Bouncing Neutrons and the Neutron Centrifuge

The recent observation of the quantum state of the neutron bouncing freely under gravity allows some novel experiments. A method of purifying the ground state is given, and possible applications to the measurement of the electric dipole moment of the neutron and the short distance behaviour of gravity are discussed.Comment: 7 pages, 7 figure

Modelling spatially regulated B-catenin dynamics & invasion in intestinal crypts

Experimental data (e.g., genetic lineage and cell population studies) on intestinal crypts reveal that regulatory features of crypt behavior, such as control via morphogen gradients, are remarkably well conserved among numerous organisms (e.g., from mouse and rat to human) and throughout the different regions of the small and large intestines. In this article, we construct a partial differential equation model of a single colonic crypt that describes the spatial distribution of Wnt pathway proteins along the crypt axis. The novelty of our continuum model is that it is based upon assumptions that can be directly related to processes at the cellular and subcellular scales. We use the model to predict how the distributions of Wnt pathway proteins are affected by mutations. The model is then extended to investigate how mutant cell populations can invade neighboring crypts. The model simulations suggest that cell crowding caused by increased proliferation and decreased cell loss may be sufficient for a mutant cell population to colonize a neighboring healthy crypt

Modeling the growth of multicellular cancer spheroids in a\ud bioengineered 3D microenvironment and their treatment with an\ud anti-cancer drug

A critical step in the dissemination of ovarian cancer cells is the formation of multicellular spheroids from cells shed from the primary tumor. The objectives of this study were to establish and validate bioengineered three-dimensional (3D) microenvironments for culturing ovarian cancer cells in vitro and simultaneously to develop computational models describing the growth of multicellular spheroids in these bioengineered matrices. Cancer cells derived from human epithelial ovarian carcinoma were embedded within biomimetic hydrogels of varying stiffness and cultured for up to 4 weeks. Immunohistochemistry was used to quantify the dependence of cell proliferation and apoptosis on matrix stiffness, long-term culture and treatment with the anti-cancer drug paclitaxel.\ud \ud Two computational models were developed. In the first model, each spheroid was treated as an incompressible porous medium, whereas in the second model the concept of morphoelasticity was used to incorporate details about internal stresses and strains. Each model was formulated as a free boundary problem. Functional forms for cell proliferation and apoptosis motivated by the experimental work were applied and the predictions of both models compared with the output from the experiments. Both models simulated how the growth of cancer spheroids was influenced by mechanical and biochemical stimuli including matrix stiffness, culture time and treatment with paclitaxel. Our mathematical models provide new perspectives on previous experimental results and have informed the design of new 3D studies of multicellular cancer spheroids

Four-terminal resistance of an interacting quantum wire with weakly invasive contacts

We analyze the behavior of the four-terminal resistance, relative to the two-terminal resistance of an interacting quantum wire with an impurity, taking into account the invasiveness of the voltage probes. We consider a one-dimensional Luttinger model of spinless fermions for the wire. We treat the coupling to the voltage probes perturbatively, within the framework of non-equilibrium Green function techniques. Our investigation unveils the combined effect of impurities, electron-electron interactions and invasiveness of the probes on the possible occurrence of negative resistance.Comment: 10 pages, 7 figure

Growth of confined cancer spheroids: a combined experimental and mathematical modelling approach

We have integrated a bioengineered three-dimensional platform by generating multicellular cancer spheroids in a controlled microenvironment with a mathematical model to investigate\ud confined tumour growth and to model its impact on cellular processes

The Evaluation of V_{ud}, Experiment and Theory

The value of the V_{ud} matrix element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix can be derived from nuclear superallowed beta decays, neutron decay, and pion beta decay. We survey current world data for all three. Today, the most precise value of V_{ud} comes from the nuclear decays; however, the precision is limited not by experimental error but by the estimated uncertainty in theoretical corrections. Experimental uncertainty does limit the neutron-decay result, which, though statistically consistent with the nuclear result, is approximately a factor of three poorer in precision. The value obtained for $V_{ud}$ leads to a result that differs at the 98% confidence level from the unitarity condition for the CKM matrix. We examine the reliability of the small calculated corrections that have been applied to the data, and assess the likelihood of even higher quality nuclear data becoming available to confirm or deny the discrepancy. Some of the required experiments depend upon the availability of intense radioactive beams. Others are possible today.Comment: 21 pages, 1 figure, LaTe

Initial/boundary-value problems of tumor growth within a host tissue

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly degenerate parabolic equations, which include phenomenological terms related to specific cell functions. The paper discusses general modeling guidelines for such terms, as well as for initial and boundary conditions, aiming at both biological consistency and mathematical robustness of the resulting problems. Particularly, it addresses some qualitative properties such as a priori nonnegativity, boundedness, and uniqueness of the solutions. Existence of the solutions is studied in the one-dimensional time-independent case.Comment: 30 pages, 5 figure