction of inflationary and equalizing bias. Harmonic counting could also offer unrivalled accuracy in automated assessments of scientific productivity, impact and achievement. PMID:19107201

Combination of High Rate, Real-Time GNSS and Accelerometer Observations and Rapid Seismic Event Notification for Earthquake Early Warning and Volcano Monitoring with a Focus on the Pacific Rim.

NASA Astrophysics Data System (ADS)

Zimakov, L. G.; Passmore, P.; Raczka, J.; Alvarez, M.; Jackson, M.

2014-12-01

Scientific GNSS networks are moving towards a model of real-time data acquisition, epoch-by-epoch storage integrity, and on-board real-time position and displacement calculations. This new paradigm allows the integration of real-time, high-rate GNSS displacement information with acceleration and velocity data to create very high-rate displacement records. The mating of these two instruments allows the creation of a new, very high-rate (200 sps) displacement observable that has the full-scale displacement characteristics of GNSS and high-precision dynamic motions of seismic technologies. It is envisioned that these new observables can be used for earthquake early warning studies, volcano monitoring, and critical infrastructure monitoring applications. Our presentation will focus on the characteristics of GNSS, seismic, and strong motion sensors in high dynamic environments, including historic earthquakes in Southern California and the Pacific Rim, replicated on a shake table, over a range of displacements and frequencies. We will explore the optimum integration of these sensors from a filtering perspective including simple harmonic impulses over varying frequencies and amplitudes and under the dynamic conditions of various earthquake scenarios. In addition we will discuss implementation of a Rapid Seismic Event Notification System that provides quick delivery of digital data from seismic stations to the acquisition and processing center and a full data integrity model for real-time earthquake notification that provides warning prior to significant ground shaking.

The kinematics and kinetics of pedestrians on a laterally swaying footbridge

NASA Astrophysics Data System (ADS)

Claff, D.; Williams, M. S.; Blakeborough, A.

2017-10-01

Progress in understanding human-structure interaction (HSI) on footbridges has been hampered by the shortage of quality data collected in realistic environments. This paper reports a novel experiment conducted on a naturally-swaying 7 m footbridge of frequency 0.67 Hz and amplitudes up to 125 mm. Subjects crossed the bridge while wearing infrared motion-tracking markers and pressure-sensing insoles. The bridge was fitted with bespoke force plates, allowing investigators to simultaneously record kinematic and kinetic reactions to the structure's motion, which was assumed simple harmonic. The bridge was naturally excited by the test subjects, who were allowed to walk at a comfortable self-chosen pace. The data show that the subjects adopted a fixed-in-space Centre of Mass (CoM) strategy but their Centres of Pressure (CoP) were highly correlated to the position of the bridge deck within its lateral oscillation cycle (henceforth 'bridge phase'), allowing for the prediction of wide and crossed steps. Ground forces generally correlated to CoM-CoP separation, which reflected the phase of the bridge at the previous heel-strike. Instantaneous step width was correlated to the bridge phase and is proportional to the offset in the Medial-Lateral (M-L) ground force between consecutive steps. The Inverted Pendulum Model (IPM) was evaluated using the data, exhibiting a limited fit to the recorded ground forces. Finally, the pedestrian-induced work on the bridge and system stability boundaries are also calculated, revealing mechanisms for bridge instability to occur.

Relativistic satellite orbits: central body with higher zonal harmonics

NASA Astrophysics Data System (ADS)

Schanner, Maximilian; Soffel, Michael

2018-06-01

Satellite orbits around a central body with arbitrary zonal harmonics are considered in a relativistic framework. Our starting point is the relativistic Celestial Mechanics based upon the first post-Newtonian approximation to Einstein's theory of gravity as it has been formulated by Damour et al. (Phys Rev D 43:3273-3307, 1991; 45:1017-1044, 1992; 47:3124-3135, 1993; 49:618-635, 1994). Since effects of order (GM/c^2R) × J_k with k ≥ 2 for the Earth are very small (of order 7 × 10^{-10} × J_k) we consider an axially symmetric body with arbitrary zonal harmonics and a static external gravitational field. In such a field the explicit J_k/c^2-terms (direct terms) in the equations of motion for the coordinate acceleration of a satellite are treated first with first-order perturbation theory. The derived perturbation theoretical results of first order have been checked by purely numerical integrations of the equations of motion. Additional terms of the same order result from the interaction of the Newtonian J_k-terms with the post-Newtonian Schwarzschild terms (relativistic terms related to the mass of the central body). These `mixed terms' are treated by means of second-order perturbation theory based on the Lie-series method (Hori-Deprit method). Here we concentrate on the secular drifts of the ascending node <{\\dot{Ω }}> and argument of the pericenter <{\\dot{ω }}>. Finally orders of magnitude are given and discussed.

Dark-dark-soliton dynamics in two density-coupled Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Morera, I.; Mateo, A. Muñoz; Polls, A.; Juliá-Díaz, B.

2018-04-01

We study the one-dimensional dynamics of dark-dark solitons in the miscible regime of two density-coupled Bose-Einstein condensates having repulsive interparticle interactions within each condensate (g >0 ). By using an adiabatic perturbation theory in the parameter g12/g , we show that, contrary to the case of two solitons in scalar condensates, the interactions between solitons are attractive when the interparticle interactions between condensates are repulsive g12>0 . As a result, the relative motion of dark solitons with equal chemical potential μ is well approximated by harmonic oscillations of angular frequency wr=(μ /ℏ ) √{(8 /15 ) g12/g } . We also show that, in finite systems, the resonance of this anomalous excitation mode with the spin-density mode of lowest energy gives rise to alternating dynamical instability and stability fringes as a function of the perturbative parameter. In the presence of harmonic trapping (with angular frequency Ω ) the solitons are driven by the superposition of two harmonic motions at a frequency given by w2=(Ω/√{2 }) 2+wr2 . When g12<0 , these two oscillators compete to give rise to an overall effective potential that can be either single well or double well through a pitchfork bifurcation. All our theoretical results are compared with numerical solutions of the Gross-Pitaevskii equation for the dynamics and the Bogoliubov equations for the linear stability. A good agreement is found between them.

In vivo feasibility of real-time monitoring of focused ultrasound surgery (FUS) using harmonic motion imaging (HMI).

PubMed

Maleke, Caroline; Konofagou, Elisa E

2010-01-01

In this study, the Harmonic Motion Imaging for Focused Ultrasound (HMIFU) technique is applied to monitor changes in mechanical properties of tissues during thermal therapy in a transgenic breast cancer mouse model in vivo. An HMIFU system, composed of a 4.5-MHz focused ultrasound (FUS) and a 3.3-MHz phased-array imaging transducer, was mechanically moved to image and ablate the entire tumor. The FUS transducer was driven by an amplitude-modulated (AM) signal at 15 Hz. The acoustic intensity ( I(spta)) was equal to 1050 W/cm(2) at the focus. A digital low-pass filter was used to filter out the spectrum of the FUS beam and its harmonics prior to displacement estimation. The resulting axial displacement was estimated using 1-D cross-correlation on the acquired RF signals. Results from two mice with eight lesions formed in each mouse (16 lesions total) showed that the average peak-to-peak displacement amplitude before and after lesion formation was respectively equal to 17.34 +/- 1.34 microm and 10.98 +/- 1.82 microm ( p < 0.001). Cell death was also confirmed by hematoxylin and eosin histology. HMI displacement can be used to monitor the relative tissue stiffness changes in real time during heating so that the treatment procedure can be performed in a time-efficient manner. The HMIFU system may, therefore, constitute a cost-efficient and reliable alternative for real-time monitoring of thermal ablation.

Temporal analysis of regional wall motion from cine cardiac MRI

NASA Astrophysics Data System (ADS)

Ratib, Osman M.; Didier, Dominique; Chretien, Anne; Rosset, Antoine; Magnin, Isabelle E.; Ligier, Yves

1996-04-01

The purpose of this work is to develop and to evaluate an automatic analysis technique for quantitative assessment of cardiac function from cine MRI and to identify regional alterations in synchronicity based on Fourier analysis of ventricular wall motion (WM). A temporal analysis technique of left ventricular wall displacement was developed for quantitative analysis of temporal delays in wall motion and applied to gated cine 'dark blood' cardiac MRI. This imaging technique allows the user to saturate the blood both above and below the imaging slice simultaneously by using a specially designed rf presaturation pulse. The acquisition parameters are: TR equals 25 - 60 msec, TE equals 5 - 7 msec, 0 equals 25 degrees, slice thickness equals 10 mm, 16 to 32 frames/cycle. Automatic edge detection was used to outline the ventricular cavities on all frames of a cardiac cycle. Two different segmentation techniques were applied to all studies and lead to similar results. Further improvement in edge detection accuracy was achieved by temporal interpolation of individual contours on each image of the cardiac cycle. Radial analysis of the ventricular wall motion was then performed along 64 radii drawn from the center of the ventricular cavity. The first harmonic of the Fourier transform of each radial motion curve is calculated. The phase of the fundamental Fourier component is used as an index of synchrony (delay) of regional wall motion. Results are displayed in color-coded maps of regional alterations in the amplitude and synchrony of wall motion. The temporal delays measured from individual segments are evaluated through a histogram of phase distribution, where the width of the main peak is used as an index of overall synchrony of wall motion. The variability of this technique was validated in 10 normal volunteers and was used to identify regions with asynchronous WM in 15 patients with documented CAD. The standard deviation (SD) of phase distribution measured in short axis views was calculated and used to identify regions with asynchronous wall motion in patients with coronary artery disease. Results suggest that this technique is more sensitive than global functional parameters such as ejection fraction for the detection of ventricular dysfunction. Color coded parametric display offers a more convenient way for the identification and localization of regional wall motion asynchrony. Data obtained from endocardial wall motion analysis were not significantly different from wall thickening measurements. The innovative approach of evaluating the temporal behavior of regional wall motion anomalies is expected to provide clinically relevant data about subtle alteration that cannot be detected through simple analysis of the extent (amplitude) of wall motion or myocardial thickening. Temporal analysis of regional WM abnormality from cine MRI offers an innovative and promising means for objective quantitative evaluation of subtle regional abnormalities. Color coded parametric maps allowed a better identification and localization of regional WM asynchrony.

Using the Graphing Calculator--in Two-Dimensional Motion Plots.

ERIC Educational Resources Information Center

Brueningsen, Chris; Bower, William

1995-01-01

Presents a series of simple activities involving generalized two-dimensional motion topics to prepare students to study projectile motion. Uses a pair of motion detectors, each connected to a calculator-based-laboratory (CBL) unit interfaced with a standard graphics calculator, to explore two-dimensional motion. (JRH)

Modeling and visualization of carrier motion in organic films by optical second harmonic generation and Maxwell-displacement current

NASA Astrophysics Data System (ADS)

Iwamoto, Mitsumasa; Manaka, Takaaki; Taguchi, Dai

2015-09-01

The probing and modeling of carrier motions in materials as well as in electronic devices is a fundamental research subject in science and electronics. According to the Maxwell electromagnetic field theory, carriers are a source of electric field. Therefore, by probing the dielectric polarization caused by the electric field arising from moving carriers and dipoles, we can find a way to visualize the carrier motions in materials and in devices. The techniques used here are an electrical Maxwell-displacement current (MDC) measurement and a novel optical method based on the electric field induced optical second harmonic generation (EFISHG) measurement. The MDC measurement probes changes of induced charge on electrodes, while the EFISHG probes nonlinear polarization induced in organic active layers due to the coupling of electron clouds of molecules and electro-magnetic waves of an incident laser beam in the presence of a DC field caused by electrons and holes. Both measurements allow us to probe dynamical carrier motions in solids through the detection of dielectric polarization phenomena originated from dipolar motions and electron transport. In this topical review, on the basis of Maxwell’s electro-magnetism theory of 1873, which stems from Faraday’s idea, the concept for probing electron and hole transport in solids by using the EFISHG is discussed in comparison with the conventional time of flight (TOF) measurement. We then visualize carrier transit in organic devices, i.e. organic field effect transistors, organic light emitting diodes, organic solar cells, and others. We also show that visualizing an EFISHG microscopic image is a novel way for characterizing anisotropic carrier transport in organic thin films. We also discuss the concept of the detection of rotational dipolar motions in monolayers by means of the MDC measurement, which is capable of probing the change of dielectric spontaneous polarization formed by dipoles in organic monolayers. Finally we conclude that the ideas and experiments on EFISHG and MDC lead to a novel way of analyzing dynamical motions of electrons, holes, and dipoles in solids, and thus are available in organic electronic device application.

Fundamental analysis and ex vivo validation of thermal lesion mapping using harmonic motion imaging for focused ultrasound (HMIFU)

NASA Astrophysics Data System (ADS)

Hou, Gary Y.; Luo, Jianwen; Maleke, Caroline; Vappou, Jonathan; Marquet, Fabrice; Konofagou, Elisa E.

2012-10-01

Harmonic Motion Imaging for Focused Ultrasound (HMIFU) is a novel high-intensity focused ultrasound (HIFU) therapy monitoring method with feasibilities demonstrated in vitro, ex vivo and in vivo. Its principle is based on Amplitude-modulated (AM) - Harmonic Motion Imaging (HMI), an oscillatory radiation force used for imaging the tissue mechanical response during thermal ablation. In this study, a theoretical framework of HMIFU is presented, comprising a customized nonlinear wave propagation model, a finite-element (FE) analysis module, and an image-formation model. The objective of this study is to develop such a framework in order to 1) assess the fundamental performance of HMIFU in detecting HIFU lesions based on the change in tissue apparent elasticity, i.e., the increasing Young's modulus, and the HIFU lesion size with respect to the HIFU exposure time and 2) validate the simulation findings ex vivo. The same HMI and HMIFU parameters as in the experimental studies were used, i.e., 4.5-MHz HIFU frequency and 25-Hz AM frequency. For a lesion-to-background Young's modulus ratio of 3, 6, and 9, the estimated HMI displacement ratios were equal to 1.65, 3.19, 4.59, respectively. In experiments, the HMI displacement followed a similar increasing trend of 1.19, 1.28, 1.78 at 10-s, 20-s, and 30-s HIFU exposure, respectively. In addition, moderate agreement in lesion size growth was also found in both simulations (16.2, 73.1 and 334.7 mm2) and experiments (26.2, 94.2 and 206.2 mm2). Therefore, the feasibility of HMIFU for HIFU lesion detection based on the underlying tissue elasticity changes was verified through the developed theoretical framework, i.e., validation of the fundamental performance of the HMIFU system for lesion detection, localization and quantification, was demonstrated both theoretically and ex vivo.

Performance assessment of HIFU lesion detection by Harmonic Motion Imaging for Focused Ultrasound (HMIFU): A 3D finite-element-based framework with experimental validation

PubMed Central

Hou, Gary Y.; Luo, Jianwen; Marquet, Fabrice; Maleke, Caroline; Vappou, Jonathan; Konofagou, Elisa E.

