Dispersive Estimates for Harmonic Oscillator Systems

We consider a large class of harmonic systems, each defined as a quasi-free dynamics on the Weyl algebra over $\ell^2(\mathbb{Z}^d)$. In contrast to recently obtained, short-time locality estimates, known as Lieb-Robinson bounds, we prove a number of long-time dispersive estimates for these models

Information, Animal Spirits, and the Meaning of Innovations in Consumer Confidence

Innovations to measures of consumer confidence convey incremental information about economic activity far into the future. Comparing the shapes of impulse responses to confidence innovations in the data with the predictions of a calibrated New Keynesian model, we find little evidence of a strong causal channel from autonomous movements in sentiment to economic outcomes (the "animal spirits" interpretation). Rather, these impulse responses support an alternative hypothesis that the surprise movements in confidence reflect information about future economic prospects (the "information" view). Confidence innovations are best characterized as noisy measures of changes in expected productivity growth over a relatively long horizon.

News Shocks

We implement a new approach for the identification of "news shocks" about future technology. In a VAR featuring a measure of aggregate technology and several forward-looking variables, we identify the news shock as the shock orthogonal to technology innovations that best explains future variation in technology. In the data, news shocks account for the bulk of low frequency variation in technology. News shocks are positively correlated with consumption, stock price, and consumer confidence innovations, and negatively correlated with inflation innovations. The disinflationary nature of news shocks is consistent with the implications of sensibly modified versions of a New Keynesian model.

A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states

We prove that quantum many-body systems on a one-dimensional lattice locally relax to Gaussian states under non-equilibrium dynamics generated by a bosonic quadratic Hamiltonian. This is true for a large class of initial states - pure or mixed - which have to satisfy merely weak conditions concerning the decay of correlations. The considered setting is a proven instance of a situation where dynamically evolving closed quantum systems locally appear as if they had truly relaxed, to maximum entropy states for fixed second moments. This furthers the understanding of relaxation in suddenly quenched quantum many-body systems. The proof features a non-commutative central limit theorem for non-i.i.d. random variables, showing convergence to Gaussian characteristic functions, giving rise to trace-norm closeness. We briefly relate our findings to ideas of typicality and concentration of measure.Comment: 27 pages, final versio

Redox-Active Nanomaterials For Nanomedicine Applications

Nanomedicine utilizes the remarkable properties of nanomaterials for the diagnosis, treatment, and prevention of disease. Many of these nanomaterials have been shown to have robust antioxidative properties, potentially functioning as strong scavengers of reactive oxygen species. Conversely, several nanomaterials have also been shown to promote the generation of reactive oxygen species, which may precipitate the onset of oxidative stress, a state that is thought to contribute to the development of a variety of adverse conditions. As such, the impacts of nanomaterials on biological entities are often associated with and influenced by their specific redox properties. In this review, we overview several classes of nanomaterials that have been or projected to be used across a wide range of biomedical applications, with discussion focusing on their unique redox properties. Nanomaterials examined include iron, cerium, and titanium metal oxide nanoparticles, gold, silver, and selenium nanoparticles, and various nanoscale carbon allotropes such as graphene, carbon nanotubes, fullerenes, and their derivatives/variations. Principal topics of discussion include the chemical mechanisms by which the nanomaterials directly interact with biological entities and the biological cascades that are thus indirectly impacted. Selected case studies highlighting the redox properties of nanomaterials and how they affect biological responses are used to exemplify the biologically-relevant redox mechanisms for each of the described nanomaterials

The Bandwidth of Transient Yaw Effects on Vehicle Aerodynamics

A vehicle on the road encounters an unsteady flow due to turbulence in the natural wind, the unsteady wakes from other vehicles and as a result of traversing through the stationary wakes of road side obstacles. There is increasing concern about potential differences in aerodynamic behaviour measured in steady flow wind tunnel conditions and that which occurs for vehicles on the road. It is possible to introduce turbulence into the wind tunnel environment (e.g. by developing active turbulence generators) but on-road turbulence is wide ranging in terms of both its intensity and frequency and it would be beneficial to better understand what aspects of the turbulence are of greatest importance to the aerodynamic performance of vehicles. There has been significant recent work on the characterisation of turbulent airflow relevant to road vehicles. The simulation of this time-varying airflow is now becoming possible in wind tunnels and in CFD. Less is known about the range of turbulence length scales and intensities that are significant to the performance of vehicles. It is only necessary to simulate (experimentally or computationally) the Venn intersection of the range of conditions experienced and the range that are important to the vehicle's performance. The focus of this work is on transient yaw fluctuations. Time-resolved simulations of simple two dimensional parametric geometries subjected to yaw transients at a range of different time scales were conducted using Exa Powerflow. The effects of model geometry, Reynolds number yaw fluctuation amplitude and superposition were investigated. It was found that, in general, the flow could be treated as quasi-steady for reduced frequencies below 0.3 (based on model length and freestream velocity), which is consistent with theory. The most significant changes were observed in a critical reduced frequency range between ω R = 0.3 and ω R = 1.5 (scales of 4-20 vehicle lengths, or periods of 0.6 to 3s for a vehicle at 30 m/s). Higher frequencies will have significant effects, but these were observed to show little sensitivity to frequency above the critical range. Small physical features on real vehicles will add importance to smaller, but not larger, scales. The dynamic effects were largely independent of Reynolds number, including for near-inviscid conditions, indicating that the sources of the non-quasi-steady response were not viscous in origin. Increasing yaw amplitude or combining multiple frequency components did not have a summative impact suggesting that it may not be possible to describe vehicle response to transient conditions using linear concepts such as transfer or admittance functions

Pipeline network features and leak detection by cross-correlation analysis of reflected waves

This paper describes progress on a new technique to detect pipeline features and leaks using signal processing of a pressure wave measurement. Previous work (by the present authors) has shown that the analysis of pressure wave reflections in fluid pipe networks can be used to identify specific pipeline features such as open ends, closed ends, valves, junctions, and certain types of bends. It was demonstrated that by using an extension of cross-correlation analysis, the identification of features can be achieved using fewer sensors than are traditionally employed. The key to the effectiveness of the technique lies in the artificial generation of pressure waves using a solenoid valve, rather than relying upon natural sources of fluid excitation. This paper uses an enhanced signal processing technique to improve the detection of leaks. It is shown experimentally that features and leaks can be detected around a sharp bend and up to seven reflections from features/ leaks can be detected, by which time the wave has traveled over 95 m. The testing determined the position of a leak to within an accuracy of 5%, even when the location of the reflection from a leak is itself dispersed over a certain distance and, therefore, does not cause an exact reflection of the wave

The inverse resonance problem for perturbations of algebro-geometric potentials

We prove that a compactly supported perturbation of a rational or simply periodic algebro-geometric potential of the one-dimensional Schr\"odinger equation on the half line is uniquely determined by the location of its Dirichlet eigenvalues and resonances.Comment: 14 page

Isolated Eigenvalues of the Ferromagnetic Spin-J XXZ Chain with Kink Boundary Conditions

We investigate the low-lying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy Delta and kink boundary conditions. Since the third component of the total magnetization, M, is conserved, it is meaningful to study the spectrum for each fixed value of M. We prove that for J>= 3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum