Metastability of a granular surface in a spinning bucket

The surface shape of a spinning bucket of granular material is studied using a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. An experimentally observed central subcritical region is reproduced by the model. The subcritical region occurs when a metastable surface becomes unstable via a nonlinear instability mechanism. The nonlinear instability mechanism destabilizes the surface in large systems while a linear instability mechanism is relevant for smaller systems. The range of angles in which the granular surface is metastable vanishes with increasing system size.Comment: 8 pages with postscript figures, RevTex, to appear in Phys. Rev.

T Cell Receptor Signaling That Regulates the Development of Intrathymic Natural Regulatory T Cells

T cell receptor (TCR) signaling plays a critical role in T cell development, survival and differentiation. In the thymus, quantitative and/or qualitative differences in TCR signaling determine the fate of developing thymocytes and lead to positive and negative selection. Recently, it has been suggested that self-reactive T cells, escape from negative selection, should be suppressed in the periphery by regulatory T cells (Tregs) expressing Foxp3 transcription factor. Foxp3 is a master factor that is critical for not only development and survival but also suppressive activity of Treg. However, signals that determine Treg fate are not completely understood. The availability of mutant mice which harbor mutations in TCR signaling mediators will certainly allow to delineate signaling events that control intrathymic (natural) Treg (nTreg) development. Thus, we summarize the recent progress on the role of TCR signaling cascade components in nTreg development from the studies with murine model

Some problems on spatial patterns in nonequilibrium systems

In this thesis, we study the evolution of spatial patterns in two nonequilibrium systems.In Chapter 1, we study the steady state of a 1-d cellular automata (CA) model of chemical turbulence. Empirically there are two interesting types of space-time patterns (depending on model parameters): a S phase which seems to contain solitons and a T phase which seems to be turbulent. We show that the macroscopic phases can be predicted from the microscopic dynamics. We define the thermodynamic limit of the steady state of CAs and show that the steady state of the S phase is trivial and the T phase exhibits a Gibbs state. We explicitly calculate the T phase steady state and find an approximate form for the energy functional which generates the Gibbs state. We show that there is no adequate characterization of turbulent behavior in CAs and introduce a quantity the "P-entropy" which is positive if the CA patterns are turbulent and zero otherwise. We show the P-entropy for the T phase is positive.In Chapter 2, we consider the consequences of the dynamical scaling hypothesis in phase ordering dynamics. We assume that the dynamics are governed by the Cahn-Hilliard-Cook (CHC) and time-dependent Ginzburg-Landau equations and show that the scaling hypothesis restricts the asymptotic growth rate of the length-scale of the patterns and the small wavevector behavior of the form factor. Specifically, if the form factor S\sb{k}($t$) grows as k\sp{\delta} for small $\delta$, then $\delta\geq$ 4 (for the CHC dynamics). We find that experimental data indicates $\delta$ = 4. We also show that the CHC equation is sometimes inadequate for describing phase ordering dynamics. An alternative to the CHC model by Oono, Kitahara and Jasnow is examined. We find that many features of phase ordering dynamics are robust with respect to changing the dynamics.U of I OnlyETDs are only available to UIUC Users without author permissio

Estrogen and progesterone receptors in transplantable Noble art mammary tumors

The relationship between sex steroid hormone receptors and hormone dependent status of mammary tumors has been studied using an animal model. Hormone-induced Noble rat mammary tumor lines were maintained by serial transplantations. Transplants were carried out by injecting small pieces of viable tissues into the backs of animals. Depending on the hormonal status of the tumors, exogenous estrogen was supplemented. Tumors (5-10 g) were harvested and their cytoplasmic estrogen receptors (ERc), nuclear estrogen receptors (ERn) and cytoplasmic progesterone receptors (PgR) profiles were analyzed. The majority of the tumors studied did not depend on exogenous estrogen for growth i.e. they were hormone autonomous. They arose from transplants of a hormone dependent tumor, an autonomous tumor, or a tumor which had undergone a transition from dependency to autonomy upon removal of the exogenous estrogen source from the host. Histologically they appeared very homogeneous. Characterization of the receptor profiles of the autonomous tumors were intended to answer whether or not (1) the measurements of ERc, or ERn and PgR can indicate the autonomous status of these tumors (2) the levels of ERc, ERn and PgR are influenced by sequential transplantation (3) there is a change in the receptor profiles concurrent to tumor progression from dependency to autonomy. Receptors were measured by isolating the cytoplasmic and nuclear fractions prior to an exchange assay with radioactive hormone ligand. Cytoplasmic contamination of the ERn assay was avoided by the development of a procedure to isolate clean intact nuclei as starting material. Almost all of the autonomous tumors reported in this study (48 out of 52) have measurable amounts of cytoplasmic estrogen receptors (ERc+). This supports the general belief that ERc alone is not a sufficient indicator of hormone dependence. The level of receptors was also found to be quite constant in transplants over a number of generations of male and female hosts. This is consistent with the postulate that production of receptors is "genetically" coded by individual cell type and is not greatly influenced by the hormonal milieu. Noble rat mammary tumors began to progress towards autonomy when the estrogen pellets were removed. Changes in receptor profiles were studied with respect to tumor progression while under some degree of estrogen stimulation. Transplants were carried out in either intact female animals or males supplemented with an estrogen pellet, after the tumor had undergone a transition from dependency to autonomy. Results show that such tumors seemed to maintain an intact stimulatory pathway i.e. ERc+/ERn+/PgR+ if transplants were performed shortly after the removal of the estrogen pellets from the dependent tumors (<13 weeks). However, if duration of progression was extended, receptor profile would become negative and implied a total autonomous state. Therefore, it is suggested that tumor progression might be attenuated with hormone supplement. This would keep the estrogenic mechanism intact; thus maintaining an avenue for controlling growth via hormone manipulation. Two major groups of autonomous tumors with different receptor profiles were also observed. Group I tumours were shown to have measurable amounts of cytoplasmic estrogen receptors, nuclear estrogen receptors and cytoplasmic progesterone receptors (ERc+/ERn+/PgR+). Further investigation is necessary to elucidate whether these tumors might be hormone responsive thus required the maintenance of their estrogen stimulatory mechanism. In contrast, group II was ERc+/ERn +or- /PgR-. The absence of PgR in this group implies the presence of biochemical lesions or hormone nonresponsiveness and would agree with their autonomous behavior. This suggests that the measurement of PgR, which is believed to be an end product of estrogen- stimulation, might be more informative concerning the condition of the estrogenic stimulatory mechanism than the assays of ERc or ERn.Medicine, Faculty ofPathology and Laboratory Medicine, Department ofGraduat

