Scalar conservation laws on constant and time-dependent Riemannian manifolds

In this paper we establish well-posedness for scalar conservation laws on closed manifolds M endowed with a constant or a time-dependent Riemannian metric for initial values in L^\infty(M). In particular we show the existence and uniqueness of entropy solutions as well as the L^1 contraction property and a comparison principle for these solutions. Throughout the paper the flux function is allowed to depend on time and to have non-vanishing divergence. Furthermore, we derive estimates of the total variation of the solution for initial values in BV(M), and we give, in the case of a time-independent metric, a simple geometric characterisation of flux functions that give rise to total variation diminishing estimates.Comment: 23 pages, no figure

Diffusion of Macromolecules across the Nuclear Pore Complex

Nuclear pore complexes (NPCs) are very selective filters that monitor the transport between the cytoplasm and the nucleoplasm. Two models have been suggested for the plug of the NPC. They are (i) it is a reversible hydrogel or (ii) it is a polymer brush. We propose a mesoscopic model for the transport of a protein through the plug, that is general enough to cover both. The protein stretches the plug and creates a local deformation. The bubble so created (prtoein+deformation) executes random walk in the plug. We find that for faster relaxation of the gel, the diffusion of the bubble is greater. Further, on using parameters appropriate for the brush, we find that the diffusion coefficient is much lower. Hence the gel model seems to be more likely explanation for the workings of the plug

Model of SNARE-Mediated Membrane Adhesion Kinetics

SNARE proteins are conserved components of the core fusion machinery driving diverse membrane adhesion and fusion processes in the cell. In many cases micron-sized membranes adhere over large areas before fusion. Reconstituted in vitro assays have helped isolate SNARE mechanisms in small membrane adhesion-fusion and are emerging as powerful tools to study large membrane systems by use of giant unilamellar vesicles (GUVs). Here we model SNARE-mediated adhesion kinetics in SNARE-reconstituted GUV-GUV or GUV-supported bilayer experiments. Adhesion involves many SNAREs whose complexation pulls apposing membranes into contact. The contact region is a tightly bound rapidly expanding patch whose growth velocity increases with SNARE density . We find three patch expansion regimes: slow, intermediate, fast. Typical experiments belong to the fast regime where depends on SNARE diffusivities and complexation binding constant. The model predicts growth velocities s. The patch may provide a close contact region where SNAREs can trigger fusion. Extending the model to a simple description of fusion, a broad distribution of fusion times is predicted. Increasing SNARE density accelerates fusion by boosting the patch growth velocity, thereby providing more complexes to participate in fusion. This quantifies the notion of SNAREs as dual adhesion-fusion agents

Sewer System Alternatives Evaluation for Potential Creswell Area Expansion in Harford County

Final project for ENCE422: Project Cost Accounting and Economics (Fall 2018). University of Maryland, College Park.This report summarizes the findings of the ENCE422 Fall 2018 class term project. Students were tasked with evaluating sewer system alternatives for the Creswell area expansion in Harford County. Student groups were to consider environmental impacts, community/social impacts, and perform financial analysis for the alternatives they chose to evaluate. This report extracts information from 14 separate team presentations and synthesizes it around the following structure; 1. Systems that Utilize Septic Tanks a. Traditional Septic System b. Orenco Effluent System c. Small Diameter Gravity Sewer System 2. System that Do Not Utilize Septic Tanks a. Traditional Gravity System b. Vacuum System c. Grinder Pump SystemHarford Count

Discovery of Clinical Candidate 4‑[2-(5-Amino‑1<i>H</i>‑pyrazol-4-yl)-4-chlorophenoxy]-5-chloro-2-fluoro‑<i>N</i>‑1,3-thiazol-4-ylbenzenesulfonamide (PF-05089771): Design and Optimization of Diaryl Ether Aryl Sulfonamides as Selective Inhibitors of Na_V1.7

A series of acidic diaryl ether heterocyclic sulfonamides that are potent and subtype selective Na_V1.7 inhibitors is described. Optimization of early lead matter focused on removal of structural alerts, improving metabolic stability and reducing cytochrome P450 inhibition driven drug–drug interaction concerns to deliver the desired balance of preclinical in vitro properties. Concerns over nonmetabolic routes of clearance, variable clearance in preclinical species, and subsequent low confidence human pharmacokinetic predictions led to the decision to conduct a human microdose study to determine clinical pharmacokinetics. The design strategies and results from preclinical PK and clinical human microdose PK data are described leading to the discovery of the first subtype selective Na_V1.7 inhibitor clinical candidate PF-05089771 (<b>34</b>) which binds to a site in the voltage sensing domain