Dynamics of an Unbounded Interface Between Ordered Phases

We investigate the evolution of a single unbounded interface between ordered phases in two-dimensional Ising ferromagnets that are endowed with single-spin-flip zero-temperature Glauber dynamics. We examine specifically the cases where the interface initially has either one or two corners. In both examples, the interface evolves to a limiting self-similar form. We apply the continuum time-dependent Ginzburg-Landau equation and a microscopic approach to calculate the interface shape. For the single corner system, we also discuss a correspondence between the interface and the Young tableau that represents the partition of the integers.Comment: 9 pages, 11 figures, 2-column revtex4 format. V2: references added and discussion section expanded slightly. Final version for PRE. V3: A few small additional editorial change

Free boundary problems describing two-dimensional pulse recycling and motion in semiconductors

An asymptotic analysis of the Gunn effect in two-dimensional samples of bulk n-GaAs with circular contacts is presented. A moving pulse far from contacts is approximated by a moving free boundary separating regions where the electric potential solves a Laplace equation with subsidiary boundary conditions. The dynamical condition for the motion of the free boundary is a Hamilton-Jacobi equation. We obtain the exact solution of the free boundary problem (FBP) in simple one-dimensional and axisymmetric geometries. The solution of the FBP is obtained numerically in the general case and compared with the numerical solution of the full system of equations. The agreement is excellent so that the FBP can be adopted as the basis for an asymptotic study of the multi-dimensional Gunn effect.Comment: 19 pages, 9 figures, Revtex. To appear in Phys. Rev.

Pattern Formation of Glioma Cells: Effects of Adhesion

We investigate clustering of malignant glioma cells. \emph{In vitro} experiments in collagen gels identified a cell line that formed clusters in a region of low cell density, whereas a very similar cell line (which lacks an important mutation) did not cluster significantly. We hypothesize that the mutation affects the strength of cell-cell adhesion. We investigate this effect in a new experiment, which follows the clustering dynamics of glioma cells on a surface. We interpret our results in terms of a stochastic model and identify two mechanisms of clustering. First, there is a critical value of the strength of adhesion; above the threshold, large clusters grow from a homogeneous suspension of cells; below it, the system remains homogeneous, similarly to the ordinary phase separation. Second, when cells form a cluster, we have evidence that they increase their proliferation rate. We have successfully reproduced the experimental findings and found that both mechanisms are crucial for cluster formation and growth.Comment: 6 pages, 6 figure

Level Set Approach to Reversible Epitaxial Growth

We generalize the level set approach to model epitaxial growth to include thermal detachment of atoms from island edges. This means that islands do not always grow and island dissociation can occur. We make no assumptions about a critical nucleus. Excellent quantitative agreement is obtained with kinetic Monte Carlo simulations for island densities and island size distributions in the submonolayer regime.Comment: 7 pages, 9 figure

MRI of Neuronal Recovery After Low-Dose Methamphetamine Treatment of Traumatic Brain Injury in Rats

We assessed the effects of low dose methamphetamine treatment of traumatic brain injury (TBI) in rats by employing MRI, immunohistology, and neurological functional tests. Young male Wistar rats were subjected to TBI using the controlled cortical impact model. The treated rats (n = 10) received an intravenous (iv) bolus dose of 0.42 mg/kg of methamphetamine at eight hours after the TBI followed by continuous iv infusion for 24 hrs. The control rats (n = 10) received the same volume of saline using the same protocol. MRI scans, including T2-weighted imaging (T2WI) and diffusion tensor imaging (DTI), were performed one day prior to TBI, and at 1 and 3 days post TBI, and then weekly for 6 weeks. The lesion volumes of TBI damaged cerebral tissue were demarcated by elevated values in T2 maps and were histologically identified by hematoxylin and eosin (H&E) staining. The fractional anisotropy (FA) values within regions-of-interest (ROI) were measured in FA maps deduced from DTI, and were directly compared with Bielschowsky’s silver and Luxol fast blue (BLFB) immunohistological staining. No therapeutic effect on lesion volumes was detected during 6 weeks after TBI. However, treatment significantly increased FA values in the recovery ROI compared with the control group at 5 and 6 weeks after TBI. Myelinated axons histologically measured using BLFB were significantly increased (p,0.001) in the treated group (25.8461.41%) compared with the control group (17.0562.95%). Significant correlations were detected between FA and BLFB measures in the recovery ROI (R = 0.54, p,0.02). Methamphetamine treatment significantly reduced modified neurological severity scores from 2 to 6 weeks (p,0.05) and foot-fault errors from 3 days to 6 weeks (p,0.05) after TBI. Thus, the FA data suggest that methamphetamine treatment improves white matter reorganization from 5 to 6 weeks after TBI in rats compared with saline treatment, which may contribute to the observed functional recovery

