Heat kernels and regularity for rough metrics on smooth manifolds

We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Hölder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.     

High Charge Mobility of a Perylene Bisimide Dye with Hydrogen-bond Formation Group

Charge carrier mobility is one of the most important parameters concerning the performance of organic electronic devices1.High mobility usually leads to high calculation speed in computer and high short-circuit current in organic solar cells.Unfortunately,the intrinsic charge mobilities for organic semiconductors are of orders of magnitude lower than amorphous silicon.As a promising n-type organic semiconductor,N,N′-n-alkyl-perylene bisimides have shown their electron mobility to be up to10-…     

Statistical modeling and comparison with experimental data of tire–soil interaction for combined longitudinal and lateral slip

The interaction of a tire with a soft terrain has multiple sources of uncertainties such as the mechanical properties of the terrain, and the interfacial properties between the tire and the terrain. These uncertainties are best characterized using statistical methods such as the development of stochastic models of tire–soil interaction. The quality of the models can be assessed via statistical validation measures or metrics. Although validation of stochastic tire–soil interaction models has recently been reported with good results, it involves longitudinal slip only without considering lateral slip which can occur simultaneously with longitudinal motion. This paper presents results of the validation of a simple stochastic tire–soil interaction model for the more complicated case of combined slip. The statistical methods used for validation include the development of a Gaussian process metamodel, the calibration of model parameters using the approach of the maximum likelihood estimate in conjunction with new test data. The validation of the calibrated model, when compared with test data, is obtained using four validation metrics with good results.     

Characterisation of martian soil simulants for the ExoMars rover testbed

The European Space Agency (ESA) ExoMars mission involves landing a rover on the surface of Mars on an exobiology mission to extend the search for life. The locomotion capabilities of the ExoMars rover will enable it to use its scientific instruments in a wide variety of locations. Before it is sent to Mars, this locomotion system must be tested and its performance limitations understood. To test the locomotion performance of the ExoMars rover, three martian regolith simulants were selected: a fine dust analogue, a fine Aeolian sand analogue, and a coarse sand analogue. To predict the performance of the ExoMars rover locomotion system in these three regolith simulants, it is necessary to measure some fundamental macroscopic properties of the materials: cohesion, friction angle, and various bearing capacity constants. This paper presents the tests conducted to determine these properties. During these tests, emphasis was placed on preparing the regolith simulants at different levels of density in order to evaluate its impact on the value of the parameters in particular. It was shown that compaction can influence the Bekker coefficients of pressure-sinkage. The shear properties are consistent with the critical state model at normal stresses similar to those of the ExoMars rover in all but one of the simulants, which showed behaviour more consistent with transitional soil behaviour. It is necessary to give due consideration to these variations to ensure a robust test regime is developed when testing the tractive ability of the ExoMars mobility system.     

Prediction of tractive response for flexible wheels with application to planetary rovers

Planetary rovers are typically developed for high-risk missions. Locomotion requires traction to provide forward thrust on the ground. In soft soils, traction is limited by the mechanical properties of the soil, therefore lack of traction and wheel slippage cause difficulties during the operation of the rover. A possible solution to increase the traction force is to increase the size of the wheel-ground contact area. Flexible wheels provide this due to the deformation of the loaded wheel and hence this decreases the ground pressure on the soil surface. This study focuses on development of an analytical model which is an extension to the Bekker theory to predict the tractive performance for a metal flexible wheel by using the geometric model of the wheel in deformation. We demonstrate that the new analytical model closely matches experimental results. Hence this model can be used in the design of robust and optimal traction control algorithms for planetary rovers and for the design and the optimisation of flexible wheels.     

Barbilian’s metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics

In the present paper we answer two questions raised by Barbilian in 1960. First, we study how far can the hypothesis of Barbilian’s metrization procedure can be relaxed. Then, we prove that Barbilian’s metrization procedure in the plane generates either Riemannian metrics or Lagrance generalized metrics not reducible to Finslerian or Langrangian metrics.     

Spaces and moduli spaces of Riemannian metrics

These notes present and survey results about spaces and moduli spaces of complete Riemannian metrics with curvature bounds on open and closed manifolds, here focussing mainly on connectedness and disconnectedness properties. They also discuss several open problems and questions in the field.     

Affinely equivalent Khler-Finsler metrics on a complex manifold

The purpose of the present paper is to investigate affinely equivalent Khler-Finsler metrics on a complex manifold.We give two facts (1) Projectively equivalent Khler-Finsler metrics must be affinely equivalent;(2) a Khler-Finsler metric is a Khler-Berwald metric if and only if it is affinely equivalent to a Khler metric.Furthermore,we give a formula to describe the affine equivalence of two weakly Khler-Finsler metrics.     

Measuring Lineup Difficulty By Matching Distance Metrics With Subject Choices in Crowd-Sourced Data

Graphics play a crucial role in statistical analysis and data mining. Being able to quantify structure in data that is visible in plots, and how people read the structure from plots is an ongoing challenge. The lineup protocol provides a formal framework for data plots, making inference possible. The data plot is treated like a test statistic, and lineup protocol acts like a comparison with the sampling distribution of the nulls. This article describes metrics for describing structure in data plots and evaluates them in relation to the choices that human readers made during several large Amazon Turk studies using lineups. The metrics that were more specific to the plot types tended to better match subject choices, than generic metrics. The process that we followed to evaluate metrics will be useful for general development of numerically measuring structure in plots, and also in future experiments on lineups for choosing blocks of pictures. Supplementary materials for this article are available online.     

Kähler Surfaces of Positive Scalar Curvature

We construct Kähler metrics of positive scalar curvature on almost all blown-up ruled surfaces of arbitrary genus. The metrics have an explicit form on ruled surfaces blown up at most twice successively from a minimal model. Our surfaces are generic in the sense that they make up a dense set in the deformations of a given ruled surface.