On the determination of the earthquake slip distribution via linear programming techniques

The description that one can have of the seismic source is the mani- festation of an imagined model, obviously outlined from Physic Theories and supported by mathematical methods. In that context, the modelling of earthquake rupture consists in finding values of the parameters of the selected physics-mathematical model, through which it becomes possible to reproduce numerically the records of earthquake effects on the Earths surface. We present and test a Linear Programming (LP) inversion in dual form, for reconstructing the kinematics of the rupture of large earthquakes through space-time seismic slip distribution on finite faults planes

Geoengineering: Whiter skies?

One proposed side effect of geoengineering with stratospheric sulfate aerosols is sky whitening during the day and afterglows near sunset, as is seen after large volcanic eruptions. Sulfate aerosols in the stratosphere would increase diffuse light received at the surface, but with a non-uniform spectral distribution. We use a radiative transfer model to calculate spectral irradiance for idealized size distributions of sulfate aerosols. A 2% reduction in total irradiance, approximately enough to offset anthropogenic warming for a doubling of CO_2 concentrations, brightens the sky (increase in diffuse light) by 3 to 5 times, depending on the aerosol size distribution. The relative increase is less when optically thin cirrus clouds are included in our simulations. Particles with small radii have little influence on the shape of the spectra. Particles of radius ∼0.5 μm preferentially increase diffuse irradiance in red wavelengths, whereas large particles (∼0.9 μm) preferentially increase diffuse irradiance in blue wavelengths. Spectra show little change in dominant wavelength, indicating little change in sky hue, but all particle size distributions produce an increase in white light relative to clear sky conditions. Diffuse sky spectra in our simulations of geoengineering with stratospheric aerosols are similar to those of average conditions in urban areas today

Phase Diagram of the Dissipative Hofstadter Model

The dissipative quantum mechanics of a charged particle in a uniform magnetic field and periodic potential has delocalization critical points which correspond to backgrounds for the open string. We study the phase diagram of this system (in the magnetic field/dissipation constant plane) and find a fractal structure which, in the limit of zero dissipation, matches the fractal energy level structure of the pure quantum mechanical version of this problem (Hofstadter model).Comment: 23 page

Biogeochemical modeling at mass extinction boundaries

The causes of major mass extinctions is a subject of considerable interest to those concerned with the history and evolution of life on earth. The primary objectives of the proposed plan of research are: (1) to develop quantitative time-dependent biogeochemical cycle models, coupled with an ocean atmosphere in order to improve the understanding of global scale physical, chemical, and biological processes that control the distribution of elements important for life at times of mass extinctions; and (2) to develop a comprehensive data base of the best available geochemical, isotopic, and other relevant geologic data from sections across mass extinction boundaries. These data will be used to constrain and test the biogeochemical model. These modeling experiments should prove useful in: (1) determining the possible cause(s) of the environmental changes seen at bio-event boundaries; (2) identifying and quantifying little-known feedbacks among the oceans, atmosphere, and biosphere; and (3) providing additional insights into the possible responses of the earth system to perturbations of various timescales. One of the best known mass extinction events marks the Cretaceous/Tertiary (K/T) boundary (66 Myr ago). Data from the K/T boundary are used here to constrain a newly developed time-dependent biogeochemical cycle model that is designed to study transient behavior of the earth system. Model results predict significant fluctuations in ocean alkalinity, atmospheric CO2, and global temperatures caused by extinction of calcareous plankton and reduction in the sedimentation rates of pelagic carbonates and organic carbon. Oxygen-isotome and other paleoclimatic data from K/T time provide some evidence that such climatic fluctuations may have occurred, but stabilizing feedbacks may have acted to reduce the ocean alkalinity and carbon dioxide fluctuations

