C1,αC^{1,\alpha} regularity of solutions of degenerate fully non-linear elliptic equations

In the present paper, a class of fully non-linear elliptic equations are considered, which are degenerate as the gradient becomes small. H\"older estimates obtained by the first author (2011) are combined with new Lipschitz estimates obtained through the Ishii-Lions method in order to get $C^{1,\alpha}$ estimates for solutions of these equations.Comment: Submitte

Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations

The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic integro-differential equations, players choose smooth functions on the whole space

On the Numerical Approximations of an Optimal Correction Problem

The numerical solution of an optimal correction problem for a damped random linear oscillator is studied. A numerical algorithm for the discretized system of the associated dynamic programming equation is given. To initiate the computation, we adopt a numerical scheme derived from the deterministic version of the problem. Next, a correction-type algorithm based on a discrete maximum principle is introduced to ensure the convergence of the iteration procedure

Contribution to the search for binaries among Am stars - VII. Orbital elements of seven new spectroscopic binaries, implications on tidal effects

International audienceWe present the results of a radial-velocity study of seven Am stars (HD 3970, 35035, 93946, 151746, 153286, 204751 and 224002) observed at the Observatoire de Haute-Provence (OHP) and the Cambridge Observatories with CORAVEL instruments. We find that these systems are single-lined spectroscopic binaries whose orbital elements are determined for the first time. Among this sample, HD 35035 and 153286 have long periods, with P = 2.8 and 9.5yr, respectively, which is rather unusual for Am stars. Four systems have orbits with large eccentricities (with e >= 0.4). Physical parameters are inferred from this study for the primaries of those systems. We then investigate the influence of tidal interaction, which has already led to the synchronism of the primaries and/or to the circularization of the orbits of some systems belonging to this sample. We extend this study to the list of 33 objects studied in this series of papers and derive values of the critical fractional radii r = R/a for circularization and synchronization of Am-type binaries. We find that the stars with r >~ 0.15 are orbiting on circular orbits and that synchronism is likely for all components with r >~ 0.20

Amplitude-based generalized plane waves: New quasi-trefftz functions for scalar equations in two dimensions

Generalized plane waves (GPWs) were introduced to take advantage of Trefftz methods for problems modeled by variable coefficient equations. Despite the fact that GPWs do not satisfy the Trefftz property, i.e., they are not exact solutions to the governing equation, they instead satisfy a quasi-Trefftz property: They are only approximate solutions. They lead to high-order numerical methods, and this quasi-Trefftz property is critical for their numerical analysis. The present work introduces a new family of GPWs: amplitude-based. The motivation lies in the poor behavior of the phase-based GPW approximations in the preasymptotic regime, which will be tamed by avoiding high-degree polynomials within an exponential. The new ansatz introduces higher-order terms in the amplitude rather than in the phase of a plane wave as was initially proposed. The new functions' construction and the study of their approximation properties are guided by the road map proposed in [L.-M. Imbert-Gérard and G. Sylvand, Numer. Math., to appear]. For the sake of clarity, the first focus is on the two-dimensional Helmholtz equation with spatially varying wave number. The extension to a range of operators allowing for anisotropy in the first- and second-order terms follows. Numerical simulations illustrate the theoretical study of the new quasi-Trefftz functions. © 2021 Society for Industrial and Applied MathematicsImmediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Snake (Colubridae: Thamnophis) Predatory Responses to Chemical Cues from Native and Introduced Prey Species

Several aquatic vertebrates have been introduced into freshwater systems in California over the past 100 years. Some populations of the two-striped garter snake (Thamnophis hammondii) have lived in sympatry with these species since their introduction; other populations have never encountered them. To assess the possible adaptation to a novel prey, we tested the predatory responses of T. hammondii from different populations to different chemosensory cues from native and introduced prey species. We presented chemical extracts from potential prey types and 2 control odors to individual snakes on cotton swabs and recorded the number of tongue flicks and attacks directed at each swab. Subject response was higher for prey odors than control substances. Odors from introduced centrarchid fish (Lepomis) elicited higher response levels than other prey types, including native anuran larvae (Pseudacris regilla). The pattern of response was similar for both populations of snakes (experienced and naïve, with respect to the introduced prey). We suggest that the generalist aquatic lifestyle of T. hammondii has allowed it to take advantage of increasing populations of introduced prey. Decisions on the management strategies for some of these introduced prey species should include consideration of how T. hammondii populations might respond in areas of sympatry