2014-01-01

Harmonic Motion Imaging for Focused Ultrasound (HMIFU) is a novel high-intensity focused ultrasound (HIFU) therapy monitoring method with feasibilities demonstrated in vitro, ex vivo and in vivo. Its principle is based on Amplitude-modulated (AM) - Harmonic Motion Imaging (HMI), an oscillatory radiation force used for imaging the tissue mechanical response during thermal ablation. In this study, a theoretical framework of HMIFU is presented, comprising a customized nonlinear wave propagation model, a finite-element (FE) analysis module, and an image-formation model. The objective of this study is to develop such a framework in order to 1) assess the fundamental performance of HMIFU in detecting HIFU lesions based on the change in tissue apparent elasticity, i.e., the increasing Young's modulus, and the HIFU lesion size with respect to the HIFU exposure time and 2) validate the simulation findings ex vivo. The same HMI and HMIFU parameters as in the experimental studies were used, i.e., 4.5-MHz HIFU frequency and 25 Hz AM frequency. For a lesion-to-background Young's modulus ratio of 3, 6, and 9, the FE and estimated HMI displacement ratios were equal to 1.83, 3.69, 5.39 and 1.65, 3.19, 4.59, respectively. In experiments, the HMI displacement followed a similar increasing trend of 1.19, 1.28, and 1.78 at 10-s, 20-s, and 30-s HIFU exposure, respectively. In addition, moderate agreement in lesion size growth was also found in both simulations (16.2, 73.1 and 334.7 mm2) and experiments (26.2, 94.2 and 206.2 mm2). Therefore, the feasibility of HMIFU for HIFU lesion detection based on the underlying tissue elasticity changes was verified through the developed theoretical framework, i.e., validation of the fundamental performance of the HMIFU system for lesion detection, localization and quantification, was demonstrated both theoretically and ex vivo. PMID:22036637

Catalytic micromotor generating self-propelled regular motion through random fluctuation.

PubMed

Yamamoto, Daigo; Mukai, Atsushi; Okita, Naoaki; Yoshikawa, Kenichi; Shioi, Akihisa

2013-07-21

Most of the current studies on nano∕microscale motors to generate regular motion have adapted the strategy to fabricate a composite with different materials. In this paper, we report that a simple object solely made of platinum generates regular motion driven by a catalytic chemical reaction with hydrogen peroxide. Depending on the morphological symmetry of the catalytic particles, a rich variety of random and regular motions are observed. The experimental trend is well reproduced by a simple theoretical model by taking into account of the anisotropic viscous effect on the self-propelled active Brownian fluctuation.

Catalytic micromotor generating self-propelled regular motion through random fluctuation

NASA Astrophysics Data System (ADS)

Yamamoto, Daigo; Mukai, Atsushi; Okita, Naoaki; Yoshikawa, Kenichi; Shioi, Akihisa

2013-07-01

Most of the current studies on nano/microscale motors to generate regular motion have adapted the strategy to fabricate a composite with different materials. In this paper, we report that a simple object solely made of platinum generates regular motion driven by a catalytic chemical reaction with hydrogen peroxide. Depending on the morphological symmetry of the catalytic particles, a rich variety of random and regular motions are observed. The experimental trend is well reproduced by a simple theoretical model by taking into account of the anisotropic viscous effect on the self-propelled active Brownian fluctuation.

Analysis of 3-D Tongue Motion From Tagged and Cine Magnetic Resonance Images

PubMed Central

Woo, Jonghye; Lee, Junghoon; Murano, Emi Z.; Stone, Maureen; Prince, Jerry L.

2016-01-01

Purpose Measuring tongue deformation and internal muscle motion during speech has been a challenging task because the tongue deforms in 3 dimensions, contains interdigitated muscles, and is largely hidden within the vocal tract. In this article, a new method is proposed to analyze tagged and cine magnetic resonance images of the tongue during speech in order to estimate 3-dimensional tissue displacement and deformation over time. Method The method involves computing 2-dimensional motion components using a standard tag-processing method called harmonic phase, constructing superresolution tongue volumes using cine magnetic resonance images, segmenting the tongue region using a random-walker algorithm, and estimating 3-dimensional tongue motion using an incompressible deformation estimation algorithm. Results Evaluation of the method is presented with a control group and a group of people who had received a glossectomy carrying out a speech task. A 2-step principal-components analysis is then used to reveal the unique motion patterns of the subjects. Azimuth motion angles and motion on the mirrored hemi-tongues are analyzed. Conclusion Tests of the method with a various collection of subjects show its capability of capturing patient motion patterns and indicate its potential value in future speech studies. PMID:27295428

Passive wide spectrum harmonic filter for adjustable speed drives in oil and gas industry

NASA Astrophysics Data System (ADS)

Al Jaafari, Khaled Ali

Non-linear loads such as variable speed drives constitute the bulky load of oil and gas industry power systems. They are widely used in driving induction and permanent magnet motors for variable speed applications. That is because variable speed drives provide high static and dynamic performance. Moreover, they are known of their high energy efficiency and high motion quality, and high starting torque. However, these non-linear loads are main sources of current and voltage harmonics and lower the quality of electric power system. In fact, it is the six-pulse and twelve-pulse diode and thyristor rectifiers that spoil the AC power line with the dominant harmonics (5th, 7th, 11th). They provide DC voltage to the inverter of the variable speed drives. Typical problems that arise from these harmonics are Harmonic resonances', harmonic losses, interference with electronic equipment, and line voltage distortion at the Point of Common Coupling (PCC). Thus, it is necessary to find efficient, reliable, and economical harmonic filters. The passive filters have definite advantage over active filters in terms of components count, cost and reliability. Reliability and maintenance is a serious issue in drilling rigs which are located in offshore and onshore with extreme operating conditions. Passive filters are tuned to eliminate a certain frequency and therefore there is a need to equip the system with more than one passive filter to eliminate all unwanted frequencies. An alternative solution is Wide Spectrum Harmonic passive filter. The wide spectrum harmonic filters are becoming increasingly popular in these applications and found to overcome some of the limitations of conventional tuned passive filter. The most important feature of wide spectrum harmonic passive filters is that only one capacitor is required to filter a wide range of harmonics. Wide spectrum filter is essentially a low-pass filter for the harmonic at fundamental frequency. It can also be considered as a single-stage passive filter plus input and output inductors. The work proposed gives a complete analysis of wide spectrum harmonic passive filters, the methodology to choose its parameters according to the operational condition, effect of load and source inductance on its characteristics. Also, comparison of the performance of the wide band passive filter with tuned filter is given. The analyses are supported with the simulation results and were verified experimentally. The analysis given in this thesis will be useful for the selection of proper wide spectrum harmonic filters for harmonic mitigation applications in oil and gas industry.

Instantaneous and dynamical decoherence

NASA Astrophysics Data System (ADS)

Polonyi, Janos

2018-04-01

Two manifestations of decoherence, called instantaneous and dynamical, are investigated. The former reflects the suppression of the interference between the components of the current state while the latter reflects that within the initial state. These types of decoherence are computed in the case of the Brownian motion and the harmonic and anharmonic oscillators within the semiclassical approximation. A remarkable phenomenon, namely the opposite orientation of the time arrow of the dynamical variables compared to that of the quantum fluctuations generates a double exponential time dependence of the dynamical decoherence in the presence of a harmonic force. For the weakly anharmonic oscillator the dynamical decoherence is found to depend in a singular way on the amount of the anharmonicity.

Concept of quasi-periodic undulator - control of radiation spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sasaki, Shigemi

1995-02-01

A new type of undulator, the quasi-periodic undulator (QPU) is considered which generates the irrational harmonics in the radiation spectrum. This undulator consists of the arrays of magnet blocks aligned in a quasi-periodic order, and consequentially lead to a quasi-periodic motion of electron. A combination of the QPU and a conventional crystal/grating monochromator provides pure monochromatic photon beam for synchrotron radiation users because the irrational harmonics do not be diffracted in the same direction by a monochromator. The radiation power and width of each radiation peak emitted from this undulator are expected to be comparable with those of the conventionalmore » periodic undulator.« less

Analysing simple motions using the Doppler effect—‘seeing’ sound

NASA Astrophysics Data System (ADS)

Stonawski, Tamás; Gálik, Tamás

2017-01-01

The Doppler effect has seen widespread use in the past hundred years. It is used for medical imaging, for measuring speed, temperature, direction, etc, and it makes the spatial relations of motion easy to map. The Doppler effect also allows GPS receivers to measure the speed of a vehicle significantly more accurately than dashboard speedometers. Its diverse applications have prompted us to revisit the simple motions from kinematics with the help of everyday objects in our experiments.

Conformational statistics of stiff macromolecules as solutions to partial differential equations on the rotation and motion groups

PubMed

Chirikjian; Wang

2000-07-01

Partial differential equations (PDE's) for the probability density function (PDF) of the position and orientation of the distal end of a stiff macromolecule relative to its proximal end are derived and solved. The Kratky-Porod wormlike chain, the Yamakawa helical wormlike chain, and the original and revised Marko-Siggia models are examples of stiffness models to which the present formulation is applied. The solution technique uses harmonic analysis on the rotation and motion groups to convert PDE's governing the PDF's of interest into linear algebraic equations which have mathematically elegant solutions.

Analytical solutions for the motion of a charged particle in electric and magnetic fields via non-singular fractional derivatives

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Gómez-Aguilar, J. F.; Taneco-Hernandez, M. A.

2017-12-01

In this work we propose fractional differential equations for the motion of a charged particle in electric, magnetic and electromagnetic fields. Exact solutions are obtained for the fractional differential equations by employing the Laplace transform method. The temporal fractional differential equations are considered in the Caputo-Fabrizio-Caputo and Atangana-Baleanu-Caputo sense. Application examples consider constant, ramp and harmonic fields. In addition, we present numerical results for different values of the fractional order. In all cases, when α = 1, we recover the standard electrodynamics.

Multidimensional Attosecond Resonant X-Ray Spectroscopy of Molecules: Lessons from the Optical Regime

PubMed Central

Mukamel, Shaul; Healion, Daniel; Zhang, Yu; Biggs, Jason D.

2013-01-01

New free-electron laser and high-harmonic generation X-ray light sources are capable of supplying pulses short and intense enough to perform resonant nonlinear time-resolved experiments in molecules. Valence-electron motions can be triggered impulsively by core excitations and monitored with high temporal and spatial resolution. We discuss possible experiments that employ attosecond X-ray pulses to probe the quantum coherence and correlations of valence electrons and holes, rather than the charge density alone, building on the analogy with existing studies of vibrational motions using femtosecond techniques in the visible regime. PMID:23245522

Non-linear analysis of stick/slip motion

NASA Astrophysics Data System (ADS)

Pratt, T. K.; Williams, R.

1981-02-01

The steady state relative motion of two masses with dry (Coulomb) friction contact is investigated. The bodies are assumed to have the same mass and stiffness and are subjected to harmonic excitation. By means of a combined analytical—numerical procedure, results are obtained for arbitrary values of Coulomb friction, excitation frequency, and natural frequencies of the bodies. For certain values of these parameters, multiple lockups per cycle are possible. In this respect, the problem investigated here is a natural extension of the one considered by Den Hartog, who in obtaining his closed form solution assumed a maximum of two lockups per cycle.

Beyond harmonic sounds in a simple model for birdsong production.

PubMed

Amador, Ana; Mindlin, Gabriel B

2008-12-01

In this work we present an analysis of the dynamics displayed by a simple bidimensional model of labial oscillations during birdsong production. We show that the same model capable of generating tonal sounds can present, for a wide range of parameters, solutions which are spectrally rich. The role of physiologically sensible parameters is discussed in each oscillatory regime, allowing us to interpret previously reported data.

Acoustic resonances in cylinder bundles oscillating in a compressibile fluid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, W.H.; Raptis, A.C.

1984-12-01

This paper deals with an analytical study on acoustic resonances of elastic oscillations of a group of parallel, circular, thin cylinders in an unbounded volume of barotropic, compressible, inviscid fluid. The perturbed motion of the fluid is assumed due entirely to the flexural oscillations of the cylinders. The motion of the fluid disturbances is first formulated in a three-dimensional wave form and then casted into a two-dimensional Helmholtz equation for the harmonic motion in time and in axial space. The acoustic motion in the fluid and the elastic motion in the cylinders are solved simultaneously. Acoustic resonances were approximately determinedmore » from the secular (eigenvalue) equation by the method of successive iteration with the use of digital computers for a given set of the fluid properties and the cylinders' geometry and properties. Effects of the flexural wavenumber and the configuration of and the spacing between the cylinders on the acoustic resonances were thoroughly investigated.« less

The soft embodiment of culture: camera angles and motion through time and space.

PubMed

Leung, Angela K-y; Cohen, Dov

2007-09-01

Cultural assumptions about one's relation to others and one's place in the world can be literally embodied in the way one cognitively maps out one's position and motion in time and space. In three experiments, we examined the psychological perspective that Asian American and Euro-American participants embodied as they both comprehended and produced narratives and mapped out metaphors of time and space. In social situations, Euro-American participants were more likely to embody their own perspective and a sense of their own motion (rather than those of a friend), whereas Asian American participants were more likely to embody a friend's perspective and sense of motion (rather than their own). We discuss how these psychological perspectives represent the soft embodiment of culture by implicitly instantiating cultural injunctions (a) to think about how you look to others and to harmonize with them or (b) to know yourself, trust yourself, and act with confidence.

Physiological motion modeling for organ-mounted robots.

PubMed

Wood, Nathan A; Schwartzman, David; Zenati, Marco A; Riviere, Cameron N

2017-12-01

Organ-mounted robots passively compensate heartbeat and respiratory motion. In model-guided procedures, this motion can be a significant source of information that can be used to aid in localization or to add dynamic information to static preoperative maps. Models for estimating periodic motion are proposed for both position and orientation. These models are then tested on animal data and optimal orders are identified. Finally, methods for online identification are demonstrated. Models using exponential coordinates and Euler-angle parameterizations are as accurate as models using quaternion representations, yet require a quarter fewer parameters. Models which incorporate more than four cardiac or three respiration harmonics are no more accurate. Finally, online methods estimate model parameters as accurately as offline methods within three respiration cycles. These methods provide a complete framework for accurately modelling the periodic deformation of points anywhere on the surface of the heart in a closed chest. Copyright © 2017 John Wiley & Sons, Ltd.

Approaches to creating and controlling motion in MRI.

PubMed

Fischer, Gregory S; Cole, Gregory; Su, Hao

2011-01-01

Magnetic Resonance Imaging (MRI) can provide three dimensional (3D) imaging with excellent resolution and sensitivity making it ideal for guiding and monitoring interventions. The development of MRI-compatible interventional devices is complicated by factors including: the high magnetic field strength, the requirement that such devices should not degrade image quality, and the confined physical space of the scanner bore. Numerous MRI guided actuated devices have been developed or are currently being developed utilizing piezoelectric actuators as their primary means of mechanical energy generation to enable better interventional procedure performance. While piezoelectric actuators are highly desirable for MRI guided actuation for their precision, high holding force, and non-magnetic operation they are often found to cause image degradation on a large enough to scale to render live imaging unusable. This paper describes a newly developed piezoelectric actuator driver and control system designed to drive a variety of both harmonic and non-harmonic motors that has been demonstrated to be capable of operating both harmonic and non-harmonic piezoelectric actuators with less than 5% SNR loss under closed loop control. The proposed system device allows for a single controller to control any supported actuator and feedback sensor without any physical hardware changes.