Scaling and the Damage Algorithm in Phase-Ordering Dynamics

Recent scaling, analytic and experimental work suggests that, in phaseordering dynamics, the nonequilibrium two-time correlation functions display scaling behaviour distinctly different from that of single-point functions such as the local density. In this paper we argue, through scaling arguments and numerical results, that the damage algorithm is directly related to the underlying physical mechanism of this scaling behaviour, and allows direct measurement of the new scaling exponent . Simulation results are shown for Ising model quenches to T = 0 in both 2d and 3d. We find 2d = 1:28 \Sigma 04, 3d = xxx. Typeset using REVT E X The dynamical behaviour of a system approaching equilbrium following a rapid quench from well above to well below the critical temperature is one of the seminal problems of modern condensed matter physics. The canonical experiment is simple, both in theory and in practice: take a system, initially well above its critical temperature T c , and quench it rapi..

Exact results and the effect of monomer–monomer bond type for a grafted ideal chain

We determine the equilibrium chain end probability density $$P_N(x)$$ for a one-dimensional ideal chain of N monomers grafted to a planar surface. This distribution is also the distribution function of a three-dimensional chain where the tangential dimensions y, z are integrated out of the distribution. With a small modification of the analysis of Erukhimovich, Johner, and Joanny for free chains near a wall, we are able to obtain exact results for $$P_N(x)$$ for any monomer number N though with the restriction that the monomer–monomer bonds lengths are exponentially distributed. In particular, we obtain exact values for $$P_N$$ and its derivative $$\textrm{d}P_N/\textrm{d}x$$ at the surface for any N and the full profile $$P_N(x)$$ for selected values of N. To determine the effect of the bond distribution, we find $$P_N(x)$$ numerically for Gaussian and uniformly distributed one-dimensional bonds and compare with the exact results for exponential bonds. We suggest several ways to quantify the effect of bond type based both on $$P_N (x)$$ near the surface and in the scaling region $$x\sim \sqrt{N} a$$. We then extract the large N limit of $$P_N(x)$$ and show that it is similar to the chain end probability for continuous chains but shifted toward smaller x. We show the amount of shift is a measure of the magnitude of the correction to the continuous chain $$P_N(x)$$. We derive the value of the shift for exponential bonds and show that the value is different for other bond types. We argue the shift can be interpreted as an effective surface behind the actual surface

Bounds on the decay of the auto-correlation in phase ordering dynamics

We investigate the decay of temporal correlations in phase ordering dynamics by obtaining bounds on the decay exponent &#955; of the autocorrelation function [defined by limt2»t17lt; &#966;(r,t1)&#966;(r,t2)&gt;~L (t2)-&#955;]. For a nonconserved order parameter, we recover the Fisher and Huse inequality, &#955;&#8805;d/2. For a conserved order parameter, we find &#955;&#8805;d/2 only if t1 = 0. If t1 is in the scaling regime, then &#955;&#8805;d/2+2 for d&#8805;2 and &#955;&#8805;3/2 for d=1. For the one-dimensional scalar case, this, in conjunction with previous results, implies that the value of &#955; depends on whether t1=0 or t1»1. Our numerical simulations for the two-dimensional, conserved scalar order parameter show that &#955;?4 for t1 in the scaling regime, consistent with our bound. The asymptotic decay when t1=0, while exhibiting an unexpected sensitivity to the amplitude of the initial correlations, is slower than when t1»1 and obeys the bound &#955;&#8805;d/2