Helicoidal surfaces rotating/translating under the mean curvature flow

We describe all possible self-similar motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding hypersurface equations. Then we present a new two-parameter family of immersed helicoidal surfaces that rotate/translate with constant velocity under the flow. We look at their limiting behaviour as the pitch of the helicoidal motion goes to 0 and compare it with the limiting behaviour of the classical helicoidal minimal surfaces. Finally, we give a classification of the immersed cylinders in the family of constant mean curvature helicoidal surfaces.Comment: 21 pages, 22 figures, final versio

A mathematical model of quorum sensing regulated EPS production in biofilm communities

<p>Abstract</p> <p>Background</p> <p>Biofilms are microbial communities encased in a layer of extracellular polymeric substances (EPS). The EPS matrix provides several functional purposes for the biofilm, such as protecting bacteria from environmental stresses, and providing mechanical stability. Quorum sensing is a cell-cell communication mechanism used by several bacterial taxa to coordinate gene expression and behaviour in groups, based on population densities.</p> <p>Model</p> <p>We mathematically model quorum sensing and EPS production in a growing biofilm under various environmental conditions, to study how a developing biofilm impacts quorum sensing, and conversely, how a biofilm is affected by quorum sensing-regulated EPS production. We investigate circumstances when using quorum-sensing regulated EPS production is a beneficial strategy for biofilm cells.</p> <p>Results</p> <p>We find that biofilms that use quorum sensing to induce increased EPS production do not obtain the high cell populations of low-EPS producers, but can rapidly increase their volume to parallel high-EPS producers. Quorum sensing-induced EPS production allows a biofilm to switch behaviours, from a colonization mode (with an optimized growth rate), to a protection mode.</p> <p>Conclusions</p> <p>A biofilm will benefit from using quorum sensing-induced EPS production if bacteria cells have the objective of acquiring a thick, protective layer of EPS, or if they wish to clog their environment with biomass as a means of securing nutrient supply and outcompeting other colonies in the channel, of their own or a different species.</p

31P magnetic resonance spectroscopy as a predictor of efficacy in photodynamic therapy using differently charged zinc phthalocyanines

Photodynamic therapy (PDT) is a developing approach to the treatment of solid tumours which requires the combined action of light and a photosensitizing drug in the presence of adequate levels of molecular oxygen. We have developed a novel series of photosensitizers based on zinc phthalocyanine which are water-soluble and contain neutral (TDEPC), positive (PPC) and negative (TCPC) side-chains. The PDT effects of these sensitizers have been studied in a mouse model bearing the RIF-1 murine fibrosarcoma line studying tumour regrowth delay, phosphate metabolism by magnetic resonance spectroscopy (MRS) and blood flow, using D2O uptake and MRS. The two main aims of the study were to determine if MRS measurements made at the time of PDT treatment could potentially be predictive of ultimate PDT efficacy and to assess the effects of sensitizer charge on PDT in this model. It was clearly demonstrated that there is a relationship between MRS measurements during and immediately following PDT and the ultimate effect on the tumour. For all three drugs, tumour regrowth delay was greater with a 1-h time interval between drug and light administration than with a 24-h interval. In both cases, the order of tumour regrowth delay was PPC > TDEPC = TCPC (though the data at 24 h were not statistically significant). Correspondingly, there were greater effects on phosphate metabolism (measured at the time of PDT or soon after) for the 1-h than for the 24-h time interval. Again effects were greatest with the cationic PPC, with the sequence being PPC > TDEPC > TCPC. A parallel sequence was observed for the blood flow effects, demonstrating that reduction in blood flow is an important factor in PDT with these sensitizers. © 1999 Cancer Research Campaig