Formability and Damage in Electromagnetically Formed AA5754 and AA6111

This paper presents the results of experiments carried out to determine the formability of AA5754 and AA6111 using electromagnetic forming (EMF), and the effect of the tool/sheet interaction on damage evolution and failure. The experiments consisted of forming 1mm sheets into conical dies of 40° and 45° side angle, using a spiral coil. The experiments showed that both alloys could successfully be formed into the 40?? die, with strains above the conventional forming limit diagram (FLD) of both alloys. Forming into the higher 45° cone resulted in failure for both materials. Metallographic analysis indicated that damage is suppressed during the forming process. Micrographs of the necked and fractured areas of the part show evidence that the materials do not fail in pure ductile fracture, but rather in what could be a combination of plastic collapse, ductile fracture and shear band fracture. The failure modes are different for each material; with the AA5754 parts failing by necking and fracture, with significant thinning at the fracture tip. The AA6111 exhibited a saw tooth pattern fractures, a crosshatch pattern of shear bands in the lower half of the part, and tears in the area close to the tip. Both areas showed evidence of shear fracture. This experimental study indicates that there is increased formability for AA5754 and AA6111 when these alloys are formed using EMF. A major factor in this increase in formability is the reduction in damage caused by the tool/sheet interaction

Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

Increased intensity of treatment and decreased mortality in elderly patients in an intensive care unit over a decade

Objectives: Data collected from two cohorts of patients aged ≥80 yrs and admitted to an intensive care unit in France were compared to determine whether intensive care unit care and survival had evolved from the 1990s to the 2000s.Design: Retrospective cohort study on patient data attained during intensive care unit stays. Setting: 18-bed intensive care unit in an academic medical center. Patients: Two cohorts of patients aged ≥80 yrs, admitted to an intensive care unit at a 10-yr interval. Interventions: None. Measurements and Main Results: The first cohort comprised 348 patients admitted between January 1992 and December 1995, and the second cohort, 373 patients admitted between January 2001 and December 2004. There was no difference in age between the two cohorts, but patients in the second had significantly less history of functional limitation and significantly more acute illness (Simplified Acute Physiology Score II 43 ± 18 vs. 57 ± 25, respectively, p < .0001). Patients in the second cohort had a significantly higher Omega Score, had a higher occurrence of renal replacement therapy, and received vasopressors more frequently than the patients in the first cohort, even when adjusted for age, sex, Knaus classification, Simplified Acute Physiology Score II, and intensive care unit admission cause. Intensive care unit mortality was 65% and 64% for the first and second cohorts, respectively. In multivariate analysis (including age, Knaus classification, Simplified Acute Physiology Score II and first vs. second period) for association with intensive care unit survival, the 2001–2004 period was associated with a near tripling of chances of survival (odds ratio 2.9; 95% confidence interval, 1.92–4.47, p < .0001). Conclusions: The characteristics and intensity of treatment for elderly people admitted to the intensive care unit changed significantly over a decade. The intensity of treatments has increased over time and survival has improved over time as well. A potential link between increased treatment and improved survival in the elderly may be evoked

High Mass Triple Systems: The Classical Cepheid Y Car

We have obtained an HST STIS ultraviolet high dispersion Echelle mode spectrum the binary companion of the double mode classical Cepheid Y Car. The velocity measured for the hot companion from this spectrum is very different from reasonable predictions for binary motion, implying that the companion is itself a short period binary. The measured velocity changed by 7 km/ s during the 4 days between two segments of the observation confirming this interpretation. We summarize "binary" Cepheids which are in fact members of triple system and find at least 44% are triples. The summary of information on Cepheids with orbits makes it likely that the fraction is under-estimated.Comment: accepted by A