Solvability and regularity for an elliptic system prescribing the curl, divergence, and partial trace of a vector field on Sobolev-class domains

We provide a self-contained proof of the solvability and regularity of a Hodge-type elliptic system, wherein the divergence and curl of a vector field are prescribed in an open, bounded, Sobolev-class domain, and either the normal component or the tangential components of the vector field are prescribed on the boundary. The proof is based on a regularity theory for vector elliptic equations set on Sobolev-class domains and with Sobolev-class coefficients.Comment: 49 Pages, improved exposition and corrected typo

Global existence and decay for solutions of the Hele-Shaw flow with injection

We study the global existence and decay to spherical equilibrium of Hele-Shaw flows with surface tension. We prove that without injection of fluid, perturbations of the sphere decay to zero exponentially fast. On the other hand, with a time-dependent rate of fluid injection into the Hele-Shaw cell, the distance from the moving boundary to an expanding sphere (with time-dependent radius) also decays to zero but with an algebraic rate, which depends on the injection rate of the fluid.Comment: 25 Page

On the Motion of Vortex Sheets with Surface Tension in the 3D Euler Equations with Vorticity

We prove well-posedness of vortex sheets with surface tension in the 3D incompressible Euler equations with vorticity.Comment: 28 page

Navier-Stokes equations interacting with a nonlinear elastic fluid shell

We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic fluid shell. The fluid motion is governed by the Navier-Stokes equations, while the fluid shell is modeled by a bending energy which extremizes the Willmore functional and a membrane energy that extremizes the surface area of the shell. The fluid flow and shell deformation are coupled together by continuity of displacements and tractions (stresses) along the moving material interface. We prove existence and uniqueness of solutions in Sobolev spaces.Comment: 56 pages, 1 figur

Surface Plasmon Studies of Composition Control in Mixed Acid Alkanethiol SAMs

In this study, surface plasmon resonance (SPR) was used to investigate the adsorption of MUA (11-mercapto-undecanoic acid), MPA (3-mercapto-propionic acid) and MHX (6-mercapto-1-hexanol) onto a gold SPR sensor surface. MUA, MPA, and MHX were dissolved in phosphate buffers of ionic strengths varying from 0.1 mM to 1 M and at pH values between 2 and 11, and monolayer formation experiments were performed. Our results illustrate how the adsorption of these charged and neutral alkanethiols depends on solution ionic strength and pH. Results indicate that, for single-component MUA or MPA layers, low pH and elevated solution ionic strength may promote denser layer formation. For binary MUA-MHX monolayers, potentiostatic control was important to establish reproducible SAM formation. Surprisingly, for 0.00 V potentiostatic depositions from mixed MUA-MHX solutions, MUA was substantially incorporated into the monolayer only at pH 3; whereas, at pH 7 and 11, MHX strongly predominated in the monolayer phase

INVESTIGATIONS INTO THE FATIGUE-RELATED REDUCTION IN TORQUE, SHORTENING VELOCITY, AND JOINT RANGE OF MOTION IN HUMANS

Studies in humans and animals have derived much understanding of neuromuscular function from isometric (static) contractions. In comparison, fewer studies have evaluated dynamic contractions, which are relevant to everyday movements and activities of daily living. The primary purpose of this thesis was to investigate and compare the contributing factors to fatigue during different voluntary contraction tasks. The interpolated twitch technique is commonly used to assess voluntary activation, but with changes in muscle length, musculotendinous slackness can diminish the amplitude of electrically-evoked twitches used to calculate voluntary activation. This might result in erroneous measurements of voluntary activation. Chapter 2 describes an experiment in which at the short muscle lengths, when voluntary activation is 80% or lower, actual activation will be underestimated. Maximum voluntary isometric contraction (MVC) torque is often used to assess overall neuromuscular function, and any activity-induced decline in MVC torque is indicative of fatigue. However, a reduction in shortening velocity is also an important feature of fatigue. Results from Chapter 3 indicate that shortening velocity was an important and perhaps more sensitive measure of fatigue following both isometric and dynamic contraction tasks than MVC torque per se. These findings are further supported in Chapter 4, in which, following comparable repetitive shortening contraction tasks in two different muscles, shortening velocity was reduced to a greater extent at task failure but was restored more rapidly than MVC torque. Shortening contractions are also characterized by a fatigue-related reduction in joint range of motion (ROM) and it was suggested that the reduction in ROM might be due to length-dependent alterations in torque or contractile slowing with fatigue. Results iii presented in Chapter 5, suggest that length-dependent alterations in torque or contractile slowing cannot explain the fatigue-related reduction in dorsiflexion ROM. Thus, in addition to fatigue-related reductions in torque, decreases in shortening velocity and joint range of motion are important indicators of a fatigue-induced impairment in muscle shortening capacity

Minority Games and stylized facts

The Minority Game is a generic model of competing adaptive agents, which is often believed to be a model of financial markets. We discuss to which extend this is a reasonable statement, and present minimal modifications that make this model reproduce stylized facts. The resulting model shows that without speculators, prices follow random walks, and that stylized facts disappear if enough speculators take into account their market impact.Comment: 6 pages, 2 figures. Proceedings of the NATO Advanced Research Workshop on Application of Physics in Economic Modelling, Prague 2001. 2nd version: small modification of the abstrac

Destabilizing the autoinhibitory conformation of Zap70 induces up-regulation of inhibitory receptors and T cell unresponsiveness.

Zap70 plays a critical role in normal T cell development and T cell function. However, little is known about how perturbation of allosteric autoinhibitory mechanisms in Zap70 impacts T cell biology. Here, we analyze mice with a hypermorphic Zap70 mutation, W131A, which destabilizes the autoinhibitory conformation of Zap70, rendering the kinase in a semiactive state. W131A mutant mice with wild-type T cell receptor (TCR) repertoires exhibited relatively normal T cell development. However, crossing the W131A mutant mice to OTII TCR transgenic mice resulted in increased negative selection of OTII+ thymocytes and in increased thymic and peripheral T regulatory cells. Strikingly, increased basal TCR signaling was associated with a marked increase in inhibitory receptor expression and with T cells that were relatively refractory to TCR stimulation. PD-1 inhibitory receptor blockade partially reversed T cell unresponsiveness. Collectively, disruption of normal Zap70 autoinhibition engaged negative feedback mechanisms by which negative selection and inhibitory receptors restrain TCR signaling to enforce both central and peripheral tolerance

Hierarchical Lattice Models of Hydrogen Bond Networks in Water

We develop a graph-based model of the hydrogen bond network in water, with a view towards quantitatively modeling the molecular-level correlational structure of the network. The networks are formed are studied by the constructing the model on two infinite-dimensional lattices. Our models are built \emph{bottom up}, based on microscopic information coming from atomistic simulations, and we show that the predictions of the model are consistent with known results from ab-initio simulations of liquid water. We show that simple entropic models can predict the correlations and clustering of local-coordination defects around tetrahedral waters observed in the atomistic simulations. We also find that orientational correlations between bonds are longer ranged than density correlations, and determine the directional correlations within closed loops and show that the patterns of water wires within these structures are also consistent with previous atomistic simulations. Our models show the existence of density and compressibility anomalies, as seen in the real liquid, and the phase diagram of these models is consistent with the singularity-free scenario previously proposed by Sastry and co-workers (Sastry et al, PRE 53, 6144 (1996)).Comment: 17 pages, published versio