Quasireversibility Methods for Non-Well-Posed Problems

The nal value problem, ae u t + Au = 0 ; 0 ! t ! T u(T ) = f with positive self-adjoint unbounded A is known to be ill-posed. One approach to dealing with this has been the method of quasireversibility, where the operator is perturbed to obtain a well-posed problem which approximates the original problem. In this work, we will use a quasi-boundary-value method, where we perturb the nal condition to form an approximate non-local problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions u converge on 0; T] if and only if the original problem has a classical solution. We obtain several other results, including some explicit convergence rates

Seismic tomography and deformation modeling of the junction of the San Andreas and Calaveras faults

Local earthquake P traveltime data is inverted to obtain a three‐dimensional tomographic image of the region centered on the junction of the San Andreas and Calaveras faults. The resulting velocity model is then used to relocate more than 17,000 earthquakes and to produce a model of fault structure in the region. These faults serve as the basis for modeling the topography using elastic dislocation methods. The region is of interest because active faults join, it marks the transition zone from creeping to locked fault behavior on the San Andreas fault, it exhibits young topography, and it has a good spatial distribution of seismicity. The tomographic data set is extensive, consisting of 1445 events, 96 stations, and nearly 95,000 travel time readings. Tomographic images are resolvable to depths of 12 km and show significant velocity contrasts across the San Andreas and Calaveras faults, a low‐velocity zone associated with the creeping section of the San Andreas fault, and shallow low‐velocity sediments in the southern Santa Clara valley and northern Salinas valley. Relocated earthquakes only occur where vp > 5 km/s and indicate that portions of the San Andreas and Calaveras faults are non vertical, although we cannot completely exclude the possibility that all or part of this results from ray tracing problems. The new dips are more consistent with geological observations that dipping faults intersect the surface where surface traces have been mapped. The topographic modeling predicts extensive subsidence in regions characterized by shallow low‐velocity material, presumably the result of recent sedimentation. Some details of the topography at the junction of the San Andreas and Calaveras faults are not consistent with the modeling results, suggesting that the current position of this “triple junction” has changed with time. The model also predicts those parts of the fault subject to contraction or extension perpendicular to the fault strike and hence the sense of any dip‐slip component. In each locality the relative vertical motion across the fault is consistent with the fault dips found with the new hypocentral locations

Eigenvalues of the 2p3pP3 and 2p3dD1,3 bound states of the helium isoelectronic sequence

The 1Z expansion method is used to calculate the eigenvalues of the 2p3pP3 and 2p3dD1,3 states of the helium isoelectronic sequence. The results are compared to variational calculations for neutral helium. Wavelengths are predicted for a number of transitions originating in doubly excited states of the heliumlike ions up to Fe xxv. The results for neutral helium are compared to recent beam-foil experiments and alternative line identifications are made. The predicted wavelength for the 2p3dD3-2p2P3 transition is 3014, in close agreement with the line observed by Berry et al. at 3012 ± 2. © 1972 The American Physical Society

The Flux Auto- and Cross-Correlation of the Lyman-alpha Forest. II. Modelling Anisotropies with Cosmological Hydrodynamic Simulations

The isotropy of the Lyman-alpha forest in real-space uniquely provides a measurement of cosmic geometry at z > 2. The angular diameter distance for which the correlation function along the line of sight and in the transverse direction agree corresponds to the correct cosmological model. However, the Lyman-alpha forest is observed in redshift-space where distortions due to Hubble expansion, bulk flows, and thermal broadening introduce anisotropy. Similarly, a spectrograph's line spread function affects the autocorrelation and cross-correlation differently. In this the second paper of a series on using the Lyman-alpha forest observed in pairs of QSOs for a new application of the Alcock-Paczynski (AP) test, these anisotropies and related sources of potential systematic error are investigated with cosmological hydrodynamic simulations. Three prescriptions for galactic outflow were compared and found to have only a marginal effect on the Lyman-alpha flux correlation (which changed by at most 7% with use of the currently favored variable-momentum wind model vs. no winds at all). An approximate solution for obtaining the zero-lag cross-correlation corresponding to arbitrary spectral resolution directly from the zero-lag cross-correlation computed at full-resolution (good to within 2% at the scales of interest) is presented. Uncertainty in the observationally determined mean flux decrement of the Lyman-alpha forest was found to be the dominant source of systematic error; however, this is reduced significantly when considering correlation ratios. We describe a simple scheme for implementing our results, while mitigating systematic errors, in the context of a future application of the AP test.Comment: 20 page

