Morphological Bedload Transport in Gravel-Bed Braided Rivers

Gravel-bed braided rivers, defined by their multi-thread planform and dynamic morphology, are commonly found in proglacial mountainous areas. With little cohesive sediment and a lack of stabilizing vegetation, the dynamic morphology of these rivers is fundamentally the result of bedload transport processes but our understanding of the fundamental relationships between channel form and bedload processes remains incomplete. For example, the area of the bed actively transporting bedload, known as the active width, is strongly linked to bedload transport rates but these relationships have not been investigated systematically in braided rivers. This research builds on previous research to investigate the relationships between morphology, bedload transport rates, and bed-material mobility using physical models of braided rivers over a range of constant channel-forming discharges and event hydrographs. Morphology changes were estimated using the morphological method, which infers information from changes in channel topography over time, from an extensive dataset of digital elevation models (DEMs) generated using digital photogrammetry and ‘Structure-from-Motion’ principles. Results suggest that the morphological active width is highly variable even at constant discharge, but increases with stream power and is positively related to bedload transport rates, bulk change (i.e. total volume of erosion and deposition), and active braiding intensity. Morphologically-derived sediment budgets provided reasonable estimates of bedload transport rates that were similar to independent measurements of bedload transport rates from sediment baskets. In addition, grain size distributions and bed mobility evolved from a state of partial mobility towards equal mobility with increasing discharge. This is rare in most gravel-bed rivers but in braided rivers the high levels of sediment supply and lack of armouring allow for greater mobility of the channel bed and subsurface. Finally, the lower detection threshold for the morphological active width, bedload transport, and transition to selective mobility all coincided with a dimensionless stream power of ~0.08. Overall, these results suggest that while braided rivers are dynamic, they may be restricted in ways like their single-threaded counterparts so that measures of morphology (i.e. the active width) can be used as general predictors of bedload transport rates and the morphological stability of the river. This knowledge contributes to our overall understanding of braided river morphodynamics while also building on theory for use in applied geomorphology and engineering practices for the management, conservation, and restoration of complex braided rivers systems

Onset of Localization in Heterogeneous Interfacial Failure

We study numerically the failure of an interface joining two elastic materials under load using a fiber bundle model connected to an elastic half space. We find that the breakdown process follows the equal load sharing fiber bundle model without any detectable spatial correlations between the positions of the failing fibers until localization sets in. The onset of localization is an instability, not a phase transition. Depending on the elastic constant describing the elastic half space, localization sets in before or after the critical load causing the interface to fail completely, is reached. There is a crossover between failure due to localization or failure without spatial correlations when tuning the elastic constant, not a phase transition. Contrary to earlier claims based on models different from ours, we find that a finite fraction of fibers must fail before the critical load is attained, even in the extreme localization regime, i.e.\ for very small elastic constant. We furthermore find that the critical load remains finite for all values of the elastic constant in the limit of an infinitely large system.Comment: 4 pages, 5 figure

Failure properties of loaded fiber bundles having a lower cutoff in fiber threshold distribution

Presence of lower cutoff in fiber threshold distribution may affect the failure properties of a bundle of fibers subjected to external load. We investigate this possibility both in a equal load sharing (ELS) fiber bundle model and in local load sharing (LLS) one. We show analytically that in ELS model, the critical strength gets modified due to the presence of lower cutoff and it becomes bounded by an upper limit. Although the dynamic exponents for the susceptibility and relaxation time remain unchanged, the avalanche size distribution shows a permanent deviation from the mean-fiels power law. In the LLS model, we analytically estimate the upper limit of the lower cutoff above which the bundle fails at one instant. Also the system size variation of bundle's strength and the avalanche statistics show strong dependence on the lower cutoff level.Comment: 7 pages and 7 figure

Dynamic model for failures in biological systems

A dynamic model for failures in biological organisms is proposed and studied both analytically and numerically. Each cell in the organism becomes dead under sufficiently strong stress, and is then allowed to be healed with some probability. It is found that unlike the case of no healing, the organism in general does not completely break down even in the presence of noise. Revealed is the characteristic time evolution that the system tends to resist the stress longer than the system without healing, followed by sudden breakdown with some fraction of cells surviving. When the noise is weak, the critical stress beyond which the system breaks down increases rapidly as the healing parameter is raised from zero, indicative of the importance of healing in biological systems.Comment: To appear in Europhys. Let

A random fiber bundle with many discontinuities in the threshold distribution

We study the breakdown of a random fiber bundle model (RFBM) with $n$-discontinuities in the threshold distribution using the global load sharing scheme. In other words, $n+1$ different classes of fibers identified on the basis of their threshold strengths are mixed such that the strengths of the fibers in the $i-th$ class are uniformly distributed between the values $\sigma_{2i-2}$ and $\sigma_{2i-1}$ where $1 \leq i \leq n+1$. Moreover, there is a gap in the threshold distribution between $i-th$ and $i+1-th$ class. We show that although the critical stress depends on the parameter values of the system, the critical exponents are identical to that obtained in the recursive dynamics of a RFBM with a uniform distribution and global load sharing. The avalanche size distribution (ASD), on the other hand, shows a non-universal, non-power law behavior for smaller values of avalanche sizes which becomes prominent only when a critical distribution is approached. We establish that the behavior of the avalanche size distribution for an arbitrary $n$ is qualitatively similar to a RFBM with a single discontinuity in the threshold distribution ($n=1$), especially when the density and the range of threshold values of fibers belonging to strongest ($n+1$)-th class is kept identical in all the cases.Comment: 6 pages, 4 figures, Accepted in Phys. Rev.

Tailoring laser pulses with spectral and fluence constraints using optimal control theory

Within the framework of optimal control theory we develop a simple iterative scheme to determine optimal laser pulses with spectral and fluence constraints. The algorithm is applied to a one-dimensional asymmetric double well where the control target is to transfer a particle from the ground state, located in the left well, to the first excited state, located in the right well. Extremely high occupations of the first excited state are obtained for a variety of spectral and/or energetic constraints. Even for the extreme case where no resonance frequency is allowed in the pulse the algorithm achieves an occupation of almost 100%

Energy bursts in fiber bundle models of composite materials

As a model of composite materials, a bundle of many fibers with stochastically distributed breaking thresholds for the individual fibers is considered. The bundle is loaded until complete failure to capture the failure scenario of composite materials under external load. The fibers are assumed to share the load equally, and to obey Hookean elasticity right up to the breaking point. We determine the distribution of bursts in which an amount of energy $E$ is released. The energy distribution follows asymptotically a universal power law $E^{-5/2}$, for any statistical distribution of fiber strengths. A similar power law dependence is found in some experimental acoustic emission studies of loaded composite materials.Comment: 5 pages, 4 fig

Effect of discontinuity in threshold distribution on the critical behaviour of a random fiber bundle

The critical behaviour of a Random Fiber Bundle Model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different parameters of the distribution. The discontinuity in the threshold strength distribution of fibers non-trivially modifies the critical stress as well as puts a restriction on the allowed values of parameters for which the recursive dynamics approach holds good. The discontinuity leads to a non-universal behaviour in the avalanche size distribution for smaller values of avalanche size. We observe that apart from the mean field behaviour for larger avalanches, a new behaviour for smaller avalanche size is observed as a critical threshold distribution is approached. The phenomenological understanding of the above result is provided using the exact analytical result for the avalanche size distribution. Most interestingly,the prominence of non-universal behaviour in avalanche size distribution depends on the system parameters.Comment: 6 pages, 4 figures, text and figures modifie