Application of the Method of Matched Asymptotic Expansions to Solve a Nonlinear Pseudo-Parabolic Equation: The Saturation Convection-Dispersion Equation

In this work, we apply the method of matched asymptotic expansions to solve the one-dimensional saturation convection-dispersion equation, a nonlinear pseudo-parabolic partial differential equation. This equation is one of the governing equations for two-phase flow in a porous media when including capillary pressure effects, for the specific initial and boundary conditions arising when injecting water in an infinite radial piecewise homogeneous horizontal medium containing oil and water. The method of matched asymptotic expansions combines inner and outer expansions to construct the global solution. In here, the outer expansion corresponds to the solution of the nonlinear first-order hyperbolic equation obtained when the dispersion effects driven by capillary pressure became negligible. This equation has a monotonic flux function with an inflection point, and its weak solution can be found by applying the method of characteristics. The inner expansion corresponds to the shock layer, which is modeled as a traveling wave obtained by a stretching transformation of the partial differential equation. In the transformed domain, the traveling wave solution is solved using regular perturbation theory. By combining the solution for saturation with the so-called Thompson-Reynolds steady-state theory for obtaining the pressure, one can obtain an approximate analytical solution for the wellbore pressure, which can be used as the forward solution which analyzes pressure data by pressure-transient analysis

A core function for p120-catenin in cadherin turnover

p120-catenin stabilizes epithelial cadherin (E-cadherin) in SW48 cells, but the mechanism has not been established. Here, we show that p120 acts at the cell surface to control cadherin turnover, thereby regulating cadherin levels. p120 knockdown by siRNA expression resulted in dose-dependent elimination of epithelial, placental, neuronal, and vascular endothelial cadherins, and complete loss of cell–cell adhesion. ARVCF and δ-catenin were functionally redundant, suggesting that proper cadherin-dependent adhesion requires the presence of at least one p120 family member. The data reveal a core function of p120 in cadherin complexes, and strongly predict a dose-dependent loss of E-cadherin in tumors that partially or completely down-regulate p120

Intrinsic Absorption Lines in Seyfert 1 Galaxies. I. Ultraviolet Spectra from the Hubble Space Telescope

We present a study of the intrinsic absorption lines in the ultraviolet spectra of Seyfert 1 galaxies. We find that the fraction of Seyfert 1 galaxies that show absorption associated with their active nuclei is more than one-half (10/17), which is much higher than previous estimates (3 - 10%) . There is a one-to-one correspondence between Seyferts that show intrinsic UV absorption and X-ray ``warm absorbers''. The intrinsic UV absorption is generally characterized by high ionization: C IV and N V are seen in all 10 Seyferts with detected absorption (in addition to Ly-alpha), whereas Si IV is present in only four of these Seyferts, and Mg II absorption is only detected in NGC 4151. The absorption lines are blueshifted (or in a few cases at rest) with respect to the narrow emission lines, indicating that the absorbing gas is undergoing net radial outflow. At high resolution, the absorption often splits into distinct kinematic components that show a wide range in widths (20 - 400 km/s FWHM), indicating macroscopic motions (e.g., radial velocity subcomponents or turbulence) within a component. The strong absorption components have cores that are much deeper than the continuum flux levels, indicating that the regions responsible for these components lie completely outside of the broad emission-line regions. The covering factor of the absorbing gas in the line of sight, relative to the total underlying emission, is C > 0.86, on average. The global covering factor, which is the fraction of emission intercepted by the absorber averaged over all lines of sight, is C > 0.5.Comment: 56 pages, Latex, includes 4 figures (encapsulated postscript), Fig. 1 has 2 parts and Fig. 2 has 3 parts, to appear in the Astrophysical Journa

Fast TeV variability from misaligned minijets in the jet of M87

The jet of the radio galaxy M87 is misaligned, resulting in a Doppler factor delta~1 for emission of plasma moving parallel to the jet. This makes the observed fast TeV flares on timescales of t_v~5R_g/c harder to understand as emission from the jet. In previous work, we have proposed a jets-in-a-jet model for the ultra-fast TeV flares with t_v<<R_g/c seen in Mrk 501 and PKS 2155-304. Here, we show that about half of the minijets beam their emission outside the jet cone. Minijets emitting off the jet axis result in rapidly evolving TeV (and maybe lower energy) flares that can be observed in nearby radio galaxies. The TeV flaring from M87 fits well into this picture, if M87 is a misaligned blazar.Comment: 9 pages, 5 figures, minor changes, MNRAS, accepte

Incremental Reduction in Risk of Death Associated with Use of Guideline-Recommended Therapies in Patients with Heart Failure: A Nested Case-Control Analysis of IMPROVE HF

