Maze solvers demystified and some other thoughts

There is a growing interest towards implementation of maze solving in spatially-extended physical, chemical and living systems. Several reports of prototypes attracted great publicity, e.g. maze solving with slime mould and epithelial cells, maze navigating droplets. We show that most prototypes utilise one of two phenomena: a shortest path in a maze is a path of the least resistance for fluid and current flow, and a shortest path is a path of the steepest gradient of chemoattractants. We discuss that substrates with so-called maze-solving capabilities simply trace flow currents or chemical diffusion gradients. We illustrate our thoughts with a model of flow and experiments with slime mould. The chapter ends with a discussion of experiments on maze solving with plant roots and leeches which show limitations of the chemical diffusion maze-solving approach.Comment: This is a preliminary version of the chapter to be published in Adamatzky A. (Ed.) Shortest path solvers. From software to wetware. Springer, 201

Breakdown of smoothness for the Muskat problem

In this paper we show that there exist analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down i.e. no longer belongs to $C^4$.Comment: 93 pages, 10 figures (6 added

Cavitation-induced force transition in confined viscous liquids under traction

We perform traction experiments on simple liquids highly confined between parallel plates. At small separation rates, we observe a simple response corresponding to a convergent Poiseuille flow. Dramatic changes in the force response occur at high separation rates, with the appearance of a force plateau followed by an abrupt drop. By direct observation in the course of the experiment, we show that cavitation accounts for these features which are reminiscent of the utmost complex behavior of adhesive films under traction. Surprisingly enough, this is observed here in purely viscous fluids.Comment: Submitted to Physical Review Letters on May 31, 2002. Related informations on http://www.crpp.u-bordeaux.fr/tack.htm

Particle dynamics of a cartoon dune

The spatio-temporal evolution of a downsized model for a desert dune is observed experimentally in a narrow water flow channel. A particle tracking method reveals that the migration speed of the model dune is one order of magnitude smaller than that of individual grains. In particular, the erosion rate consists of comparable contributions from creeping (low energy) and saltating (high energy) particles. The saltation flow rate is slightly larger, whereas the number of saltating particles is one order of magnitude lower than that of the creeping ones. The velocity field of the saltating particles is comparable to the velocity field of the driving fluid. It can be observed that the spatial profile of the shear stress reaches its maximum value upstream of the crest, while its minimum lies at the downstream foot of the dune. The particle tracking method reveals that the deposition of entrained particles occurs primarily in the region between these two extrema of the shear stress. Moreover, it is demonstrated that the initial triangular heap evolves to a steady state with constant mass, shape, velocity, and packing fraction after one turnover time has elapsed. Within that time the mean distance between particles initially in contact reaches a value of approximately one quarter of the dune basis length

Boltzmann-conserving classical dynamics in quantum time-correlation functions: "Matsubara dynamics".

We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or "classical Wigner approximation") results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their "Matsubara" values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of ħ(2) at ħ(0) (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting "Matsubara" dynamics is inherently classical (since all terms O(ħ(2)) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.T.J.H.H., M.J.W., and S.C.A. acknowledge funding from the U.K. Engineering and Physical Sciences Research Council. A.M. acknowledges the European Lifelong Learning Programme (LLP) for an Erasmus student placement scholarship. T.J.H.H. also acknowledges a Research Fellowship from Jesus College, Cambridge and helpful discussions with Dr. Adam Harper.This is the author accepted manuscript. The final version is available from AIP via http://dx.doi.org/10.1063/1.491631

Passivation of black silicon boron emitters with atomic layer deposited aluminum oxide

The nanostructured surface – also called black silicon (b-Si) – is a promising texture for solar cells because of its extremely low reflectance combined with low surface recombination obtained with atomic layer deposited (ALD) thin films. However, the challenges in keeping the excellent optical properties and passivation in further processing have not been addressed before. Here we study especially the applicability of the ALD passivation on highly boron doped emitters that is present in crystalline silicon solar cells. The results show that the nanostructured boron emitters can be passivated efficiently using ALD Al2O3 reaching emitter saturation current densities as low as 51 fA/cm2. Furthermore, reflectance values less than 0.5% after processing show that the different process steps are not detrimental for the low reflectance of b-Si.Peer reviewe

FLUID MAPPERS AS VISUAL ANALOGS FOR POTENTIAL FIELDS

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73340/1/j.1749-6632.1955.tb40080.x.pd

ExROPPP: Fast, accurate, and spin-pure calculation of the electronically excited states of organic hydrocarbon radicals

Recent years have seen an explosion of interest in organic radicals due to their promise for highly efficient organic light-emitting diodes and molecular qubits. However, accurately and inexpensively computing their electronic structure has been challenging, especially for excited states, due to the spin-contamination problem. Furthermore, while alternacy or "pseudoparity" rules have guided the interpretation and prediction of the excited states of closed-shell hydrocarbons since the 1950s, similar general rules for hydrocarbon radicals have not to our knowledge been found yet. In this article, we present solutions to both of these challenges. First, we combine the extended configuration interaction singles method with Pariser-Parr-Pople (PPP) theory to obtain a method that we call ExROPPP (Extended Restricted Open-shell PPP) theory. We find that ExROPPP computes spin-pure excited states of hydrocarbon radicals with comparable accuracy to experiment as high-level general multi-configurational quasi-degenerate perturbation theory calculations but at a computational cost that is at least two orders of magnitude lower. We then use ExROPPP to derive widely applicable rules for the spectra of alternant hydrocarbon radicals, which are completely consistent with our computed results. These findings pave the way for highly accurate and efficient computation and prediction of the excited states of organic radicals

ExROPPP: Fast, Accurate and Spin-Pure Calculation of the Electronically Excited States of Organic Hydrocarbon Radicals

Recent years have seen an explosion of interest in organic radicals due to their promise for highly efficient organic light-emitting diodes (OLEDs) and molecular qubits. However, accurately and inexpensively computing their electronic structure has been challenging, especially for excited states, due to the spin-contamination problem. Furthermore, while alternacy or `pseudoparity' rules have guided the interpretation and prediction of the excited states of closed-shell hydrocarbons since the 1950s, similarly general rules for hydrocarbon radicals have not to our knowledge yet been found. In this article we present solutions to both of these challenges. We firstly combine the extended configuration interaction singles (XCIS) method with Pariser-Parr-Pople (PPP) theory to obtain a method which we call ExROPPP (Extended Restricted Open-shell PPP theory). We find that ExROPPP computes spin-pure excited states of hydrocarbon radicals with comparable accuracy to experiment as high-level GMC-QDPT calculations but at a computational cost that is at least two orders of magnitude lower. We then use ExROPPP to derive widely-applicable rules for the spectra of alternant hydrocarbon radicals which are completely consistent with our computed results. These findings pave the way for the highly accurate and efficient computation and prediction of the excited states of organic radicals.Comment: 39 page