Uniqueness and Stability near Stationary Solutions for the Thin-Film Equation in Multiple Space Dimensions with Small Initial Lipschitz Perturbations

In any number of space variables, we study the Cauchy problem related to the thin-film equation in the simplest case of a linearly degenerate mobility. This equation, derived from a lubrication approximation, also models the surface-tension dominated flow of a thin viscous film in the Hele-Shaw cell. Our focus is on uniqueness of weak solutions in the complete wetting regime, when a zero contact angle between liquid and solid is imposed. In this case, we transform the problem by zooming into the free boundary and look at small Lipschitz perturbations of a quadratic stationary solution. In the perturbational setting, the main difficulty is to construct scale invariant function spaces based on time-space cylinders. Here we rely on the theory of singular integrals in spaces of homogeneous type to obtain linear estimates in these functions spaces which provide optimal conditions on the initial data under which a unique solution exists. In fact, this solution can be used to define a class of functions in which the original initial value problem has a unique (weak) solution. Moreover, we show that the (moving) interface between empty and occupied regions is an analytic hypersurface in time and space.Eindeutigkeit und Stabilität nahe stationärer Lösungen für die Dünnfilmgleichung in mehreren Raumdimensionen mit kleinen Lipschitz-Anfangsstörungen Betrachtet man im freien Randwertproblem für den Stokes-Fluss mit Oberflächenspannung den Grenzübergang für dünne Schichten, so ergibt sich formal aus den Navier-Stokes-Gleichungen für inkompressible Flüssigkeiten die Dünnfilmgleichung. Diese ist eine partielle Differentialgleichung vierter Ordnung mit degenerierter Parabolizität. In der vorliegenden Arbeit befassen wir uns mit dem einfachsten Fall einer linearen Mobilität (Hele-Shaw Fluss) und arbeiten Bedingungen an die Anfangswerte heraus, unter welchen eine eindeutige globale Lösung des dazugehörigen Anfangswertproblems existiert. Im ersten Schritt fixieren wir den freien Rand, indem wir auf der Positivitätsmenge unabhängige und abhängige Variablen vertauschen (von Mises-Transformation), und anschließend die resultierende Gleichung um eine quadratische stationäre Lösung linearisieren. In der linearen Konfiguration konstruieren wir basierend auf Zeit-Raum-Zylindern Skalierungs-invariante Funktionenräume. In diesen beweisen wir mithilfe der Theorie singulärer Integrale in Räumen vom homogenen Typ lineare Abschätzungen und erhalten somit optimale Bedingungen an die Anfangswerte, unter denen eine eindeutige Lösung existiert. Tatsächlich können wir diese Lösung verwenden, um eine Funktionenklasse zu definieren, in der das ursprüngliche Problem eine eindeutige (schwache) Lösung besitzt. Darüber hinaus zeigen wir, dass die Kontaktlinie zwischen leeren und benetzten Regionen eine analytische Hyperfläche in Zeit und Raum ist

PPSZ for General k-SAT - Making Hertli\u27s Analysis Simpler and 3-SAT Faster

The currently fastest known algorithm for k-SAT is PPSZ named after its inventors Paturi, Pudlak, Saks, and Zane. Analyzing its running time is much easier for input formulas with a unique satisfying assignment. In this paper, we achieve three goals. First, we simplify Hertli\u27s analysis for input formulas with multiple satisfying assignments. Second, we show a "translation result": if you improve PPSZ for k-CNF formulas with a unique satisfying assignment, you will immediately get a (weaker) improvement for general k-CNF formulas. Combining this with a result by Hertli from 2014, in which he gives an algorithm for Unique-3-SAT slightly beating PPSZ, we obtain an algorithm beating PPSZ for general 3-SAT, thus obtaining the so far best known worst-case bounds for 3-SAT

Random triangular Burnside groups

We introduce a model for random groups in varieties of $n$-periodic groups as $n$-periodic quotients of triangular random groups. We show that for an explicit $d_{\mathrm{crit}}\in(1/3,1/2)$, for densities $d\in(1/3,d_{\mathrm{crit}})$ and for $n$ large enough, the model produces \emph{infinite} $n$-periodic groups. As an application, we obtain, for every fixed large enough $n$, for every $p\in (1,\infty)$ an infinite $n$-periodic group with fixed points for all isometric actions on $L^p$-spaces. Our main contribution is to show that certain random triangular groups are uniformly acylindrically hyperbolic.Comment: v1: 9 pages, 1 figure; v2: 14 pages, 1 figure. Expanded exposition, final versio

Stabilizing a Leading-edge Boundary Layer Subject to Wall Suction by Increasing the Reynolds Number

AbstractLaminar fiow in the boundary layer at the leading edge of swept airplane wings typically becomes transitional and turbulent shortly downstream of the attachment line. Flow control techniques to maintain the fiow laminar, such as suction into the wall, therefore must focus on this instability, which otherwise leads to turbulent fiow and thus contaminates the fiow over the entire wing chord.The present paper presents new results on how the linear leading-edge boundary layer (LEBL) instability of swept-cylinders fiow, which models swept-wing fiow, may be avoided. The classical Reynolds number definition is employed, which is based on the far-field velocity Q∞, the cylinder radius R*, and the sweep angle Λ. It is demonstrated that the fiow can be stabilized by increasing the Reynolds number at constant wall suction through an increase of R* or Λ, but not of Q∞.The stability analysis is carried out for the swept Hiemenz boundary layer (SHBL), a widely used fiat-plate approximation of the swept-cylinder LEBL. As demonstrated recently 1, the SHBL with suction becomes similar to the two-dimensional asymptotic suction boundary layer (ASBL) when increasing the classical Reynolds number ReSH to large values. In the limit of ReSH→∞, the SHBL with suction becomes identical to the highly stable ASBL, and hence inherits its linear stability properties. The transformation of these recent findings concerning the linear stability of the SHBL with suction to the swept-cylinder LEBL unveils that stabilization of fiow with constant suction can be observed by increasing ReSH

