Fractional diffusion emulates a human mobility network during a simulated disease outbreak

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between contact nodes. In some cases, transport can be parameterized with gravity-type models or approximated by a diffusive random walk. As a alternative, we have isolated intranational commercial air traffic as a case study for the utility of non-diffusive, heavy-tailed transport models. We implemented new stochastic simulations of a prototypical influenza-like infection, focusing on the dense, highly-connected United States air travel network. We show that mobility on this network can be described mainly by a power law, in agreement with previous studies. Remarkably, we find that the global evolution of an outbreak on this network is accurately reproduced by a two-parameter space-fractional diffusion equation, such that those parameters are determined by the air travel network.Comment: 26 pages, 4 figure

Scattering by ensembles of small particles experiment, theory and application

A hypothetical self consistent picture of evolution of prestellar intertellar dust through a comet phase leads to predictions about the composition of the circum-solar dust cloud. Scattering properties of thus resulting conglomerates with a bird's-nest type of structure are investigated using a micro-wave analogue technique. Approximate theoretical methods of general interest are developed which compared favorably with the experimental results. The principal features of scattering of visible radiation by zodiacal light particles are reasonably reproduced. A component which is suggestive of (ALPHA)-meteoroids is also predicted

Quasi-analytical solutions for APSIDAL motion in the three-body problem: Sun—minor planet—Jupiter

This paper deals with the effect of a third body on the apsidal motion of two bodies. The specific case involves a third body-planet Jupiter and the apsidal line motion of a minor planet that orbits the Sun and has its apsidal line go through the major axis of an ellipse. The third body (Jupiter) which satisfies the Langrangian solution will affect the apsidal line motion and therefore affects the ascending and descending motions of the minor planet. In this case no analytical solutions can be obtained, and therefore specific assumptions are made along with numerical solutions. For convenience, we adopt the Lagrangian solution in the three-body problem and obtain quasi-analytical results, which are used to evaluate the effect of the planet on the d Omega/dt (Omega ascending node) of each minor planet. This method is beneficial for improving our knowledge of the orbital elements of the asteroids, and perhaps even much smaller effects such as the effects of the planets on the interplanetary dust complex. Information on the latter may be provided by using this method to investigate Jupiter\u27s effect on the inclination of the symmetry surface of the zodiacal dust cloud

Quantum Zeno subspaces

The quantum Zeno effect is recast in terms of an adiabatic theorem when the measurement is described as the dynamical coupling to another quantum system that plays the role of apparatus. A few significant examples are proposed and their practical relevance discussed. We also focus on decoherence-free subspaces.Comment: 5 pages, 1 figure, to be published in Phys. Rev. Let

Control sideband generation for dual-recycled laser interferometric gravitational wave detectors

We present a discussion of the problems associated with generation of multiple control sidebands for length sensing and control of dual-recycled, cavity-enhanced Michelson interferometers and the motivation behind more complicated sideband generation methods. We focus on the Mach–Zehnder interferometer as a topological solution to the problem and present results from tests carried out at the Caltech 40 m prototype gravitational wave detector. The consequences for sensing and control for advanced interferometry are discussed, as are the implications for future interferometers such as Advanced LIGO

Thermal noise in half infinite mirrors with non-uniform loss: a slab of excess loss in a half infinite mirror

We calculate the thermal noise in half-infinite mirrors containing a layer of arbitrary thickness and depth made of excessively lossy material but with the same elastic material properties as the substrate. For the special case of a thin lossy layer on the surface of the mirror, the excess noise scales as the ratio of the coating loss to the substrate loss and as the ratio of the coating thickness to the laser beam spot size. Assuming a silica substrate with a loss function of 3x10-8 the coating loss must be less than 3x10-5 for a 6 cm spot size and a 7 micrometers thick coating to avoid increasing the spectral density of displacement noise by more than 10%. A similar number is obtained for sapphire test masses.Comment: Passed LSC (internal) review. Submitted to Phys. Rev. D. (5/2001) Replacement: Minor typo in Eq. 17 correcte

Dust Distribution in Gas Disks. A Model for the Ring Around HR 4796A

There have been several model analyses of the near and mid IR flux from the circumstellar ring around HR4796A. In the vicinity of a young star, the possibility that the dust ring is embedded within a residual protostellar gas disk cannot be ruled out. In a gas-rich environment, larger sizes ($>100 \mu m$) are needed for the particles to survive the radiative blow out. The total dust mass required to account for the IR flux is $< 10^{-1} M_\oplus$. The combined influence of gas and stellar radiation may also account for the observed sharp inner boundary and rapidly fading outer boundary of the ring. The pressure gradient induced by a small (10%) amplitude variation in the surface density distribution of a low-mass gaseous disk would be sufficient to modify the rotation speed of the gas.Comment: proof read version, 26 pages, LaTex, 11 figures. To appear in The Astronomical Journal June 200

Laser-interferometer gravitational-wave optical-spring detectors

Using a quantum mechanical approach, we show that in a gravitational-wave interferometer composed of arm cavities and a signal recycling cavity, e.g., the LIGO-II configuration, the radiation-pressure force acting on the mirrors not only disturbs the motion of the free masses randomly due to quantum fluctuations, but also and more fundamentally, makes them respond to forces as though they were connected to an (optical) spring with a specific rigidity. This oscillatory response gives rise to a much richer dynamics than previously known, which enhances the possibilities for reshaping the LIGO-II's noise curves. However, the optical-mechanical system is dynamically unstable and an appropriate control system must be introduced to quench the instability.Comment: 7 pages, 3 figures; to appear in the Proceedings of 4th Edoardo Amaldi Conference on Gravitational Waves, Perth, Australia, 8-13 July 200

The hybrid spectral problem and Robin boundary conditions

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented and the conformal determinant on a 2-disc, where the D and N regions are semi-circles, is derived. Comments on higher coefficients are made. A hemisphere hybrid problem is introduced that involves Robin boundary conditions and leads to logarithmic terms in the heat--kernel expansion which are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added. Substantial Robin additions. Substantial revisio