Renormalization study of two-dimensional convergent solutions of the porous medium equation

In the focusing problem we study a solution of the porous medium equation $u_t=\Delta (u^m)$ whose initial distribution is positive in the exterior of a closed non-circular two dimensional region, and zero inside. We implement a numerical scheme that renormalizes the solution each time that the average size of the empty region reduces by a half. The initial condition is a function with circular level sets distorted with a small sinusoidal perturbation of wave number $k\geq 3$. We find that for nonlinearity exponents m smaller than a critical value which depends on k, the solution tends to a self-similar regime, characterized by rounded polygonal interfaces and similarity exponents that depend on m and on the discrete rotational symmetry number k. For m greater than the critical value, the final form of the interface is circular.Comment: 26 pages, Latex, 13 ps figure

Degenerate neckpinches in Ricci flow

In earlier work, we derived formal matched asymptotic profiles for families of Ricci flow solutions developing Type-II degenerate neckpinches. In the present work, we prove that there do exist Ricci flow solutions that develop singularities modeled on each such profile. In particular, we show that for each positive integer $k\geq3$, there exist compact solutions in all dimensions $m\geq3$ that become singular at the rate (T-t)^{-2+2/k}$

Formal matched asymptotics for degenerate Ricci flow neckpinches

Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on $S^m$, for all $m\geq 3$. In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit

Complete Embedded Self-Translating Surfaces under Mean Curvature Flow

We describe a construction of complete embedded self-translating surfaces under mean curvature flow by desingularizing the intersection of a finite family of grim reapers in general position.Comment: 42 pages, 8 figures. v2: typos correcte

MADS-box genes controlling inflorescence morphogenesis in sunflower

MADS-box genes play an important role in plant ontogeny, particularly, in the regulation of floral organ induction and development. Eight full-length cDNAs of HAM genes (Helianthus annuus MADS) have been isolated from sunflower. They encode MADS-box transcription factors expressed in inflorescence tissues. In the frames of the ABCDE model, the HAM proteins were classified according to their structural homology to known MADS-box transcription factors. The HAM45 and HAM59 genes encode the homeotic C function and are involved in the control of the identity of pistil and stamens, while the HAM75 and HAM92 genes determine the A function and identity of floral and inflorescence meristems and petal identity. The HAM31, HAM2, HAM63, and HAM91 genes encode the B function and are involved in the formation of petals and stamens; and the HAM137 gene encodes the E function. Analysis of the expression of HAM genes in sunflower has demonstrated that the structural and functional differences between the ray and tubular flowers in the inflorescence could be a consequence of the lack of HAM59 expression during ray flower initiation

Finsler Active Contours

©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TPAMI.2007.70713In this paper, we propose an image segmentation technique based on augmenting the conformal (or geodesic) active contour framework with directional information. In the isotropic case, the euclidean metric is locally multiplied by a scalar conformal factor based on image information such that the weighted length of curves lying on points of interest (typically edges) is small. The conformal factor that is chosen depends only upon position and is in this sense isotropic. Although directional information has been studied previously for other segmentation frameworks, here, we show that if one desires to add directionality in the conformal active contour framework, then one gets a well-defined minimization problem in the case that the factor defines a Finsler metric. Optimal curves may be obtained using the calculus of variations or dynamic programming-based schemes. Finally, we demonstrate the technique by extracting roads from aerial imagery, blood vessels from medical angiograms, and neural tracts from diffusion-weighted magnetic resonance imagery

Genetische modificatie tomaat en chrysant

Gedurende 1999 en 2000 zijn in dit project tomaten en chrysanten getransformeerd met genen waarvan kon worden aangenomen dat ze van invloed zijn op de energiehuishouding. Deze aanname berust op effecten die door deze genen in andere planten zijn opgewekt bijv. een andere gewasopbouw en lichtonderschepping. De werkelijke effecten op de energiebehoefte van de genetisch gemodificeerde tomaten en chrysanten worden in het project "Teeltanalyse transgene planten tomaat en crysant" onderzocht. In het vervolg traject "Genetische modificatie van tomaat en chrysant, analyse op plantniveau" zijn de effecten van verhoogde niveaus van phyA, phyB1 en phyB2 op de schaduw-vermijdings-reactie (SAR) onderzocht, door fytochroomgenen in tomaat tot overexpressie te brenge

Development of a new high-rate anaerobic process for the treatment of industrial and domestic wastewaters: the anaerobic migrating blanket reactor (AMBR)

The anaerobic migrating blanket reactor (AMBR) was developed as a new high-rate system for the treatment of industrial and domestic wastewaters, at Iowa State University. The AMBR, a continuously fed, compartmentalized reactor, required mechanical mixing to obtain a sufficient biomass/substrate contact. The formation of granular biomass was not dependent on a hydraulic upflow pattern in the reactor, but was dependent on biomass migration over the horizontal plane of the reactor and the settling characteristics of the final compartment. To prevent acclimation of biomass in the final compartment, the flow was reversed in a horizontal matter. Keeping the pH sufficiently high in the initial compartment without recycling effluent was another advantage of reversing the flow. This also prevented total phase separation of acidogenesis and methanogenesis in the AMBR;Laboratory-scale AMBR systems have achieved high organic removal efficiencies when fed with non-acidified sucrose as a substrate at chemical oxygen demand (COD) loading rates up to 30 g/L/d. Furthermore, the AMBR was able to retain high levels of granular biomass at these loading rates. Due to moderate shear forces by mechanical mixing, the laboratory-scale AMBR was able to treat non-acidified sucrose at food to microorganism (FIM) ratios higher than found for other high rate systems. The AMBR out-competed the upflow anaerobic sludge blanket (UASB) and anaerobic sequencing batch reactor (ASBR) in a laboratory-scale comparison in terms of reactor performances and maximum organic loading rates;A mature granular blanket was formed after four months of operating a 54-liter AMBR, seeded with flocculent primary digester sludge. This was accomplished with moderate hydraulic selection pressures at the start of the run, in which reactor performances were sufficient to build up an active biomass, without losing the selection mechanism for better settling biomass;A 20-liter AMBR was able to effectively remove organic material from dilute non-fat dry milk (NFDM) solution at a concentration of 600 mg/L under psychrophilic conditions. Moreover, this reactor was able to retain its granular biomass after the hydraulic retention time (HRT) was decreased from four to one hour during hydraulic shock load studies. Finally, staging or partial phase separation was found in the AMBR in which relatively more methanogens were present in the inside compartments