Cycle-Level Products in Equivariant Cohomology of Toric Varieties

In this paper, we define an action of the group of equivariant Cartier divisors on a toric variety X on the equivariant cycle groups of X, arising naturally from a choice of complement map on the underlying lattice. If X is nonsingular, this gives a lifting of the multiplication in equivariant cohomology to the level of equivariant cycles. As a consequence, one naturally obtains an equivariant cycle representative of the equivariant Todd class of any toric variety. These results extend to equivariant cohomology the results of Thomas and Pommersheim. In the case of a complement map arising from an inner product, we show that the equivariant cycle Todd class obtained from our construction is identical to the result of the inductive, combinatorial construction of Berline-Vergne. In the case of arbitrary complement maps, we show that our Todd class formula yields the local Euler-Maclarurin formula introduced in Garoufalidis-Pommersheim.Comment: 15 pages, to be published in Michigan Mathematical Journal; LaTe

Growth and decay of localized disturbances on a surfactant-coated spreading film

If the surface of a quiescent thin liquid film is suddenly coated by a patch of surface active material like a surfactant monolayer, the film is set in motion and begins spreading. An insoluble surfactant will rapidly attempt to coat the entire surface of the film thereby minimizing the liquid's surface tension. The shear stress that develops during the spreading process produces a maximum in surface velocity in the region where the moving film meets the quiescent layer. This region is characterized by a shock front with large interfacial curvature and a corresponding local buildup of surfactant which creates a spike in the concentration gradient. In this paper, we investigate the sensitivity of this region to infinitesimal disturbances. Accordingly, we introduce a measure of disturbance amplification and transient growth analogous to a kinetic energy that couples variations in film thickness to the surfactant concentration. These variables undergo significant amplification during the brief period in which they are convected past the downstream tip of the monolayer, where the variation in concentration gradient and surface curvature are largest. Once they migrate past this sensitive area, the perturbations weaken considerably and the system approaches a stable configuration. It appears that the localized disturbances of the type we consider here, cannot sustain asymptotic instability. Nonetheless, our study of the dynamics leading to the large transient growth clearly illustrates how the coupling of Marangoni and capillary forces work in unison to stabilize the spreading process against localized perturbations

Work Incentives and the Cost of Redistribution via Tax-transfer Reforms under Constrained Labor Supply

Using information on desired and actual hours of work, we formulate a discrete choice model of constrained labor supply. Using the German Socio-Economic Panel and the microsimulation model STSM, we find that hours and participation elasticities are substantially smaller than those in the conventional model. We evaluate two reforms for Germany. Both redistribute to the working poor. The first reform is financed through an increase in the effective marginal tax rate for welfare recipients, the second through an increase in taxes. The first reform is desirable with equal weights, the second if the social planner has substantial redistributive taste

Thinning and disturbance growth in liquid films mobilized by continuous surfactant delivery

A generalized linear stability analysis is applied to the case of a thin liquid film propelled to spread by a continuous supply of surfactant. The time-dependent base states for the film thickness and surfactant concentration give rise to a nonautonomous system describing disturbance propagation. As a first approximation, the nonautonomous operator is treated as time independent, thereby reducing the system of equations to a standard eigenvalue problem. For the range of parameters investigated, this modal approximation reveals a band of unstable modes corresponding to the growth of transverse, sinusoidal corrugations. A transient growth analysis of the fully time-dependent system, which requires the solution of an initial value problem, also signals the possibility of large disturbance growth. In both cases, significant amplification of infinitesimal disturbances can be traced to the region of the film most rapidly thinned by Marangoni stresses, which is characterized by large interfacial curvature and a sharp variation in shear stress. In contrast to previous models implementing a finite surfactant source that predict asymptotic stability, large transient growth and asymptotic instability are possible for the case of sustained surfactant release

Projection-based curve clustering

This paper focuses on unsupervised curve classification in the context of nuclear industry. At the Commissariat à l'Energie Atomique (CEA), Cadarache (France), the thermal-hydraulic computer code CATHARE is used to study the reliability of reactor vessels. The code inputs are physical parameters and the outputs are time evolution curves of a few other physical quantities. As the CATHARE code is quite complex and CPU-time consuming, it has to be approximated by a regression model. This regression process involves a clustering step. In the present paper, CATHARE output curves are clustered using a k-means scheme, with a projection onto a lower dimensional space. We study the properties of the empirically optimal cluster centers found by the clustering method based on projections, compared to the “true” ones. The choice of the projection basis is discussed, and an algorithm is implemented to select the best projection basis among a library of orthonormal bases. The approach is illustrated on a simulated example and then applied to the industrial problem

Some inverse problems around the tokamak Tore Supra

International audienceWe consider two inverse problems related to the tokamak \textsl{Tore Supra} through the study of the magnetostatic equation for the poloidal flux. The first one deals with the Cauchy issue of recovering in a two dimensional annular domain boundary magnetic values on the inner boundary, namely the limiter, from available overdetermined data on the outer boundary. Using tools from complex analysis and properties of genereralized Hardy spaces, we establish stability and existence properties. Secondly the inverse problem of recovering the shape of the plasma is addressed thank tools of shape optimization. Again results about existence and optimality are provided. They give rise to a fast algorithm of identification which is applied to several numerical simulations computing good results either for the classical harmonic case or for the data coming from \textsl{Tore Supra}

A brief review of low-dose rate (LDR) and high-dose rate (HDR) brachytherapy boost for high-risk prostate

For patients with unfavorable or high-risk prostate cancer, dose escalated radiation therapy leads to improved progression free survival but attempts to deliver increased dose by external beam radiation therapy (EBRT) alone can be limited by late toxicities to nearby genitourinary and gastrointestinal organs at risk. Brachytherapy is a method to deliver dose escalation in conjunction with EBRT with a potentially improved late toxicity profile and improved prostate cancer related outcomes. At least three randomized controlled trials have demonstrated improved biochemical control with the addition of either low-dose rate (LDR) or high-dose rate (HDR) brachytherapy to EBRT, although only ASCENDE-RT compared brachytherapy to dose-escalated EBRT but did report an over 50% improvement in biochemical failure with a LDR boost. Multiple single institution and comparative research series also support the use of a brachytherapy boost in the DE-EBRT era and demonstrate excellent prostate cancer specific outcomes. Despite improved oncologic outcomes with a brachytherapy boost in the high-risk setting, the utilization of both LDR, and HDR brachytherapy use is declining. The acute genitourinary toxicities when brachytherapy boost is combined with EBRT, particularly a LDR boost, are of concern in comparison to EBRT alone. HDR brachytherapy boost has many physical properties inherent to its rapid delivery of a large dose which may reduce acute toxicities and also appeal to the radiobiology of prostate cancer. We herein review the evidence for use of either LDR or HDR brachytherapy boost for high-risk prostate cancer and summarize comparisons between the two treatment modalities