Corrosion process monitoring by AFM higher harmonic imaging

NASA Astrophysics Data System (ADS)

Babicz, S.; Zieliński, A.; Smulko, J.; Darowicki, K.

2017-11-01

The atomic force microscope (AFM) was invented in 1986 as an alternative to the scanning tunnelling microscope, which cannot be used in studies of non-conductive materials. Today the AFM is a powerful, versatile and fundamental tool for visualizing and studying the morphology of material surfaces. Moreover, additional information for some materials can be recovered by analysing the AFM’s higher cantilever modes when the cantilever motion is inharmonic and generates frequency components above the excitation frequency, usually close to the resonance frequency of the lowest oscillation mode. This method has been applied and developed to monitor corrosion processes. The higher-harmonic imaging is especially helpful for sharpening boundaries between objects in heterogeneous samples, which can be used to identify variations in steel structures (e.g. corrosion products, steel heterogeneity). The corrosion products have different chemical structures because they are composed of chemicals other than the original metal base (mainly iron oxides). Thus, their physicochemical properties are different from the primary basis. These structures have edges at which higher harmonics should be more intense because of stronger interference between the tip and the specimen structure there. This means that the AFM’s higher-harmonic imaging is an excellent tool for monitoring surficial effects of the corrosion process.

Zombie states for description of structure and dynamics of multi-electron systems

NASA Astrophysics Data System (ADS)

Shalashilin, Dmitrii V.

2018-05-01

Canonical Coherent States (CSs) of Harmonic Oscillator have been extensively used as a basis in a number of computational methods of quantum dynamics. However, generalising such techniques for fermionic systems is difficult because Fermionic Coherent States (FCSs) require complicated algebra of Grassmann numbers not well suited for numerical calculations. This paper introduces a coherent antisymmetrised superposition of "dead" and "alive" electronic states called here Zombie State (ZS), which can be used in a manner of FCSs but without Grassmann algebra. Instead, for Zombie States, a very simple sign-changing rule is used in the definition of creation and annihilation operators. Then, calculation of electronic structure Hamiltonian matrix elements between two ZSs becomes very simple and a straightforward technique for time propagation of fermionic wave functions can be developed. By analogy with the existing methods based on Canonical Coherent States of Harmonic Oscillator, fermionic wave functions can be propagated using a set of randomly selected Zombie States as a basis. As a proof of principles, the proposed Coupled Zombie States approach is tested on a simple example showing that the technique is exact.

Relationships between scalp, brain, and skull motion estimated using magnetic resonance elastography.

PubMed

Badachhape, Andrew A; Okamoto, Ruth J; Johnson, Curtis L; Bayly, Philip V

2018-05-17

The objective of this study was to characterize the relationships between motion in the scalp, skull, and brain. In vivo estimates of motion transmission from the skull to the brain may illuminate the mechanics of traumatic brain injury. Because of challenges in directly sensing skull motion, it is useful to know how well motion of soft tissue of the head, i.e., the scalp, can approximate skull motion or predict brain tissue deformation. In this study, motion of the scalp and brain were measured using magnetic resonance elastography (MRE) and separated into components due to rigid-body displacement and dynamic deformation. Displacement estimates in the scalp were calculated using low motion-encoding gradient strength in order to reduce "phase wrapping" (an ambiguity in displacement estimates caused by the 2 π-periodicity of MRE phase contrast). MRE estimates of scalp and brain motion were compared to skull motion estimated from three tri-axial accelerometers. Comparison of the relative amplitudes and phases of harmonic motion in the scalp, skull, and brain of six human subjects indicate that data from scalp-based sensors should be used with caution to estimate skull kinematics, but that fairly consistent relationships exist between scalp, skull, and brain motion. In addition, the measured amplitude and phase relationships of scalp, skull, and brain can be used to evaluate and improve mathematical models of head biomechanics. Copyright © 2018 Elsevier Ltd. All rights reserved.

Support for Simulation-Based Learning; The Effects of Model Progression and Assignments on Learning about Oscillatory Motion.

ERIC Educational Resources Information Center

Swaak, Janine; And Others

In this study, learners worked with a simulation of harmonic oscillation. Two supportive measures were introduced: model progression and assignments. In model progression, the model underlying the simulation is not offered in its full complexity from the start, but variables are gradually introduced. Assignments are small exercises that help the…

Anharmonic phonons and second-order phase-transitions by the stochastic self-consistent harmonic approximation

NASA Astrophysics Data System (ADS)

Mauri, Francesco

Anharmonic effects can generally be treated within perturbation theory. Such an approach breaks down when the harmonic solution is dynamically unstable or when the anharmonic corrections of the phonon energies are larger than the harmonic frequencies themselves. This situation occurs near lattice-related second-order phase-transitions such as charge-density-wave (CDW) or ferroelectric instabilities or in H-containing materials, where the large zero-point motion of the protons results in a violation of the harmonic approximation. Interestingly, even in these cases, phonons can be observed, measured, and used to model transport properties. In order to treat such cases, we developed a stochastic implementation of the self-consistent harmonic approximation valid to treat anharmonicity in the nonperturbative regime and to obtain, from first-principles, the structural, thermodynamic and vibrational properties of strongly anharmonic systems. I will present applications to the ferroelectric transitions in SnTe, to the CWD transitions in NbS2 and NbSe2 (in bulk and monolayer) and to the hydrogen-bond symmetrization transition in the superconducting hydrogen sulfide system, that exhibits the highest Tc reported for any superconductor so far. In all cases we are able to predict the transition temperature (pressure) and the evolution of phonons with temperature (pressure). This project has received funding from the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore1.

Predicting Mercury's precession using simple relativistic Newtonian dynamics

NASA Astrophysics Data System (ADS)

Friedman, Y.; Steiner, J. M.

2016-03-01

We present a new simple relativistic model for planetary motion describing accurately the anomalous precession of the perihelion of Mercury and its origin. The model is based on transforming Newton's classical equation for planetary motion from absolute to real spacetime influenced by the gravitational potential and introducing the concept of influenced direction.

A harmonic adiabatic approximation to calculate highly excited vibrational levels of ``floppy molecules''

NASA Astrophysics Data System (ADS)

Lauvergnat, David; Nauts, André; Justum, Yves; Chapuisat, Xavier

2001-04-01

The harmonic adiabatic approximation (HADA), an efficient and accurate quantum method to calculate highly excited vibrational levels of molecular systems, is presented. It is well-suited to applications to "floppy molecules" with a rather large number of atoms (N>3). A clever choice of internal coordinates naturally suggests their separation into active, slow, or large amplitude coordinates q', and inactive, fast, or small amplitude coordinates q″, which leads to an adiabatic (or Born-Oppenheimer-type) approximation (ADA), i.e., the total wave function is expressed as a product of active and inactive total wave functions. However, within the framework of the ADA, potential energy data concerning the inactive coordinates q″ are required. To reduce this need, a minimum energy domain (MED) is defined by minimizing the potential energy surface (PES) for each value of the active variables q', and a quadratic or harmonic expansion of the PES, based on the MED, is used (MED harmonic potential). In other words, the overall picture is that of a harmonic valley about the MED. In the case of only one active variable, we have a minimum energy path (MEP) and a MEP harmonic potential. The combination of the MED harmonic potential and the adiabatic approximation (harmonic adiabatic approximation: HADA) greatly reduces the size of the numerical computations, so that rather large molecules can be studied. In the present article however, the HADA is applied to our benchmark molecule HCN/CNH, to test the validity of the method. Thus, the HADA vibrational energy levels are compared and are in excellent agreement with the ADA calculations (adiabatic approximation with the full PES) of Light and Bačić [J. Chem. Phys. 87, 4008 (1987)]. Furthermore, the exact harmonic results (exact calculations without the adiabatic approximation but with the MEP harmonic potential) are compared to the exact calculations (without any sort of approximation). In addition, we compare the densities of the bending motion during the HCN/CNH isomerization, computed with the HADA and the exact wave function.

Disorders of motion and depth.

PubMed

Nawrot, Mark

2003-08-01

Damage to the human homologue of area MT produces a motion perception deficit similar to that found in the monkey with MT lesions. Even temporary disruption of MT processing with transcranial magnetic stimulation can produce a temporary akinetopsia [127]. Motion perception deficits, however, also are found with a variety of subcortical lesions and other neurologic disorders that can best be described as causing a disconnection within the motion processing stream. The precise role of these subcortical structures, such as the cerebellum, remains to be determined. Simple motion perception, moreover, is only a part of MT function. It undoubtedly has an important role in the perception of depth from motion and stereopsis [112]. Psychophysical studies using aftereffects in normal observers suggest a link between stereo mechanisms and the perception of depth from motion [9-11]. There is even a simple correlation between stereo acuity and the perception of depth from motion [128]. Future studies of patients with cortical lesions will take a closer look at depth perception in association with motion perception and should provide a better understanding of how motion and depth are processed together.

Complex demodulation in VLBI estimation of high frequency Earth rotation components

NASA Astrophysics Data System (ADS)

Böhm, S.; Brzeziński, A.; Schuh, H.

2012-12-01

The spectrum of high frequency Earth rotation variations contains strong harmonic signal components mainly excited by ocean tides along with much weaker non-harmonic fluctuations driven by irregular processes like the diurnal thermal tides in the atmosphere and oceans. In order to properly investigate non-harmonic phenomena a representation in time domain is inevitable. We present a method, operating in time domain, which is easily applicable within Earth rotation estimation from Very Long Baseline Interferometry (VLBI). It enables the determination of diurnal and subdiurnal variations, and is still effective with merely diurnal parameter sampling. The features of complex demodulation are used in an extended parameterization of polar motion and universal time which was implemented into a dedicated version of the Vienna VLBI Software VieVS. The functionality of the approach was evaluated by comparing amplitudes and phases of harmonic variations at tidal periods (diurnal/semidiurnal), derived from demodulated Earth rotation parameters (ERP), estimated from hourly resolved VLBI ERP time series and taken from a recently published VLBI ERP model to the terms of the conventional model for ocean tidal effects in Earth rotation recommended by the International Earth Rotation and Reference System Service (IERS). The three sets of tidal terms derived from VLBI observations extensively agree among each other within the three-sigma level of the demodulation approach, which is below 6 μas for polar motion and universal time. They also coincide in terms of differences to the IERS model, where significant deviations primarily for several major tidal terms are apparent. An additional spectral analysis of the as well estimated demodulated ERP series of the ter- and quarterdiurnal frequency bands did not reveal any significant signal structure. The complex demodulation applied in VLBI parameter estimation could be demonstrated a suitable procedure for the reliable reproduction of high frequency Earth rotation components and thus represents a qualified tool for future studies of irregular geophysical signals in ERP measured by space geodetic techniques.

Cavity enhanced third harmonic generation in graphene

NASA Astrophysics Data System (ADS)

Beckerleg, Chris; Constant, Thomas J.; Zeimpekis, Ioannis; Hornett, Samuel M.; Craig, Chris; Hewak, Daniel W.; Hendry, Euan

2018-01-01

Graphene displays a surprisingly large third order nonlinearity. Here, we report that conversion efficiencies approaching 10-4 are possible for third harmonic generation (THG). Moreover, the atomically thin nature of graphene allows for simple integration in cavity designs to increase this even further. We demonstrate a 117-fold enhancement, of resonant vs non-resonant wavelengths in the THG from graphene due to the integration of a graphene layer with a resonant cavity. This large enhancement occurs as the cavity is resonant for both the fundamental field and the third harmonic. We model this effect using the finite difference time domain approach. By comparing our model with experiment, we are able to deduce the value of a bulk third order susceptibility of graphene of |χ(3)|=4 ×10-17(m/V ) 2 .

Generation of Crystal-Structure Transverse Patterns via a Self-Frequency-Doubling Laser

PubMed Central

Yu, Haohai; Zhang, Huaijin; Wang, Yicheng; Wang, Zhengping; Wang, Jiyang; Petrov, V.

2013-01-01

Two-dimensional (2D) visible crystal-structure patterns analogous to the quantum harmonic oscillator (QHO) have been experimentally observed in the near- and far-fields of a self-frequency-doubling (SFD) microchip laser. Different with the fundamental modes, the localization of the SFD light is changed with the propagation. Calculation based on Hermite-Gaussian (HG) functions and second harmonic generation theory reproduces well the patterns both in the near- and far-field which correspond to the intensity distribution in coordinate and momentum spaces, respectively. Considering the analogy of wave functions of the transverse HG mode and 2D harmonic oscillator, we propose that the simple monolithic SFD lasers can be used for developing of new materials and devices and testing 2D quantum mechanical theories. PMID:23336067

Generation of crystal-structure transverse patterns via a self-frequency-doubling laser.

PubMed

Yu, Haohai; Zhang, Huaijin; Wang, Yicheng; Wang, Zhengping; Wang, Jiyang; Petrov, V

2013-01-01

Two-dimensional (2D) visible crystal-structure patterns analogous to the quantum harmonic oscillator (QHO) have been experimentally observed in the near- and far-fields of a self-frequency-doubling (SFD) microchip laser. Different with the fundamental modes, the localization of the SFD light is changed with the propagation. Calculation based on Hermite-Gaussian (HG) functions and second harmonic generation theory reproduces well the patterns both in the near- and far-field which correspond to the intensity distribution in coordinate and momentum spaces, respectively. Considering the analogy of wave functions of the transverse HG mode and 2D harmonic oscillator, we propose that the simple monolithic SFD lasers can be used for developing of new materials and devices and testing 2D quantum mechanical theories.

Development and applications of algorithms for calculating the transonic flow about harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Weatherill, W. H.; Yip, E. L.

1984-01-01

A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.

Development and application of a program to calculate transonic flow around an oscillating three-dimensional wing using finite difference procedures

NASA Technical Reports Server (NTRS)

Weatherill, Warren H.; Ehlers, F. Edward

1989-01-01

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. Difference equations are derived for harmonic transonic flow to include a coordinate transformation for swept and tapered planforms. A pilot program is developed for three-dimensional planar lifting surface configurations (including thickness) for the CRAY-XMP at Boeing Commercial Airplanes and for the CYBER VPS-32 at the NASA Langley Research Center. An investigation is made of the effect of the location of the outer boundaries on accuracy for very small reduced frequencies. Finally, the pilot program is applied to the flutter analysis of a rectangular wing.

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation formore » the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.« less

Simple lock-in detection technique utilizing multiple harmonics for digital PGC demodulators.

PubMed

Duan, Fajie; Huang, Tingting; Jiang, Jiajia; Fu, Xiao; Ma, Ling

2017-06-01

A simple lock-in detection technique especially suited for digital phase-generated carrier (PGC) demodulators is proposed in this paper. It mixes the interference signal with rectangular waves whose Fourier expansions contain multiple odd or multiple even harmonics of the carrier to recover the quadrature components needed for interference phase demodulation. In this way, the use of a multiplier is avoided and the efficiency of the algorithm is improved. Noise performance with regard to light intensity variation and circuit noise is analyzed theoretically for both the proposed technique and the traditional lock-in technique, and results show that the former provides a better signal-to-noise ratio than the latter with proper modulation depth and average interference phase. Detailed simulations were conducted and the theoretical analysis was verified. A fiber-optic Michelson interferometer was constructed and the feasibility of the proposed technique is demonstrated.

