Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the tumor induced ingiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators

Architecture of a Bench-Type Carbonate Lake Margin and Its Relation to Fluvially Dominated Deltas, Las Minas Basin, Upper Miocene, Spain

The Upper Miocene stratigraphic succession of the Las Minas Basin, located at the external zone of the Betic Chain in SE Spain, preserves several examples of lake carbonate bench deposits. Excellent exposures of the carbonate benches allow detailed observation of the architecture of these sediments and provide new insights for the ‘‘steep-gradient bench margin–low energy’’ model proposed by Platt and Wright (1991). The lake carbonate benches developed in close association with fluvially dominated shallow deltas that exhibit typical Gilbert-type profiles. The delta sequences comprise bottomset prodelta marl facies, distal to proximal foreset facies, deposited mainly in a delta-front environment, and topset facies, the latter reflecting both subaqueous delta-front and subaerial delta-plain environments. The development of the carbonate benches was constrained by the convexupward morphology of the deltaic deposits, which led to the available accommodation space for the growth of the steep-gradient platforms. The benches display a progradational pattern characterized by sigmoid-oblique internal geometries and offlap upper boundary relationships, which suggests that the carbonate benches developed under slow though continuous lake-level rise. Both the dimensions of the benches and the dominant carbonate components (i.e., encrusted charophyte stems and calcified cyanobaterial remains), allow comparisons with the progradational marl benches recognized in modern temperate hardwater lakes. Accordingly, the case study presented here provides a good ancient sedimentary analog for low-energy lake carbonate benches. Moreover, the evolutionary trend inferred from the fossil example offers new insights into the depositional conditions of this type of sediment and allows recognition of the transitional pattern from bench to ramp carbonate lake margins.