Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction

Bose-Einstein Condensates in Superlattices

We consider the Gross--Pitaevskii (GP) equation in the presence of periodic and quasi-periodic superlattices to study cigar-shaped Bose--Einstein condensates (BECs) in such potentials. We examine spatially extended wavefunctions in the form of modulated amplitude waves (MAWs). With a coherent structure ansatz, we derive amplitude equations describing the evolution of spatially modulated states of the BEC. We then apply second-order multiple scale perturbation theory to study harmonic resonances with respect to a single lattice substructure as well as ultrasubharmonic resonances that result from interactions of both substructures of the superlattice. In each case, we determine the resulting system's equilibria, which represent spatially periodic solutions, and subsequently examine the stability of the corresponding wavefunctions by direct simulations of the GP equation, identifying them as typically stable solutions of the model. We then study subharmonic resonances using Hamiltonian perturbation theory, tracing robust spatio-temporally periodic patterns

Microwave radiometer for subsurface temperature measurement

A UHF radiometer, operating at a frequency of 800 MHz, was modified to provide an integral, three frequency voltage standing wave ratio (VSWR) circuit in the radio frequency (RF) head. The VSWR circuit provides readings of power transmission at the antenna-material interface with an accuracy of plus or minus 5 percent. The power transmission readings are numerically equal to the emissivity of the material under observation. Knowledge of material emissivity is useful in the interpretation of subsurface apparent temperatures obtained on phantom models of biological tissue. The emissivities of phantom models consisting of lean beefsteak were found to lie in the range 0.623 to 0.779, depending on moisture content. Radiometric measurements performed on instrumented phantoms showed that the radiometer was capable of sensing small temperature changes occurring at depths of at least 19 to 30 mm. This is consistent with previously generated data which showed that the radiometer could sense temperatures at a depth of 38 mm

Ocean foam generation and modeling

A laboratory investigation was conducted to determine the physical and microwave properties of ocean foam. Special foam generators were designed and fabricated, using porous glass sheets, known as glass frits, as the principal element. The glass frit was sealed into a water-tight vertical box, a few centimeters from the bottom. Compressed air, applied to the lower chamber, created ocean foam from sea water lying on the frit. Foam heights of 30 cm were readily achieved, with relatively low air pressures. Special photographic techniques and analytical procedures were employed to determine foam bubble size distributions. In addition, the percentage water content of ocean foam was determined with the aid of a particulate sampling procedure. A glass frit foam generator, with pore diameters in the range 70 - 100 micrometers, produced foam with bubble distributions very similar to those found on the surface of natural ocean foam patches

Dark Matter Searches with Astroparticle Data

The existence of dark matter (DM) was first noticed by Zwicky in the 1930s, but its nature remains one of the great unsolved problems of physics. A variety of observations indicate that it is non-baryonic and non-relativistic. One of the preferred candidates for non-baryonic DM is a weakly interacting massive particle (WIMP) that in most models is stable. WIMP self-annihilation can produce cosmic rays, gamma rays, and other particles with signatures that may be detectable. Hints of anomalous cosmic-ray spectra found by recent experiments, such as PAMELA, have motivated interesting interpretations in terms of DM annihilation and/or decay. However, these signatures also have standard astrophysical interpretations, so additional evidence is needed in order to make a case for detection of DM annihilation or decay. Searches by the Fermi Large Area Telescope for gamma-ray signals from clumps, nearby dwarf spheroidal galaxies, and galaxy clusters have also been performed, along with measurements of the diffuse Galactic and extragalactic gamma-ray emission. In addition, imaging atmospheric Cherenkov telescopes like HESS, MAGIC, and VERITAS have reported on searches for gamma-ray emission from dwarf galaxies. In this review, we examine the status of searches for particle DM by these instruments and discuss the interpretations and resulting DM limits.Comment: Solicited review article to appear in Annual Reviews of Astronomy and Astrophysics. 52 pages, 10 figures (higher resolution figures will appear in the journal article

Narrow scope for resolution-limit-free community detection

Detecting communities in large networks has drawn much attention over the years. While modularity remains one of the more popular methods of community detection, the so-called resolution limit remains a significant drawback. To overcome this issue, it was recently suggested that instead of comparing the network to a random null model, as is done in modularity, it should be compared to a constant factor. However, it is unclear what is meant exactly by "resolution-limit-free", that is, not suffering from the resolution limit. Furthermore, the question remains what other methods could be classified as resolution-limit-free. In this paper we suggest a rigorous definition and derive some basic properties of resolution-limit-free methods. More importantly, we are able to prove exactly which class of community detection methods are resolution-limit-free. Furthermore, we analyze which methods are not resolution-limit-free, suggesting there is only a limited scope for resolution-limit-free community detection methods. Finally, we provide such a natural formulation, and show it performs superbly

Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein Condensates

We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length $a$ subjected to a spatially periodic modulation, $a=a(x)=a(x+L)$. This "collisionally inhomogeneous" BEC is described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of $x$. We transform this equation into a GP equation with constant coefficient $a$ and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization of the Ince equation. In the small-amplitude limit, we use averaging to construct analytical solutions for modulated amplitude waves (MAWs), whose stability we subsequently examine using both numerical simulations of the original GP equation and fixed-point computations with the MAWs as numerically exact solutions. We show that "on-site" solutions, whose maxima correspond to maxima of $a(x)$, are significantly more stable than their "off-site" counterparts.Comment: 25 pages, 10 figures (many with several parts), to appear in Physica D; higher resolution versions of some figures are available at http://www.its.caltech.edu/~mason/paper

Control in the technical societies: a brief history

By the time control engineering emerged as a coherent body of knowledge and practice (during and just after WW2) professional engineering societies had existed for many decades. Since control engineering is an interdisciplinary branch of the profession, new sections devoted to control were quickly established within the various existing technical societies. In addition, some new bodies devoted specifically or primarily to control were established. This article, a revised version of a paper presented at the IEEE 2009 Conference on the History of Technical Societies, describes how control engineering as a distinct branch of engineering became represented in technical societies in a number of countries

Hadronic Gamma Rays from Supernova Remnants

A gas cloud near a supernova remnant (SNR) provides a target for pp-collisions leading to subsequent gamma-ray emission through neutral pion decay. The assumption of a power-law ambient spectrum of accelerated particles with index near -2 is usually built into models predicting the spectra of very-high energy (VHE) gamma-ray emission from SNRs. However, if the gas cloud is located at some distance from the SNR shock, this assumption is not necessarily correct. In this case, the particles which interact with the cloud are those leaking from the shock and their spectrum is approximately monoenergetic with the injection energy gradually decreasing as the SNR ages. In the GLAST energy range the gamma-ray spectrum resulting from particle interactions with the gas cloud will be flatter than expected, with the cutoff defined by the pion momentum distribution in the laboratory frame. We evaluate the flux of particles escaping from a SNR shock and apply the results to the VHE diffuse emission detected by the HESS at the Galactic centre.Comment: 4 pages, 3 figures. Contribution to the 30th ICRC, Merida, Mexico, 2007 (final version