A study of the effect of space-dependent neutronics on stochastically-induced bifurcations in BWR dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Analytis, G.T.

1995-09-01

A non-linear one-group space-dependent neutronic model for a finite one-dimensional core is coupled with a simple BWR feed-back model. In agreement with results obtained by the authors who originally developed the point-kinetics version of this model, we shall show numerically that stochastic reactivity excitations may result in limit-cycles and eventually in a chaotic behaviour, depending on the magnitude of the feed-back coefficient K. In the framework of this simple space-dependent model, the effect of the non-linearities on the different spatial harmonics is studied and the importance of the space-dependent effects is exemplified and assessed in terms of the importance ofmore » the higher harmonics. It is shown that under certain conditions, when the limit-cycle-type develop, the neutron spectra may exhibit strong space-dependent effects.« less

Asymmetric network connectivity using weighted harmonic averages

NASA Astrophysics Data System (ADS)

Morrison, Greg; Mahadevan, L.

2011-02-01

We propose a non-metric measure of the "closeness" felt between two nodes in an undirected, weighted graph using a simple weighted harmonic average of connectivity, that is a real-valued Generalized Erdös Number (GEN). While our measure is developed with a collaborative network in mind, the approach can be of use in a variety of artificial and real-world networks. We are able to distinguish between network topologies that standard distance metrics view as identical, and use our measure to study some simple analytically tractable networks. We show how this might be used to look at asymmetry in authorship networks such as those that inspired the integer Erdös numbers in mathematical coauthorships. We also show the utility of our approach to devise a ratings scheme that we apply to the data from the NetFlix prize, and find a significant improvement using our method over a baseline.

Euler flow predictions for an oscillating cascade using a high resolution wave-split scheme

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Swafford, Timothy W.; Reddy, T. S. R.

1991-01-01

A compressible flow code that can predict the nonlinear unsteady aerodynamics associated with transonic flows over oscillating cascades is developed and validated. The code solves the two dimensional, unsteady Euler equations using a time-marching, flux-difference splitting scheme. The unsteady pressures and forces can be determined for arbitrary input motions, although only harmonic pitching and plunging motions are addressed. The code solves the flow equations on a H-grid which is allowed to deform with the airfoil motion. Predictions are presented for both flat plate cascades and loaded airfoil cascades. Results are compared to flat plate theory and experimental data. Predictions are also presented for several oscillating cascades with strong normal shocks where the pitching amplitudes, cascade geometry and interblade phase angles are varied to investigate nonlinear behavior.

Negative-Mass Instability of the Spin and Motion of an Atomic Gas Driven by Optical Cavity Backaction

NASA Astrophysics Data System (ADS)

Kohler, Jonathan; Gerber, Justin A.; Dowd, Emma; Stamper-Kurn, Dan M.

2018-01-01

We realize a spin-orbit interaction between the collective spin precession and center-of-mass motion of a trapped ultracold atomic gas, mediated by spin- and position-dependent dispersive coupling to a driven optical cavity. The collective spin, precessing near its highest-energy state in an applied magnetic field, can be approximated as a negative-mass harmonic oscillator. When the Larmor precession and mechanical motion are nearly resonant, cavity mediated coupling leads to a negative-mass instability, driving exponential growth of a correlated mode of the hybrid system. We observe this growth imprinted on modulations of the cavity field and estimate the full covariance of the resulting two-mode state by observing its transient decay during subsequent free evolution.

Cyclotron Phase-Coherent Ion Spatial Dispersion in a Non-Quadratic Trapping Potential is Responsible for FT-ICR MS at the Cyclotron Frequency

NASA Astrophysics Data System (ADS)

Nagornov, Konstantin O.; Kozhinov, Anton N.; Tsybin, Yury O.

2018-01-01

Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) at the cyclotron frequency instead of the reduced cyclotron frequency has been experimentally demonstrated using narrow aperture detection electrode (NADEL) ICR cells. Here, based on the results of SIMION simulations, we provide the initial mechanistic insights into the cyclotron frequency regime generation in FT-ICR MS. The reason for cyclotron frequency regime is found to be a new type of a collective motion of ions with a certain dispersion in the initial characteristics, such as pre-excitation ion velocities, in a highly non-quadratic trapping potential as realized in NADEL ICR cells. During ion detection, ions of the same m/z move in phase for cyclotron ion motion but out of phase for magnetron (drift) ion motion destroying signals at the fundamental and high order harmonics that comprise reduced cyclotron frequency components. After an initial magnetron motion period, ion clouds distribute into a novel type of structures - ion slabs, elliptical cylinders, or star-like structures. These structures rotate at the Larmor (half-cyclotron) frequency on a plane orthogonal to the magnetic field, inducing signals at the true cyclotron frequency on each of the narrow aperture detection electrodes. To eliminate the reduced cyclotron frequency peak upon dipolar ion detection, a number of slabs or elliptical cylinders organizing a star-like configuration are formed. In a NADEL ICR cell with quadrupolar ion detection, a single slab or an elliptical cylinder is sufficient to minimize the intensity of the reduced cyclotron frequency components, particularly the second harmonic. [Figure not available: see fulltext.

Series expansions of rotating two and three dimensional sound fields.

PubMed

Poletti, M A

2010-12-01

The cylindrical and spherical harmonic expansions of oscillating sound fields rotating at a constant rate are derived. These expansions are a generalized form of the stationary sound field expansions. The derivations are based on the representation of interior and exterior sound fields using the simple source approach and determination of the simple source solutions with uniform rotation. Numerical simulations of rotating sound fields are presented to verify the theory.

Extracting harmonic signal from a chaotic background with local linear model

NASA Astrophysics Data System (ADS)

Li, Chenlong; Su, Liyun

2017-02-01

In this paper, the problems of blind detection and estimation of harmonic signal in strong chaotic background are analyzed, and new methods by using local linear (LL) model are put forward. The LL model has been exhaustively researched and successfully applied for fitting and forecasting chaotic signal in many chaotic fields. We enlarge the modeling capacity substantially. Firstly, we can predict the short-term chaotic signal and obtain the fitting error based on the LL model. Then we detect the frequencies from the fitting error by periodogram, a property on the fitting error is proposed which has not been addressed before, and this property ensures that the detected frequencies are similar to that of harmonic signal. Secondly, we establish a two-layer LL model to estimate the determinate harmonic signal in strong chaotic background. To estimate this simply and effectively, we develop an efficient backfitting algorithm to select and optimize the parameters that are hard to be exhaustively searched for. In the method, based on sensitivity to initial value of chaos motion, the minimum fitting error criterion is used as the objective function to get the estimation of the parameters of the two-layer LL model. Simulation shows that the two-layer LL model and its estimation technique have appreciable flexibility to model the determinate harmonic signal in different chaotic backgrounds (Lorenz, Henon and Mackey-Glass (M-G) equations). Specifically, the harmonic signal can be extracted well with low SNR and the developed background algorithm satisfies the condition of convergence in repeated 3-5 times.

Hydrological signal in polar motion excitation from a combination of geophysical and gravimetric series

NASA Astrophysics Data System (ADS)

Nastula, Jolanta; Winska, Malgorzata; Salstein, David A.

2015-08-01

One can estimate the hydrological signal in polar motion excitation as a residual, namely the difference between observed geodetic excitation functions (Geodetic Angular Momentum, GAM) and the sum of Atmospheric Angular Momentum (AAM) and Oceanic Angular Momentum (OAM).The aim of this study is to find the optimal model and results for hydrological excitation functions in terms of their agreement with the computed difference between GAM and atmospheric and oceanic signals.The atmospheric and oceanic model-based data that we use in this study are the geophysical excitation functions of AAM, OAM available from the Special Bureaus for the Atmosphere and Oceans of the Geophysical Global Fluids Center (GGFC) of the International Earth Rotation and Reference Systems Service (IERS). For the atmosphere and ocean, these functions are based on the mass and motion fields of the fluids.Global models of land hydrology are used to estimate hydrological excitation functions of polar motion (Hydrological Angular Momentum - HAM). These HAM series are the mass of water substance determined from the various types of land-based hydrological reservoirs. In addition the HAM are estimated from spherical harmonic coefficients of the Earth’s gravity field. We use several sets of degree-2, order-1 harmonics of the Earth’s gravity field, derived from the Gravity Recovery and Climate Experiment (GRACE), Satellite Laser Ranging (SLR), and Global Navigation Satellite Systems (GNSS) data.Finally, these several different HAM series are used to determine the best model of hydrological excitation of polar motion. The model is found by looking for the combination of these series that fits the geodetic residuals using the least-square method.In addition, we will access model results from the Coupled Model Intercomparison Project, fifth experiment (CMIP-5) to examine atmospheric excitations from the twentieth century and estimates for the twenty-first century to see the possible signals and trends of these excitation series to help understand the potential range in the derived of hydrological excitation results.

Bottom boundary layer forced by finite amplitude long and short surface waves motions

NASA Astrophysics Data System (ADS)

Elsafty, H.; Lynett, P.

2018-04-01

A multiple-scale perturbation approach is implemented to solve the Navier-Stokes equations while including bottom boundary layer effects under a single wave and under two interacting waves. In this approach, fluid velocities and the pressure field are decomposed into two components: a potential component and a rotational component. In this study, the two components are exist throughout the entire water column and each is scaled with appropriate length and time scales. A one-way coupling between the two components is implemented. The potential component is assumed to be known analytically or numerically a prior, and the rotational component is forced by the potential component. Through order of magnitude analysis, it is found that the leading-order coupling between the two components occurs through the vertical convective acceleration. It is shown that this coupling plays an important role in the bottom boundary layer behavior. Its effect on the results is discussed for different wave-forcing conditions: purely harmonic forcing and impurely harmonic forcing. The approach is then applied to derive the governing equations for the bottom boundary layer developed under two interacting wave motions. Both motions-the shorter and the longer wave-are decomposed into two components, potential and rotational, as it is done in the single wave. Test cases are presented wherein two different wave forcings are simulated: (1) two periodic oscillatory motions and (2) short waves interacting with a solitary wave. The analysis of the two periodic motions indicates that nonlinear effects in the rotational solution may be significant even though nonlinear effects are negligible in the potential forcing. The local differences in the rotational velocity due to the nonlinear vertical convection coupling term are found to be on the order of 30% of the maximum boundary layer velocity for the cases simulated in this paper. This difference is expected to increase with the increase in wave nonlinearity.

Revisiting the hypothesis of equating the 6-year oscillation in the length-of-day to the mantle-inner core gravitational coupling

NASA Astrophysics Data System (ADS)

Chao, B. F.

2016-12-01

The steady 6-year oscillation observed in the length-of-day variation (ΔLOD) has been postulated to be, among others, an intrinsic oscillatory mode of the Earth's axial spin due to the mantle-inner core gravitational (MICG) coupling [Buffett and Mound, 2005]. Here I develop the general equation of motion of the 3-D MICG system from first principles in terms of multipole-multipole interactions (as in molecular electric field) under simple but realistic assumptions including the buoyancy effect of the fluid outer core. When specialized to the governing of the simple-harmonic oscillation in ΔLOD, the restoring force thereof is predominated, not surprisingly, by the [degree-2, order-2] density anomalies in the lower mantle and the upper inner core. Equating the corresponding "spring constant" to that belonging to the 6-year ΔLOD oscillation, one can estimate the difference between the two inner-core equatorial principal moments of inertia to be (BIC-AIC) ≈ 1.08 x 1031 kg m2 accurate perhaps to within a factor of 2, or a tri-axiality factor about 8 times larger than that of the whole Earth. Moreover, the orientation of the two principal axes can be identified in accordance with the timing of the 6-year ΔLOD oscillation. The physical excitation of the 6-year ΔLOD oscillation, ±0.12 ms in amplitude, is beyond the present scope.

Decoding Mode-mixing in Black-hole Merger Ringdown

NASA Technical Reports Server (NTRS)

Kelly, Bernard J.; Baker, John G.

2013-01-01

Optimal extraction of information from gravitational-wave observations of binary black-hole coalescences requires detailed knowledge of the waveforms. Current approaches for representing waveform information are based on spin-weighted spherical harmonic decomposition. Higher-order harmonic modes carrying a few percent of the total power output near merger can supply information critical to determining intrinsic and extrinsic parameters of the binary. One obstacle to constructing a full multi-mode template of merger waveforms is the apparently complicated behavior of some of these modes; instead of settling down to a simple quasinormal frequency with decaying amplitude, some |m| = modes show periodic bumps characteristic of mode-mixing. We analyze the strongest of these modes the anomalous (3, 2) harmonic mode measured in a set of binary black-hole merger waveform simulations, and show that to leading order, they are due to a mismatch between the spherical harmonic basis used for extraction in 3D numerical relativity simulations, and the spheroidal harmonics adapted to the perturbation theory of Kerr black holes. Other causes of mode-mixing arising from gauge ambiguities and physical properties of the quasinormal ringdown modes are also considered and found to be small for the waveforms studied here.

Improving Students’ Science Process Skills through Simple Computer Simulations on Linear Motion Conceptions

NASA Astrophysics Data System (ADS)

Siahaan, P.; Suryani, A.; Kaniawati, I.; Suhendi, E.; Samsudin, A.

2017-02-01

The purpose of this research is to identify the development of students’ science process skills (SPS) on linear motion concept by utilizing simple computer simulation. In order to simplify the learning process, the concept is able to be divided into three sub-concepts: 1) the definition of motion, 2) the uniform linear motion and 3) the uniformly accelerated motion. This research was administered via pre-experimental method with one group pretest-posttest design. The respondents which were involved in this research were 23 students of seventh grade in one of junior high schools in Bandung City. The improving process of students’ science process skill is examined based on normalized gain analysis from pretest and posttest scores for all sub-concepts. The result of this research shows that students’ science process skills are dramatically improved by 47% (moderate) on observation skill; 43% (moderate) on summarizing skill, 70% (high) on prediction skill, 44% (moderate) on communication skill and 49% (moderate) on classification skill. These results clarify that the utilizing simple computer simulations in physics learning is be able to improve overall science skills at moderate level.

The phantom robot - Predictive displays for teleoperation with time delay

NASA Technical Reports Server (NTRS)

Bejczy, Antal K.; Kim, Won S.; Venema, Steven C.

1990-01-01

An enhanced teleoperation technique for time-delayed bilateral teleoperator control is discussed. The control technique selected for time delay is based on the use of a high-fidelity graphics phantom robot that is being controlled in real time (without time delay) against the static task image. Thus, the motion of the phantom robot image on the monitor predicts the motion of the real robot. The real robot's motion will follow the phantom robot's motion on the monitor with the communication time delay implied in the task. Real-time high-fidelity graphics simulation of a PUMA arm is generated and overlaid on the actual camera view of the arm. A simple camera calibration technique is used for calibrated graphics overlay. A preliminary experiment is performed with the predictive display by using a very simple tapping task. The results with this simple task indicate that predictive display enhances the human operator's telemanipulation task performance significantly during free motion when there is a long time delay. It appears, however, that either two-view or stereoscopic predictive displays are necessary for general three-dimensional tasks.

