Sufficient conditions for unique global solutions in optimal control of semilinear equations with C1−C^1-nonlinearity

We consider a $C^1-$semilinear elliptic optimal control problem possibly subject to control and/or state constraints. Generalizing previous work we provide a condition which guarantees that a solution of the necessary first order conditions is a global minimum. A similiar result also holds at the discrete level where the corresponding condition can be evaluated explicitly. Our investigations are motivated by G\"unter Leugering, who raised the question whether our previous results can be extended to the nonlinearity $\phi(s)=s|s|$. We develop a corresponding analysis and present several numerical test examples demonstrating its usefulness in practice

Simulation of a particle-laden turbulent channel flow using an improved stochastic Lagrangian model

The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift velocity in the limits of low and high particle inertia, is derived. It is also shown that some previously proposed stochastic models are not compatible with this transport equation in the limit of high particle inertia. The drift and diffusion parameters of these stochastic differential equations are then estimated using direct numerical simulation (DNS) data. It is observed that, contrary to the conventional modeling, they are highly space dependent and anisotropic. To investigate the performance of the present stochastic model, a comparison is made with DNS data as well as with two different stochastic models. A good prediction of the first and second order statistical moments of the particle and fluid seen velocities is obtained with the three models considered. Even for some components of the triple particle velocity correlations, an acceptable accordance is noticed. The performance of the three different models mainly diverges for the particle concentration and the drift velocity. The proposed model is seen to be the only one which succeeds in predicting the good evolution of these latter statistical quantities for the range of particle inertia studied

Measuring Endocytosis During Proliferative Cell Quiescence

Quiescence (also called "G0") is the state in which cells have exited the cell cycle but are capable to reenter as required. Though poorly understood, it represents one of the most prevalent cell states across all life. Many biologically important cell types reside in quiescence including mature hepatocytes, endothelial cells, and dormant adult stem cells. Furthermore, the quiescence program occurs in both short- and long-term varieties, depending on the physiological environments. A barrier slowing our understanding of quiescence has been a scarcity of available in vitro model systems to allow for the exploration of key regulatory pathways, such as endocytosis. Endocytosis, the internalization of extracellular material into the cell, is a fundamental and highly regulated process that impacts many cell biological functions. Accordingly, we have developed an in vitro model of deep quiescence in hTERT-immortalized RPE1 cells, combining both long-term contact inhibition and mitogen removal, to measure endocytosis. In addition, we present an analytical approach employing automated high-throughput microscopy and image analysis that yields high-content data allowing for meaningful and statistically robust interpretation. Importantly, the methods presented herein provide a suitable platform that can be easily adapted to investigate other regulatory processes across the cell cycle

Coherence-controlled transparency and far-from-degenerate parametric gain in a strongly-absorbing Doppler-broadened medium

An inversionless gain of anti-Stokes radiation above the oscillation threshold in an optically-dense far-from-degenerate double-Lambda Doppler-broadened medium accompanied by Stokes gain is predicted. The outcomes are illustrated with numerical simulations applied to sodium dimer vapor. Optical switching from absorption to gain via transparency controlled by a small variation of the medium and of the driving radiation parameters which are at a level less than one photon per molecule is shown. Related video/audio clips see in: A.K. Popov, S.A. Myslivets, and T.F. George, Optics Express Vol. 7, No 3, 148 (2000)(http://epubs.osa.org/oearchive/source/22947.htm) or download: http://kirensky.krasn.ru/popov/opa/opa.htmComment: 4 pages, 3 eps figures, to be published in Optics Letters, vol.25, No 18 (2000), minor style changes and reference correctio

Characterization of All-Chromium Tunnel Junctions and Single Electron Tunneling Devices Fabricated by Direct-Writing Multilayer Technique

We report about the fabrication and analysis of the properties of Cr/CrO_x/Cr tunnel junctions and SET transistors, prepared by different variants of direct-writing multilayer technique. In all cases, the CrO_x tunnel barriers were formed in air under ambient conditions. From the experiments on single junctions, values for the effective barrier height and thickness were derived. For the Cr/CrO_x/Cr SET transistors we achieved minimal junction areas of 17 x 60 nm^2 using a scanning transmission electron microscope for the e-beam exposure on Si_3N_4 membrane substrate. We discuss the electrical performance of the transistor samples as well as their noise behavior.Comment: 19 pages, 9 figure

J004457+4123 (Sharov 21): not a remarkable nova in M31 but a background quasar with a spectacular UV flare

We announce the discovery of a quasar behind the disk of M31, which was previously classified as a remarkable nova in our neighbour galaxy. The paper is primarily aimed at the outburst of J004457+4123 (Sharov 21), with the first part focussed on the optical spectroscopy and the improvement in the photometric database. Both the optical spectrum and the broad band spectral energy distribution of Sharov 21 are shown to be very similar to that of normal, radio-quiet type 1 quasars. We present photometric data covering more than a century and resulting in a long-term light curve that is densely sampled over the past five decades. The variability of the quasar is characterized by a ground state with typical fluctuation amplitudes of ~0.2 mag around B~20.5, superimposed by a singular flare of ~2 yr duration (observer frame) with the maximum at 1992.81 where the UV flux has increased by a factor of ~20. The total energy in the flare is at least three orders of magnitudes higher than the radiated energy of the most luminous supernovae, provided that it comes from an intrinsic process and the energy is radiated isotropically. The profile of the flare light curve appears to be in agreement with the standard predictions for a stellar tidal disruption event where a ~10 M_sun giant star was shredded in the tidal field of a ~2...5 10^8 M_sun black hole. The short fallback time derived from the light curve requires an ultra-close encounter where the pericentre of the stellar orbit is deep within the tidal disruption radius. Gravitational microlensing provides an alternative explanation, though the probability of such a high amplification event is very low.Comment: Accepted for publication in Astronomy and Astrophysics, 14 pages, 11 figure

Inertial range scaling in numerical turbulence with hyperviscosity

Numerical turbulence with hyperviscosity is studied and compared with direct simulations using ordinary viscosity and data from wind tunnel experiments. It is shown that the inertial range scaling is similar in all three cases. Furthermore, the bottleneck effect is approximately equally broad (about one order of magnitude) in these cases and only its height is increased in the hyperviscous case--presumably as a consequence of the steeper decent of the spectrum in the hyperviscous subrange. The mean normalized dissipation rate is found to be in agreement with both wind tunnel experiments and direct simulations. The structure function exponents agree with the She-Leveque model. Decaying turbulence with hyperviscosity still gives the usual t^{-1.25} decay law for the kinetic energy, and also the bottleneck effect is still present and about equally strong.Comment: Final version (7 pages

Constructing applicative functors

Applicative functors define an interface to computation that is more general, and correspondingly weaker, than that of monads. First used in parser libraries, they are now seeing a wide range of applications. This paper sets out to explore the space of non-monadic applicative functors useful in programming. We work with a generalization, lax monoidal functors, and consider several methods of constructing useful functors of this type, just as transformers are used to construct computational monads. For example, coends, familiar to functional programmers as existential types, yield a range of useful applicative functors, including left Kan extensions. Other constructions are final fixed points, a limited sum construction, and a generalization of the semi-direct product of monoids. Implementations in Haskell are included where possible