Potts Models with (17) Invisible States on Thin Graphs

The order of a phase transition is usually determined by the nature of the symmetry breaking at the phase transition point and the dimension of the model under consideration. For instance, q-state Potts models in two dimensions display a second order, continuous transition for q = 2,3,4 and first order for higher q. Tamura et al recently introduced Potts models with "invisible" states which contribute to the entropy but not the internal energy and noted that adding such invisible states could transmute continuous transitions into first order transitions. This was observed both in a Bragg-Williams type mean-field calculation and 2D Monte-Carlo simulations. It was suggested that the invisible state mechanism for transmuting the order of a transition might play a role where transition orders inconsistent with the usual scheme had been observed. In this paper we note that an alternative mean-field approach employing 3-regular random ("thin") graphs also displays this change in the order of the transition as the number of invisible states is varied, although the number of states required to effect the transmutation, 17 invisible states when there are 2 visible states, is much higher than in the Bragg-Williams case. The calculation proceeds by using the equivalence of the Potts model with 2 visible and r invisible states to the Blume-Emery-Griffiths (BEG) model, so a by-product is the solution of the BEG model on thin random graphs.Comment: (2) Minor typos corrected, references update

Synchronized voltage contrast display analysis system

An apparatus and method for comparing internal voltage potentials of first and second operating electronic components such as large scale integrated circuits (LSI's) in which voltage differentials are visually identified via an appropriate display means are described. More particularly, in a first embodiment of the invention a first and second scanning electron microscope (SEM) are configured to scan a first and second operating electronic component respectively. The scan pattern of the second SEM is synchronized to that of the first SEM so that both simultaneously scan corresponding portions of the two operating electronic components. Video signals from each SEM corresponding to secondary electron signals generated as a result of a primary electron beam intersecting each operating electronic component in accordance with a predetermined scan pattern are provided to a video mixer and color encoder

Variable renewal rate and growth properties of cell populations in colon crypts

A nonlinear mathematical model is used to investigate the time evolution of the cell populations in colon crypts (stem, semidifferentiated and fully differentiated cells). To mimic pathological alteration of the biochemical pathways leading to abnormal proliferative activity of the population of semidifferentiated cells their renewal rate is assumed to be dependent on the population size. Then, the effects of such perturbation on the population dynamics are investigated theoretically. Using both theoretical methods and numerical simulations it is shown that the increase in the renewal rate of semidifferentiated cells strongly impacts the dynamical behavior of the cell populations

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

Superconductivity and Physical Properties of CaPd2Ge2 Single Crystals

We present the superconducting and normal state properties of CaPd2Ge2 single crystal investigated by magnetic susceptibility \chi, isothermal magnetization M, heat capacity C_p, in-plane electrical resistivity \rho and London penetration depth \lambda versus temperature T and magnetic field H measurements. Bulk superconductivity is inferred from the \rho(T) and C_p(T) data. The \rho(T) data exhibit metallic behavior and undergoes a superconducting transition with T_c onset = 1.98 K and zero resistivity state at T_c 0 = 1.67 K. The \chi(T) reveal the onset of superconductivity at 2.0 K. For T>2.0 K, the \chi(T) and M(H) are weakly anisotropic paramagnetic with \chi_ab > \chi_c. The C_p(T) confirm the bulk superconductivity below T_c = 1.69(3) K. The superconducting state electronic heat capacity is analyzed within the framework of a single-band \alpha-model of BCS superconductivity and various normal and superconducting state parameters are estimated. Within the \alpha-model, the C_p(T) data and the ab plane \lambda(T) data consistently indicate a moderately anisotropic s-wave gap with \Delta(0)/k_B T_c ~ 1.6, somewhat smaller than the BCS value of 1.764. The relationship of the heat capacity jump at T_c and the penetration depth measurement to the anisotropy in the s-wave gap is discussed.Comment: 12 pages, 9 figures, 2 Tables; Submitted to PR

Film cooling on a convex wall: Heat transfer and hydrodynamic measurements for full and partial coverage

Turbine-blade cooling is an important issue for high-efficiency turbine engines, and discrete-hole injection is widely used as a cooling method. In the present study, detailed measurements were made of the heat transfer and hydrodynamics of a film-cooled flow on a convex wall, both for full and partial coverage. Two important parameters were altered: the blowing ratio, m, and the number of rows of injection holes. Three values of m were tested: m = 0.2, 0.4, and 0.6. In the blown region, m = 0.4 results in the lowest Stanton numbers of the three blowing ratios tested. This indicates that the value of m = 0.4 is near optimum on the convex wall from the point of view of cooling effect by injection. In the recovery region, Stanton numbers gradually approach the no injection values. Although the heat-transfer behavior during recovery from injection looks relatively complicated, the behavior of Stanton number can be explained in terms of two mechanisms: recovery from the thermal effect of injection and recovery from the turbulence augmentation. This interpretation of the data is supported by the hydrodynamic and temperture-profile measurements. For partial blowing cases, the data follow the full-coverage values inside the blown region. In the unblown region, both in the curved and in the flat plate, the effect of the number of blown rows is clearly seen. Hydrodynamic boundary-layer profiles were measured with the aid of a triple hot-water probe. Three mean-velocity components and six turbulence quantities were simultaneously measured, and inside the blown region strong three-dimensionality was observed