The nature of the long time decay at a second order transition point

We show that at a second order phase transition, of \phi^4 like system, a necessary condition for streched exponential decay of the time structure factor is obeyed. Using the ideas presented in this proof a crude estimate of the decay of the structure factor is obtained and shown to yield stretched exponential decay under very reasonable conditions.Comment: 7 page

Examples of mathematical modeling tales from the crypt

Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al. (2007) Proc. Natl. Acad. Sci. USA 104, 4008-4013, to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters

On the proportion of cancer stem cells in a tumour

It is now generally accepted that cancers contain a sub-population, the cancer stem cells (CSCs), which initiate and drive a tumour’s growth. At least until recently it has been widely assumed that only a small proportion of the cells in a tumour are CSCs. Here we use a mathematical model, supported by experimental evidence, to show that such an assumption is unwarranted. We show that CSCs may comprise any possible proportion of the tumour, and that the higher the proportion the more aggressive the tumour is likely to be

Force correlations and arches formation in granular assemblies

In the context of a simple microscopic schematic scalar model we study the effects of spatial correlations in force transmission in granular assemblies. We show that the parameters of the normalized weights distribution function, $P(v)\sim v^{\alpha}\exp(-v/\phi)$, strongly depend on the spatial extensions, $\xi_V$, of such correlations. We show, then, the connections between measurable macroscopic quantities and microscopic mechanisms enhancing correlations. In particular we evaluate how the exponential cut-off, $\phi(\xi_V)$, and the small forces power law exponent, $\alpha(\xi_V)$, depend on the correlation length, $\xi_V$. If correlations go to infinity, weights are power law distributed.Comment: 6 page

Nucleon-Nucleon Scattering From Fully-Dynamical Lattice QCD

We present results of the first fully-dynamical lattice QCD determination of nucleon-nucleon scattering lengths in the 1S0 channel and 3S1-3D1 coupled channels. The calculations are performed with domain-wall valence quarks on the MILC staggered configurations with lattice spacing of b=0.125 fm in the isospin-symmetric limit, and in the absence of electromagnetic interactions.Comment: 4 pages, 4 figure

Collective excitations of Bose-Einstein condensed gases at finite temperatures

We have applied the Popov version of the Hartree-Fock-Bogoliubov (HFB) approximation to calculate the finite-temperature excitation spectrum of a Bose-Einstein condensate (BEC) of $^{87}$Rb atoms. For lower values of the temperature, we find excellent agreement with recently-published experimental data for the JILA TOP trap. In contrast to recent comparison of the results of HFB--Popov theory with experimental condensate fractions and specific heats, there is disagreement of the theoretical and recent experimental results near the BEC phase transition temperature.Comment: 4 pages, Latex, with 4 figures. More info at http://amo.phy.gasou.edu/bec.htm

Results of cross-faculty 'capstone' assessments involving nursing and performing arts students

This article describes how ‘capstone’ assessments were created to provide two different student groups, nursing and performing arts students, with a lived experience of learning together about their own fields of practice. Capstone assessments combine ‘live’ human simulation with self‑reflection and peer review. A capstone assessment is the integration of a body of relatively fragmented knowledge and learning to form a unified whole and can be used as a transitional assessment and a bridging experience to connect knowledge between modules or courses. The capstone assessments involved two faculties and four modules, three nursing and one performing arts. Case studies were designed to represent real-life situations that students were likely to encounter during their careers, either playing a patient as an actor or performing a caring role as a nurse. Assessments for the capstone simulation were formative, and involved the students engaging in self-reflection and peer review. Videos were available to enhance the self-reflection and peer-review process. Evaluation was undertaken through verbal feedback during debrief, written feedback, video footage and nursing student and acting student peer review. The experience of capstone assessments for two diverse student groups provided valuable learning from their own and from a different group outside their subject area

Biophysically motivated efficient estimation of the spatially isotropic R*2 component from a single gradient‐recalled echo measurement

Purpose To propose and validate an efficient method, based on a biophysically motivated signal model, for removing the orientation‐dependent part of R*2 using a single gradient‐recalled echo (GRE) measurement. Methods The proposed method utilized a temporal second‐order approximation of the hollow‐cylinder‐fiber model, in which the parameter describing the linear signal decay corresponded to the orientation‐independent part of R*2. The estimated parameters were compared to the classical, mono‐exponential decay model for R*2 in a sample of an ex vivo human optic chiasm (OC). The OC was measured at 16 distinct orientations relative to the external magnetic field using GRE at 7T. To show that the proposed signal model can remove the orientation dependence of R*2, it was compared to the established phenomenological method for separating R*2 into orientation‐dependent and ‐independent parts. Results Using the phenomenological method on the classical signal model, the well‐known separation of R*2 into orientation‐dependent and ‐independent parts was verified. For the proposed model, no significant orientation dependence in the linear signal decay parameter was observed. Conclusions Since the proposed second‐order model features orientation‐dependent and ‐independent components at distinct temporal orders, it can be used to remove the orientation dependence of R*2 using only a single GRE measurement