Oscillations of a Simple Pendulum with Extremely Large Amplitudes

ERIC Educational Resources Information Center

Butikov, Eugene I.

2012-01-01

Large oscillations of a simple rigid pendulum with amplitudes close to 180[degrees] are treated on the basis of a physically justified approach in which the cycle of oscillation is divided into several stages. The major part of the almost closed circular path of the pendulum is approximated by the limiting motion, while the motion in the vicinity…

Simple motion correction strategy reduces respiratory-induced motion artifacts for k-t accelerated and compressed-sensing cardiovascular magnetic resonance perfusion imaging.

PubMed

Zhou, Ruixi; Huang, Wei; Yang, Yang; Chen, Xiao; Weller, Daniel S; Kramer, Christopher M; Kozerke, Sebastian; Salerno, Michael

2018-02-01

Cardiovascular magnetic resonance (CMR) stress perfusion imaging provides important diagnostic and prognostic information in coronary artery disease (CAD). Current clinical sequences have limited temporal and/or spatial resolution, and incomplete heart coverage. Techniques such as k-t principal component analysis (PCA) or k-t sparcity and low rank structure (SLR), which rely on the high degree of spatiotemporal correlation in first-pass perfusion data, can significantly accelerate image acquisition mitigating these problems. However, in the presence of respiratory motion, these techniques can suffer from significant degradation of image quality. A number of techniques based on non-rigid registration have been developed. However, to first approximation, breathing motion predominantly results in rigid motion of the heart. To this end, a simple robust motion correction strategy is proposed for k-t accelerated and compressed sensing (CS) perfusion imaging. A simple respiratory motion compensation (MC) strategy for k-t accelerated and compressed-sensing CMR perfusion imaging to selectively correct respiratory motion of the heart was implemented based on linear k-space phase shifts derived from rigid motion registration of a region-of-interest (ROI) encompassing the heart. A variable density Poisson disk acquisition strategy was used to minimize coherent aliasing in the presence of respiratory motion, and images were reconstructed using k-t PCA and k-t SLR with or without motion correction. The strategy was evaluated in a CMR-extended cardiac torso digital (XCAT) phantom and in prospectively acquired first-pass perfusion studies in 12 subjects undergoing clinically ordered CMR studies. Phantom studies were assessed using the Structural Similarity Index (SSIM) and Root Mean Square Error (RMSE). In patient studies, image quality was scored in a blinded fashion by two experienced cardiologists. In the phantom experiments, images reconstructed with the MC strategy had higher SSIM (p < 0.01) and lower RMSE (p < 0.01) in the presence of respiratory motion. For patient studies, the MC strategy improved k-t PCA and k-t SLR reconstruction image quality (p < 0.01). The performance of k-t SLR without motion correction demonstrated improved image quality as compared to k-t PCA in the setting of respiratory motion (p < 0.01), while with motion correction there is a trend of better performance in k-t SLR as compared with motion corrected k-t PCA. Our simple and robust rigid motion compensation strategy greatly reduces motion artifacts and improves image quality for standard k-t PCA and k-t SLR techniques in setting of respiratory motion due to imperfect breath-holding.

Rhythmic crowd bobbing on a grandstand simulator

NASA Astrophysics Data System (ADS)

Comer, A. J.; Blakeborough, A.; Williams, M. S.

2013-01-01

It is widely accepted that concerted human activity such as bouncing or bobbing can excite cantilever grandstands. Crowd coordination can be unwitting and may be exacerbated by structural motion caused by resonant structural response. This is an area of uncertainty in the design and analysis of modern grandstands. This paper presents experimental measurement and analysis of rhythmic crowd bobbing loads obtained from tests on a grandstand simulator with two distinct support conditions; (a) rigid, and; (b) flexible. It was found that significant structural vibration at the bobbing frequency did not increase the effective bobbing load. Structural motion at the bobbing frequency caused a reduction in the dynamic load factor (DLF) at the frequency of the second harmonic while those at the first and third harmonics were unaffected. Two plausible reasons for this are: (a) the bobbing group were unable to supply significant energy to the system at the frequency of the second harmonic; (b) the bobbing group altered their bobbing style to reduce the response of the grandstand simulator. It was deduced that the bobbing group did not absorb energy from the dynamic system. Furthermore, dynamic load factors for groups of test subjects bobbing on a rigid structure were typically greater than those of synthesised groups derived from individuals bobbing alone, possibly due to group effects such as audio and visual stimuli from neighbouring test subjects. Last, the vibration levels experienced by the test subjects appear to be below levels likely to cause discomfort. This is to be expected as the test subjects were themselves controlling the magnitude and duration of vibration for the bobbing tests considered.

A novel approach for quantitative harmonization in PET.

PubMed

Namías, M; Bradshaw, T; Menezes, V O; Machado, M A D; Jeraj, R

2018-05-04

Positron emission tomography (PET) imaging allows for measurement of activity concentrations of a given radiotracer in vivo. The quantitative capabilities of PET imaging are particularly important in the context of monitoring response to treatment, where quantitative changes in tracer uptake could be used as a biomarker of treatment response. Reconstruction algorithms and settings have a significant impact on PET quantification. In this work we introduce a novel harmonization methodology requiring only a simple cylindrical phantom and show that it can match the performance of more complex harmonization approaches based on phantoms with spherical inserts. Resolution and noise measurements from cylindrical phantoms are used to simulate the spherical inserts from NEMA image quality phantoms. An optimization algorithm was used to find the optimal smoothing filters for the simulated NEMA phantom images to identify those that best harmonized the PET scanners. Our methodology was tested on seven different PET models from two manufacturers installed at five institutions. Our methodology is able to predict contrast recovery coefficients (CRCs) from NEMA phantoms with errors within  ±5.2% for CRCmax and  ±3.7% for CRCmean (limits of agreement  =  95%). After applying the proposed harmonization protocol, all the CRC values were within the tolerances from EANM. Quantitative harmonization in compliance with the EARL FDG-PET/CT accreditation program is achieved in a simpler way, without the need of NEMA phantoms. This may lead to simplified scanner harmonization workflows more accessible to smaller institutions.

Guitar Strings as Standing Waves: A Demonstration

ERIC Educational Resources Information Center

Davis, Michael

2007-01-01

The study demonstrates the induction of one-dimensional standing waves, called "natural-harmonics" on a guitar to provide a unique tone. The analysis shows that a normally complex vibration is composed of a number of simple and discrete vibrations.

On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator

ERIC Educational Resources Information Center

Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru

2009-01-01

The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.

Harmonic oscillator representation in the theory of scattering and nuclear reactions

NASA Technical Reports Server (NTRS)

Smirnov, Yuri F.; Shirokov, A. M.; Lurie, Yuri, A.; Zaitsev, S. A.

1995-01-01

The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.

Combined study of the solar neighbourhood kinematics - Spherical harmonics and Taylor expansions

NASA Astrophysics Data System (ADS)

Hernandez-Pajares, M.; Nunez, J.

1990-08-01

This paper relates two methods of analyzing the kinematic parameters of the local macroscopic motions of the Galaxy: (1) the Ogorodnikov-Milne model (OM) that consists in the three-dimensional Taylor expansion of the mean velocity field, and (2) the two-dimensional spherical harmonic development of the velocity components (SH). The theoretical relations between the SH coefficients and the second-order OM ones for the radial velocity v(r), and the galactic heliocentric components of the velocity U, V, W are presented. Only the hypothesis of separability of the stellar density function of the sample into angular and radial parts is needed. They are applied to 4732 A-M stars included in the Figueras (1986) sample.

Full thermomechanical coupling in modelling of micropolar thermoelasticity

NASA Astrophysics Data System (ADS)

Murashkin, E. V.; Radayev, Y. N.

2018-04-01

The present paper is devoted to plane harmonic waves of displacements and microrotations propagating in fully coupled thermoelastic continua. The analysis is carried out in the framework of linear conventional thermoelastic micropolar continuum model. The reduced energy balance equation and the special form of the Helmholtz free energy are discussed. The constitutive constants providing fully coupling of equations of motion and heat conduction are considered. The dispersion equation is derived and analysed in the form bi-cubic and bi-quadratic polynoms product. The equation are analyzed by the computer algebra system Mathematica. Algebraic forms expressed by complex multivalued square and cubic radicals are obtained for wavenumbers of transverse and longitudinal waves. The exact forms of wavenumbers of a plane harmonic coupled thermoelastic waves are computed.

Preliminary design study of a higher harmonic blade feathering control system

NASA Technical Reports Server (NTRS)

Powers, R. W.

1980-01-01

The feasibility to incorporate an active higher harmonic control (HHC) system on an OH-6A rotorcraft was demonstrated. The introduction of continuously modulated low amplitude 4P feathering showed potential for reducing rotor transmitted oscillatory loads. The design implementation of this system on a baseline OH-6A required generation of a hydraulic power system, control actuator placement and design integration of an electronic subsystem comprised of an electronic control unit (ECU) and digital microcomputer. Various placements of the HHC actuators in the primary control system are evaluated. Assembly drawings of the actuator concepts and control rigging are presented. The advantages of generating both hydraulic power and 4F control motions in the nonrotating system is confirmed.

Endoplasmic motility spectral characteristics in plasmodium of Physarum polycephalum

NASA Astrophysics Data System (ADS)

Avsievich, T. I.; Ghaleb, K. E. S.; Frolov, S. V.; Proskurin, S. G.

2015-03-01

Spectral Fourier analysis of experimentally acquired velocity time dependencies, V(t), of shuttle endoplasmic motility in an isolated strand of plasmodium of slime mold Physarum Polycephalum has been realized. V(t) registration was performed in normal conditions and after the treatment by respiration inhibitors, which lead to a complete cessation of endoplasmic motion in the strand. Spectral analysis of the velocity time dependences of the endoplasm allows obtaining two distinct harmonic components in the spectra. Their ratio appeared to be constant in all cases, ν2/ν1=1.97±0.17. After the inhibitors are washed out respiratory system becomes normal, gradually restoring the activity of both harmonic oscillatory sources with time. Simulated velocity time dependences correspond to experimental data with good accuracy.

Molecular sensing with magnetic nanoparticles using magnetic spectroscopy of nanoparticle Brownian motion.

PubMed

Zhang, Xiaojuan; Reeves, Daniel B; Perreard, Irina M; Kett, Warren C; Griswold, Karl E; Gimi, Barjor; Weaver, John B

2013-12-15

Functionalized magnetic nanoparticles (mNPs) have shown promise in biosensing and other biomedical applications. Here we use functionalized mNPs to develop a highly sensitive, versatile sensing strategy required in practical biological assays and potentially in vivo analysis. We demonstrate a new sensing scheme based on magnetic spectroscopy of nanoparticle Brownian motion (MSB) to quantitatively detect molecular targets. MSB uses the harmonics of oscillating mNPs as a metric for the freedom of rotational motion, thus reflecting the bound state of the mNP. The harmonics can be detected in vivo from nanogram quantities of iron within 5s. Using a streptavidin-biotin binding system, we show that the detection limit of the current MSB technique is lower than 150 pM (0.075 pmole), which is much more sensitive than previously reported techniques based on mNP detection. Using mNPs conjugated with two anti-thrombin DNA aptamers, we show that thrombin can be detected with high sensitivity (4 nM or 2 pmole). A DNA-DNA interaction was also investigated. The results demonstrated that sequence selective DNA detection can be achieved with 100 pM (0.05 pmole) sensitivity. The results of using MSB to sense these interactions, show that the MSB based sensing technique can achieve rapid measurement (within 10s), and is suitable for detecting and quantifying a wide range of biomarkers or analytes. It has the potential to be applied in variety of biomedical applications or diagnostic analyses. © 2013 Elsevier B.V. All rights reserved.

Harmonic Motion Imaging (HMI) for Tumor Imaging and Treatment Monitoring.

PubMed

Konofagou, Elisa E; Maleke, Caroline; Vappou, Jonathan

2012-01-01

Palpation is an established screening procedure for the detection of several superficial cancers including breast, thyroid, prostate, and liver tumors through both self and clinical examinations. This is because solid masses typically have distinct stiffnesses compared to the surrounding normal tissue. In this paper, the application of Harmonic Motion Imaging (HMI) for tumor detection based on its stiffness as well as its relevance in thermal treatment is reviewed. HMI uses a focused ultrasound (FUS) beam to generate an oscillatory acoustic radiation force for an internal, non-contact palpation to internally estimate relative tissue hardness. HMI studies have dealt with the measurement of the tissue dynamic motion in response to an oscillatory acoustic force at the same frequency, and have been shown feasible in simulations, phantoms, ex vivo human and bovine tissues as well as animals in vivo. Using an FUS beam, HMI can also be used in an ideal integration setting with thermal ablation using high-intensity focused ultrasound (HIFU), which also leads to an alteration in the tumor stiffness. In this paper, a short review of HMI is provided that encompasses the findings in all the aforementioned areas. The findings presented herein demonstrate that the HMI displacement can accurately depict the underlying tissue stiffness, and the HMI image of the relative stiffness could accurately detect and characterize the tumor or thermal lesion based on its distinct properties. HMI may thus constitute a non-ionizing, cost-efficient and reliable complementary method for noninvasive tumor detection, localization, diagnosis and treatment monitoring.

Harmonic Motion Imaging (HMI) for Tumor Imaging and Treatment Monitoring

PubMed Central

Maleke, Caroline; Vappou, Jonathan

2014-01-01

Palpation is an established screening procedure for the detection of several superficial cancers including breast, thyroid, prostate, and liver tumors through both self and clinical examinations. This is because solid masses typically have distinct stiffnesses compared to the surrounding normal tissue. In this paper, the application of Harmonic Motion Imaging (HMI) for tumor detection based on its stiffness as well as its relevance in thermal treatment is reviewed. HMI uses a focused ultrasound (FUS) beam to generate an oscillatory acoustic radiation force for an internal, non-contact palpation to internally estimate relative tissue hardness. HMI studies have dealt with the measurement of the tissue dynamic motion in response to an oscillatory acoustic force at the same frequency, and have been shown feasible in simulations, phantoms, ex vivo human and bovine tissues as well as animals in vivo. Using an FUS beam, HMI can also be used in an ideal integration setting with thermal ablation using high-intensity focused ultrasound (HIFU), which also leads to an alteration in the tumor stiffness. In this paper, a short review of HMI is provided that encompasses the findings in all the aforementioned areas. The findings presented herein demonstrate that the HMI displacement can accurately depict the underlying tissue stiffness, and the HMI image of the relative stiffness could accurately detect and characterize the tumor or thermal lesion based on its distinct properties. HMI may thus constitute a non-ionizing, cost-efficient and reliable complementary method for noninvasive tumor detection, localization, diagnosis and treatment monitoring. PMID:25364321

Conical Euler analysis and active roll suppression for unsteady vortical flows about rolling delta wings

NASA Technical Reports Server (NTRS)

Lee-Rausch, Elizabeth M.; Batina, John T.

