On the Variational Regularity of Cameron-Martin paths

It is a well-known fact that finite rho-variation of the covariance (in 2D sense) of a general Gaussian process implies finite rho-variation of Cameron-Martin paths. In the special case of fractional Brownian motion (think: 2H=1/rho), in the rougher than Brownian regime, a sharper result holds thanks to a Besov-type embedding [Friz-Victoir, JFA, 2006]. In the present note we give a general result which closes this gap. We comment on the importance of this result for various applications.Comment: The contents of this paper are now included in arXiv:1307.346

From rough path estimates to multilevel Monte Carlo

New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential equations driven by Gaussian noise in the aforementioned sense. Our focus lies on numerical implementations, and more specifically on the saving possible via multilevel methods. Our analysis relies on a subtle combination of pathwise estimates, Gaussian concentration, and multilevel ideas. Numerical examples are given which both illustrate and confirm our findings.Comment: 34 page

Young Stars with SALT

We present a spectroscopic and kinematic analysis of 79 nearby M dwarfs in 77 systems. All are low-proper-motion southern hemisphere objects and were identified in a nearby star survey with a demonstrated sensitivity to young stars. Using low-resolution optical spectroscopy from the Red Side Spectrograph (RSS) on the South African Large Telescope (SALT), we have determined radial velocities, H-alpha, Lithium 6708\AA, and Potassium 7699\AA~equivalent widths linked to age and activity, and spectral types for all our targets. Combined with astrometric information from literature sources, we identify 44 young stars. Eighteen are previously known members of moving groups within 100 parsecs of the Sun. Twelve are new members, including one member of the TW Hydra moving group, one member of the 32 Orionis moving group, nine members of Tucana-Horologium, one member of Argus, and two new members of AB Doradus. We also find fourteen young star systems that are not members of any known groups. The remaining 33 star systems do not appear to be young. This appears to be evidence of a new population of nearby young stars not related to the known nearby young moving groups.Comment: 23 pages, 11 figures, 6 tables. Accepted to Ap

Assessment of slope failures off Vancouver Island revealed in EM300 multibeam bathymetry data

Multibeam bathymetric data acquired off Vancouver Island across the accretionary prism of the Cascadia subduction zone reveal a prominent segmentation of the deformation front with dominant azimuths of the ridges at ~120° and ~150° and abundant submarine landslides. Both these ridge-orientations are oblique to the direction of subduction (~45°). Ridges at a strike of ~120° show dominantly rectangular-shaped failure head-scarps and intact blocks of sediments within the failed sediment mass, whereas ridges with an azimuth of ~150° show curved head-scarps and incoherent debris in the failure mass. We propose that this systematic change in failure-style is related to the underlying thrust fault system producing steeper and taller ridges for azimuths around 150°, but less steep and tall ridges at 120°. Thus, debris-flow style failure is simply a result of higher kinetic forcing of the down-sliding sediment mass: more mixing and destruction of the coherent blocks for taller and steeper ridges, and blocks of intact sediment for gentle slopes and less elevated ridges. A segmentation of the deformation front and ridge alignment into two dominant azimuths could be a result of: a) complex interaction and competing forces from overall slab-pull (45°), b) re-activated faults orientated almost N-S (~175°) on the oceanic plate and overlying sediment cover (reflected in the magnetic stripes and abyssal plain strike-slip faulting), and c) relative orientation of the back-stop off Vancouver Island and accreted terranes (at ~127° following the coastline between Nootka Island and Port Renfrew). Extensional faulting is observed only at ridges with debris-flow style failure, which also are the ridges with larger height and steeper slopes. These extensional faults may be the result of over-steepening of the ridges and collapse of the sediment pile that can no longer withstand its own weight due to limited internal shear strength

High and low molecular weight crossovers in the longest relaxation time dependence of linear cis-1,4 polyisoprene by dielectric relaxations

The dielectric relaxation of cis-1,4 Polyisoprene [PI] is sensitive not only to the local and segmental dynamics but also to the larger scale chain (end-to-end) fluctuations. We have performed a careful dielectric investigation on linear PI with various molecular weights in the range of 1 to 320 kg/mol. The broadband dielectric spectra of all samples were measured isothermally at the same temperature to avoid utilizing shift factors. For the low and medium molecular weight range, the comparisons were performed at 250 K to access both the segmental relaxation and normal mode peaks inside the available frequency window (1 mHz–10 MHz). In this way, we were able to observe simultaneously the effect of molecular mass on the segmental dynamics—related with the glass transition process—and on the end-to-end relaxation time of PI and thus decouple the direct effect of molecular weight on the normal mode from that due to the effect on the monomeric friction coefficient. The latter effect is significant for low molecular weight (M w < 33 kg/mol), i.e., in the range where the crossover from Rouse dynamics to entanglement limited flow occurs. Despite the conductivity contribution at low frequency, careful experiments allowed us to access to the normal mode signal for molecular weights as high as M w = 320 kg/mol, i.e., into the range of high molecular weights where the pure reptation behavior could be valid, at least for the description of the slowest chain modes. The comparison between the dielectric relaxations of PI samples with medium and high molecular weight was performed at 320 K. We found two crossovers in the molecular weight dependence of the longest relaxation time, the first around a molecular weight of 6.5 ± 0.5 kg/mol corresponding to the end of the Rouse regime and the second around 75 ± 10 kg/mol. Above this latter value, we find a power law compatible with exponent 3 as predicted by the De Gennes theory