A perspective on using experiment and theory to identify design principles in dye-sensitized solar cells

Dye-sensitized solar cells (DSCs) have been the subject of wide-ranging studies for many years because of their potential for large-scale manufacturing using roll-to-roll processing allied to their use of earth abundant raw materials. Two main challenges exist for DSC devices to achieve this goal; uplifting device efficiency from the 12 to 14% currently achieved for laboratory-scale ‘hero’ cells and replacement of the widely-used liquid electrolytes which can limit device lifetimes. To increase device efficiency requires optimized dye injection and regeneration, most likely from multiple dyes while replacement of liquid electrolytes requires solid charge transporters (most likely hole transport materials – HTMs). While theoretical and experimental work have both been widely applied to different aspects of DSC research, these approaches are most effective when working in tandem. In this context, this perspective paper considers the key parameters which influence electron transfer processes in DSC devices using one or more dye molecules and how modelling and experimental approaches can work together to optimize electron injection and dye regeneration. This paper provides a perspective that theory and experiment are best used in tandem to study DSC device

Discrete Information from CHL Black Holes

AdS_2/CFT_1 correspondence predicts that the logarithm of a Z_N twisted index over states carrying a fixed set of charges grows as 1/N times the entropy of the black hole carrying the same set of charges. In this paper we verify this explicitly by calculating the microscopic Z_N twisted index for a class of states in the CHL models. This demonstrates that black holes carry more information about the microstates than just the total degeneracy.Comment: LaTeX file, 24 pages; v2: references adde

Crossings, Motzkin paths and Moments

Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain $q$-analogues of Laguerre and Charlier polynomials. The moments of these orthogonal polynomials have combinatorial models in terms of crossings in permutations and set partitions. The aim of this article is to prove simple formulas for the moments of the $q$-Laguerre and the $q$-Charlier polynomials, in the style of the Touchard-Riordan formula (which gives the moments of some $q$-Hermite polynomials, and also the distribution of crossings in matchings). Our method mainly consists in the enumeration of weighted Motzkin paths, which are naturally associated with the moments. Some steps are bijective, in particular we describe a decomposition of paths which generalises a previous construction of Penaud for the case of the Touchard-Riordan formula. There are also some non-bijective steps using basic hypergeometric series, and continued fractions or, alternatively, functional equations.Comment: 21 page

A Twist in the Dyon Partition Function

In four dimensional string theories with N=4 and N=8 supersymmetries one can often define twisted index in a subspace of the moduli space which captures additional information on the partition function than the ones contained in the usual helicity trace index. We compute several such indices in type IIB string theory on K3 x T^2 and T^6, and find that they share many properties with the usual helicity trace index that captures the spectrum of quarter BPS states in N=4 supersymmetric string theories. In particular the partition function is a modular form of a subgroup of Sp(2,Z) and the jumps across the walls of marginal stability are controlled by the residues at the poles of the partition function. However for large charges the logarithm of this index grows as 1/n times the entropy of a black hole carrying the same charges where n is the order of the symmetry generator that is used to define the twisted index. We provide a macroscopic explanation of this phenomenon using quantum entropy function formalism. The leading saddle point corresponding to the attractor geometry fails to contribute to the twisted index, but a Z_n orbifold of the attractor geometry produces the desired contribution.Comment: LaTeX file, 35 pages; v2: references adde

Borcherds Algebras and N=4 Topological Amplitudes

The perturbative spectrum of BPS-states in the E_8 x E_8 heterotic string theory compactified on T^2 is analysed. We show that the space of BPS-states forms a representation of a certain Borcherds algebra G which we construct explicitly using an auxiliary conformal field theory. The denominator formula of an extension G_{ext} \supset G of this algebra is then found to appear in a certain heterotic one-loop N=4 topological string amplitude. Our construction thus gives an N=4 realisation of the idea envisioned by Harvey and Moore, namely that the `algebra of BPS-states' controls the threshold corrections in the heterotic string.Comment: 39 page

Urban Biodiversity and Landscape Ecology: Patterns, Processes and Planning

Effective planning for biodiversity in cities and towns is increasingly important as urban areas and their human populations grow, both to achieve conservation goals and because ecological communities support services on which humans depend. Landscape ecology provides important frameworks for understanding and conserving urban biodiversity both within cities and considering whole cities in their regional context, and has played an important role in the development of a substantial and expanding body of knowledge about urban landscapes and communities. Characteristics of the whole city including size, overall amount of green space, age and regional context are important considerations for understanding and planning for biotic assemblages at the scale of entire cities, but have received relatively little research attention. Studies of biodiversity within cities are more abundant and show that longstanding principles regarding how patch size, configuration and composition influence biodiversity apply to urban areas as they do in other habitats. However, the fine spatial scales at which urban areas are fragmented and the altered temporal dynamics compared to non-urban areas indicate a need to apply hierarchical multi-scalar landscape ecology models to urban environments. Transferring results from landscape-scale urban biodiversity research into planning remains challenging, not least because of the requirements for urban green space to provide multiple functions. An increasing array of tools is available to meet this challenge and increasingly requires ecologists to work with planners to address biodiversity challenges. Biodiversity conservation and enhancement is just one strand in urban planning, but is increasingly important in a rapidly urbanising world

Remote detection of invasive alien species

The spread of invasive alien species (IAS) is recognized as the most severe threat to biodiversity outside of climate change and anthropogenic habitat destruction. IAS negatively impact ecosystems, local economies, and residents. They are especially problematic because once established, they give rise to positive feedbacks, increasing the likelihood of further invasions and spread. The integration of remote sensing (RS) to the study of invasion, in addition to contributing to our understanding of invasion processes and impacts to biodiversity, has enabled managers to monitor invasions and predict the spread of IAS, thus supporting biodiversity conservation and management action. This chapter focuses on RS capabilities to detect and monitor invasive plant species across terrestrial, riparian, aquatic, and human-modified ecosystems. All of these environments have unique species assemblages and their own optimal methodology for effective detection and mapping, which we discuss in detail