1993-01-01

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling, highly swept delta wings undergoing either forced motions or free-to-roll motions that include active roll suppression. The flow solver of the code involves a multistage, Runge-Kutta time-stepping scheme that uses a cell-centered, finite-volume, spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free to-roll case by simultaneously integrating in time the rigid-body equation of motion with the governing flow equations. Results are presented for a delta wing with a 75 deg swept, sharp leading edge at a free-stream Mach number of 1.2 and at 10 deg, 20 deg, and 30 deg angle of attack alpha. At the lower angles of attack (10 and 20 deg), forced-harmonic analyses indicate that the rolling-moment coefficients provide a positive damping, which is verified by free-to-roll calculations. In contrast, at the higher angle of attack (30 deg), a forced-harmonic analysis indicates that the rolling-moment coefficient provides negative damping at the small roll amplitudes. A free-to-roll calculation for this case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation, which is characteristic of highly swept delta wings. This limit cycle oscillation may be actively suppressed through the use of a rate-feedback control law and antisymmetrically deflected leading-edge flaps. Descriptions of the conical Euler flow solver and the free-to roll analysis are included in this report. Results are presented that demonstrate how the systematic analysis of the forced response of the delta wing can be used to predict the stable, neutrally stable, and unstable free response of the delta wing. These results also give insight into the flow physics associated with unsteady vortical flows about delta wings undergoing forced motions and free-to-roll motions, including the active suppression of the wing-rock type phenomenon. The conical Euler methodology developed is directly extend able to three-dimensional calculations.

Force-Free Time-Harmonic Plasmoids

DTIC Science & Technology

1992-10-01

effect of currents or vortical motion are absolutely required for stability. What makes the present model attractive is the minimization of the body ...radiative-mode effects may be very fruitful in the future. For example: Rigid non-radiative composite "particles" containing large numbers of fus- able...12 7. The neutral plasma .......... .......................... 12 8. Forces on a moving electron ....... ......... .............. 13 9. Effects of

Optimum design of a Lanchester damper for a viscously damped single degree of freedom system subjected to inertial excitation

NASA Astrophysics Data System (ADS)

Bapat, V. A.; Prabhu, P.

1980-11-01

The problem of designing an optimum Lanchester damper for a viscously damped single degree of freedom system subjected to inertial harmonic excitation is investigated. Two criteria are used for optimizing the performance of the damper: (i) minimum motion transmissibility; (ii) minimum force transmissibility. Explicit expressions are developed for determining the absorber parameters.

Observed tidal braking in the earth/moon/sun system

NASA Technical Reports Server (NTRS)

Christodoulidis, D. C.; Smith, D. E.; Williamson, R. G.; Klosko, S. M.

1988-01-01

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century-squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century-squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 X 10 to the -22 rad/second-squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change in the earth's rotation rate of -4.69 + or - 0.36 X 10 to the -22 rad/second-squared.

Two-dimensional multi-frequency imaging of a tumor inclusion in a homogeneous breast phantom using the harmonic motion Doppler imaging method.

PubMed

Tafreshi, Azadeh Kamali; Top, Can Barış; Gençer, Nevzat Güneri

2017-06-21

Harmonic motion microwave Doppler imaging (HMMDI) is a novel imaging modality for imaging the coupled electrical and mechanical properties of body tissues. In this paper, we used two experimental systems with different receiver configurations to obtain HMMDI images from tissue-mimicking phantoms at multiple vibration frequencies between 15 Hz and 35 Hz. In the first system, we used a spectrum analyzer to obtain the Doppler data in the frequency domain, while in the second one, we used a homodyne receiver that was designed to acquire time-domain data. The developed phantoms mimicked the elastic and dielectric properties of breast fat tissue, and included a [Formula: see text] mm cylindrical inclusion representing the tumor. A focused ultrasound probe was mechanically scanned in two lateral dimensions to obtain two-dimensional HMMDI images of the phantoms. The inclusions were resolved inside the fat phantom using both experimental setups. The image resolution increased with increasing vibration frequency. The designed receiver showed higher sensitivity than the spectrum analyzer measurements. The results also showed that time-domain data acquisition should be used to fully exploit the potential of the HMMDI method.

Development of a linearized unsteady Euler analysis for turbomachinery blade rows

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Kousen, Kenneth A.

1995-01-01

A linearized unsteady aerodynamic analysis for axial-flow turbomachinery blading is described in this report. The linearization is based on the Euler equations of fluid motion and is motivated by the need for an efficient aerodynamic analysis that can be used in predicting the aeroelastic and aeroacoustic responses of blade rows. The field equations and surface conditions required for inviscid, nonlinear and linearized, unsteady aerodynamic analyses of three-dimensional flow through a single, blade row operating within a cylindrical duct, are derived. An existing numerical algorithm for determining time-accurate solutions of the nonlinear unsteady flow problem is described, and a numerical model, based upon this nonlinear flow solver, is formulated for the first-harmonic linear unsteady problem. The linearized aerodynamic and numerical models have been implemented into a first-harmonic unsteady flow code, called LINFLUX. At present this code applies only to two-dimensional flows, but an extension to three-dimensions is planned as future work. The three-dimensional aerodynamic and numerical formulations are described in this report. Numerical results for two-dimensional unsteady cascade flows, excited by prescribed blade motions and prescribed aerodynamic disturbances at inlet and exit, are also provided to illustrate the present capabilities of the LINFLUX analysis.

Two-dimensional multi-frequency imaging of a tumor inclusion in a homogeneous breast phantom using the harmonic motion Doppler imaging method

NASA Astrophysics Data System (ADS)

Kamali Tafreshi, Azadeh; Barış Top, Can; Güneri Gençer, Nevzat

2017-06-01

Harmonic motion microwave Doppler imaging (HMMDI) is a novel imaging modality for imaging the coupled electrical and mechanical properties of body tissues. In this paper, we used two experimental systems with different receiver configurations to obtain HMMDI images from tissue-mimicking phantoms at multiple vibration frequencies between 15 Hz and 35 Hz. In the first system, we used a spectrum analyzer to obtain the Doppler data in the frequency domain, while in the second one, we used a homodyne receiver that was designed to acquire time-domain data. The developed phantoms mimicked the elastic and dielectric properties of breast fat tissue, and included a 14~\\text{mm}× 9 mm cylindrical inclusion representing the tumor. A focused ultrasound probe was mechanically scanned in two lateral dimensions to obtain two-dimensional HMMDI images of the phantoms. The inclusions were resolved inside the fat phantom using both experimental setups. The image resolution increased with increasing vibration frequency. The designed receiver showed higher sensitivity than the spectrum analyzer measurements. The results also showed that time-domain data acquisition should be used to fully exploit the potential of the HMMDI method.

A semi-analytic theory for the motion of a close-earth artificial satellite with drag

NASA Technical Reports Server (NTRS)

Liu, J. J. F.; Alford, R. L.

1979-01-01

A semi-analytic method is used to estimate the decay history/lifetime and to generate orbital ephemeris for close-earth satellites perturbed by the atmospheric drag and earth oblateness due to the spherical harmonics J2, J3, and J4. The theory maintains efficiency through the application of the theory of a method of averaging and employs sufficient numerical emphasis to include a rather sophisticated atmospheric density model. The averaged drag effects with respect to mean anomaly are evaluated by a Gauss-Legendre quadrature while the averaged variational equations of motion are integrated numerically with automatic step size and error control.

Hybrid Quantum Systems with Trapped Charged Particles

NASA Astrophysics Data System (ADS)

Kotler, Shlomi; Leibfried, Dietrich; Simmonds, Raymond; Wineland, Dave

We will review a joint effort by the Ion Storage Group and the Advanced Microwave Photonics Group at NIST (Boulder, CO) to design a hybrid system that interfaces charged particles with macroscopic high-Q resonators. We specifically consider coupling trapped charges to superconducting LC resonators, the mechanical modes of Silicon-Nitride membranes, and piezo-electric materials. We aim to achieve the strong coupling regime, where a single quantum of motion of the trapped charge can be coherently exchanged with harmonic motion of the macroscopic entity (electrical and/or mechanical). These kind of devices could potentially take advantage of both macroscopic control techniques and the long quantum coherence of its trapped charged particles.

Noncontact rack-pinion-rack device as a differential vibration sensor.

PubMed

Miri, MirFaez; Nasiri, Mojtaba

2010-07-01

We study a nanoscale system composed of one corrugated cylinder (pinion) placed between two corrugated plates (racks). The pinion and racks have no mechanical contact, but are coupled via the lateral Casimir force-one of the most spectacular consequences of quantum fluctuations of the electromagnetic field. The noncontact design of the device could help with the noteworthy wear problem in nanoscale mechanical systems. We consider the case where both racks undergo harmonic lateral motion. We assume that the amplitude, frequency, and phase of one of the racks are known. We show that probing the pinion motion, one can determine the vibration characteristics of the other rack.

SMSIM--Fortran programs for simulating ground motions from earthquakes: Version 2.0.--a revision of OFR 96-80-A

USGS Publications Warehouse

Boore, David M.

2000-01-01

A simple and powerful method for simulating ground motions is based on the assumption that the amplitude of ground motion at a site can be specified in a deterministic way, with a random phase spectrum modified such that the motion is distributed over a duration related to the earthquake magnitude and to distance from the source. This method of simulating ground motions often goes by the name "the stochastic method." It is particularly useful for simulating the higher-frequency ground motions of most interest to engineers, and it is widely used to predict ground motions for regions of the world in which recordings of motion from damaging earthquakes are not available. This simple method has been successful in matching a variety of ground-motion measures for earthquakes with seismic moments spanning more than 12 orders of magnitude. One of the essential characteristics of the method is that it distills what is known about the various factors affecting ground motions (source, path, and site) into simple functional forms that can be used to predict ground motions. SMSIM is a set of programs for simulating ground motions based on the stochastic method. This Open-File Report is a revision of an earlier report (Boore, 1996) describing a set of programs for simulating ground motions from earthquakes. The programs are based on modifications I have made to the stochastic method first introduced by Hanks and McGuire (1981). The report contains source codes, written in Fortran, and executables that can be used on a PC. Programs are included both for time-domain and for random vibration simulations. In addition, programs are included to produce Fourier amplitude spectra for the models used in the simulations and to convert shear velocity vs. depth into frequency-dependent amplification. The revision to the previous report is needed because the input and output files have changed significantly, and a number of new programs have been included in the set.

Characterization of Deficiencies in the Frequency Domain Forced Response Analysis Technique for Turbine Bladed Disks

NASA Technical Reports Server (NTRS)

Brown, Andrew M.; Schmauch, Preston

2012-01-01

Turbine blades in rocket and jet engine turbomachinery experience enormous harmonic loading conditions. These loads result from the integer number of upstream and downstream stator vanes as well as the other turbine stages. The standard technique for forced response analysis to assess structural integrity is to decompose a CFD generated flow field into its harmonic components, and to then perform a frequency response analysis at the problematic natural frequencies. Recent CFD analysis and water-flow testing at NASA/MSFC, though, indicates that this technique may miss substantial harmonic and non-harmonic excitation sources that become present in complex flows. These complications suggest the question of whether frequency domain analysis is capable of capturing the excitation content sufficiently. Two studies comparing frequency response analysis with transient response analysis, therefore, have been performed. The first is of a bladed disk with each blade modeled by simple beam elements. It was hypothesized that the randomness and other variation from the standard harmonic excitation would reduce the blade structural response, but the results showed little reduction. The second study was of a realistic model of a bladed-disk excited by the same CFD used in the J2X engine program. The results showed that the transient analysis results were up to 10% higher for "clean" nodal diameter excitations and six times larger for "messy" excitations, where substantial Fourier content around the main harmonic exists.

Symmetry based frequency domain processing to remove harmonic noise from surface nuclear magnetic resonance measurements

NASA Astrophysics Data System (ADS)

Hein, Annette; Larsen, Jakob Juul; Parsekian, Andrew D.

2017-02-01

Surface nuclear magnetic resonance (NMR) is a unique geophysical method due to its direct sensitivity to water. A key limitation to overcome is the difficulty of making surface NMR measurements in environments with anthropogenic electromagnetic noise, particularly constant frequency sources such as powerlines. Here we present a method of removing harmonic noise by utilizing frequency domain symmetry of surface NMR signals to reconstruct portions of the spectrum corrupted by frequency-domain noise peaks. This method supplements the existing NMR processing workflow and is applicable after despiking, coherent noise cancellation, and stacking. The symmetry based correction is simple, grounded in mathematical theory describing NMR signals, does not introduce errors into the data set, and requires no prior knowledge about the harmonics. Modelling and field examples show that symmetry based noise removal reduces the effects of harmonics. In one modelling example, symmetry based noise removal improved signal-to-noise ratio in the data by 10 per cent. This improvement had noticeable effects on inversion parameters including water content and the decay constant T2*. Within water content profiles, aquifer boundaries and water content are more accurate after harmonics are removed. Fewer spurious water content spikes appear within aquifers, which is especially useful for resolving multilayered structures. Within T2* profiles, estimates are more accurate after harmonics are removed, especially in the lower half of profiles.

Second- and third-harmonic generation in metal-based structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scalora, M.; Akozbek, N.; Bloemer, M. J.

We present a theoretical approach to the study of second- and third-harmonic generation from metallic structures and nanocavities filled with a nonlinear material in the ultrashort pulse regime. We model the metal as a two-component medium, using the hydrodynamic model to describe free electrons and Lorentz oscillators to account for core electron contributions to both the linear dielectric constant and harmonic generation. The active nonlinear medium that may fill a metallic nanocavity, or be positioned between metallic layers in a stack, is also modeled using Lorentz oscillators and surface phenomena due to symmetry breaking are taken into account. We studymore » the effects of incident TE- and TM-polarized fields and show that a simple reexamination of the basic equations reveals additional, exploitable dynamical features of nonlinear frequency conversion in plasmonic nanostructures.« less

Synthetic dimensions for cold atoms from shaking a harmonic trap

NASA Astrophysics Data System (ADS)

Price, Hannah M.; Ozawa, Tomoki; Goldman, Nathan

2017-02-01

We introduce a simple scheme to implement synthetic dimensions in ultracold atomic gases, which only requires two basic and ubiquitous ingredients: the harmonic trap, which confines the atoms, combined with a periodic shaking. In our approach, standard harmonic oscillator eigenstates are reinterpreted as lattice sites along a synthetic dimension, while the coupling between these lattice sites is controlled by the applied time modulation. The phase of this modulation enters as a complex hopping phase, leading straightforwardly to an artificial magnetic field upon adding a second dimension. We show that this artificial gauge field has important consequences, such as the counterintuitive reduction of average energy under resonant driving, or the realization of quantum Hall physics. Our approach offers significant advantages over previous implementations of synthetic dimensions, providing an intriguing route towards higher-dimensional topological physics and strongly-correlated states.

An empirical model for ocean radar backscatter and its application in inversion routine to eliminate wind speed and direction effects

NASA Technical Reports Server (NTRS)

Dome, G. J.; Fung, A. K.; Moore, R. K.

