Convergence to equilibrium for the discrete coagulation-fragmentation equations with detailed balance

Under the condition of detailed balance and some additional restrictions on the size of the coefficients, we identify the equilibrium distribution to which solutions of the discrete coagulation-fragmentation system of equations converge for large times, thus showing that there is a critical mass which marks a change in the behavior of the solutions. This was previously known only for particular cases as the generalized Becker-D\"oring equations. Our proof is based on an inequality between the entropy and the entropy production which also gives some information on the rate of convergence to equilibrium for solutions under the critical mass.Comment: 28 page

Primordial black holes in braneworld cosmologies: Formation, cosmological evolution and evaporation

We consider the population evolution and evaporation of primordial black holes in the simplest braneworld cosmology, Randall-Sundrum type II. We demonstrate that black holes forming during the high-energy phase of this theory (where the expansion rate is proportional to the density) have a modified evaporation law, resulting in a longer lifetime and lower temperature at evaporation, while those forming in the standard regime behave essentially as in the standard cosmology. For sufficiently large values of the AdS radius, the high-energy regime can be the one relevant for primordial black holes evaporating at key epochs such as nucleosynthesis and the present. We examine the formation epochs of such black holes, and delimit the parameter regimes where the standard scenario is significantly modified.Comment: 9 pages RevTeX4 file with four figures incorporated, minor changes to match published versio

Bounds from Primordial Black Holes with a Near Critical Collapse Initial Mass Function

Recent numerical evidence suggests that a mass spectrum of primordial black holes (PBHs) is produced as a consequence of near critical gravitational collapse. Assuming that these holes formed from the initial density perturbations seeded by inflation, we calculate model independent upper bounds on the mass variance at the reheating temperature by requiring the mass density not exceed the critical density and the photon emission not exceed current diffuse gamma-ray measurements. We then translate these results into bounds on the spectral index n by utilizing the COBE data to normalize the mass variance at large scales, assuming a constant power law, then scaling this result to the reheating temperature. We find that our bounds on n differ substantially (\delta n > 0.05) from those calculated using initial mass functions derived under the assumption that the black hole mass is proportional to the horizon mass at the collapse epoch. We also find a change in the shape of the diffuse gamma-ray spectrum which results from the Hawking radiation. Finally, we study the impact of a nonzero cosmological constant and find that the bounds on n are strengthened considerably if the universe is indeed vacuum-energy dominated today.Comment: 24 pages, REVTeX, 5 figures; minor typos fixed, two refs added, version to be published in PR

Organoids and bioengineered intestinal models: Potential solutions to the Cryptosporidium culturing dilemma

Cryptosporidium is a major cause of severe diarrhea-related disease in children in developing countries, but currently no vaccine or effective treatment exists for those who are most at risk of serious illness. This is partly due to the lack of in vitro culturing methods that are able to support the entire Cryptosporidium life cycle, which has led to research in Cryptosporidium biology lagging behind other protozoan parasites. In vivo models such as gnotobiotic piglets are complex, and standard in vitro culturing methods in transformed cell lines, such as HCT-8 cells, have not been able to fully support fertilization occurring in vitro. Additionally, the Cryptosporidium life cycle has also been reported to occur in the absence of host cells. Recently developed bioengineered intestinal models, however, have shown more promising results and are able to reproduce a whole cycle of infectivity in one model system. This review evaluates the recent advances in Cryptosporidium culturing techniques and proposes future directions for research that may build upon these successes

Stability of Attractive Bose-Einstein Condensates in a Periodic Potential

Using a standing light wave trap, a stable quasi-one-dimensional attractive dilute-gas Bose-Einstein condensate can be realized. In a mean-field approximation, this phenomenon is modeled by the cubic nonlinear Schr\"odinger equation with attractive nonlinearity and an elliptic function potential of which a standing light wave is a special case. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger equation. Their stability is examined using analytic and numerical methods. Trivial-phase solutions are experimentally stable provided they have nodes and their density is localized in the troughs of the potential. Stable time-periodic solutions are also examined.Comment: 12 pages, 18 figure

Vav Proteins in Development of the Brain: A Potential Relationship to the Pathogenesis of Congenital Zika Syndrome?