Compact stars in the standard model - and beyond

In the context of the standard model of particle physics, there is a definite upper limit to the density of stable compact stars. However, if there is a deeper layer of constituents, below that of quarks and leptons, stability may be re-established far beyond this limiting density and a new class of compact stars could exist. These objects would cause gravitational lensing of white dwarfs and gamma-ray bursts, which might be observable as a diffraction pattern in the spectrum. Such observations could provide means for obtaining new clues about the fundamental particles and the origin of cold dark matter.Comment: 16 pages, 6 figures, contribution to the 42nd course of the international school of subnuclear physics, 'How and where to go beyond the standard model', Erice, Aug. 29 - Sep. 7, 200

Diffusing wild type and sterile mosquitoes in an optimal control setting

This paper develops an optimal control framework to investigate the introduction of sterile type mosquitoes to reduce the overal moquito population. As is well known, mosquitoes are vectors of disease. For instance the WHO lists, among other diseases, Malaria, Dengue Fever, Rift Valley Fever, Yellow Fever, Chikungunya Fever and Zika. [http://www.who.int/mediacentre/factsheets/fs387/en/ ] The goal is to establish the existence of a solution given an optimal sterilization protocol as well as to develop the corresponding optimal control representation to minimize the infiltrating mosquito population while minimizing fecundity and the number of sterile type mosquitoes introduced into the environment per unit time. This paper incorporates the diffusion of the mosquitoes into the controlled model and presents a number of numerical simulations

A mini-survey for variability in early L dwarfs

We report differential I-band photometry of four early L-dwarfs obtained to study variability. We detect variability on the timescale of hours in two objects, 2M0746425+200032 (at a level of 0.007 mag -- 6.5 sigma) and 2M1108307+683017 (0.012 mag -- 5 sigma). We also place upper limits of 0.02 mag (1 sigma) on the variability of two others.Comment: 5 pages. MNRAS, in pres

Observations of Ultracool White Dwarfs

We present new spectroscopic and photometric measurements of the white dwarfs LHS 3250 and WD 0346+246. Along with F351-50, these white dwarfs are the coolest ones known, all with effective temperatures below 4000 K. Their membership in the Galactic halo population is discussed, and detailed comparisons of all three objects with new atmosphere models are presented. The new models consider the effects of mixed H/He atmospheres and indicate that WD 0346+246 and F351-50 have predominantly helium atmospheres with only traces of hydrogen. LHS 3250 may be a double degenerate whose average radiative temperature is between 2000 and 4000 K, but the new models fail to explain this object

Gravitational Collapse with a Cosmological Constant

We consider the effect of a positive cosmological constant on spherical gravitational collapse to a black hole for a few simple, analytic cases. We construct the complete Oppenheimer-Snyder-deSitter (OSdS) spacetime, the generalization of the Oppenheimer-Snyder solution for collapse from rest of a homogeneous dust ball in an exterior vacuum. In OSdS collapse, the cosmological constant may affect the onset of collapse and decelerate the implosion initially, but it plays a diminishing role as the collapse proceeds. We also construct spacetimes in which a collapsing dust ball can bounce, or hover in unstable equilibrium, due to the repulsive force of the cosmological constant. We explore the causal structure of the different spacetimes and identify any cosmological and black hole event horizons which may be present.Comment: 7 pages, 10 figures; To appear in Phys. Rev.