Weak formulation for singular diffusion equation with dynamic boundary condition

In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs.Comment: 23 page

On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.Comment: 28 page

The demography of the lizard Tropidurus torquatus (Squamata, Tropiduridae) in a highly seasonal Neotropical savanna

The demography of a population of Tropidurus torquatus was studied from March 1996 until December 1998, in the Cerrado biome of the Central Brazil, using the method of capture and recapture. Population size, number of incoming individuals in the population, and age structure varied seasonally, reflecting the reproductive cycle of the species. The instantaneous rate of population increase did not differ from zero throughout the study. In general, the permanence rate of juveniles and adults were low, indicating a large turnover of individuals in the population, with a maximum life expectancy of three years. The sex-ratio among adults was biased toward females. Since no bias was observed among juveniles and there was no difference in adults permanence between sexes, we suggestet that the biased adult sex-ratio resulted from a lower permanence of males during a short ontogenetic period, when secondary sexual characteristics develop. When compared to T. itambere, the studied population of T. torquatus attained a higher density and a greater female bias in the sex-ratio. In general, the studied population presented characteristics that, according to life history theory, should be associated with early age at maturity and polyginy: short life expectancy, high population turnover, and female biased sex-ratios

A philosophical context for methods to estimate origin-destination trip matrices using link counts.

This paper creates a philosophical structure for classifying methods which estimate origin-destination matrices using link counts. It is claimed that the motivation for doing so is to help real-life transport planners use matrix estimation methods effectively, especially in terms of trading-off observational data with prior subjective input (typically referred to as 'professional judgement'). The paper lists a number of applications that require such methods, differentiating between relatively simple and highly complex applications. It is argued that a sound philosophical perspective is particularly important for estimating trip matrices in the latter type of application. As a result of this argument, a classification structure is built up through using concepts of realism, subjectivity, empiricism and rationalism. Emphasis is put on the fact that, in typical transport planning applications, none of these concepts is useful in its extreme form. The structure is then used to make a review of methods for estimating trip matrices using link counts, covering material published over the past 30 years. The paper concludes by making recommendations, both philosophical and methodological, concerning both practical applications and further research

Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency

We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitely many sinksnear the generic unfolding of a quadratic homoclinic tangency of a dissipative saddle, can be perturbed along an infinite dimensional manifold of $C^3$ diffeomorphisms such that infinitely many sinks persist simultaneously. On the other hand, if they are perturbed along one-parameter families that unfold generically the quadratic tangencies, then at most a finite number of those sinks have continuation

Intrarenal Resistance Index as a Prognostic Parameter in Patients with Liver Cirrhosis Compared with Other Hepatic Scoring Systems

Background and Aims: Patients with advanced liver cirrhosis who develop renal dysfunction have a poor prognosis. Elevated intrarenal resistance indices (RIs) due to renal vascular constriction have been described before in cirrhotic patients. In the current study, we prospectively investigated the course of intrarenal RIs and compared their prognostic impact with those of the Model for End-Stage Liver Disease (MELD) and the Child-Pugh scores. Methods: Sixty-three patients with liver cirrhosis underwent a baseline visit which included a sonographic examination and laboratory tests. Forty-four patients were prospectively monitored. The end points were death or survival at the day of the follow-up visit. Results: In 28 patients, a follow-up visit was performed after 22 8 months (group 1). Sixteen patients died during follow-up after 12 8 months (group 2). Group 2 patients showed a significantly higher baseline RI (0.76 +/- 0.05) than group 1 patients (RI = 0.72 +/- 0.06; p < 0.05). As shown by receiver operating characteristic analysis, the RI and the MELD score achieved similar sensitivity and specificity {[}area under the curve (AUC): 0.722; 95% confidence interval (95% CI): 0.575-0.873 vs. AUC: 0.724; 95% CI: 0.575-0.873, z = 0.029, n.s.] in predicting survival and were superior to the Child-Pugh score (AUC: 0.677; 96% Cl: 0.518-0.837). Conclusion: The RI is not inferior in sensitivity and specificity to the MELD score. Cirrhotic patients with elevated RIs have impaired short- and long-term survival. The RI may help identify high-risk patients that require special therapeutic care. Copyright (C) 2012 S. Karger AG, Base

On a Cahn--Hilliard--Darcy system for tumour growth with solution dependent source terms

We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn--Hilliard--Darcy system coupled with an elliptic reaction-diffusion equation. The Darcy law gives rise to an elliptic equation for the pressure that is coupled to the convective Cahn--Hilliard equation through convective and source terms. Both Dirichlet and Robin boundary conditions are considered for the pressure variable, which allows for the source terms to be dependent on the solution variables.Comment: 18 pages, changed proof from fixed point argument to Galerkin approximatio

Rapid South Atlantic spreading changes and coeval vertical motion in surrounding continents: Evidence for temporal changes of pressure-driven upper mantle flow

International audienceThe South Atlantic region displays (1) a topographic gradient across the basin, with Africa elevated relative to South America, (2) a bimodal spreading history with fast spreading rates in Late Cretaceous and Eo-Oligocene, and (3) episodic regional uplift events in the adjacent continents concentrated in Late Cretaceous and Oligocene. Here we show that these observations can be linked by dynamic processes within Earth's mantle, through temporal changes in asthenosphere flow beneath the region. The topographic gradient implies westward, pressure-driven mantle flow beneath the basin, while the rapid spreading rate changes, on order 10 million years, require significant decoupling of regional plate motion from the large-scale mantle buoyancy distribution through a mechanically weak asthenosphere. Andean topographic growth in late Miocene can explain the most recent South Atlantic spreading velocity reduction, arising from increased plate boundary forcing associated with the newly elevated topography. But this mechanism is unlikely to explain the Late Cretaceous/Tertiary spreading variations, as changes in Andean paleoelevation at the time are small. We propose an unsteady pressure-driven flow component in the asthenosphere beneath the South Atlantic region to explain the Late Cretaceous/Tertiary spreading rate variations. Temporal changes in mantle flow due to temporal changes in regional mantle pressure gradients imply a correlation of horizontal and vertical motions: we find that this prediction from our models agrees with geologic and geophysical observations of the South Atlantic region, including episodes of passive margin uplift, regional basin reactivation, and magmatic activity