Non-local dispersal and bistability

The scalar initial value problem [ u_t = ho Du + f(u), ] is a model for dispersal. Here $u$ represents the density at point $x$ of a compact spatial region $Omega in mathbb{R}^n$ and time $t$, and $u(cdot)$ is a function of $t$ with values in some function space $B$. $D$ is a bounded linear operator and $f(u)$ is a bistable nonlinearity for the associated ODE $u_t = f(u)$. Problems of this type arise in mathematical ecology and materials science where the simple diffusion model with $D=Delta$ is not sufficiently general. The study of the dynamics of the equation presents a difficult problem which crucially differs from the diffusion case in that the semiflow generated is not compactifying. We study the asymptotic behaviour of solutions and ask under what conditions each positive semi-orbit converges to an equilibrium (as in the case $D=Delta$). We develop a technique for proving that indeed convergence does hold for small $ho$ and show by constructing a counter-example that this result does not hold in general for all $ho$

Non-local dispersal

We consider a model of spatial spread that has applications in both material science and biology. The classical models are based upon partial differential equations, in particular reaction-diffusion equations. Here the dispersal term is given in terms of an integral operator and we restrict ourselves to the scalar case

Instantons, supersymmetric vacua, and emergent geometries

We study instanton solutions and superpotentials for the large number of vacua of the plane-wave matrix model and a 2+1 dimensional Super Yang-Mills theory on $R\times S^2$ with sixteen supercharges. We get the superpotential in the weak coupling limit from the gauge theory description. We study the gravity description of these instantons. Perturbatively with respect to a background, they are Euclidean branes wrapping cycles in the dual gravity background. Moreover, the superpotential can be given by the energy of the electric charge system characterizing each vacuum. These charges are interpreted as the eigenvalues of matrices from a reduction for the 1/8 BPS sector of the gauge theories. We also discuss qualitatively the emergence of the extra spatial dimensions appeared on the gravity side.Comment: 29 pages, 3 figures, latex. v2: references added, comments added. v3: accepted version in PR

Interaction of surface acoustic waves with a two-dimensional electron gas in the presence of spin splitting of the Landau bands

The absorption and variation of the velocity of a surface acoustic wave of frequency $f$= 30 MHz interacting with two-dimensional electrons are investigated in GaAs/AlGaAs heterostructures with an electron density $n=(1.3 - 2.8) \times 10^{11} cm^{-2}$ at $T$=1.5 - 4.2 K in magnetic fields up to 7 T. Characteristic features associated with spin splitting of the Landau level are observed. The effective g factor and the width of the spin-split Landau bands are determined: $g^* \simeq 5$ and $A$=0.6 meV. The greater width of the orbital-split Landau bands (2 meV) relative to the spin-split bands is attributed to different shielding of the random fluctuation potential of charged impurities by 2D electrons. The mechanisms of the nonlinearities manifested in the dependence of the absorption and the velocity increment of the SAW on the SAW power in the presence of spin splitting of the Landau levels are investigated.Comment: Revtex 5 pages + 5 EPS Figures, v.2 - minor corrections in text and pic

Phonon-Coupled Electron Tunneling in Two and Three-Dimensional Tunneling Configurations

We treat a tunneling electron coupled to acoustical phonons through a realistic electron phonon interaction: deformation potential and piezoelectric, in two or three-dimensional tunneling configurations. Making use of slowness of the phonon system compared to electron tunneling, and using a Green function method for imaginary time, we are able to calculate the change in the transition probability due to the coupling to phonons. It is shown using standard renormalization procedure that, contrary to the one-dimensional case, second order perturbation theory is sufficient in order to treat the deformation potential coupling, which leads to a small correction to the transmission coefficient prefactor. In the case of piezoelectric coupling, which is found to be closely related to the piezoelectric polaron problem, vertex corrections need to be considered. Summing leading logarithmic terms, we show that the piezoelectric coupling leads to a significant change of the transmission coefficient.Comment: 17 pages, 4 figure

Intrauterine exposure to mild analgesics during pregnancy and the occurrence of cryptorchidism and hypospadia in the offspring: The Generation R Study

This article is available open access through the publisher’s website. Copyright @ 2012 The Authors.BACKGROUND - Recently, over-the-counter mild analgesic use during pregnancy has been suggested to influence the risk of reproductive disorders in the offspring. We examined the influence of maternal exposure to mild analgesics during pregnancy on the occurrence of cryptorchidism and hypospadia in their offspring. METHODS - Associations between maternal exposure to mild analgesics during pregnancy and cryptorchidism or hypospadia in the offspring were studied in 3184 women participating in a large population-based prospective birth cohort study from early pregnancy onwards in the Netherlands (2002–2006), the Generation R Study. Cryptorchidism and hypospadia were identified during routine screening assessments performed in child health care centres by trained physicians. The use of mild analgesics was assessed in three prenatal questionnaires in pregnancy, resulting in four periods of use, namely, periconception period, first 14 weeks of gestation, 14–22 weeks of gestation and 20–32 weeks of gestation. Logistic regression analyses were used to study the associations between maternal exposure to mild analgesics and cryptorchidism and hypospadia. RESULTS - The cumulative prevalence over 30 months of follow up was 2.1% for cryptorchidism and 0.7% for hypospadia. Use of mild analgesics in the second period of pregnancy (14–22 weeks) increased the risk of congenital cryptorchidism [adjusted odds ratio (OR) 2.12; 95% confidence interval (CI) 1.17–3.83], primarily due to the use of acetaminophen (paracetamol) (adjusted OR 1.89; 95% CI 1.01–3.51). Among mothers of cryptorchid sons, 33.8% reported (23 of 68) the use of mild analgesics during pregnancy, compared with 31.8% (7 of 22) of mothers with a boy with hypospadia and 29.9% (926 of 3094) of mothers with healthy boys. CONCLUSIONS - Our results suggest that intrauterine exposure to mild analgesics, primarily paracetamol, during the period in pregnancy when male sexual differentiation takes place, increases the risk of cryptorchidism.Erasmus University Rotterdam, School of Law and Faculty of Social Sciences, the Municipal Health Service Rotterdam area, Rotterdam, the Rotterdam Homecare Foundation, Rotterdam and the Stichting Trombosedienst & Artsenlaboratorium Rijnmond (STAR), Rotterdam