Robust Detection of Dynamic Community Structure in Networks

We describe techniques for the robust detection of community structure in some classes of time-dependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural modules in semi-decomposable systems. Null models play an important role both in the optimization of quality functions such as modularity and in the subsequent assessment of the statistical validity of identified community structure. We examine the sensitivity of such methods to model parameters and show how comparisons to null models can help identify system scales. By considering a large number of optimizations, we quantify the variance of network diagnostics over optimizations (`optimization variance') and over randomizations of network structure (`randomization variance'). Because the modularity quality function typically has a large number of nearly-degenerate local optima for networks constructed using real data, we develop a method to construct representative partitions that uses a null model to correct for statistical noise in sets of partitions. To illustrate our results, we employ ensembles of time-dependent networks extracted from both nonlinear oscillators and empirical neuroscience data.Comment: 18 pages, 11 figure

Nonlinear Waves in Disordered Diatomic Granular Chains

We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin", so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: In low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatio-temporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for such a transition. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.Comment: 10 pages, 8 figures (some with multiple parts), to appear in Physical Review E; summary of changes: new title, one new figure, additional discussion of several points (including both background and results

Mechanics of Granular Materials (MGM)

The constitutive behavior of uncemented granular materials such as strength, stiffness, and localization of deformations are to a large extend derived from interparticle friction transmitted between solid particles and particle groups. Interparticle forces are highly dependent on gravitational body forces. At very low effective confining pressures, the true nature of the Mohr envelope, which defines the Mohr-Coulomb failure criterion for soils, as well as the relative contribution of each of non-frictional components to soil's shear strength cannot be evaluated in terrestrial laboratories. Because of the impossibility of eliminating gravitational body forces on earth, the weight of soil grains develops interparticle compressive stresses which mask true soil constitutive behavior even in the smallest samples of models. Therefore the microgravity environment induced by near-earth orbits of spacecraft provides unique experimental opportunities for testing theories related to the mechanical behavior of terrestrial granular materials. Such materials may include cohesionless soils, industrial powders, crushed coal, etc. This paper will describe the microgravity experiment, 'Mechanics of Granular Materials (MGM)', scheduled to be flown on Space Shuttle-MIR missions. The paper will describe the experiment's hardware, instrumentation, specimen preparation procedures, testing procedures in flight, as well as a brief summary of the post-mission analysis. It is expected that the experimental results will significantly improve the understanding of the behavior of granular materials under very low effective stress levels

Magnetism and magnetotransport in sputtered Co-doped FeSi films

FeSi is a non-magnetic narrow-gap semiconductor that can be doped n-type by Co, which also gives rise to magnetic order. Here we report on the growth of sputtered thin films of Fe 0.8 Co 0.2 Si, which are predominantlyphase (B20 lattice structure), and possess that phase's characteristic magnetotransport properties. The ordinary Hall coefficient shows that each Co atom donates roughly one electron, whilst the magnetometry suggests that each gives rise to close to one Bohr magneton of moment. These results indicate that a highly spinpolarised electron gas persists despite the inevitable disorder in these thin films, suitable for spintronic devices

Cross-linked structure of network evolution

We study the temporal co-variation of network co-evolution via the cross-link structure of networks, for which we take advantage of the formalism of hypergraphs to map cross-link structures back to network nodes. We investigate two sets of temporal network data in detail. In a network of coupled nonlinear oscillators, hyperedges that consist of network edges with temporally co-varying weights uncover the driving co-evolution patterns of edge weight dynamics both within and between oscillator communities. In the human brain, networks that represent temporal changes in brain activity during learning exhibit early co-evolution that then settles down with practice. Subsequent decreases in hyperedge size are consistent with emergence of an autonomous subgraph whose dynamics no longer depends on other parts of the network. Our results on real and synthetic networks give a poignant demonstration of the ability of cross-link structure to uncover unexpected co-evolution attributes in both real and synthetic dynamical systems. This, in turn, illustrates the utility of analyzing cross-links for investigating the structure of temporal networks

Helical magnetic structure and the anomalous and topological Hall effects in epitaxial B20 Fe1−y_{1-y}Coy_yGe films

Epitaxial films of the B20-structure alloy Fe$_{1-y}$Co$_y$Ge were grown by molecular beam epitaxy on Si (111) substrates. The magnetization varied smoothly from the bulk-like values of one Bohr magneton per Fe atom for FeGe to zero for non-magnetic CoGe. The chiral lattice structure leads to a Dzyaloshinskii-Moriya interaction (DMI), and the films' helical magnetic ground state was confirmed using polarized neutron reflectometry measurements. The pitch of the spin helix, measured by this method, varies with Co content $y$ and diverges at $y \sim 0.45$. This indicates a zero-crossing of the DMI, which we reproduced in calculations using first principle methods. We also measured the longitudinal and Hall resistivity of our films as a function of magnetic field, temperature, and Co content $y$. The Hall resistivity is expected to contain contributions from the ordinary, anomalous, and topological Hall effects. Both the anomalous and topological Hall resistivities show peaks around $y \sim 0.5$. Our first principles calculations show a peak in the topological Hall constant at this value of $y$, related to the strong spin-polarisation predicted for intermediate values of $y$. Half-metallicity is predicted for $y = 0.6$, consistent with the experimentally observed linear magnetoresistance at this composition. Whilst it is possible to reconcile theory with experiment for the various Hall effects for FeGe, the large topological Hall resistivities for $y \sim 0.5$ are much larger then expected when the very small emergent fields associated with the divergence in the DMI are taken into account

Multiabsorber Transition-Edge Sensors for X-Ray Astronomy

We are developing arrays of position-sensitive microcalorimeters for future x-ray astronomy applications. These position-sensitive devices commonly referred to as hydras consist of multiple x-ray absorbers, each with a different thermal coupling to a single-transition-edge sensor microcalorimeter. Their development is motivated by a desire to achieve very large pixel arrays with some modest compromise in performance. We report on the design, optimization, and first results from devices with small pitch pixels (<75 m) being developed for a high-angular and energy resolution imaging spectrometer for Lynx. The Lynx x-ray space telescope is a flagship mission concept under study for the National Academy of Science 2020 decadal survey. Broadband full-width-half-maximum (FWHM) resolution measurements on a 9-pixel hydra have demonstrated E(FWHM) = 2.23 0.14 eV at Al-K, E(FWHM) = 2.44 0.29 eV at Mn-K, and E(FWHM) = 3.39 0.23 eV at Cu-K. Position discrimination is demonstrated to energies below <1 keV and the device performance is well-described by a finite-element model. Results from a prototype 20-pixel hydra with absorbers on a 50-m pitch have shown E(FWHM) = 3.38 0.20 eV at Cr-K1. We are now optimizing designs specifically for Lynx and extending the number of absorbers up to 25/hydra. Numerical simulation suggests optimized designs could achieve 3 eV while being compatible with the bandwidth requirements of the state-of-the art multiplexed readout schemes, thus making a 100,000 pixel microcalorimeter instrument a realistic goal