Modeling reaction-diffusion of molecules on surface and in volume spaces with the E-Cell System

The-Cell System is an advanced open-source simulation platform to model and analyze biochemical reaction networks. The present algorithm modules of the system assume that the reacting molecules are all homogeneously distributed in the reaction compartments, which is not the case in some cellular processes. The MinCDE system in Escherichia coli, for example, relies on intricately controlled reaction, diffusion and localization of Min proteins on the membrane and in the cytoplasm compartments to inhibit cell division at the poles of the rod-shaped cell. To model such processes, we have extended the E-Cell System to support reaction-diffusion and dynamic localization of molecules in volume and surface compartments. We evaluated our method by modeling the in vivo dynamics of MinD and MinE and comparing their simulated localization patterns to the observations in experiments and previous computational work. In both cases, our simulation results are in good agreement

Long wavelength iteration of Einstein's equations near a spacetime singularity

We clarify the links between a recently developped long wavelength iteration scheme of Einstein's equations, the Belinski Khalatnikov Lifchitz (BKL) general solution near a singularity and the antinewtonian scheme of Tomita's. We determine the regimes when the long wavelength or antinewtonian scheme is directly applicable and show how it can otherwise be implemented to yield the BKL oscillatory approach to a spacetime singularity. When directly applicable we obtain the generic solution of the scheme at first iteration (third order in the gradients) for matter a perfect fluid. Specializing to spherical symmetry for simplicity and to clarify gauge issues, we then show how the metric behaves near a singularity when gradient effects are taken into account.Comment: 35 pages, revtex, no figure

Second-order power spectra of CMB anisotropies due to primordial random perturbations in flat cosmological models

Second-order power spectra of Cosmic Microwave Background (CMB) anisotropies due to random primordial perturbations at the matter dominant stage are studied, based on the relativistic second-order theory of perturbations in flat cosmological models and on the second-order formula of CMB anisotropies derived by Mollerach and Matarrese. So far the second-order integrated Sachs-Wolfe effect has been analyzed using the three-point correlation or bispectrum. In this paper we derive the second-order term of power spectra given using the two-point correlation of temperature fluctuations. The second-order density perturbations are small, compared with the first-order ones. The second-order power spectra of CMB anisotropies, however, are not small at all, compared with the first-order power spectra, because at the early stage the first-order integrated Sachs-Wolfe effect is very small and the second-order integrated Sachs-Wolfe effect may be dominant over the first-order ones. So their characteristic behaviors may be measured through the future precise observation and bring useful informations on the structure and evolution of our universe in the future.Comment: 11 page

Spin-fluctuations in the quarter-filled Hubbard ring : significances to LiV2_2O4_4

Using the quantum Monte Carlo method, we investigate the spin dynamics of itinerant electrons in the one-dimensional Hubbard system. Based on the model calculation, we have studied the spin-fluctuations in the quarter-filled metallic Hubbard ring, which is aimed at the vanadium ring or chain defined along corner-sharing tetrahedra of LiV$_2$O$_4$, and found the dramatic changes of magnetic responses and spin-fluctuation characteristics with the temperature. Such results can explain the central findings in the recent neutron scattering experiment for LiV$_2$O$_4$.Comment: 5 pages, 3 figure

Some clarifications about Lema\^itre-Tolman models of the Universe used to deal with the dark energy problem

During the past fifteen years, inhomogeneous cosmological models have been put forward to explain the observed dimming of the SNIa luminosity without resorting to dark energy. The simplest models are the spherically symmetric Lema\^itre-Tolman (LT) solutions with a central observer. Their use must be considered as a mere first step towards more sophisticated models. Spherical symmetry is but a mathematical simplification and one must consider spherical symmetric models as exhibiting an energy density smoothed out over angles around us. However, they have been taken at face value by some authors who tried to use them for either irrelevant purposes or to put them to the test as if they were robust models of our Universe. We wish to clarify how these models must be used in cosmology. We first use the results obtained by Iguchi and collaborators to derive the density profiles of the pure growing and decaying mode LT models. We then discuss the relevance of the different test proposals in the light of the interpretation given above. We show that decaying-mode (parabolic) LT models always exhibit an overdensity near their centre and growing-mode (elliptic or hyperbolic) LT models, a void. This is at variance with some statements in the literature. We dismiss all previous proposals merely designed to test the spherical symmetry of the LT models, and we agree that the value of $H_0$ and the measurement of the redshift drift are valid tests of the models. However, we suspect that this last test, which is the best in principle, will be more complicated to implement than usually claimed.Comment: 18 pages, no figure, section 3 modified, results of section 3.2 changed, sections 4.3 and 4.4 added, other minor changes and references adde