Analysis of Compatible Discrete Operator Schemes for the Stokes Equations on Polyhedral Meshes

Compatible Discrete Operator schemes preserve basic properties of the continuous model at the discrete level. They combine discrete differential operators that discretize exactly topological laws and discrete Hodge operators that approximate constitutive relations. We devise and analyze two families of such schemes for the Stokes equations in curl formulation, with the pressure degrees of freedom located at either mesh vertices or cells. The schemes ensure local mass and momentum conservation. We prove discrete stability by establishing novel discrete Poincar\'e inequalities. Using commutators related to the consistency error, we derive error estimates with first-order convergence rates for smooth solutions. We analyze two strategies for discretizing the external load, so as to deliver tight error estimates when the external load has a large irrotational or divergence-free part. Finally, numerical results are presented on three-dimensional polyhedral meshes

Anomalous fluctuation regimes at the FFLO transition

Recently some experimental evidences have been obtained in favour of the existence of the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state in heavy-fermion superconductor CeCoIn_{5} and organic superconductor -(BETS)_{2}FeCl_{4}. However the unambiguous identification of FFLO state remains very difficult. We present the theoretical studies of the Gaussian fluctuations near the tricritical point (where the FFLO modulation appears) and demonstrate that the behavior of the fluctuational specific heat, paraconductivity and diamagnetism is qualitatively different from the usual superconducting transition. Special values of the critical exponent and the crossovers between different fluctuational regimes may provide a unique test for the FFLO state appearance.Comment: 6 pages, 2 figures. Work supported by ANR Extreme Conditions Correlated Electrons (ANR-06-BLAN-0220

Erasure Codes with a Banded Structure for Hybrid Iterative-ML Decoding

This paper presents new FEC codes for the erasure channel, LDPC-Band, that have been designed so as to optimize a hybrid iterative-Maximum Likelihood (ML) decoding. Indeed, these codes feature simultaneously a sparse parity check matrix, which allows an efficient use of iterative LDPC decoding, and a generator matrix with a band structure, which allows fast ML decoding on the erasure channel. The combination of these two decoding algorithms leads to erasure codes achieving a very good trade-off between complexity and erasure correction capability.Comment: 5 page

How do Clusters/Pipelines and Core/Periphery Structures Work Together in Knowledge Processes?

This paper contributes to the empirical identification of geographical and structural properties of innovative networks, focusing on the particular case of Global Navigation Satellite Systems (GNSS) at the European level. We show that knowledge bases of organizations and knowledge phases of the innovation process are the critical factors in determining the nature of the interplay between structural and geographical features of knowledge networks. Developing a database of R&D collaborative projects of the 5th and 6th European Framework Programs, we propose a methodology based on social network analysis. Its originality consists in starting from a bimodal network, in order to deduce two affiliation matrixes that allow us to study both the properties of the organization network and the properties of the project network. The results are discussed in the light of the mutual influence of the cognitive, structural and geographical dimensions on knowledge production and diffusion, and in the light of the knowledge drivers that give rise to the coexistence of a relational core-periphery structure with a geographical cluster and pipeline structure.Economic Geography, Knowledge networks, Social network analysis, EU Framework Programs, GNSS

Enhanced Recursive Reed-Muller Erasure Decoding

Recent work have shown that Reed-Muller (RM) codes achieve the erasure channel capacity. However, this performance is obtained with maximum-likelihood decoding which can be costly for practical applications. In this paper, we propose an encoding/decoding scheme for Reed-Muller codes on the packet erasure channel based on Plotkin construction. We present several improvements over the generic decoding. They allow, for a light cost, to compete with maximum-likelihood decoding performance, especially on high-rate codes, while significantly outperforming it in terms of speed

MSE lower bounds for deterministic parameter estimation

This paper presents a simple approach for deriving computable lower bounds on the MSE of deterministic parameter estimators with a clear interpretation of the bounds. We also address the issue of lower bounds tightness in comparison with the MSE of ML estimators and their ability to predict the SNR threshold region. Last, as many practical estimation problems must be regarded as joint detection-estimation problems, we remind that the estimation performance must be conditional on detection performance

Detection and manipulation of Majorana fermions in circuit QED

Motivated by recent experimental progress towards the measurement and manipulation of Majorana fermions with superconducting circuits, we propose a device interfacing Majorana fermions with circuit quantum electrodynamics. The proposed circuit acts as a charge parity detector changing the resonance frequency of a superconducting lambda/4 resonator conditioned on the parity of charges on nearby gates. Operating at both charge and flux sweet spots, this device is highly insensitive to environmental noise. It enables high-fidelity single-shot quantum nondemolition readout of the state of a pair of Majorana fermions encoding a topologically protected qubit. Additionally, the interaction permits the realization of an arbitrary phase gate on the topological qubit, closing the loop for computational completeness. Away from the charge sweet spot, this device can be used as a highly sensitive charge detector with a sensitivity better than 10(-4) e/root Hz and bandwidth larger than 1 MHz

Modeling and experimental investigation of transverse mode dynamics in VECSEL

We present a new method to simulate the formation of transverse modes in VECSELs. An expression for the gain as a function of carrier density and temperature is derived from a simulation of the structure reflectivity, while the field propagation in the cavity is computed with the Huygens-Fresnel integral. A rate equation model is employed to calculate the field and gain dynamics over numerous round-trips. The optimal mode size for single mode operation for a given pump shape is calculated and compared to experimental results. The effect of pump geometry, thermal lensing and structure design will be discussed.Air Force Office of Scientific Research [FA9550-17-1-0246]This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Dual-drive LiNbO_3 interferometric Mach-Zehnder architecture with extended linear regime for high peak-to-average OFDM-based communication systems

A dual-drive LiNbO3 architecture modulator with chirp management is proposed and developed offering SFDR > 25 dB in a 1.4 V bias excursion compared to only 0.5 V bias excursion in a conventional Mach-Zehnder electro-optical modulator (MZ-EOM). The architecture effectively extends the linear regime and enables the optical transmission of wireless systems employing orthogonal division multiplexing (OFDM) modulation such as ultra-wide band (UWB) which require high linearity over a broad frequency range due to their high peak-to-average power ratio (PARP). Radio-over-fiber UWB transmission in a passive optical network is experimentally demonstrated employing this technique, exhibiting an enhancement of 2.2 dB in EVM after 57 km SSMF when the dual-drive developed modulator is employed. © 2011 Optical Society of America