Efficient photosynthesis of carbon monoxide from CO2 using perovskite photovoltaics

Artificial photosynthesis, mimicking nature in its efforts to store solar energy, has received considerable attention from the research community. Most of these attempts target the production of H2 as a fuel and our group recently demonstrated solar-to-hydrogen conversion at 12.3% efficiency. Here, in an effort to take this approach closer to real photosynthesis, which is based on the conversion of CO2, we demonstrate the efficient reduction of CO2 to carbon monoxide driven solely by simulated sunlight using water as the electron source. Employing series-connected perovskite photovoltaics and high-performance catalyst electrodes, we reach a solar-to-CO efficiency exceeding 6.5%, which represents a new benchmark in sunlight-driven CO2 conversion. Considering hydrogen as a secondary product, an efficiency exceeding 7% is observed. Furthermore, this study represents one of the first demonstrations of extended, stable operation of perovskite photovoltaics, whose large open-circuit voltage is shown to be particularly suited for this process

How to Test for Diagonalizability: The Discretized PT-Invariant Square-Well Potential

Given a non-hermitean matrix M, the structure of its minimal polynomial encodes whether M is diagonalizable or not. This note will explain how to determine the minimal polynomial of a matrix without going through its characteristic polynomial. The approach is applied to a quantum mechanical particle moving in a square well under the influence of a piece-wise constant PT-symmetric potential. Upon discretizing the configuration space, the system is decribed by a matrix of dimension three. It turns out not to be diagonalizable for a critical strength of the interaction, also indicated by the transition of two real into a pair of complex energy eigenvalues. The systems develops a three-fold degenerate eigenvalue, and two of the three eigenfunctions disappear at this exceptional point, giving a difference between the algebraic and geometric multiplicity of the eigenvalue equal to two.Comment: 5 page

Fatou flowers and parabolic curves

In this survey we collect the main results known up to now (July 2015) regarding possible generalizations to several complex variables of the classical Leau-Fatou flower theorem about holomorphic parabolic dynamics

Abstract basins of attraction

Abstract basins appear naturally in different areas of several complex variables. In this survey we want to describe three different topics in which they play an important role, leading to interesting open problems

Penetration depth for shallow impact cratering

We present data for the penetration of a variety of spheres, dropped from rest, into a level non-cohesive granular medium. We improve upon our earlier work [Uehara {\it et al.} Phys. Rev. Lett. {\bf 90}, 194301 (2003)] in three regards. First, we explore the behavior vs sphere diameter and density more systematically, by holding one of these parameters constant while varying the other. Second, we prepare the granular medium more reproducibly and, third, we measure the penetration depth more accurately. The new data support our previous conclusion that the penetration depth is proportional to the 1/2 power of sphere density, the 2/3 power of sphere diameter, and the 1/3 power of total drop distance

On hyperbolicity of SU(2)-equivariant, punctured disc bundles over the complex affine quadric

Given a holomorphic line bundle over the complex affine quadric $Q^2$, we investigate its Stein, SU(2)-equivariant disc bundles. Up to equivariant biholomorphism, these are all contained in a maximal one, say $\Omega_{max}$. By removing the zero section to $\Omega_{max}$ one obtains the unique Stein, SU(2)-equivariant, punctured disc bundle over $Q^2$ which contains entire curves. All other such punctured disc bundles are shown to be Kobayashi hyperbolic.Comment: 15 pages, v2: minor changes, to appear in Transformation Group

Statistical characterization of the forces on spheres in an upflow of air

The dynamics of a sphere fluidized in a nearly-levitating upflow of air were previously found to be identical to those of a Brownian particle in a two-dimensional harmonic trap, consistent with a Langevin equation [Ojha {\it et al.}, Nature {\bf 427}, 521 (2004)]. The random forcing, the drag, and the trapping potential represent different aspects of the interaction of the sphere with the air flow. In this paper we vary the experimental conditions for a single sphere, and report on how the force terms in the Langevin equation scale with air flow speed, sphere radius, sphere density, and system size. We also report on the effective interaction potential between two spheres in an upflow of air.Comment: 7 pages, experimen

Experimental Biological Protocols with Formal Semantics

Both experimental and computational biology is becoming increasingly automated. Laboratory experiments are now performed automatically on high-throughput machinery, while computational models are synthesized or inferred automatically from data. However, integration between automated tasks in the process of biological discovery is still lacking, largely due to incompatible or missing formal representations. While theories are expressed formally as computational models, existing languages for encoding and automating experimental protocols often lack formal semantics. This makes it challenging to extract novel understanding by identifying when theory and experimental evidence disagree due to errors in the models or the protocols used to validate them. To address this, we formalize the syntax of a core protocol language, which provides a unified description for the models of biochemical systems being experimented on, together with the discrete events representing the liquid-handling steps of biological protocols. We present both a deterministic and a stochastic semantics to this language, both defined in terms of hybrid processes. In particular, the stochastic semantics captures uncertainties in equipment tolerances, making it a suitable tool for both experimental and computational biologists. We illustrate how the proposed protocol language can be used for automated verification and synthesis of laboratory experiments on case studies from the fields of chemistry and molecular programming