Transient landscapes at fault tips

Fault growth produces patterns of displacement and slip rate that are highly variable in both space and time. This transience is most pronounced near fault tips, where along‐strike displacement gradients vary in time as the fault array lengthens. We use a set of statistical and field observations to quantify the response of catchments and their associated fans in three large normal fault arrays to transient patterns of displacement and slip rate. Catchments near the fault tips show distinct scaling of channel slope with drainage area compared with catchments near the strike center. This scaling becomes uniform beyond about ∼10 km from the fault tips and is therefore like footwall relief, largely decoupled from the fault displacement profile. The estimated catchment response times to a change in slip rate also vary between fault tips and strike center. The response times for tip catchments are much longer than the inferred time since fault activity began, indicating that they are unlikely to be in equilibrium with the current fault displacement field. This disequilibrium, combined with the decoupling of slope‐area scaling from displacement, indicates that landscapes are most sensitive to fault activity near fault tips. Active faults characterized by along‐strike variation in slip rate thus provide excellent opportunities to explore the transient response of landscapes to tectonic forcing

Landscape evolution at extensional relay zones

It is commonly argued that the extensional relay zones between adjacent crustal-scale normal fault segments are associated with large catchment-fan systems that deliver significant amounts of sediment to hanging wall basins. This conceptual model of extensional basin development, while useful, overlooks some of the physical constraints on catchment evolution and sediment supply in relay zones. We argue that a key factor in the geomorphic evolution of relay zones is the interplay between two different timescales, the time over which the fault array develops, and the time over which the footwall catchment-fan systems are established. Results of numerical experiments using a landscape evolution model suggest that, in isolated fault blocks, footwall catchment evolution is highly dependent on the pattern and rate of fault array growth. A rapidly linked en echelon fault geometry gives rise to capture of relay zone drainage by aggressive catchment incision in the relay zone and to consequent increases in the rate of sediment supply to the hanging wall. Capture events do not occur when the fault segments are allowed to propagate slowly toward an en echelon geometry. In neither case, however, are large relay zone catchment-fan systems developed. We propose several physical reasons for this, including geometric constraints and limits on catchment incision and sediment transport rates in relay zones. Future research efforts should focus on the timescales over which fault array development occurs, and on the quantitative variations in catchment-fan system morphology at relay zones

Towards flavour diffusion coefficient and electrical conductivity without ultraviolet contamination

By subtracting from a recent lattice measurement of the thermal vector-current correlator the known 5-loop vacuum contribution, we demonstrate that the remainder is small and shows no visible short-distance divergence. It can therefore in principle be subjected to model-independent analytic continuation. Testing a particular implementation, we obtain estimates for the flavour-diffusion coefficient (2 pi T D \gsim 0.8) and electrical conductivity which are significantly smaller than previous results. Although systematic errors remain beyond control at present, some aspects of our approach could be of a wider applicability.Comment: 7 pages. v2: clarifications added, published versio

Line-distortion, Bandwidth and Path-length of a graph

We investigate the minimum line-distortion and the minimum bandwidth problems on unweighted graphs and their relations with the minimum length of a Robertson-Seymour's path-decomposition. The length of a path-decomposition of a graph is the largest diameter of a bag in the decomposition. The path-length of a graph is the minimum length over all its path-decompositions. In particular, we show: - if a graph $G$ can be embedded into the line with distortion $k$, then $G$ admits a Robertson-Seymour's path-decomposition with bags of diameter at most $k$ in $G$; - for every class of graphs with path-length bounded by a constant, there exist an efficient constant-factor approximation algorithm for the minimum line-distortion problem and an efficient constant-factor approximation algorithm for the minimum bandwidth problem; - there is an efficient 2-approximation algorithm for computing the path-length of an arbitrary graph; - AT-free graphs and some intersection families of graphs have path-length at most 2; - for AT-free graphs, there exist a linear time 8-approximation algorithm for the minimum line-distortion problem and a linear time 4-approximation algorithm for the minimum bandwidth problem

Single parameter scaling in 1-D localized absorbing systems

Numerical study of the scaling of transmission fluctuations in the 1-D localization problem in the presence of absorption is carried out. Violations of single parameter scaling for lossy systems are found and explained on the basis of a new criterion for different types of scaling behavior derived by Deych et al [Phys. Rev. Lett., {\bf 84}, 2678 (2000)].Comment: 7 pages, 6 figures, RevTex, submitted to Phys. Rev.

