Metabelian SL(n,C) representations of knot groups IV: twisted Alexander polynomials

In this paper we will study properties of twisted Alexander polynomials of knots corresponding to metabelian representations. In particular we answer a question of Wada about the twisted Alexander polynomial associated to the tensor product of two representations, and we settle several conjectures of Hirasawa and Murasugi

Tunable reflection minima of nanostructured antireflective surfaces

Broadband antireflection schemes for silicon surfaces based on the moth-eye principle and comprising arrays of subwavelength-scale pillars are applicable to solar cells, photodetectors, and stealth technologies and can exhibit very low reflectances. We show that rigorous coupled wave analysis can be used to accurately model the intricate reflectance behavior of these surfaces and so can be used to explore the effects of variations in pillar height, period, and shape. Low reflectance regions are identified, the extent of which are determined by the shape of the pillars. The wavelengths over which these low reflectance regions operate can be shifted by altering the period of the array. Thus the subtle features of the reflectance spectrum of a moth-eye array can be tailored for optimum performance for the input spectrum of a specific application

Temperature dependence of the charge carrier mobility in gated quasi-one-dimensional systems

The many-body Monte Carlo method is used to evaluate the frequency dependent conductivity and the average mobility of a system of hopping charges, electronic or ionic on a one-dimensional chain or channel of finite length. Two cases are considered: the chain is connected to electrodes and in the other case the chain is confined giving zero dc conduction. The concentration of charge is varied using a gate electrode. At low temperatures and with the presence of an injection barrier, the mobility is an oscillatory function of density. This is due to the phenomenon of charge density pinning. Mobility changes occur due to the co-operative pinning and unpinning of the distribution. At high temperatures, we find that the electron-electron interaction reduces the mobility monotonically with density, but perhaps not as much as one might intuitively expect because the path summation favour the in-phase contributions to the mobility, i.e. the sequential paths in which the carriers have to wait for the one in front to exit and so on. The carrier interactions produce a frequency dependent mobility which is of the same order as the change in the dc mobility with density, i.e. it is a comparably weak effect. However, when combined with an injection barrier or intrinsic disorder, the interactions reduce the free volume and amplify disorder by making it non-local and this can explain the too early onset of frequency dependence in the conductivity of some high mobility quasi-one-dimensional organic materials.Comment: 9 pages, 8 figures, to be published in Physical Review

The Alchemy of an Indeterminate Visual Matrix: Perception within Light and Shadows

The primary objective of this thesis paper is to articulate the concepts, context, methodology, and materials within my artistic practice. As a document this paper offers an overview of my past work as it progressed through to the work as developed for my thesis exhibition. My artistic practice has its roots in themes relating to the phenomenological aspects of photography, specifically emphasizing the psychological experience of light and shadows within visual perception. While the foundation of my work is rooted in traditional lens-based photography, my materials and processes of producing work have expanded to incorporate camera-less alternative processes such as the cyanotype and photogram along with painting, collage, and various other print-based techniques. Once printed, images are cut and then assembled into various forms of installation-based work. Visual patterns extracted through the printing of imagery and through the physical process of piecing images together are various ways in which I present my interpretation and expression of ideas

Strategies for successful field deployment in a resource-poor region: Arsenic remediation technology for drinking water

Strong long-term international partnership in science, technology, finance and policy is critical for sustainable field experiments leading to successful commercial deployment of novel technology at community-scale. Although technologies already exist that can remediate arsenic in groundwater, most are too expensive or too complicated to operate on a sustained basis in resource-poor communities with the low technical skill common in rural South Asia. To address this specific problem, researchers at University of California-Berkeley (UCB) and Lawrence Berkeley National Laboratory (LBNL) invented a technology in 2006 called electrochemical arsenic remediation (ECAR). Since 2010, researchers at UCB and LBNL have collaborated with Global Change Program of Jadavpur University (GCP-JU) in West Bengal, India for its social embedding alongside a local private industry group, and with financial support from the Indo-US Technology Forum (IUSSTF) over 2012–2017. During the first 10 months of pilot plant operation (April 2016 to January 2017) a total of 540 m3 (540,000 L) of arsenic-safe water was produced, consistently and reliably reducing arsenic concentrations from initial 252 ± 29 to final 2.9 ± 1 parts per billion (ppb). This paper presents the critical strategies in taking a technology from a lab in the USA to the field in India for commercialization to address the technical, socio-economic, and political aspects of the arsenic public health crisis while targeting several sustainable development goals (SDGs). The lessons learned highlight the significance of designing a technology contextually, bridging the knowledge divide, supporting local livelihoods, and complying with local regulations within a defined Critical Effort Zone period with financial support from an insightful funding source focused on maturing inventions and turning them into novel technologies for commercial scale-up. Along the way, building trust with the community through repetitive direct interactions, and communication by the scientists, proved vital for bridging the technology-society gap at a critical stage of technology deployment. The information presented here fills a knowledge gap regarding successful case studies in which the arsenic remediation technology obtains social acceptance and sustains technical performance over time, while operating with financial viability

The Gould's Belt distance survey

Very Long Baseline Interferometry (VLBI) observations can provide the position of compact radio sources with an accuracy of order 50 micro-arcseconds. This is sufficient to measure the trigonometric parallax and proper motions of any object within 500 pc of the Sun to better than a few percent. Because they are magnetically active, young stars are often associated with compact radio emission detectable using VLBI techniques. Here we will show how VLBI observations have already constrained the distance to the most often studied nearby regions of star-formation (Taurus, Ophiuchus, Orion, etc.) and have started to provide information on their internal structure and kinematics. We will then briefly describe a large project (called The Gould's Belt Distance Survey) designed to provide a detailed view of star-formation in the Solar neighborhood using VLBI observations.Comment: To be published in the Revista Mexicana de Astronomia y Astrofisica (Serie de Conferencias

Adequate links in thickened surfaces and the generalized Tait conjectures

The Kauffman bracket of classical links extends to an invariant of links in an arbitrary oriented 3-manifold $M$ with values in the skein module of $M$. In this paper, we consider the skein bracket in case $M$ is a thickened surface. We develop a theory of adequacy for link diagrams on surfaces and show that any alternating link diagram on a surface is skein adequate. We apply our theory to establish the first and second Tait conjectures for adequate link diagrams on surfaces. These are the statements that any adequate link diagram has minimal crossing number, and any two adequate diagrams of the same link have the same writhe. Given a link diagram $D$ on a surface $\Sigma$, we use $[D]_\Sigma$ to denote its skein bracket. If $D$ has minimal genus, we show that $${\rm span}([D]_\Sigma) \leq 4c(D) + 4 |D|-4g(\Sigma),$$ where $|D|$ is the number of connected components of $D$, $c(D)$ is the number of crossings, and $g(\Sigma)$ is the genus of $\Sigma.$ This extends a classical result proved by Kauffman, Murasugi, and Thistlethwaite. We further show that the above inequality is an equality if and only if $D$ is weakly alternating, namely if $D$ is the connected sum of an alternating link diagram on $\Sigma$ with one or more alternating link diagrams on $S^2$. This last statement is a generalization of a well-known result for classical links due to Thistlethwaite, and it implies that the skein bracket detects the crossing number for weakly alternating links. As an application, we show that the crossing number is additive under connected sum for adequate links in thickened surfaces.Comment: 24 pages, 13 figure