Approach to Equilibrium for a Forced Burgers Equation

We show that approach to equilibrium in certain forced Burgers equations is implied by a decay estimate on a suitable intrinsic semigroup estimate, and we verify this estimate in a variety of cases including a periodic force.Comment: To appear in Journal of Evolution Equation

Lifshitz tails for alloy type models in a constant magnetic field

In this note, we study Lifshitz tails for a 2D Landau Hamiltonian perturbed by a random alloy-type potential constructed with single site potentials decaying at least at a Gaussian speed. We prove that, if the Landau level stays preserved as a band edge for the perturbed Hamiltonian, at the Landau levels, the integrated density of states has a Lifshitz behavior of the type $e^{-\log^2|E-2bq|}$

Books

Portrait of Don Craib In Search of Truth - A Portrait of Don Craib: By E.B. Adams pp. xi + 123. Illustrated.London and New York: Royal Society of Medicine Services. 1990.Internal medicine Harrison's Principles of Internal Medicine. 12th ed. Bd. by ].D. Wilson, E. Braunwald, K.]. Isselbacher, et al. pp. xxx + 2208. Illustrated. USA: McGraw-Hill. 1991.HPV and cervical cancer Human Papillomavirus and Cervical Cancer. Ed. by N. Munoz, F. X. Bosch and O. M. Jensen. Pp. xii + 155. Illustrated. France: International Agency for Research on Cancer. 1989

Editorial: Hendrik Hanekom - innovator, facilitator and transformer

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Convective cold pools in long-term boundary layer mast observations

Cold pools are mesoscale features that are key for understanding the organization of convection, but are insufficiently captured in conventional observations. This study conducts a statistical characterization of cold-pool passages observed at a 280-m-high boundary layer mast in Hamburg (Germany) and discusses factors controlling their signal strength. During 14 summer seasons 489 cold-pool events are identified from rapid temperature drops below 22K associated with rainfall. The cold-pool activity exhibits distinct annual and diurnal cycles peaking in July and midafternoon, respectively. The median temperature perturbation is -3.3K at 2-m height and weakens above. Also the increase in hydrostatic air pressure and specific humidity is largest near the surface. Extrapolation of the vertically weakening pressure signal suggests a characteristic cold-pool depth of about 750 m. Disturbances in the horizontal and vertical wind speed components document a lifting-induced circulation of air masses prior to the approaching cold-pool front. According to a correlation analysis, the near-surface temperature perturbation is more strongly controlled by the pre-event saturation deficit (r = -0.71) than by the event-accumulated rainfall amount (r = -0.35). Simulating the observed temperature drops as idealized wet-bulb processes suggests that evaporative cooling alone explains 64 of the variability in cold-pool strength. This number increases to 92 for cases that are not affected by advection of midtropospheric low-Qe air masses under convective downdrafts. © 2021 American Meteorological Society

In-orbit Vignetting Calibrations of XMM-Newton Telescopes

We describe measurements of the mirror vignetting in the XMM-Newton Observatory made in-orbit, using observations of SNR G21.5-09 and SNR 3C58 with the EPIC imaging cameras. The instrument features that complicate these measurements are briefly described. We show the spatial and energy dependences of measured vignetting, outlining assumptions made in deriving the eventual agreement between simulation and measurement. Alternate methods to confirm these are described, including an assessment of source elongation with off-axis angle, the surface brightness distribution of the diffuse X-ray background, and the consistency of Coma cluster emission at different position angles. A synthesis of these measurements leads to a change in the XMM calibration data base, for the optical axis of two of the three telescopes, by in excess of 1 arcminute. This has a small but measureable effect on the assumed spectral responses of the cameras for on-axis targets.Comment: Accepted by Experimental Astronomy. 26 pages, 18 figure

Density of Surface States in Discrete Models

We consider a simple quantum model with a surface and prove the existence of a surface density of states. We show that the energy spectrum of the model is the union of the support of the bulk densities of states of the media forming the surface and the support of the surface density of states

Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.Comment: 9 page

Carbon-Carbon Single Bond Activation for Nucleophilic Addition to Michael Acceptors

Intramolecular alkene carboacylation has previously been achieved under rhodium catalysis using quinolinyl ketones. Utilizing insight gained from mechanistic studies, new substrates containing ortho-substitution have been prepared and subjected to rhodium catalysis with an exogenous alkene. This research provides an overview of substrate synthesis as well as the unexpected product—rather than the anticipated carboacylation these substrates have been observed to undergo carbon-carbon bond activation followed by conjugate addition to Michael acceptors