Background: Several therapies are guideline-recommended to reduce mortality in patients with heart failure (HF) and reduced left ventricular ejection fraction, but the incremental clinical effectiveness of these therapies has not been well studied. We aimed to evaluate the individual and incremental benefits of guideline-recommended HF therapies associated with 24-month survival. Methods and results: We performed a nested case-control study of HF patients enrolled in IMPROVE HF. Cases were patients who died within 24 months and controls were patients who survived to 24 months, propensity-matched 1:2 for multiple prognostic variables. Logistic regression was performed, and the attributable mortality risk from incomplete application of each evidence-based therapy among eligible patients was calculated. A total of 1376 cases and 2752 matched controls were identified. β-Blocker and cardiac resynchronization therapy were associated with the greatest 24-month survival benefit (adjusted odds ratio for death 0.42, 95% confidence interval (CI), 0.34–0.52; and 0.44, 95% CI, 0.29–0.67, respectively). Angiotensin-converting enzyme inhibitors/angiotensin receptor blockers, implantable cardioverter-defibrillators, anticoagulation for atrial fibrillation, and HF education were also associated with benefit, whereas aldosterone antagonist use was not. Incremental benefits were observed with each successive therapy, plateauing once any 4 to 5 therapies were provided (adjusted odds ratio 0.31, 95% CI, 0.23–0.42 for 5 or more versus 0/1, P<0.0001). Conclusions: Individual, with a single exception, and incremental use of guideline-recommended therapies was associated with survival benefit, with a potential plateau at 4 to 5 therapies. These data provide further rationale to implement guideline-recommended HF therapies in the absence of contraindications to patients with HF and reduced left ventricular ejection fraction

MAPPING OF RESERVOIR PROPERTIES AND FACIES THROUGH INTEGRATION OF STATIC AND DYNAMIC DATA

Knowledge of the distribution of permeability and porosity in a reservoir is necessary for the prediction of future oil production, estimation of the location of bypassed oil, and optimization of reservoir management. But while the volume of data that can potentially provide information on reservoir architecture and fluid distributions has increased enormously in the past decade, it is not yet possible to make use of all the available data in an integrated fashion. While it is relatively easy to generate plausible reservoir models that honor static data such as core, log, and seismic data, it is far more difficult to generate plausible reservoir models that honor dynamic data such as transient pressures, saturations, and flow rates. As a result, the uncertainty in reservoir properties is higher than it could be and reservoir management can not be optimized. The goal of this project is to develop computationally efficient automatic history matching techniques for generating geologically plausible reservoir models which honor both static and dynamic data. Solution of this problem is necessary for the quantification of uncertainty in future reservoir performance predictions and for the optimization of reservoir management. Facies (defined here as regions of relatively uniform petrophysical properties) are common features of all reservoirs. Because the flow properties of the various facies can vary greatly, knowledge of the location of facies boundaries is of utmost importance for the prediction of reservoir performance and for the optimization of reservoir management. When the boundaries between facies are fairly well known, but flow properties are poorly known, the average properties for all facies can be determined using traditional techniques. Traditional history matching honors dynamic data by adjusting petrophysical properties in large areas, but in the process of adjusting the reservoir model ignores the static data and often results in implausible reservoir models. In general, boundary locations, average permeability and porosity, relative permeability curves, and local flow properties may all need to be adjusted to achieve a plausible reservoir model that honors all data. In this project, we will characterize the distribution of geologic facies as an indicator random field, making use of the tools of geostatistics as well as the tools of inverse and probability theory for data integration

A fast Monte Carlo algorithm for site or bond percolation

We describe in detail a new and highly efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time which scales linearly with the size of the system. We demonstrate our algorithm by using it to investigate a number of issues in percolation theory, including the position of the percolation transition for site percolation on the square lattice, the stretched exponential behavior of spanning probabilities away from the critical point, and the size of the giant component for site percolation on random graphs.Comment: 17 pages, 13 figures. Corrections and some additional material in this version. Accompanying material can be found on the web at http://www.santafe.edu/~mark/percolation

Modeling bursts and heavy tails in human dynamics

Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. We provide direct evidence that for five human activity patterns the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. We discuss two queueing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can hadle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution with exponent alpha=3/2. The second model imposes limitations on the queue length, resulting in alpha=1. We provide empirical evidence supporting the relevance of these two models to human activity patterns. Finally, we discuss possible extension of the proposed queueing models and outline some future challenges in exploring the statistical mechanisms of human dynamics.Comment: RevTex, 19 pages, 8 figure

Can a Dusty Warm Absorber Model Reproduce the Soft X-ray Spectra of MCG-6-30-15 and Mrk 766?

XMM-Newton RGS spectra of MCG-6-30-15 and Mrk 766 exhibit complex discrete structure, which was interpreted in a paper by Branduardi-Raymont et al. (2001) as evidence for the existence of relativistically broadened Lyman alpha emission from carbon, nitrogen, and oxygen, produced in the inner-most regions of an accretion disk around a Kerr black hole. This suggestion was subsequently criticized in a paper by Lee et al. (2001), who argued that for MCG-6-30-15, the Chandra HETG spectrum, which is partially overlapping the RGS in spectral coverage, is adequately fit by a dusty warm absorber model, with no relativistic line emission. We present a reanalysis of the original RGS data sets in terms of the Lee et al. (2001) model, and demonstrate that spectral models consisting of a smooth continuum with ionized and dust absorption alone cannot reproduce the RGS spectra of both objects. The original relativistic line model with warm absorption proposed by Branduardi-Raymont et al. (2001) provides a superior fit to the RGS data, both in the overall shape of the spectrum and in the discrete absorption lines. Limits on the amount of X-ray absorption by dust particles are discussed. We also discuss a possible theoretical interpretation for the putative relativistic Lyman alpha line emission in terms of the photoionized surface layers of the inner regions of an accretion disk.Comment: Replaced with accepted version. To appear in ApJ; tentatively scheduled for the v596 Oct. 10, 2003 issu