On a nonlocal degenerate parabolic problem

Conditions for the existence and uniqueness of weak solutions for a class of nonlinear nonlocal degenerate parabolic equations are established. The asymptotic behaviour of the solutions as time tends to infinity are also studied. In particular, the finite time extinction and polynomial decay properties are proved

Response of a particle in a one-dimensional lattice to an applied force: Dynamics of the effective mass

We study the behaviour of the expectation value of the acceleration of a particle in a one-dimensional periodic potential when an external homogeneous force is suddenly applied. The theory is formulated in terms of modified Bloch states that include the interband mixing induced by the force. This approach allows us to understand the behaviour of the wavepacket, which responds with a mass that is initially the bare mass, and subsequently oscillates around the value predicted by the effective mass. If Zener tunneling can be neglected, the expression obtained for the acceleration of the particle is valid over timescales of the order of a Bloch oscillation, which are of interest for experiments with cold atoms in optical lattices. We discuss how these oscillations can be tuned in an optical lattice for experimental detection.Comment: 15 pages, 12 figure

Helicopter Rotor Blade Computation in Unsteady Flows Using Moving Overset Grids

An overset grid thin-layer Navier-Stokes code has been extended to include dynamic motion of helicopter rotor blades through relative grid motion. The unsteady flowfield and airloads on an AH-IG rotor in forward flight were computed to verify the methodology and to demonstrate the method's potential usefulness towards comprehensive helicopter codes. In addition, the method uses the blade's first harmonics measured in the flight test to prescribe the blade motion. The solution was impulsively started and became periodic in less than three rotor revolutions. Detailed unsteady numerical flow visualization techniques were applied to the entire unsteady data set of five rotor revolutions and exhibited flowfield features such as blade vortex interaction and wake roll-up. The unsteady blade loads and surface pressures compare well against those from flight measurements. Details of the method, a discussion of the resulting predicted flowfield, and requirements for future work are presented. Overall, given the proper blade dynamics, this method can compute the unsteady flowfield of a general helicopter rotor in forward flight

A 2d Honeycomb Photonic Crystal Under Applied Magnetic Fields

The band-structure properties of a photonic two-dimensional honeycomb lattice formed by cylindrical semiconductor shell rods with dielectric permitivities ε 1 and ε 2, and embedded in a background with permitivity ε 3, is studied by using an standard plane-wave expansion. The properties of bandgaps and density of states, considering dispersive dielectric responses, are investigated together with the possibility of fabricating systems with tunable photonic bandgaps, due to the Voigt magneto-optical effect, under the influence of an external magnetic field. © 2008 SPIE.7138J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University Press, Princeton, 1995E. Istrate and E. H. Sargent, Rev. Mod. Phys. 78, 455 (2006)Xu, C., Hu, X., Li, Y., Liu, X., Fu, R., Zi, J., (2003) Phys. Rev. B, 68, p. 193201Kee, C.-S., Kim, J.-E., Park, H.Y., Park, I., Lim, H., (2000) Phys. Rev. B, 61, p. 15523Anderson, C.M., Giapis, K.P., (1996) Phys. Rev. Lett, 77, p. 2949Rezaei, B., Kalafi, M., (2006) Optics Commun, 266, p. 159Busch, K., John, S., (1999) Phys. Rev. Lett, 83, p. 967S. B. Cavalcanti, M. de Dios-Leyva, E. Reyes-Gómez, and L. E. Oliveira, Phys. Rev. B 74, 153102 (2006)ibid., Phys. Rev. E 75, 026607 (2007)Ho, K.M., Chan, C.T., Soukoulis, C.M., (1990) Phys. Rev. Lett, 65, p. 315

The heartbeat of the city

Human activity is organised around daily and weekly cycles, which should, in turn, dominate all types of social interactions, such as transactions, communications, gatherings and so on. Yet, despite their strategic importance for policing and security, cyclical weekly patterns in crime and road incidents have been unexplored at the city and neighbourhood level. Here we construct a novel method to capture the weekly trace, or "heartbeat" of events and use geotagged data capturing the time and location of more than 200,000 violent crimes and nearly one million crashes in Mexico City. On aggregate, our findings show that the heartbeats of crime and crashes follow a similar pattern. We observe valleys during the night and peaks in the evening, where the intensity during a peak is 7.5 times the intensity of valleys in terms of crime and 12.3 times in terms of road accidents. Although distinct types of events, crimes and crashes reach their respective intensity peak on Friday night and valley on Tuesday morning, the result of a hyper-synchronised society. Next, heartbeats are computed for city neighbourhood 'tiles', a division of space within the city based on the distance to Metro and other public transport stations. We find that heartbeats are spatially heterogeneous with some diffusion, so that nearby tiles have similar heartbeats. Tiles are then clustered based on the shape of their heartbeat, e.g., tiles within groups suffer peaks and valleys of crime or crashes at similar times during the week. The clusters found are similar to those based on economic activities. This enables us to anticipate temporal traces of crime and crashes based on local amenities

Palenque de San Basilio in Colombia: genetic data support an oral history of a paternal ancestry in Congo

The Palenque, a black community in rural Colombia, have an oral history of fugitive African slaves founding a free village near Cartagena in the seventeenth century. Recently, linguists have identified some 200 words in regular use that originate in a Kikongo language, with Yombe, mainly spoken in the Congo region, being the most likely source. The non-recombining portion of the Y chromosome (NRY) and mitochondrial DNA were analysed to establish whether there was greater similarity between present-day members of the Palenque and Yombe than between the Palenque and 42 other African groups (for all individuals,n= 2799) from which forced slaves might have been taken. NRY data are consistent with the linguistic evidence that Yombe is the most likely group from which the original male settlers of Palenque came. Mitochondrial DNA data suggested substantial maternal sub-Saharan African ancestry and a strong founder effect but did not associate Palenque with any particular African group. In addition, based on cultural data including inhabitants' claims of linguistic differences, it has been hypothesized that the two districts of the village (Abajo and Arriba) have different origins, with Arriba founded by men originating in Congo and Abajo by those born in Colombia. Although significant genetic structuring distinguished the two from each other, no supporting evidence for this hypothesis was found

Contracts in Practice

Contracts are a form of lightweight formal specification embedded in the program text. Being executable parts of the code, they encourage programmers to devote proper attention to specifications, and help maintain consistency between specification and implementation as the program evolves. The present study investigates how contracts are used in the practice of software development. Based on an extensive empirical analysis of 21 contract-equipped Eiffel, C#, and Java projects totaling more than 260 million lines of code over 7700 revisions, it explores, among other questions: 1) which kinds of contract elements (preconditions, postconditions, class invariants) are used more often; 2) how contracts evolve over time; 3) the relationship between implementation changes and contract changes; and 4) the role of inheritance in the process. It has found, among other results, that: the percentage of program elements that include contracts is above 33% for most projects and tends to be stable over time; there is no strong preference for a certain type of contract element; contracts are quite stable compared to implementations; and inheritance does not significantly affect qualitative trends of contract usage

Three-dimensional Computational Fluid Dynamics Investigation of a Spinning Helicopter Slung Load

After performing steady-state Computational Fluid Dynamics (CFD) calculations using OVERFLOW to validate the CFD method against static wind-tunnel data of a box-shaped cargo container, the same setup was used to investigate unsteady flow with a moving body. Results were compared to flight test data previously collected in which the container is spinning