Filtrations on the knot contact homology of transverse knots

We construct a new invariant of transverse links in the standard contact structure on R^3. This invariant is a doubly filtered version of the knot contact homology differential graded algebra (DGA) of the link. Here the knot contact homology of a link in R^3 is the Legendrian contact homology DGA of its conormal lift into the unit cotangent bundle S^*R^3 of R^3, and the filtrations are constructed by counting intersections of the holomorphic disks of the DGA differential with two conormal lifts of the contact structure. We also present a combinatorial formula for the filtered DGA in terms of braid representatives of transverse links and apply it to show that the new invariant is independent of previously known invariants of transverse links.Comment: 23 pages, v2: minor corrections suggested by refere

A note on Reeb dynamics on the tight 3-sphere

We show that a nondegenerate tight contact form on the 3-sphere has exactly two simple closed Reeb orbits if and only if the differential in linearized contact homology vanishes. Moreover, in this case the Floquet multipliers and Conley-Zehnder indices of the two Reeb orbits agree with those of a suitable irrational ellipsoid in 4-space.Comment: 20 pages, no figure

Modelling Household Energy Access in India

Improving access to affordable modern energy is deemed to be a critical factor in improving living standards in the developing world. Particularly rural households in India are relying mostly on traditional biomass to satisfy their basic energy needs with adverse effects on human health through indoor air pollution, but also on land degradation and labor productivity. This study presents a new generic modeling approach with the aim to explore response strategies for energy poverty eradication for India. The modeling approach explores characteristics of fuel consumption of the poorest through explicit representation of the main determinants of urban and rural energy fuel choice, including the effect of income distributions and capital scarcity on energy use as well as traditionally more intangible factors such as "inconvenience costs" or private discount rates. The methodology is applied to explore how different policy mechanisms such as fuel subsidies and microfinancing can enhance the diffusion of clean and affordable energy in India. This draft summarizes preliminary initial results focusing on the attainable transition to clean and modern fuels. As a next step, a sensitivity analysis for the main uncertain parameters and an assessment of the number of households and their exposure is planned. Implications for life-expectancy will be assessed through collaboration with APD

The Minimal Length of a Lagrangian Cobordism between Legendrians

To investigate the rigidity and flexibility of Lagrangian cobordisms between Legendrian submanifolds, we investigate the minimal length of such a cobordism, which is a $1$-dimensional measurement of the non-cylindrical portion of the cobordism. Our primary tool is a set of real-valued capacities for a Legendrian submanifold, which are derived from a filtered version of Legendrian Contact Homology. Relationships between capacities of Legendrians at the ends of a Lagrangian cobordism yield lower bounds on the length of the cobordism. We apply the capacities to Lagrangian cobordisms realizing vertical dilations (which may be arbitrarily short) and contractions (whose lengths are bounded below). We also study the interaction between length and the linking of multiple cobordisms as well as the lengths of cobordisms derived from non-trivial loops of Legendrian isotopies.Comment: 33 pages, 9 figures. v2: Minor corrections in response to referee comments. More general statement in Proposition 3.3 and some reorganization at the end of Section

Revenue and risk of variable renewable electricity investment: The cannibalization effect under high market penetration

Wind and solar power depress market prices at times when they produce the most. This has been termed the ‘cannibalization effect’, and its magnitude has been established within the economic literature on current and future markets. Although it has a substantial impact on the revenue of VRE technologies, the cannibalization effect is neglected in the capital budgeting literature, including portfolio- and real options theory. In this paper, we present an analytical framework that explicitly models the correlation between VRE production and electricity price, based on the production costs of surrounding generation capacity. We derive closed-form expressions for the expected short-term and long-term revenue, the variance of the revenue and the timing of investments. The effect of including these system characteristics is illustrated with numerical examples, where we find the cannibalization effect to decrease projected profit relative to investment cost from 33% to between 13% and −40%, depending on the assumption for the future VRE capacity expansion rate. Using a real options framework, the investment threshold increases by between 13% and 67%, due to the inclusion of cannibalization

A Hardy inequality in twisted waveguides

We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page