Group testing with Random Pools: Phase Transitions and Optimal Strategy

The problem of Group Testing is to identify defective items out of a set of objects by means of pool queries of the form "Does the pool contain at least a defective?". The aim is of course to perform detection with the fewest possible queries, a problem which has relevant practical applications in different fields including molecular biology and computer science. Here we study GT in the probabilistic setting focusing on the regime of small defective probability and large number of objects, $p \to 0$ and $N \to \infty$. We construct and analyze one-stage algorithms for which we establish the occurrence of a non-detection/detection phase transition resulting in a sharp threshold, $\bar M$, for the number of tests. By optimizing the pool design we construct algorithms whose detection threshold follows the optimal scaling $\bar M\propto Np|\log p|$. Then we consider two-stages algorithms and analyze their performance for different choices of the first stage pools. In particular, via a proper random choice of the pools, we construct algorithms which attain the optimal value (previously determined in Ref. [16]) for the mean number of tests required for complete detection. We finally discuss the optimal pool design in the case of finite $p$

Solidification behavior of intensively sheared hypoeutectic Al-Si alloy liquid

The official published version of this article can be found at the link below.The effect of the processing temperature on the microstructural and mechanical properties of Al-Si (hypoeutectic) alloy solidified from intensively sheared liquid metal has been investigated systematically. Intensive shearing gives a significant refinement in grain size and intermetallic particle size. It also is observed that the morphology of intermetallics, defect bands, and microscopic defects in high-pressure die cast components are affected by intensive shearing the liquid metal. We attempt to discuss the possible mechanism for these effects.Funded by the EPSRC

Quantum effects on the BKT phase transition of two-dimensional Josephson arrays

The phase diagram of two dimensional Josephson arrays is studied by means of the mapping to the quantum XY model. The quantum effects onto the thermodynamics of the system can be evaluated with quantitative accuracy by a semiclassical method, the {\em pure-quantum self-consistent harmonic approximation}, and those of dissipation can be included in the same framework by the Caldeira-Leggett model. Within this scheme, the critical temperature of the superconductor-to-insulator transition, which is a Berezinskii-Kosterlitz-Thouless one, can be calculated in an extremely easy way as a function of the quantum coupling and of the dissipation mechanism. Previous quantum Monte Carlo results for the same model appear to be rather inaccurate, while the comparison with experimental data leads to conclude that the commonly assumed model is not suitable to describe in detail the real system.Comment: 4 pages, 2 figures, to be published in Phys. Rev.

Para to Ortho transition of metallic dimers on Si(001)

Extensive electronic structure calculations are performed to obtain the stable geometries of metals like Al, Ga and In on the Si(001) surface at 0.5 ML and 1 ML coverages. Our results coupled with previous theoretical findings explain the recent experimental data in a comprehensive fashion. At low coverages, as shown by previous works, `Para' dimers give the lowest energy structure. With increasing coverage beyond 0.5 ML, `Ortho' dimers become part of low energy configurations leading toward a `Para' to `Ortho' transition at 1 ML coverage. For In mixed staggered dimers (`Ortho' and `Para') give the lowest energy configuration. For Ga, mixed dimers are non-staggered, while for Al `Para' to `Ortho' transition of dimers is complete. Thus at intermediate coverages between 0.5 and 1 ML, the `Ortho' and `Para' dimers may coexist on the surface. Consequently, this may be an explanation of the fact that the experimental observations can be successfully interpreted using either orientation. A supported zigzag structure at 0.5 ML, which resembles ${\rm (CH)_x}$, does not undergo a dimerization transition, and hence stays semi-metallic. Also, unlike ${\rm (CH)_x}$ the soliton formation is ruled out for this structure.Comment: 8 pages, 6 figure

Three-Particle Correlations in Simple Liquids

We use video microscopy to follow the phase-space trajectory of a two-dimensional colloidal model liquid and calculate three-point correlation functions from the measured particle configurations. Approaching the fluid-solid transition by increasing the strength of the pair-interaction potential, one observes the gradual formation of a crystal-like local order due to triplet correlations, while being still deep inside the fluid phase. Furthermore, we show that in a strongly interacting system the Born-Green equation can be satisfied only with the full triplet correlation function but not with three-body distribution functions obtained from superposing pair-correlations (Kirkwood superposition approximation).Comment: 4 pages, submitted to PRL, experimental paper, 2nd version: Fig.1 and two new paragraphs have been adde