Ocean alkalinity and the Cretaceous/Tertiary boundary

A biogeochemical cycle model resolving ocean carbon and alkalinity content is applied to the Maestrichtian and Danian. The model computes oceanic concentrations and distributions of Ca(2+), Mg(2+), and Sigma-CO2. From these values an atmospheric pCO2 value is calculated, which is used to estimate rates of terrestrial weathering of calcite, dolomite, and calcium and magnesium silicates. Metamorphism of carbonate rocks and the subsequent outgassing of CO2 to the atmosphere are parameterized in terms of carbonate rock reservoir sizes, total land area, and a measure of overall tectonic activity, the sea-floor generation rate. The ocean carbon reservoir computed by the model is used with Deep Sea Drilling Project (DSDP) C-13 data to estimate organic detrital fluxes under a variety of ocean mixing rate assumptions. Using Redfield ratios, the biogenic detrital flux estimate is used to partition the ocean carbon and alkalinity reservoirs between the mixed layer and deep ocean. The calcite flux estimate and carbonate ion concentrations are used to determine the rate of biologically mediated CaCO3 titration. Oceanic productivity was severely limited for approximately 500 kyr following the K/T boundary resulting in significant increases in total ocean alkalinity. As productivity returned to the ocean, excess carbon and alkalinity was removed from the ocean as CaCO3. Model runs indicate that this resulted in a transient imbalance in the other direction. Ocean chemistry returned to near-equilibrium by about 64 mybp

The frequency response of temperature and precipitation in a climate model

Dynamic aspects of the climate's response to forcing are typically explored through transient simulations in the time domain. However, because of the large range of time-scales involved, some features are more easily observed in the frequency domain. We compute the frequency-response of the HadCM3L general circulation model (GCM) to sinusoidal perturbations in solar radiative forcing, with periods between 2^(−1/2) and 2^9 (512) years. The global mean temperature response decreases with increasing frequency, and the frequency scaling at time-scales longer than one year is consistent with the behavior of diffusion into a semi-infinite slab. The land-sea contrast and land-averaged precipitation, however, exhibit relatively little dependency on the frequency of the imposed perturbation, with significant response at both short and long periods. Understanding these relative characteristics of different climate variables in the frequency domain is important to understanding the transient response of the climate system to both anthropogenic and natural (e.g., volcanic) forcings; the frequency response is also relevant in understanding the spectrum of natural variability

Critical Theories of the Dissipative Hofstadter Model

It has recently been shown that the dissipative Hofstadter model (dissipative quantum mechanics of an electron subject to uniform magnetic field and periodic potential in two dimensions) exhibits critical behavior on a network of lines in the dissipation/magnetic field plane. Apart from their obvious condensed matter interest, the corresponding critical theories represent non-trivial solutions of open string field theory, and a detailed account of their properties would be interesting from several points of view. A subject of particular interest is the dependence of physical quantities on the magnetic field since it, much like $\theta_{\rm QCD}$, serves only to give relative phases to different sectors of the partition sum. In this paper we report the results of an initial investigation of the free energy, $N$-point functions and boundary state of this type of critical theory. Although our primary goal is the study of the magnetic field dependence of these quantities, we will present some new results which bear on the zero magnetic field case as well.Comment: 42 pages (25 reduced

Extended Seismic Source Characterisation using Linear Programming Inversion in a Dual Formulation

A linear programming (LP) inversion method in a dual formulation was applied to reconstruct the kinematics of finite seismic ruptures. In a general setting, this approach can yield results from several data sets: strong ground motion, teleseismic waveforms or/and geodesic data (static deformation). The dual formulation involves the transformation of a normal solution space into an equivalent but reduced space: the dual space. The practical result of this transformation is a simpler inversion problem that is therefore faster to resolve, more stable and more robust. The developed algorithm includes a forward problem that calculates Green’s functions using a finite differences method with a 3D structure model. To evaluate the performance of this algorithm, we applied it to the reconstitution of a realistic slip distribution model from a data set synthesised using this model, i.e., the solution of the forward problem. Several other standard inversion approaches were applied to the same synthetic data for comparison

Relic Abundances and the Boltzmann Equation

I discuss the validity of the quantum Boltzmann equation for the calculation of WIMP relic densities.Comment: 5 pages, no figures; talk given at Dark Matter 2000; an important reference is added in the revised versio

Single-Spin Measurement and Decoherence in Magnetic Resonance Force Microscopy

We consider a simple version of a cyclic adiabatic inversion (CAI) technique in magnetic resonance force microscopy (MRFM). We study the problem: What component of the spin is measured in the CAI MRFM? We show that the non-destructive detection of the cantilever vibrations provides a measurement of the spin component along the effective magnetic field. This result is based on numerical simulations of the Hamiltonian dynamics (the Schrodinger equation) and the numerical solution of the master equation.Comment: 5 pages + 5 figures (PNG format