1977-01-01

Several regression models were tested to explain the wind direction dependence of the 1975 JONSWAP (Joint North Sea Wave Project) scatterometer data. The models consider the radar backscatter as a harmonic function of wind direction. The constant term accounts for the major effect of wind speed and the sinusoidal terms for the effects of direction. The fundamental accounts for the difference in upwind and downwind returns, while the second harmonic explains the upwind-crosswind difference. It is shown that a second harmonic model appears to adequately explain the angular variation. A simple inversion technique, which uses two orthogonal scattering measurements, is also described which eliminates the effect of wind speed and direction. Vertical polarization was shown to be more effective in determining both wind speed and direction than horizontal polarization.

A New Model of Jupiter's Magnetic Field From Juno's First Nine Orbits

NASA Astrophysics Data System (ADS)

Connerney, J. E. P.; Kotsiaros, S.; Oliversen, R. J.; Espley, J. R.; Joergensen, J. L.; Joergensen, P. S.; Merayo, J. M. G.; Herceg, M.; Bloxham, J.; Moore, K. M.; Bolton, S. J.; Levin, S. M.

2018-03-01

A spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during its first nine polar orbits about the planet. Observations acquired during eight of these orbits provide the first truly global coverage of Jupiter's magnetic field with a coarse longitudinal separation of 45° between perijoves. The magnetic field is represented with a degree 20 spherical harmonic model for the planetary ("internal") field, combined with a simple model of the magnetodisc for the field ("external") due to distributed magnetospheric currents. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model ("Juno Reference Model through Perijove 9") of the planetary magnetic field with spherical harmonic coefficients well determined through degree and order 10, providing the first detailed view of a planetary dynamo beyond Earth.

SeismoGeodesy: Combination of High Rate, Real-time GNSS and Accelerometer Observations and Rapid Seismic Event Notification for Earth Quake Early Warning and Volcano Monitoring

NASA Astrophysics Data System (ADS)

Jackson, Michael; Zimakov, Leonid; Moessmer, Matthias

2015-04-01

Scientific GNSS networks are moving towards a model of real-time data acquisition, epoch-by-epoch storage integrity, and on-board real-time position and displacement calculations. This new paradigm allows the integration of real-time, high-rate GNSS displacement information with acceleration and velocity data to create very high-rate displacement records. The mating of these two instruments allows the creation of a new, very high-rate (200 Hz) displacement observable that has the full-scale displacement characteristics of GNSS and high-precision dynamic motions of seismic technologies. It is envisioned that these new observables can be used for earthquake early warning studies, volcano monitoring, and critical infrastructure monitoring applications. Our presentation will focus on the characteristics of GNSS, seismic, and strong motion sensors in high dynamic environments, including historic earthquakes replicated on a shake table over a range of displacements and frequencies. We will explore the optimum integration of these sensors from a filtering perspective including simple harmonic impulses over varying frequencies and amplitudes and under the dynamic conditions of various earthquake scenarios. We will also explore the tradeoffs between various GNSS processing schemes including real-time precise point positioning (PPP) and real-time kinematic (RTK) as applied to seismogeodesy. In addition we will discuss implementation of a Rapid Seismic Event Notification System that provides quick delivery of digital data from seismic stations to the acquisition and processing center and a full data integrity model for real-time earthquake notification that provides warning prior to significant ground shaking.

New Hybridized Surface Wave Approach for Geotechnical Modeling of Shear Wave Velocity at Strong Motion Recording Stations

NASA Astrophysics Data System (ADS)

Kayen, R.; Carkin, B.; Minasian, D.

2006-12-01

Strong motion recording (SMR) networks often have little or no shear wave velocity measurements at stations where characterization of site amplification and site period effects is needed. Using the active Spectral Analysis of Surface Waves (SASW) method, and passive H/V microtremor method we have investigated nearly two hundred SMR sites in California, Alaska, Japan, Australia, China and Taiwan. We are conducting these studies, in part, to develop a new hybridized method of site characterization that utilizes a parallel array of harmonic-wave sources for active-source SASW, and a single long period seismometer for passive-source microtremor measurement. Surface wave methods excel in their ability to non-invasively and rapidly characterize the variation of ground stiffness properties with depth below the surface. These methods are lightweight, inexpensive to deploy, and time-efficient. They have been shown to produce accurate and deep soil stiffness profiles. By placing and wiring shakers in a large parallel circuit, either side-by-side on the ground or in a trailer-mounted array, a strong in-phase harmonic wave can be produced. The effect of arraying many sources in parallel is to increase the amplitude of waves received at far-away spaced seismometers at low frequencies so as to extend the longest wavelengths of the captured dispersion curve. The USGS system for profiling uses this concept by arraying between two and eight electro-mechanical harmonic-wave shakers. With large parallel arrays of vibrators, a dynamic force in excess of 1000 lb can be produced to vibrate the ground and produce surface waves. We adjust the harmonic wave through a swept-sine procedure to profile surface wave dispersion down to a frequency of 1 Hz and out to surface wave-wavelengths of 200-1000 meters, depending on the site stiffness. The parallel-array SASW procedure is augmented using H/V microtremor data collected with the active source turned off. Passive array microtremor data reveal the natural and resonance characteristics of the ground by capturing persistent natural vibrations. These microtremors are the result of the interaction of surface waves arriving from distant sources and the stiffness structure of the site under investigation. As such, these resonance effects are effective in constraining the layer thicknesses of the SASW shear wave velocity structure and aid in determining the depth of the deepest layer. Together, the hybridized SASW and H/V procedure provides a complete data set for modeling the geotechnical aspects of ground amplification of earthquake motions. Data from these investigations are available at http://walrus.wr.usgs.gov/geotech.

Visual persistence and cinema?

PubMed

Galifret, Yves

2006-01-01

In Faraday and Plateau's days, both apparent motion and the fusion of intermittent lights, two phenomena that are hardly connected, were explained by retinal persistence. The works of Exner and of the 'Gestalt' psychologists, as well as the modern works on 'sampled' motion and smooth motion, disregarded retinal persistence. One tried, originally, to measure this persistence using intermittent stimulation, but under the pressure of practical concern, what was established in 1902 was the logarithmic relation between fusion frequency and the intensity of the stimulation. One had to wait until the 1950s for the use of harmonic analysis to finally allow a renewal in which many problems that, for decades, had only given rise to discussions that led nowhere and to groundless assertions, were correctly stated and easily solved. To cite this article: Y. Galifret, C. R. Biologies 329 (2006).

Particle confinement by a radially polarized laser Bessel beam

NASA Astrophysics Data System (ADS)

Laredo, Gilad; Kimura, Wayne D.; Schächter, Levi

2017-03-01

The stable trajectory of a charged particle in an external guiding field is an essential condition for its acceleration or for forcing it to generate radiation. Examples of possible guiding devices include a solenoidal magnetic field or permanent periodic magnet in klystrons, a wiggler in free-electron lasers, the lattice of any accelerator, and finally the crystal lattice for the case of channeling radiation. We demonstrate that the trajectory of a point-charge in a radially polarized laser Bessel beam may be stable similarly to the case of a positron that bounces back and forth in the potential well generated by two adjacent atomic planes. While in the case of channeling radiation, the transverse motion is controlled by a harmonic oscillator equation, for a Bessel beam the transverse motion is controlled by the Mathieu equation. Some characteristics of the motion are presented.

Efficient swimming of an assembly of rigid spheres at low Reynolds number.

PubMed

Felderhof, B U

2015-08-01

The swimming of an assembly of rigid spheres immersed in a viscous fluid of infinite extent is studied in low-Reynolds-number hydrodynamics. The instantaneous swimming velocity and rate of dissipation are expressed in terms of the time-dependent displacements of sphere centers about their collective motion. For small-amplitude swimming with periodically oscillating displacements, optimization of the mean swimming speed at given mean power leads to an eigenvalue problem involving a velocity matrix and a power matrix. The corresponding optimal stroke permits generalization to large-amplitude motion in a model of spheres with harmonic interactions and corresponding actuating forces. The method allows straightforward calculation of the swimming performance of structures modeled as assemblies of interacting rigid spheres. A model of three collinear spheres with motion along the common axis is studied as an example.

Comparative Analysis of Models of the Earth's Gravity: 3. Accuracy of Predicting EAS Motion

NASA Astrophysics Data System (ADS)

Kuznetsov, E. D.; Berland, V. E.; Wiebe, Yu. S.; Glamazda, D. V.; Kajzer, G. T.; Kolesnikov, V. I.; Khremli, G. P.

2002-05-01

This paper continues a comparative analysis of modern satellite models of the Earth's gravity which we started in [6, 7]. In the cited works, the uniform norms of spherical functions were compared with their gradients for individual harmonics of the geopotential expansion [6] and the potential differences were compared with the gravitational accelerations obtained in various models of the Earth's gravity [7]. In practice, it is important to know how consistently the EAS motion is represented by various geopotential models. Unless otherwise stated, a model version in which the equations of motion are written using the classical Encke scheme and integrated together with the variation equations by the implicit one-step Everhart's algorithm [1] was used. When calculating coordinates and velocities on the integration step (at given instants of time), the approximate Everhart formula was employed.

Highly eccentric hip-hop solutions of the 2 N-body problem

NASA Astrophysics Data System (ADS)

Barrabés, Esther; Cors, Josep M.; Pinyol, Conxita; Soler, Jaume

2010-02-01

We show the existence of families of hip-hop solutions in the equal-mass 2 N-body problem which are close to highly eccentric planar elliptic homographic motions of 2 N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter ɛ, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ɛ≠0, the topological transversality persists and Brouwer’s fixed point theorem shows the existence of this kind of solutions in the full system.

Reconfigurable paramagnetic microswimmers: Brownian motion affects non-reciprocal actuation.

PubMed

Du, Di; Hilou, Elaa; Biswal, Sibani Lisa

2018-05-09

Swimming at low Reynolds number is typically dominated by a large viscous drag, therefore microscale swimmers require non-reciprocal body deformation to generate locomotion. Purcell described a simple mechanical swimmer at the microscale consisting of three rigid components connected together with two hinges. Here we present a simple microswimmer consisting of two rigid paramagnetic particles with different sizes. When placed in an eccentric magnetic field, this simple microswimmer exhibits non-reciprocal body motion and its swimming locomotion can be directed in a controllable manner. Additional components can be added to create a multibody microswimmer, whereby the particles act cooperatively and translate in a given direction. For some multibody swimmers, the stochastic thermal forces fragment the arm, which therefore modifies the swimming strokes and changes the locomotive speed. This work offers insight into directing the motion of active systems with novel time-varying magnetic fields. It also reveals that Brownian motion not only affects the locomotion of reciprocal swimmers that are subject to the Scallop theorem, but also affects that of non-reciprocal swimmers.

Dynamics of a camphoric acid boat at the air-water interface

NASA Astrophysics Data System (ADS)

Akella, V. S.; Singh, Dhiraj K.; Mandre, Shreyas; Bandi, M. M.

2018-05-01

We report experiments on an agarose gel tablet loaded with camphoric acid (c-boat) spontaneously set into motion by surface tension gradients on the water surface. We observe three distinct modes of c-boat motion: harmonic mode where the c-boat speed oscillates sinusoidally in time, a steady mode where the c-boat maintains constant speed, and an intermittent mode where the c-boat maintains near-zero speed between sudden jumps in speed. Whereas all three modes have been separately reported before in different systems, controlled release of Camphoric Acid (CA) from the agarose gel matrix allowed the observation of all the three modes in the same system. These three modes are a result of a competition between the driving (surface tension gradients) and drag forces acting on the c-boat. Moreover we suggest that there exist two time scales corresponding to spreading of CA and boat motion and the mismatch of these two time scales give rise to the three modes in boat motion. We reproduced all the modes of motion by varying the air-water interfacial tension using Sodium Dodecyl Sulfate (SDS).

Actively triggered 4d cone-beam CT acquisition.

PubMed

Fast, Martin F; Wisotzky, Eric; Oelfke, Uwe; Nill, Simeon

2013-09-01

4d cone-beam computed tomography (CBCT) scans are usually reconstructed by extracting the motion information from the 2d projections or an external surrogate signal, and binning the individual projections into multiple respiratory phases. In this "after-the-fact" binning approach, however, projections are unevenly distributed over respiratory phases resulting in inefficient utilization of imaging dose. To avoid excess dose in certain respiratory phases, and poor image quality due to a lack of projections in others, the authors have developed a novel 4d CBCT acquisition framework which actively triggers 2d projections based on the forward-predicted position of the tumor. The forward-prediction of the tumor position was independently established using either (i) an electromagnetic (EM) tracking system based on implanted EM-transponders which act as a surrogate for the tumor position, or (ii) an external motion sensor measuring the chest-wall displacement and correlating this external motion to the phase-shifted diaphragm motion derived from the acquired images. In order to avoid EM-induced artifacts in the imaging detector, the authors devised a simple but effective "Faraday" shielding cage. The authors demonstrated the feasibility of their acquisition strategy by scanning an anthropomorphic lung phantom moving on 1d or 2d sinusoidal trajectories. With both tumor position devices, the authors were able to acquire 4d CBCTs free of motion blurring. For scans based on the EM tracking system, reconstruction artifacts stemming from the presence of the EM-array and the EM-transponders were greatly reduced using newly developed correction algorithms. By tuning the imaging frequency independently for each respiratory phase prior to acquisition, it was possible to harmonize the number of projections over respiratory phases. Depending on the breathing period (3.5 or 5 s) and the gantry rotation time (4 or 5 min), between ∼90 and 145 projections were acquired per respiratory phase resulting in a dose of ∼1.7-2.6 mGy per respiratory phase. Further dose savings and decreases in the scanning time are possible by acquiring only a subset of all respiratory phases, for example, peak-exhale and peak-inhale only scans. This study is the first experimental demonstration of a new 4d CBCT acquisition paradigm in which imaging dose is efficiently utilized by actively triggering only those projections that are desired for the reconstruction process.

Transverse vibration and buckling of a cantilevered beam with tip body under constant axial base acceleration

NASA Technical Reports Server (NTRS)

Storch, J.; Gates, S.

1983-01-01

The planar transverse bending behavior of a uniform cantilevered beam with rigid tip body subject to constant axial base acceleration was analyzed. The beam is inextensible and capable of small elastic transverse bending deformations only. Two classes of tip bodies are recognized: (1) mass centers located along the beam tip tangent line; and (2) mass centers with arbitrary offset towards the beam attachment point. The steady state response is studied for the beam end condition cases: free, tip mass, tip body with restricted mass center offset, and tip body with arbitrary mass center offset. The first three cases constitute classical Euler buckling problems, and the characteristic equation for the critical loads/accelerations are determined. For the last case a unique steady state solution exists. The free vibration response is examined for the two classes of tip body. The characteristic equation, eigenfunctions and their orthogonality properties are obtained for the case of restricted mass center offset. The vibration problem is nonhomogeneous for the case of arbitrary mass center offset. The exact solution is obtained as a sum of the steady state solution and a superposition of simple harmonic motions.

