On the dynamic stability of eccentrically reinforced circular cylindrical shells Technical report, Sep. 1, 1965 - Jan. 31, 1967

Dynamic stability of eccentrically reinforced circular cylindrical shell

On the Formulation of Equations of Motion of an Eccentrically Stiffened Shallow Circular Cylindrical Shell Semiannual Progress Report, Sep. 1, 1965 - Mar. 1, 1966

Motion equations formulation for eccentrically stiffened shallow circular cylindrical shel

Threshold effects for two pathogens spreading on a network

Diseases spread through host populations over the networks of contacts between individuals, and a number of results about this process have been derived in recent years by exploiting connections between epidemic processes and bond percolation on networks. Here we investigate the case of two pathogens in a single population, which has been the subject of recent interest among epidemiologists. We demonstrate that two pathogens competing for the same hosts can both spread through a population only for intermediate values of the bond occupation probability that lie above the classic epidemic threshold and below a second higher value, which we call the coexistence threshold, corresponding to a distinct topological phase transition in networked systems.Comment: 5 pages, 2 figure

Altitude-Wind-Tunnel Investigation of the 19B-2, 19B-8 and 19XB-1 Jet- Propulsion Engines

Investigations were conducted in the Cleveland altitude wind tunnel to determine the performance and operational characteristics of the 19B-2, 19B-8, and 19XS-1 turbojet engines. One objective was to determine the effect of altitude, flight Mach number, and tail-pipe-nozzle area on the performance characteristics of the six-stage and ten-stage axial-flow compressors of the 19B-8 and 19XB-1 engines, respectively, The data were obtained over a range of simulated altitudes and flight Mach numbers. At each simulated flight condition the engine was run over its full operable range of speeds. Performance characteristics of the 19B-8 and 19XB-1 compressors for the range of operation obtainable in the turboJet-engine installation are presented. Compressor characteristics are presented as functions of air flow corrected to sea-level conditions, compressor Mach number, and compressor load coefficient. For the range of compressor operation investigated, changes in Reynolds number had no measurable effect on the relations among compressor Mach number, corrected air flow, compressor load coefficient, compressor pressure ratio, and compressor efficiency. The operating lines for the 19B-8 compressor lay on the low-air-flow side of the region of maximum compressor efficiency; the 19B-8 compressor operated at higher average pressure coefficients per stage and produced a lower over-all pressure ratio than did the 19XB-1 compressor

Distribution of survival times of deliberate Plasmodium falciparum infections in tertiary syphilis patients

Survival time data of Plasmodium falciparum infections from deliberate infection of human subjects with P. falciparum between 1940 and 1963 as a treatment for neurosyphilis in the USA (Georgia) have been used to test the fits of five commonly used parametric distributions for survival times using quantile-quantile plots. Our results suggest that the best fit is obtained from the Gompertz or Weibull distributions. This result has important implications for mathematical modelling of malaria, which has for the past century exclusively assumed that the duration of malaria infections has an exponential distribution. It is desirable to know the correct distribution because its shape profoundly influences the length of monitoring needed in an intervention programme for eliminating or reducing malari

Third rank Killing tensors in general relativity. The (1+1)-dimensional case

Third rank Killing tensors in (1+1)-dimensional geometries are investigated and classified. It is found that a necessary and sufficient condition for such a geometry to admit a third rank Killing tensor can always be formulated as a quadratic PDE, of order three or lower, in a Kahler type potential for the metric. This is in contrast to the case of first and second rank Killing tensors for which the integrability condition is a linear PDE. The motivation for studying higher rank Killing tensors in (1+1)-geometries, is the fact that exact solutions of the Einstein equations are often associated with a first or second rank Killing tensor symmetry in the geodesic flow formulation of the dynamics. This is in particular true for the many models of interest for which this formulation is (1+1)-dimensional, where just one additional constant of motion suffices for complete integrability. We show that new exact solutions can be found by classifying geometries admitting higher rank Killing tensors.Comment: 16 pages, LaTe

Spectral theorem for the Lindblad equation for quadratic open fermionic systems

The spectral theorem is proven for the quantum dynamics of quadratic open systems of n fermions described by the Lindblad equation. Invariant eigenspaces of the many-body Liouvillean dynamics and their largest Jordan blocks are explicitly constructed for all eigenvalues. For eigenvalue zero we describe an algebraic procedure for constructing (possibly higher dimensional) spaces of (degenerate) non-equilibrium steady states.Comment: 19 pages, no figure

Nonperiodic echoes from mushroom billiard hats

Mushroom billiards have the remarkable property to show one or more clear cut integrable islands in one or several chaotic seas, without any fractal boundaries. The islands correspond to orbits confined to the hats of the mushrooms, which they share with the chaotic orbits. It is thus interesting to ask how long a chaotic orbit will remain in the hat before returning to the stem. This question is equivalent to the inquiry about delay times for scattering from the hat of the mushroom into an opening where the stem should be. For fixed angular momentum we find that no more than three different delay times are possible. This induces striking nonperiodic structures in the delay times that may be of importance for mesoscopic devices and should be accessible to microwave experiments.Comment: Submitted to Phys. Rev. E without the appendi

Non-Hamiltonian dynamics in optical microcavities resulting from wave-inspired corrections to geometric optics

We introduce and investigate billiard systems with an adjusted ray dynamics that accounts for modifications of the conventional reflection of rays due to universal wave effects. We show that even small modifications of the specular reflection law have dramatic consequences on the phase space of classical billiards. These include the creation of regions of non-Hamiltonian dynamics, the breakdown of symmetries, and changes in the stability and morphology of periodic orbits. Focusing on optical microcavities, we show that our adjusted dynamics provides the missing ray counterpart to previously observed wave phenomena and we describe how to observe its signatures in experiments. Our findings also apply to acoustic and ultrasound waves and are important in all situations where wavelengths are comparable to system sizes, an increasingly likely situation considering the systematic reduction of the size of electronic and photonic devices.Comment: 6 pages, 4 figures, final published versio