Erosion as a driving mechanism of intracontinental mountain growth

In nature, mountains can grow and remain as localized tectonic features over long periods of time (> 10 m.y.). By contrast, according to current knowledge of lithospheric rheology and neglecting surface processes, any intracontinental range with a width that exceeds that which can be supported by the strength of the lithosphere should collapse within a few tens of millions of years. For example, assuming a quartz-dominated crustal rheology, the relief of a range initially 3 km high and 300–400 km wide is reduced by half in about 15 m.y. as a result of lateral spreading of its crustal root. We suggest that surface processes might actually prevent such a “subsurface collapse.” Removal of material from topographic heights and deposition in the foreland oppose spreading of the crustal root and could eventually drive a net influx of material toward the orogeny. We performed a set of numerical experiments in order to validate this hypothesis. A section of a lithosphere, with a brittle-elasto-ductile rheology, initially loaded by a mountain range is submitted to horizontal shortening and to surface processes. If erosion is intense, material is removed more rapidly than it can be supplied by crustal thickening below the range, and the topography is rapidly smoothed. For example, a feature 3 km high and 300–400 km wide is halved in height in about 15 m.y. for an erosion coefficient k = 10^3 m^2/yr (the erosion rate is of the order of a few 0.1 mm/yr). This regime might be called “erosional collapse.” If erosion is not active enough, the crustal root spreads out laterally and “subsurface collapse” occurs. In the third intermediate regime, removal of the material by erosion is dynamically compensated by isostatic rebound and inward flow in the lower crust so that the range can grow. In this “mountain growth” regime the range evolves toward a characteristic graded shape that primarily depends on the erosion law. The erosion rate may be high (e.g., 0.5–0.9 mm/yr), close to the rate of tectonic uplift (e.g., 0.7–1.1 mm/yr), and few times higher than the rate of topographic uplift (0.15–0.2 mm/yr). These experiments show that surface processes can favor localized crustal shortening and participate in the development of an intracontinental mountain. Surface processes must therefore be taken into account in the interpretation and modeling of long-term deformation of continental lithosphere. Conversely, the mechanical response of the lithosphere must be accounted for when large-scale topographic features are interpreted and modeled in terms of geomorphologic processes

Tectonic evolution of a continental collision zone: A thermomechanical numerical model

We model evolution of a continent-continent collision and draw some parallels with the tectonic evolution of the Himalaya. We use a large-scale visco-plasto-elastic thermomechanical model that has a free upper surface, accounts for erosion and deposition and allows for all modes of lithospheric deformation. For quartz/olivine rheology and 60 mm/yr convergence rate, the continental subduction is stable, and the model predicts three distinct phases. During the phase 1 (120 km or 6% of shortening), deformation is characterized by back thrusting around the suture zone. Some amount of delaminated lower crust accumulates at depth. During phase 2 (120 km–420 km or 6%–22% of shortening), this crustal root is exhumed (medium- to high-grade rocks) along a newly formed major thrust fault. This stage bears similarities with the period of coeval activity of the Main Central thrust and of the South Tibetan Detachment between 20–16 Myr ago. During phase 3 (>420 km or 22% of shortening), the crust is scraped off from the mantle lithosphere and is incorporated into large crustal wedge. Deformation is localized around frontal thrust faults. This kinematics should produce only low- to medium-grade exhumation. This stage might be compared with the tectonics that has prevailed in the Himalaya over the last 15 Myr allowing for the formation of the Lesser Himalaya. The experiment is conducted at constant convergence rate, which implies increasing compressive force. Considering that this force is constant in nature, this result may be equivalent to a slowing down of the convergence rate as was observed during the India-Asia collision

Transverse Instabilities of Coasting Beams with Space Charge

Transverse beam stability is strongly affected by the beam space charge. Usually it is analyzed with the rigid-beam model. However this model is only valid when a bare (not affected by the space charge) tune spread is small compared to the space charge tune shift. This condition specifies a relatively small area of parameters which, however, is the most interesting for practical applications. The Landau damping rate and the beam Schottky spectra are computed assuming that validity condition is satisfied. The results are applied to a round Gaussian beam. The stability thresholds are described by simple fits for the cases of chromatic and octupole tune spreads.Comment: 6 pages, 2 figures, accepted by Phys. Rev. ST - Accel. Beam

Bifurcations of Relative Equilibria Sets of a Massive Point on Rough Rotating Surfaces

Dynamics of a massive point on a rotating wire or surface under dry friction force action is considered. Existence, stability and bifurcations of non-isolated relative equilibria sets of the point located on a sphere uniformly rotating about an inclined fixed axis; on a thin circular hoop rotating about an inclined fixed axis; on a paraboloidal bowl uniformly rotating about its axis are studied. The results are represented in the form of bifurcation diagrams

Random Time-Scale Invariant Diffusion and Transport Coefficients

Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement $\overline{\delta^2}$ of individual particles remains a random variable while indicating that the particle motion is subdiffusive. We investigate this type of ergodicity breaking within the continuous time random walk model and show that $\overline{\delta^2}$ differs from the corresponding ensemble average. In particular we derive the distribution for the fluctuations of the random variable $\overline{\delta^2}$. Similarly we quantify the response to a constant external field, revealing a generalization of the Einstein relation. Consequences for the interpretation of single molecule tracking data are discussed.Comment: 4 pages, 4 figures.Article accompanied by a PRL Viewpoint in Physics1, 8 (2008

Plume-like upper mantle instabilities drive subduction initiation

International audienc

Residence time statistics for NN blinking quantum dots and other stochastic processes

We present a study of residence time statistics for $N$ blinking quantum dots. With numerical simulations and exact calculations we show sharp transitions for a critical number of dots. In contrast to expectation the fluctuations in the limit of $N \to \infty$ are non-trivial. Besides quantum dots our work describes residence time statistics in several other many particle systems for example $N$ Brownian particles. Our work provides a natural framework to detect non-ergodic kinetics from measurements of many blinking chromophores, without the need to reach the single molecule limit