Experimentation on recurrent sphere collision with Audacity

NASA Astrophysics Data System (ADS)

Muradoglu, Murat; Ng, Enoch Ming Wei; Ng, Tuck Wah

2014-11-01

Under the theme of collisions that occur repeatedly, we conducted easy and inexpensive experiments of rebounding spheres and Newton’s cradle with two spheres to determine the coefficients of restitution using the sound record feature in modern laptops and a free and open source software called Audacity. In the rebounding sphere experiment, the coefficients of restitution of the golf and ping pong balls used were found to be 0.727 ± 0.025 and 0.816 ± 0.041 respectively. With the Netwon’s cradle experiment, the coefficient of restitution of two steel sphere balls was found to be 0.987 ± 0.003. The contrasts in the results obtained from both experiments permit the operational principles of a pendulum to be emphasized, and engagements to be made to consider the transfer of kinetic energy in the form of vibrational energy of the bodies’ constituents. Using a one-dimensional two-mass model with spring and damper linkages to account for harmonic motions that occur during impact, we found it possible to perform a simple analysis to account for this, and how it can be linked to high energy transfer modes such as the phenomenon of resonance and impedance matching.

Analysis and synthesis of laughter

NASA Astrophysics Data System (ADS)

Sundaram, Shiva; Narayanan, Shrikanth

2004-10-01

There is much enthusiasm in the text-to-speech community for synthesis of emotional and natural speech. One idea being proposed is to include emotion dependent paralinguistic cues during synthesis to convey emotions effectively. This requires modeling and synthesis techniques of various cues for different emotions. Motivated by this, a technique to synthesize human laughter is proposed. Laughter is a complex mechanism of expression and has high variability in terms of types and usage in human-human communication. People have their own characteristic way of laughing. Laughter can be seen as a controlled/uncontrolled physiological process of a person resulting from an initial excitation in context. A parametric model based on damped simple harmonic motion to effectively capture these diversities and also maintain the individuals characteristics is developed here. Limited laughter/speech data from actual humans and synthesis ease are the constraints imposed on the accuracy of the model. Analysis techniques are also developed to determine the parameters of the model for a given individual or laughter type. Finally, the effectiveness of the model to capture the individual characteristics and naturalness compared to real human laughter has been analyzed. Through this the factors involved in individual human laughter and their importance can be better understood.

Second-harmonic generation in shear wave beams with different polarizations

NASA Astrophysics Data System (ADS)

Spratt, Kyle S.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2015-10-01

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

Force-motion phase relations and aerodynamic performance of a plunging plate

NASA Astrophysics Data System (ADS)

Son, Onur; Cetiner, Oksan

2018-02-01

Due to the unsteady motion of a plunging plate, forces acting on the body experience a phase difference with respect to the motion. These phase relations are investigated experimentally for a harmonically plunging plate within an amplitude range of 0.05≤ {a/c}≤ 0.6, reduced frequency range of 0.78<{k}<7.06, and at a constant Reynolds number of 10,000. Both streamwise and cross-stream force components are found to have a phase lag following the motion; however, their variations are different. The phase lag of the force on the cross-stream direction increases as the amplitude increases. Drag-thrust transition has an influence on the streamwise force phase lags, which starts to increase when the thrust starts to be produced. Particle image velocimetry measurements are also performed to reveal the relations between vortex structures and force measurements. Leading edge vortex shedding characteristics are observed to be changing from drag occurring cases to thrust producing cases in parallel with the increment in phase lags.

DESIGN STREAM FLOWS BASED ON HARMONIC MEANS.

EPA Science Inventory

Design streamflows are frequently used in water quality studies to provide adequate protection against pollutant exposure periods of a given duration. By analyzing the effect that simple streamflow dilution has on x-day average exposure levels of a pollutant, it appears that the ...

Further Uses of the Analog Computer as a Teaching Tool

ERIC Educational Resources Information Center

Shonle, John I.

1976-01-01

Discusses the use of an analog computer oscilloscope to illustrate the transition from underdamped to overdamped for the simple harmonic oscillator, the maximum range for a projectile, and the behavior of charged particles in crossed electric and magnetic fields. (MLH)

Controlling the high frequency response of H2 by ultra-short tailored laser pulses: A time-dependent configuration interaction study

NASA Astrophysics Data System (ADS)

Schönborn, Jan Boyke; Saalfrank, Peter; Klamroth, Tillmann

2016-01-01

We combine the stochastic pulse optimization (SPO) scheme with the time-dependent configuration interaction singles method in order to control the high frequency response of a simple molecular model system to a tailored femtosecond laser pulse. For this purpose, we use H2 treated in the fixed nuclei approximation. The SPO scheme, as similar genetic algorithms, is especially suited to control highly non-linear processes, which we consider here in the context of high harmonic generation. Here, we will demonstrate that SPO can be used to realize a "non-harmonic" response of H2 to a laser pulse. Specifically, we will show how adding low intensity side frequencies to the dominant carrier frequency of the laser pulse and stochastically optimizing their contribution can create a high-frequency spectral signal of significant intensity, not harmonic to the carrier frequency. At the same time, it is possible to suppress the harmonic signals in the same spectral region, although the carrier frequency is kept dominant during the optimization.

Quantum-mechanical elaboration for the description of low- and high-order harmonics generated by extended gas media: prospects to the efficiency enhancement in spatially modulated media

NASA Astrophysics Data System (ADS)

Stremoukhov, Sergey Yu; Andreev, Anatoly V.

2018-03-01

A simple model fully matching the description of the low- and high-order harmonic generation in extended media interacting with multicolor laser fields is proposed. The extended atomic media is modeled by a 1D chain of atoms, the number of atoms and the distance between them depend on the pressure of the gas and the length of the gas cell. The response of the individual atoms is calculated accurately in the frame of the non-perturbative theory where the driving field for each atom is calculated with account of dispersion properties of any multicolor field component. In spite of the simplicity of the proposed model it provides the detailed description of behaviour of harmonic spectra under variation of the gas pressure and medium length, it also predicts a scaling law for harmonic generation (an invariant). To demonstrate the wide range of applications of the model we have simulated the results of recent experiments dealing with spatially modulated media and obtained good coincidence between the numerical results and the experimental ones.

IUTAM Symposium on Statistical Energy Analysis, 8-11 July 1997, Programme

DTIC Science & Technology

1997-01-01

distribution is unlimited 12b. DISTRIBUTION CODE 13. ABSTRACT (Maximum200 words) This was the first international scientific gathering devoted...energy flow, continuum dynamics, vibrational energy, statistical energy analysis (SEA) 15. NUMBER OF PAGES 16. PRICE CODE INSECURITY... correlation v=V(ɘ ’• • determination of the correlation n^, =11^, (<?). When harmonic motion and time-average are considered, the following I

Multi-parametric monitoring and assessment of high-intensity focused ultrasound (HIFU) boiling by harmonic motion imaging for focused ultrasound (HMIFU): an ex vivo feasibility study

NASA Astrophysics Data System (ADS)

Hou, Gary Y.; Marquet, Fabrice; Wang, Shutao; Konofagou, Elisa E.

2014-03-01

Harmonic motion imaging for focused ultrasound (HMIFU) is a recently developed high-intensity focused ultrasound (HIFU) treatment monitoring method with feasibilities demonstrated in vitro and in vivo. Here, a multi-parametric study is performed to investigate both elastic and acoustics-independent viscoelastic tissue changes using the Harmonic Motion Imaging (HMI) displacement, axial compressive strain and change in relative phase shift during high energy HIFU treatment with tissue boiling. Forty three (n = 43) thermal lesions were formed in ex vivo canine liver specimens (n = 28). Two-dimensional (2D) transverse HMI displacement maps were also obtained before and after lesion formation. The same method was repeated in 10 s, 20 s and 30 s HIFU durations at three different acoustic powers of 8, 10, and 11 W, which were selected and verified as treatment parameters capable of inducing boiling using both thermocouple and passive cavitation detection (PCD) measurements. Although a steady decrease in the displacement, compressive strain, and relative change in the focal phase shift (Δϕ) were obtained in numerous cases, indicating an overall increase in relative stiffness, the study outcomes also showed that during boiling, a reverse lesion-to-background displacement contrast was detected, indicating potential change in tissue absorption, geometrical change and/or, mechanical gelatification or pulverization. Following treatment, corresponding 2D HMI displacement images of the thermal lesions also mapped consistent discrepancy in the lesion-to-background displacement contrast. Despite the expectedly chaotic changes in acoustic properties with boiling, the relative change in phase shift showed a consistent decrease, indicating its robustness to monitor biomechanical properties independent of the acoustic property changes throughout the HIFU treatment. In addition, the 2D HMI displacement images confirmed and indicated the increase in the thermal lesion size with treatment duration, which was validated against pathology. In conclusion, multi-parametric HMIFU was shown capable of monitoring and mapping tissue viscoelastic response changes during and after HIFU boiling, some of which were independent of the acoustic parameter changes.

Multi-parametric monitoring and assessment of High Intensity Focused Ultrasound (HIFU) boiling by Harmonic Motion Imaging for Focused Ultrasound (HMIFU): An ex vivo feasibility study

PubMed Central

Hou, Gary Y.; Marquet, Fabrice; Wang, Shutao; Konofagou, Elisa E.

2014-01-01

Harmonic Motion Imaging for Focused Ultrasound (HMIFU) is a recently developed high-intensity focused ultrasound (HIFU) treatment monitoring method with feasibilities demonstrated in vitro and in vivo. Here, a multi-parametric study is performed to investigate both elastic and acoustics-independent viscoelastic tissue changes using the Harmonic Motion Imaging (HMI) displacement, axial compressive strain and change in relative phase-shift during high energy HIFU treatment with tissue boiling. Forty three (n=43) thermal lesions were formed in ex vivo canine liver specimens (n=28). Two dimensional (2D) transverse HMI displacement maps were also obtained before and after lesion formation. The same method was repeated in 10-s, 20-s and 30-s HIFU durations at three different acoustic powers of 8, 10, and 11W, which were selected and verified as treatment parameters capable of inducing boiling using both thermocouple and Passive Cavitation Detection (PCD) measurements. Although a steady decrease in the displacement, compressive strain, and relative change in the focal phase shift (Δφ) were obtained in numerous cases, indicating an overall increase in relative stiffness, the study outcomes also showed that during boiling, a reverse lesion-to-background displacement contrast was detected, indicating potential change in tissue absorption, geometrical change and/or, mechanical gelatification or pulverization. Following treatment, corresponding 2D HMI displacement images of the thermal lesions also mapped consistent discrepancy in the lesion-to-background displacement contrast. Despite unpredictable changes in acoustic properties with boiling, the relative change in phase shift showed a consistent decrease, indicating its robustness to monitor biomechanical properties independent of the acoustic property change throughout the HIFU treatment. In addition, the 2D HMI displacement images confirmed and indicated the increase in the thermal lesion size with treatment duration, which was validated against pathology. In conclusion, multi-parametric HMIFU was shown capable of monitoring and mapping tissue viscoelastic response changes during and after HIFU boiling, some of which were independent of the acoustic parameter changes. PMID:24556974

Performance assessment of HIFU lesion detection by harmonic motion imaging for focused ultrasound (HMIFU): a 3-D finite-element-based framework with experimental validation.

PubMed

Hou, Gary Y; Luo, Jianwen; Marquet, Fabrice; Maleke, Caroline; Vappou, Jonathan; Konofagou, Elisa E

2011-12-01

Harmonic motion imaging for focused ultrasound (HMIFU) is a novel high-intensity focused ultrasound (HIFU) therapy monitoring method with feasibilities demonstrated in vitro, ex vivo and in vivo. Its principle is based on amplitude-modulated (AM) - harmonic motion imaging (HMI), an oscillatory radiation force used for imaging the tissue mechanical response during thermal ablation. In this study, a theoretical framework of HMIFU is presented, comprising a customized nonlinear wave propagation model, a finite-element (FE) analysis module and an image-formation model. The objective of this study is to develop such a framework to (1) assess the fundamental performance of HMIFU in detecting HIFU lesions based on the change in tissue apparent elasticity, i.e., the increasing Young's modulus, and the HIFU lesion size with respect to the HIFU exposure time and (2) validate the simulation findings ex vivo. The same HMI and HMIFU parameters as in the experimental studies were used, i.e., 4.5-MHz HIFU frequency and 25 Hz AM frequency. For a lesion-to-background Young's modulus ratio of 3, 6 and 9, the FE and estimated HMI displacement ratios were equal to 1.83, 3.69 and 5.39 and 1.65, 3.19 and 4.59, respectively. In experiments, the HMI displacement followed a similar increasing trend of 1.19, 1.28 and 1.78 at 10-s, 20-s and 30-s HIFU exposure, respectively. In addition, moderate agreement in lesion size growth was found in both simulations (16.2, 73.1 and 334.7 mm(2)) and experiments (26.2, 94.2 and 206.2 mm(2)). Therefore, the feasibility of HMIFU for HIFU lesion detection based on the underlying tissue elasticity changes was verified through the developed theoretical framework, i.e., validation of the fundamental performance of the HMIFU system for lesion detection, localization and quantification, was demonstrated both theoretically and ex vivo. Copyright © 2011 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Multi-parametric monitoring and assessment of high-intensity focused ultrasound (HIFU) boiling by harmonic motion imaging for focused ultrasound (HMIFU): an ex vivo feasibility study.

PubMed

Hou, Gary Y; Marquet, Fabrice; Wang, Shutao; Konofagou, Elisa E

2014-03-07

Harmonic motion imaging for focused ultrasound (HMIFU) is a recently developed high-intensity focused ultrasound (HIFU) treatment monitoring method with feasibilities demonstrated in vitro and in vivo. Here, a multi-parametric study is performed to investigate both elastic and acoustics-independent viscoelastic tissue changes using the Harmonic Motion Imaging (HMI) displacement, axial compressive strain and change in relative phase shift during high energy HIFU treatment with tissue boiling. Forty three (n = 43) thermal lesions were formed in ex vivo canine liver specimens (n = 28). Two-dimensional (2D) transverse HMI displacement maps were also obtained before and after lesion formation. The same method was repeated in 10 s, 20 s and 30 s HIFU durations at three different acoustic powers of 8, 10, and 11 W, which were selected and verified as treatment parameters capable of inducing boiling using both thermocouple and passive cavitation detection (PCD) measurements. Although a steady decrease in the displacement, compressive strain, and relative change in the focal phase shift (Δϕ) were obtained in numerous cases, indicating an overall increase in relative stiffness, the study outcomes also showed that during boiling, a reverse lesion-to-background displacement contrast was detected, indicating potential change in tissue absorption, geometrical change and/or, mechanical gelatification or pulverization. Following treatment, corresponding 2D HMI displacement images of the thermal lesions also mapped consistent discrepancy in the lesion-to-background displacement contrast. Despite the expectedly chaotic changes in acoustic properties with boiling, the relative change in phase shift showed a consistent decrease, indicating its robustness to monitor biomechanical properties independent of the acoustic property changes throughout the HIFU treatment. In addition, the 2D HMI displacement images confirmed and indicated the increase in the thermal lesion size with treatment duration, which was validated against pathology. In conclusion, multi-parametric HMIFU was shown capable of monitoring and mapping tissue viscoelastic response changes during and after HIFU boiling, some of which were independent of the acoustic parameter changes.