Zika virus (ZIKV) infection during pregnancy can result in a significant impact on the brain and eye of the developing fetus, termed congenital zika syndrome (CZS). At a morphological level, the main serious presentations of CZS are microcephaly and retinal scarring. At a cellular level, many cell types of the brain may be involved, but primarily neuronal progenitor cells (NPC) and developing neurons. Vav proteins have guanine exchange activity in converting GDP to GTP on proteins such as Rac1, Cdc42 and RhoA to stimulate intracellular signaling pathways. These signaling pathways are known to play important roles in maintaining the polarity and self-renewal of NPC pools by coordinating the formation of adherens junctions with cytoskeletal rearrangements. In developing neurons, these same pathways are adopted to control the formation and growth of neurites and mediate axonal guidance and targeting in the brain and retina. This review describes the role of Vavs in these processes and highlights the points of potential ZIKV interaction, such as (i) the binding and entry of ZIKV in cells via TAM receptors, which may activate Vav/Rac/RhoA signaling; (ii) the functional convergence of ZIKV NS2A with Vav in modulating adherens junctions; (iii) ZIKV NS4A/4B protein effects on PI3K/AKT in a regulatory loop via PPI3 to influence Vav/Rac1 signaling in neurite outgrowth; and (iv) the induction of SOCS1 and USP9X following ZIKV infection to regulate Vav protein degradation or activation, respectively, and impact Vav/Rac/RhoA signaling in NPC and neurons. Experiments to define these interactions will further our understanding of the molecular basis of CZS and potentially other developmental disorders stemming from in utero infections. Additionally, Vav/Rac/RhoA signaling pathways may present tractable targets for therapeutic intervention or molecular rationale for disease severity in CZS.Aidan J. Norbury, Lachlan A. Jolly, Luke P. Kris, and Jillian M. Car

Superconductivity and Charge Density Wave in a Quasi-One-Dimensional Spin Gap System

We consider a model of spin-gapped chains weakly coupled by Josephson and Coulomb interactions. Combining such non-perturbative methods as bosonization and Bethe ansatz to treat the intra-chain interactions with the Random Phase Approximation for the inter-chain couplings and the first corrections to this, we investigate the phase diagram of this model. The phase diagram shows both charge density wave ordering and superconductivity. These phases are seperated by a line of critical points which exhibits an approximate an SU(2) symmetry. We consider the effects of a magnetic field on the system. We apply the theory to the material Sr_2 Ca_12 Cu_24 O_41 and suggest further experiments.Comment: 14 pages, 7 figure; submitted to PRB; Revised with new version: references added; section on the flux state remove

Comparison between chiral and meson-theoretic nucleon-nucleon potentials through (p,p') reactions

We use proton-nucleus reaction data at intermediate energies to test the emerging new generation of chiral nucleon-nucleon (NN) potentials. Predictions from a high quality one-boson-exchange (OBE) force are used for comparison and evaluation. Both the chiral and OBE models fit NN phase shifts accurately, and the differences between the two forces for proton-induced reactions are small. A comparison to a chiral model with a less accurate NN description sets the scale for the ability of such models to work for nuclear reactions.Comment: 6 pages, revtex, 4 eps-figure

Stationary solutions of the one-dimensional nonlinear Schroedinger equation: I. Case of repulsive nonlinearity

All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the attractive case. Our solutions take the form of stationary trains of dark or grey density-notch solitons. Real stationary states are in one-to-one correspondence with those of the linear Schr\"odinger equation. Complex stationary states are uniquely nonlinear, nodeless, and symmetry-breaking. Our solutions apply to many physical contexts, including the Bose-Einstein condensate and optical pulses in fibers.Comment: 11 pages, 7 figures -- revised versio

Size-structured populations: immigration, (bi)stability and the net growth rate

We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the linearised system is governed by a quasicontraction semigroup. We also establish that linear stability of equilibrium solutions is governed by a generalized net reproduction function. In a special case of the model ingredients we discuss the nonlinear dynamics of the system when the spectral bound of the linearised operator equals zero, i.e. when linearisation does not decide stability. This allows us to demonstrate, through a concrete example, how immigration might be beneficial to the population. In particular, we show that from a nonlinearly unstable positive equilibrium a linearly stable and unstable pair of equilibria bifurcates. In fact, the linearised system exhibits bistability, for a certain range of values of the external inflow, induced potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin