Computing the Arithmetic Genus of Hilbert Modular Fourfolds

The Hilbert modular fourfold determined by the totally real quartic number field k is a desingularization of a natural compactification of the quotient space Gamma(k)\H-4, where Gamma(k) = PSL2(O-k) acts on H-4 by fractional linear transformations via the four embeddings of k into R. The arithmetic genus, equal to one plus the dimension of the space of Hilbert modular cusp forms of weight (2, 2, 2, 2), is a birational invariant useful in the classification of these varieties. In this work, we describe an algorithm allowing for the automated computation of the arithmetic genus and give sample results

Computing the Arithmetic Genus of Hilbert Modular Fourfolds

The Hilbert modular fourfold determined by the totally real quartic number field k is a desingularization of a natural compactification of the quotient space Gamma(k)\H-4, where Gamma(k) = PSL2(O-k) acts on H-4 by fractional linear transformations via the four embeddings of k into R. The arithmetic genus, equal to one plus the dimension of the space of Hilbert modular cusp forms of weight (2, 2, 2, 2), is a birational invariant useful in the classification of these varieties. In this work, we describe an algorithm allowing for the automated computation of the arithmetic genus and give sample results

Hybrid simulations of lateral diffusion in fluctuating membranes

In this paper we introduce a novel method to simulate lateral diffusion of inclusions in a fluctuating membrane. The regarded systems are governed by two dynamic processes: the height fluctuations of the membrane and the diffusion of the inclusion along the membrane. While membrane fluctuations can be expressed in terms of a dynamic equation which follows from the Helfrich Hamiltonian, the dynamics of the diffusing particle is described by a Langevin or Smoluchowski equation. In the latter equations, the curvature of the surface needs to be accounted for, which makes particle diffusion a function of membrane fluctuations. In our scheme these coupled dynamic equations, the membrane equation and the Langevin equation for the particle, are numerically integrated to simulate diffusion in a membrane. The simulations are used to study the ratio of the diffusion coefficient projected on a flat plane and the intramembrane diffusion coefficient for the case of free diffusion. We compare our results with recent analytical results that employ a preaveraging approximation and analyze the validity of this approximation. A detailed simulation study of the relevant correlation functions reveals a surprisingly large range where the approximation is applicable.Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev.

Curvature-coupling dependence of membrane protein diffusion coefficients

We consider the lateral diffusion of a protein interacting with the curvature of the membrane. The interaction energy is minimized if the particle is at a membrane position with a certain curvature that agrees with the spontaneous curvature of the particle. We employ stochastic simulations that take into account both the thermal fluctuations of the membrane and the diffusive behavior of the particle. In this study we neglect the influence of the particle on the membrane dynamics, thus the membrane dynamics agrees with that of a freely fluctuating membrane. Overall, we find that this curvature-coupling substantially enhances the diffusion coefficient. We compare the ratio of the projected or measured diffusion coefficient and the free intramembrane diffusion coefficient, which is a parameter of the simulations, with analytical results that rely on several approximations. We find that the simulations always lead to a somewhat smaller diffusion coefficient than our analytical approach. A detailed study of the correlations of the forces acting on the particle indicates that the diffusing inclusion tries to follow favorable positions on the membrane, such that forces along the trajectory are on average smaller than they would be for random particle positions.Comment: 16 pages, 8 figure

Study of nuclear recoils in liquid argon with monoenergetic neutrons

For the development of liquid argon dark matter detectors we assembled a setup in the laboratory to scatter neutrons on a small liquid argon target. The neutrons are produced mono-energetically (E_kin=2.45 MeV) by nuclear fusion in a deuterium plasma and are collimated onto a 3" liquid argon cell operating in single-phase mode (zero electric field). Organic liquid scintillators are used to tag scattered neutrons and to provide a time-of-flight measurement. The setup is designed to study light pulse shapes and scintillation yields from nuclear and electronic recoils as well as from {\alpha}-particles at working points relevant to dark matter searches. Liquid argon offers the possibility to scrutinise scintillation yields in noble liquids with respect to the populations of the two fundamental excimer states. Here we present experimental methods and first results from recent data towards such studies.Comment: 9 pages, 8 figures, proceedings of TAUP 2011, to be published in Journal of Physics: Conference Series (JCPS

The Zeta Herculis binary system revisited. Calibration and seismology

We have revisited the calibration of the visual binary system Zeta Herculis with the goal to give the seismological properties of the G0 IV sub-giant Zeta Her A. We have used the most recent physical and observational data. For the age we have obtained 3387 Myr, for the masses respectively 1.45 and 0.98 solar mass, for the initial helium mass fraction 0.243, for the initial mass ratio of heavy elements to hydrogen 0.0269 and for the mixing-length parameters respectively 0.92 and 0.90 using the Canuto & Mazitelli (1991, 1992) convection theory. Our results do not exclude that Zeta Her A is itself a binary sub-system; the mass of the hypothetical unseen companion would be smaller than 0.05 solar mass. The adiabatic oscillation spectrum of Zeta Her A is found to be a complicated superposition of acoustic and gravity modes; some of them have a dual character. This greatly complicates the classification of the non-radial modes. The echelle diagram used by the observers to extract the frequencies will work for ell=0, 2, 3. The large difference is found to be of the order of 42 mu Hz, in agreement with the Martic et al. (2001) seismic observations.Comment: 12 pages, A&A in pres

Observation of the Dependence of Scintillation from Nuclear Recoils in Liquid Argon on Drift Field

We have exposed a dual-phase Liquid Argon Time Projection Chamber (LAr-TPC) to a low energy pulsed narrowband neutron beam, produced at the Notre Dame Institute for Structure and Nuclear Astrophysics to study the scintillation light yield of recoiling nuclei in a LAr-TPC. A liquid scintillation counter was arranged to detect and identify neutrons scattered in the LAr-TPC target and to select the energy of the recoiling nuclei. We report the observation of a significant dependence on drift field of liquid argon scintillation from nuclear recoils of 11 keV. This observation is important because, to date, estimates of the sensitivity of noble liquid TPC dark matter searches are based on the assumption that electric field has only a small effect on the light yield from nuclear recoils.Comment: v3 updated to reflect published version, including a set of plots for 49.9 keV dat

Effective Viscosity of a Dilute Suspension of Membrane-bound Inclusions

When particulate suspensions are sheared, perturbations in the shear flows around the rigid particles increase the local energy dissipation, so that the viscosity of the suspension is effectively higher than that of the solvent. For bulk (three-dimensional) fluids, understanding this viscosity enhancement is a classic problem in hydrodynamics that originated over a century ago with Einstein's study of a dilute suspension of spherical particles. \cite{Einstein1} In this paper, we investigate the analogous problem of the effective viscosity of a suspension of disks embedded in a two-dimensional membrane or interface. Unlike the hydrodynamics of bulk fluids, low-Reynolds number membrane hydrodynamics is characterized by an inherent length scale generated by the coupling of the membrane to the bulk fluids that surround it. As a result, we find that the size of the particles in the suspension relative to this hydrodynamic length scale has a dramatic effect on the effective viscosity of the suspension. Our study also helps to elucidate the mathematical tools needed to solve the mixed boundary value problems that generically arise when considering the motion of rigid inclusions in fluid membranes.Comment: 33 pages, 4 figures (preprint); submitted to Physics of Fluid