Geometric Phase, Hannay's Angle, and an Exact Action Variable

Canonical structure of a generalized time-periodic harmonic oscillator is studied by finding the exact action variable (invariant). Hannay's angle is defined if closed curves of constant action variables return to the same curves in phase space after a time evolution. The condition for the existence of Hannay's angle turns out to be identical to that for the existence of a complete set of (quasi)periodic wave functions. Hannay's angle is calculated, and it is shown that Berry's relation of semiclassical origin on geometric phase and Hannay's angle is exact for the cases considered.Comment: Submitted to Phys. Rev. Lett. (revised version

Unitary relation between a harmonic oscillator of time-dependent frequency and a simple harmonic oscillator with and without an inverse-square potential

The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the well-known sets of the simple harmonic oscillator. Exact invariants of the time-dependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation. The geometric phases for the wave functions of a generalized harmonic oscillator with an inverse-square potential are given.Comment: Phys. Rev. A (Brief Report), in pres

Endogeneity bias modeling using observables

This paper proposes an alternative solution to the endogeneity problem by explicitly modeling the joint interaction of the endogenous variables and the unobserved causes of the dependent variable as a function of additional observables. We derive identification of the parameters, develop an estimator, and establish its consistency and asymptotic normality

Fracture Mechanics Analyses of Subsurface Defects in Reinforced Carbon-Carbon Joggles Subjected to Thermo-Mechanical Loads

Coating spallation events have been observed along the slip-side joggle region of the Space Shuttle Orbiter wing-leading-edge panels. One potential contributor to the spallation event is a pressure build up within subsurface voids or defects due to volatiles or water vapor entrapped during fabrication, refurbishment, or normal operational use. The influence of entrapped pressure on the thermo-mechanical fracture-mechanics response of reinforced carbon-carbon with subsurface defects is studied. Plane-strain simulations with embedded subsurface defects are performed to characterize the fracture mechanics response for a given defect length when subjected to combined elevated-temperature and subsurface-defect pressure loadings to simulate the unvented defect condition. Various subsurface defect locations of a fixed-length substrate defect are examined for elevated temperature conditions. Fracture mechanics results suggest that entrapped pressure combined with local elevated temperatures have the potential to cause subsurface defect growth and possibly contribute to further material separation or even spallation. For this anomaly to occur, several unusual circumstances would be required making such an outcome unlikely but plausible

Through-the-thickness response of hybrid 2D and 3D woven composites

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106441/1/AIAA2013-1780.pd

Ultrasonic verification of five wave fronts in unidirectional graphite epoxy composite

The existence of five different waves fronts in a unidirectional graphite fiber reinforced epoxy composite with energy flux propagation at the angle of 60 deg with respect to the fiber direction is verified by measuring their corresponding group and phase velocities of longitudinal and shear waves using the through transmission technique. The experimental and theoretical values of phase velocities show excellent agreement for all three modes of wave propagation. It is also verified that the maximum output voltage amplitude is obtained when the line joining the centers of the transmitting and receiving transducers is parallel to the energy propagation direction defined by the deviation angle

On the Inability of Markov Models to Capture Criticality in Human Mobility

We examine the non-Markovian nature of human mobility by exposing the inability of Markov models to capture criticality in human mobility. In particular, the assumed Markovian nature of mobility was used to establish a theoretical upper bound on the predictability of human mobility (expressed as a minimum error probability limit), based on temporally correlated entropy. Since its inception, this bound has been widely used and empirically validated using Markov chains. We show that recurrent-neural architectures can achieve significantly higher predictability, surpassing this widely used upper bound. In order to explain this anomaly, we shed light on several underlying assumptions in previous research works that has resulted in this bias. By evaluating the mobility predictability on real-world datasets, we show that human mobility exhibits scale-invariant long-range correlations, bearing similarity to a power-law decay. This is in contrast to the initial assumption that human mobility follows an exponential decay. This assumption of exponential decay coupled with Lempel-Ziv compression in computing Fano's inequality has led to an inaccurate estimation of the predictability upper bound. We show that this approach inflates the entropy, consequently lowering the upper bound on human mobility predictability. We finally highlight that this approach tends to overlook long-range correlations in human mobility. This explains why recurrent-neural architectures that are designed to handle long-range structural correlations surpass the previously computed upper bound on mobility predictability

Exact quantum states of a general time-dependent quadratic system from classical action

A generalization of driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization which gives a general quadratic Hamiltonian system does not change the classical equation of motion. Based on the observation by Feynman and Hibbs, the propagators (kernels) of the systems are calculated from the classical action, in terms of solutions of the classical equation of motion: two homogeneous and one particular solutions. The kernels are then used to find wave functions which satisfy the Schr\"{o}dinger equation. One of the wave functions is shown to be that of a Gaussian pure state. In every case considered, we prove that the kernel does not depend on the way of choosing the classical solutions, while the wave functions depend on the choice. The generalization which gives a rather complicated quadratic Hamiltonian is simply interpreted as acting an unitary transformation to the driven harmonic oscillator system in the Hamiltonian formulation.Comment: Submitted to Phys. Rev.