Convergence of phase-field approximations to the Gibbs-Thomson law

We prove the convergence of phase-field approximations of the Gibbs-Thomson law. This establishes a relation between the first variation of the Van-der-Waals-Cahn-Hilliard energy and the first variation of the area functional. We allow for folding of diffuse interfaces in the limit and the occurrence of higher-multiplicities of the limit energy measures. We show that the multiplicity does not affect the Gibbs-Thomson law and that the mean curvature vanishes where diffuse interfaces have collided. We apply our results to prove the convergence of stationary points of the Cahn-Hilliard equation to constant mean curvature surfaces and the convergence of stationary points of an energy functional that was proposed by Ohta-Kawasaki as a model for micro-phase separation in block-copolymers.Comment: 25 page

Crystal dissolution and precipitation in porous media : L1L^1-contraction and uniqueness

In this note we continue the analysis of the pore-scale model for crystal dissolution and precipitation in porous media proposed in [C. J. van Duijn and I. S. Pop, Crystal dissolution and precipitation in porous media: pore scale analysis, J. Reine Angew. Math. 577 (2004), 171–211]. There the existence of weak solutions was shown. We prove an L1-contraction property of the pore-scale model. As a direct consequence we obtain the uniqueness of (weak) solutions

Turing instabilities in a mathematical model for signaling networks

GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for this symmetry breaking. We formulate a mathematical model that couples a reaction-diffusion system in the inner volume to a reaction-diffusion system on the membrane via a flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler non-local reaction-diffusion model and perform a stability analysis and numerical simulations for this reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion of inactivated GTPase is much faster than the diffusion of activated GTPase.Comment: 23 pages, 5 figures; The final publication is available at http://www.springerlink.com http://dx.doi.org/10.1007/s00285-011-0495-

Pathogen- and Host-Directed Antileishmanial Effects Mediated by Polyhexanide (PHMB)

BACKGROUND:Cutaneous leishmaniasis (CL) is a neglected tropical disease caused by protozoan parasites of the genus Leishmania. CL causes enormous suffering in many countries worldwide. There is no licensed vaccine against CL, and the chemotherapy options show limited efficacy and high toxicity. Localization of the parasites inside host cells is a barrier to most standard chemo- and immune-based interventions. Hence, novel drugs, which are safe, effective and readily accessible to third-world countries and/or drug delivery technologies for effective CL treatments are desperately needed. METHODOLOGY/PRINCIPAL FINDINGS:Here we evaluated the antileishmanial properties and delivery potential of polyhexamethylene biguanide (PHMB; polyhexanide), a widely used antimicrobial and wound antiseptic, in the Leishmania model. PHMB showed an inherent antileishmanial activity at submicromolar concentrations. Our data revealed that PHMB kills Leishmania major (L. major) via a dual mechanism involving disruption of membrane integrity and selective chromosome condensation and damage. PHMB's DNA binding and host cell entry properties were further exploited to improve the delivery and immunomodulatory activities of unmethylated cytosine-phosphate-guanine oligodeoxynucleotides (CpG ODN). PHMB spontaneously bound CpG ODN, forming stable nanopolyplexes that enhanced uptake of CpG ODN, potentiated antimicrobial killing and reduced host cell toxicity of PHMB. CONCLUSIONS:Given its low cost and long history of safe topical use, PHMB holds promise as a drug for CL therapy and delivery vehicle for nucleic acid immunomodulators

Orthogonality conditions and asymptotic stability in the Stefan problem with surface tension

We prove nonlinear asymptotic stability of steady spheres in the two-phase Stefan problem with surface tension. Our method relies on the introduction of appropriate orthogonality conditions in conjunction with a high-order energy method.Comment: 25 pages, important references added, two remarks added, typos correcte

Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension

The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities in a sense made precise below, it is proved that it exists globally in time and its orbit is relatively compact. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable, reminiscent of the onset of Ostwald ripening.Comment: 56 pages. Expanded introduction, added references. This revised version is published in Arch. Ration. Mech. Anal. (207) (2013), 611-66

SolarPACES Task III Project: Analyze Heliostat Field

In recent years, great efforts have been made to reach a consensus on heliostat testing best practices. A specific SolarPACES task was launched to provide a Heliostat Testing Guidelines document for single heliostat evaluation with a focus on prototype validation and qualification. Such guidelines are not well-suited for heliostat evaluation in operating commercial heliostat fields. The commercial implementation of the Central Receiver technology is burdened by the lack of a demonstrated cost-effective methodology to test solar fields, particularly during the commissioning and operation phases of the plant. To address heliostat characterization challenges, the SolarPACES funded Project Analyze Heliostat Field aims to set the basis towards a SolarPACES guideline for Heliostat Field Performance testing under a common framework. This is by means of a review of the existing methodologies, R&D and industrial stakeholders information sharing and preparation of a future quantitative comparison and validation plan. As part of the development of this project, several meetings and a workshop involving the SolarPACES community was organized to share knowledge and experience in the measurement and characterization of heliostat fields using a range of technologies and procedures. Research centers and companies from 5 different and distant countries have actively participated in these meetings, sharing their experiences, needs and interests. This paper summarizes the outcome of this international collaborative effort and the prospects for future close collaborations sustained over time

Innate PD-L1 limits T cell–mediated adipose tissue inflammation and ameliorates diet-induced obesity

Obesity has become a major health problem in the industrialized world. Immune regulation plays an important role in adipose tissue homeostasis; however, the initial events that shift the balance from a noninflammatory homeostatic environment toward inflammation leading to obesity are poorly understood. Here, we report a role for the costimulatory molecule programmed death-ligand 1 (PD-L1) in the limitation of diet-induced obesity. Functional ablation of PD-L1 on dendritic cells (DCs) using conditional knockout mice increased weight gain and metabolic syndrome during diet-induced obesity, whereas PD-L1 expression on type 2 innate lymphoid cells (ILC2s), T cells, and macrophages was dispensable for obesity control. Using in vitro cocultures, DCs interacted with T cells and ILC2s via the PD-L1:PD-1 axis to inhibit T helper type 1 proliferation and promote type 2 polarization, respectively. A role for PD-L1 in adipose tissue regulation was also shown in humans, with a positive correlation between PD-L1 expression in visceral fat of people with obesity and elevated body weight. Thus, we define a mechanism of adipose tissue homeostasis controlled by the expression of PD-L1 by DCs, which may be a clinically relevant finding with regard to immune-related adverse events during immune checkpoint inhibitor therapy