Periodic long-time behaviour for an approximate model of nematic polymers

We study the long-time behaviour of a nonlinear Fokker-Planck equation, which models the evolution of rigid polymers in a given flow, after a closure approximation. The aim of this work is twofold: first, we propose a microscopic derivation of the classical Doi closure, at the level of the kinetic equation ; second, we prove the convergence of the solution to the Fokker-Planck equation to periodic solutions in the long-time limit

Aggregation of Heterogeneous Beliefs and Asset Pricing: A Mean-Variance Analysis

The aim of this paper is to show, within the mean-variance framework, how the market belief can be constructed as the result of the aggregation of heterogeneous beliefs and how the market equilibrium prices of risky assets can thus be determined. The heterogeneous beliefs are defined in terms of not only the means but also variances and covariances. By constructing the mean and variance of the market belief, we analyze the impact of the heterogeneous beliefs on the market equilibrium asset pricing relation. In particular, we extend the standard CAPM under homogenous beliefs to the one under the heterogeneous beliefs.Mean variance analysis, heterogeneous beliefs, aggregation, asset pricing

Additively Manufactured RF Components, Packaging, Modules, and Flexible Modular Phased Arrays Enabling Widespread Massively Scalable mmWave/5G Applications

The 5G era is here and with it comes many challenges, particularily facing the high frequency mmWave adoption. This is because of the cost to implement such dense networks is much greater due to the high propagation losses of signals that range from 26 GHz to 40 GHz. Therefore there needs to be a way to utilize a method of fabrication that can change with the various environments that 5G will be deployed in, be it dense urban areas or suburban sprawl. In this research, the focus is on making these RF components utilized for 5G at low cost and modular with a focus on additive manufacturing. Since additive manufacturing is a rapid prototyping technique, the technology can be quickly adjusted and altered to meet certain specifications with negligible overhead. Several areas of research will be explored. Firstly, various RF passive components such as additively manufactured antennas and couplers with a combination hybrid inkjet and 3D printing will be discussed. Passive components are critical for evaluating the process of additive manufacturing for high frequency operation. Secondly, various structures will be evaluated specifically for packaging mmWave ICs, including interconnects, smart packaging and encapsulants for use in single or multichip modules. Thirdly, various antenna fabrication techniques will be explored which enables fully integrated ICs with antennas, called System on Antenna (SoA) which utilizes both inkjet and 3D printing to combine antennas and ICs into modules. These modules, can then be built into arrays in a modular fashion, allowing for large or smaller arrays to be assembled on the fly. Finally, a method of calibrating the arrays is introduced, utilizing inkjet printed sensors. This allows the sensor to actively detect bends and deformations in the array and restore optimal antenna array performance. Built for flexible phased arrays, the sensor is designed for implementation for ubiquitous use, meaning that its can be placed on any surface, which enables widespread use of 5G technologies.Ph.D

Mathematical analysis of a one-dimensional model for an aging fluid

We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and investigate the longtime behaviour of the solutions

Compressive Channel Estimation and Multi-user Detection in C-RAN

This paper considers the channel estimation (CE) and multi-user detection (MUD) problems in cloud radio access network (C-RAN). Assuming that active users are sparse in the network, we solve CE and MUD problems with compressed sensing (CS) technology to greatly reduce the long identification pilot overhead. A mixed L{2,1}-regularization functional for extended sparse group-sparsity recovery is proposed to exploit the inherently sparse property existing both in user activities and remote radio heads (RRHs) that active users are attached to. Empirical and theoretical guidelines are provided to help choosing tuning parameters which have critical effect on the performance of the penalty functional. To speed up the processing procedure, based on alternating direction method of multipliers and variable splitting strategy, an efficient algorithm is formulated which is guaranteed to be convergent. Numerical results are provided to illustrate the effectiveness of the proposed functional and efficient algorithm.Comment: 6 pages, 3 figure

Vector Bundle Extensions, Sheaf Cohomology, and the Heterotic Standard Model

Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the vector bundle, which yield the low energy spectrum, are computed using the Leray spectral sequence and fit the requirements of particle phenomenology. The physical properties of these vacua were discussed previously. In this paper, we systematically compute all relevant cohomology groups and explicitly prove the existence of the necessary vector bundle extensions. All mathematical details are explained in a pedagogical way, providing the technical framework for constructing heterotic standard model vacua.Comment: 62 pages, 2 figures, LaTeX. v2: references adde

A Standard Model from the E8 x E8 Heterotic Superstring

In a previous paper, we introduced a heterotic standard model and discussed its basic properties. This vacuum has the spectrum of the MSSM with one additional pair of Higgs-Higgs conjugate fields and a small number of uncharged moduli. In this paper, the requisite vector bundles are formulated; specifically, stable, holomorphic bundles with structure group SU(N) on smooth Calabi-Yau threefolds with Z_3 x Z_3 fundamental group. A method for computing bundle cohomology is presented and used to evaluate the cohomology groups of the standard model bundles. It is shown how to determine the Z_3 x Z_3 action on these groups. Finally, using an explicit method of "doublet-triplet splitting", the low-energy particle spectrum is computed.Comment: 23 pages. references and typos correcte

Detailed Diagnosis of Performance Anomalies in Sensornets

We address the problem of analysing performance anomalies in sensor networks. In this paper, we propose an approach that uses the local flash storage of the motes for logging system data, in combination with online statistical analysis. Our results show not only that this is a feasible method but that the overhead is significantly lower than that of communication-centric methods, and that interesting patterns can be revealed when calculating the correlation of large data sets of separate event types.GINSENGCONE