Differences in reactivation of tuberculosis induced from anti-tnf treatments are based on bioavailability in granulomatous tissue

The immune response to Mycobacterium tuberculosis (Mtb) infection is complex. Experimental evidence has revealed that tumor necrosis factor (TNF) plays a major role in host defense against Mtb in both active and latent phases of infection. TNF-neutralizing drugs used to treat inflammatory disorders have been reported to increase the risk of tuberculosis (TB), in accordance with animal studies. The present study takes a computational approach toward characterizing the role of TNF in protection against the tubercle bacillus in both active and latent infection. We extend our previous mathematical models to investigate the roles and production of soluble (sTNF) and transmembrane TNF (tmTNF). We analyze effects of anti-TNF therapy in virtual clinical trials (VCTs) by simulating two of the most commonly used therapies, anti-TNF antibody and TNF receptor fusion, predicting mechanisms that explain observed differences in TB reactivation rates. The major findings from this study are that bioavailability of TNF following anti-TNF therapy is the primary factor for causing reactivation of latent infection and that sTNF-even at very low levels-is essential for control of infection. Using a mathematical model, it is possible to distinguish mechanisms of action of the anti-TNF treatments and gain insights into the role of TNF in TB control and pathology. Our study suggests that a TNF-modulating agent could be developed that could balance the requirement for reduction of inflammation with the necessity to maintain resistance to infection and microbial diseases. Alternatively, the dose and timing of anti-TNF therapy could be modified. Anti-TNF therapy will likely lead to numerous incidents of primary TB if used in areas where exposure is likely. © 2007 Marino et al

Factors influencing the efficiency of a marker-assisted introgression programme in Merino sheep

This study investigated a marker-assisted introgression programme in Australian Merino sheep. The goal was to introgress an allele with a large negative effect on fibre diameter into a Merino flock possessing medium average fibre diameter. The influence of two factors was explored: the strategy used to select animals from the purebred and backcross line for backcrossing purposes and the use of selection on background markers to accelerate the return to the purebred line's genome. The results were compared to introgression based on EBVs only. Introgression using EBVs only produced almost the same response in the dollar index as marker-based introgression methods. However, this study did not account for some of the costs associated with implementing the programmes, including the costs of phenotyping and genotyping. Given that the cost of measuring fibre diameter is low, it was concluded that introgression on EBVs only would be the preferred method since the marginal profit of marker-assisted introgression would not be large enough to cover the additional cost of genotyping. In marker-assisted introgression, reciprocal crossing of male and female selection candidates from the backcross and the purebred line was the most advantageous strategy from a practical and profit point of view. Selection for background markers was less profitable in this study than recovering the donor genome by selection on phenotype

ACOUSTIC CUES OF PROSODIC BOUNDARIES IN GERMAN AT DIFFERENT SPEECH RATE

International audienceThis paper reports results of a production study on prosodic phrase boundaries at different speech rates. Our research question was to examine which acoustic cues (F0, intensity and duration) change as a function of speech rate both before and after prosodic phrase boundaries. We investigated identical sentences that differed in the placement of the prosodic boundary, i.e. before or after the critical word. Based on the data of 25 German speakers, duration was the main acoustic cue that speakers altered when marking prosodic boundaries at different speech rates. More specifically, words which appear before the boundary had longer durations, similarly to pauses at phrase-final boundaries, even if the speech rate increases. Intensity does also play a role: in faster speech words are produced with a higher intensity. Finally, F0 max was not changed on the critical words but rather it altered in comparison to F max of the preceding word

The footprint of cometary dust analogues: II. Morphology as a tracer of tensile strength and application to dust collection by the Rosetta spacecraft

The structure of cometary dust is a tracer of growth processes in the formation of planetesimals. Instrumentation on board the Rosetta mission to comet 67P/Churyumov- Gerasimenko captured dust particles and analysed them in situ. However, these deposits are a product of a collision within the instrument. We conducted laboratory experiments with cometary dust analogues, simulating the collection process by Rosetta instruments (specifically COSIMA, MIDAS). In Paper I we reported that velocity is a key driver in determining the appearance of deposits. Here in Paper II we use materials with different monomer sizes, and study the effect of tensile strength on the appearance of deposits. We find that mass transfer efficiency increases from $\sim$1 up to $\sim$10% with increasing monomer diameter from 0.3 $\mu$m to 1.5 $\mu$m (i.e. tensile strength decreasing from $\sim$12 to $\sim$3 kPa), and velocities increasing from 0.5 to 6 m/s. Also, the relative abundance of small fragments after impact is higher for material with higher tensile strength. The degeneracy between the effects of velocity and material strength may be lifted by performing a closer study of the deposits. This experimental method makes it possible to estimate the mass transfer efficiency in the COSIMA instrument. Extrapolating these results implies that more than half of the dust collected during the Rosetta mission has not been imaged. We analysed two COSIMA targets containing deposits from single collisions. The collision that occurred closest to perihelion passage led to more small fragments on the target.Comment: 13 pages, 11 figures, accepted for publication in MNRA

Способ построения интегрированной информационной среды на базе систем управления данными и систем автоматизированного проектирования

Рассмотрены аспекты построения единого информационного пространства для разработки высокотехнологичной продукции, реализованного в виде программного взаимодействия системы управления данными и систем автоматизированного проектирования. Предложены требования к интеграции систем указанных категорий, структура хранения типовых справочных данных, алгоритмы обмена информацией между интегрируемыми информационными системами с учетом состояний жизненного цикла объектов проектирования