Constraints on Supersymmetric Models of Hybrid Inflation

We point out that the inclusion of a string component contributing around 5% to the CMB power spectrum amplitude on large scales can increase the preferred value of the spectral index n_s of density fluctuations measured by CMB experiments. While this finding applies to any cosmological scenario involving strings, we consider in particular models of supersymmetric hybrid inflation, which predict n_s >= 0.98, in tension with the CMB data when strings are not included. Using MCMC analysis we constrain the parameter space allowed for F- and D-term inflation. For the F-term model, using minimal supergravity corrections, we find that \log\kappa= -2.34\pm 0.38 and M= (0.518\pm 0.059) * 10^16 GeV. The inclusion of non-minimal supergravity corrections can modify these values somewhat. In the corresponding analysis for D-term inflation, we find \log\kappa= -4.24\pm 0.19 and m_FI= (0.245\pm 0.031) * 10^16 GeV. Under the assumption that these models are correct, these results represent precision measurements of important parameters of a Grand Unified Theory. We consider the possible uncertainties in our measurements and additional constraints on the scenario from the stochastic background of gravitational waves produced by the strings. The best-fitting model predicts a B-mode polarization signal \approx 0.3 \mu K rms peaking at l \approx 1000. This is of comparable amplitude to the expected signal due to gravitational lensing of the adiabatic E-mode signal on these scales.Comment: 21 pages, 16 figure

A RANS modelling approach for predicting powering performance of ships in waves

In this paper, a modelling technique for simulating self-propelled ships in waves is presented. The flow is modelled using a RANS solver coupled with an actuator disk model for the propeller. The motion of the ship is taken into consideration in the definition of the actuator disk region as well as the advance ratio of the propeller. The RPM of the propeller is controlled using a PID-controller with constraints added on the maximum permissible RPM increase rate. Results are presented for a freely surging model in regular waves with different constraints put on the PID-controller. The described method shows promising results and allows for the studying of several factors relating to selfpropulsion. However, more validation data is needed to judge the accuracy of the mode

Szego coordinates, quadrature domains, and double quadrature domains

We define Szego coordinates on a finitely connected smoothly bounded planar domain which effect a holomorphic change of coordinates on the domain that can be as close to the identity as desired and which convert the domain to a quadrature domain with respect to boundary arc length. When these Szego coordinates coincide with Bergman coordinates, the result is a double quadrature domain with respect to both area and arc length. We enumerate a host of interesting and useful properties that such double quadrature domains possess, and we show that such domains are in fact dense in the realm of bounded finitely connected domains with smooth boundaries.Comment: 19 page

Maximizing Energy Efficiency in Multiple Access Channels by Exploiting Packet Dropping and Transmitter Buffering

Quality of service (QoS) for a network is characterized in terms of various parameters specifying packet delay and loss tolerance requirements for the application. The unpredictable nature of the wireless channel demands for application of certain mechanisms to meet the QoS requirements. Traditionally, medium access control (MAC) and network layers perform these tasks. However, these mechanisms do not take (fading) channel conditions into account. In this paper, we investigate the problem using cross layer techniques where information flow and joint optimization of higher and physical layer is permitted. We propose a scheduling scheme to optimize the energy consumption of a multiuser multi-access system such that QoS constraints in terms of packet loss are fulfilled while the system is able to maximize the advantages emerging from multiuser diversity. Specifically, this work focuses on modeling and analyzing the effects of packet buffering capabilities of the transmitter on the system energy for a packet loss tolerant application. We discuss low complexity schemes which show comparable performance to the proposed scheme. The numerical evaluation reveals useful insights about the coupling effects of different QoS parameters on the system energy consumption and validates our analytical results.Comment: in IEEE trans. Wireless communications, 201

Phase field modelling of surfactants in multi-phase flow

A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring thermodynamic consistency. By an asymptotic analysis the model can be related to a moving boundary problem in the sharp interface limit, which is derived from first principles. Results from numerical simulations support the theoretical findings. The main novelties are centred around the conditions in the triple junctions where three fluids meet. Specifically the case of local chemical equilibrium with respect to the surfactant is considered, which allows for interfacial surfactant flow through the triple junctions

Ring completion of rig categories

We offer a solution to the long-standing problem of group completing within the context of rig categories (also known as bimonoidal categories). Given a rig category R we construct a natural additive group completion R' that retains the multiplicative structure, hence has become a ring category. If we start with a commutative rig category R (also known as a symmetric bimonoidal category), the additive group completion R' will be a commutative ring category. In an accompanying paper we show how this can be used to prove the conjecture from [BDR] that the algebraic K-theory of the connective topological K-theory spectrum ku is equivalent to the algebraic K-theory of the rig category V of complex vector spaces.Comment: There was a mathematical error in arXiv:0706.0531v2: the map T in the purported proof of Lemma 3.7(2) is not well defined. Version 4 has been edited for notational consistenc