Saffman-Taylor instability in a non-Brownian suspension: finger selection and destabilization

We study the Saffman-Taylor instability in a non-Brownian suspension by injection of air. We find that flow structuration in the Hele-Shaw cell can be described by an effective viscosity depending on the volume fraction. When this viscosity is used to define the control parameter of the instability, the classical finger selection for Newtonian fluids is recovered. However, this picture breaks down when the cell thickness is decreased below approximatively 10 grain sizes. The discrete nature of the grains plays also a determinant role in the the early destabilization of the fingers observed. The grains produce a perturbation at the interface proportional to the grain size and can thus be considered as a "controlled noise". The finite amplitude instability mechanism proposed earlier by Bensimon et al. allows to link this perturbation to the actual values of the destabilization threshold.Comment: 4 pages, 4 figures, submitted to PR

Disk-planets interactions and the diversity of period ratios in Kepler's multi-planetary systems

The Kepler mission is dramatically increasing the number of planets known in multi-planetary systems. Many adjacent planets have orbital period ratios near resonant values, with a tendency to be larger than required for exact first-order mean-motion resonances. This intriguing feature has been shown to be a natural outcome of orbital circularization of resonant planetary pairs due to star-planet tidal interactions. However, this feature holds in multi-planetary systems with periods longer than ten days, for which tidal circularization is unlikely to provide efficient divergent evolution of the planets orbits. Gravitational interactions between planets and their parent protoplanetary disk may instead provide efficient divergent evolution. For a planet pair embedded in a disk, we show that interactions between a planet and the wake of its companion can reverse convergent migration, and significantly increase the period ratio from a near-resonant value. Divergent evolution due to wake-planet interactions is particularly efficient when at least one of the planets opens a partial gap around its orbit. This mechanism could help account for the diversity of period ratios in Kepler's multiple systems comprising super-Earth to sub-jovian planets with periods greater than about ten days. Diversity is also expected for planet pairs massive enough to merge their gap. The efficiency of wake-planet interactions is then much reduced, but convergent migration may stall with a variety of period ratios depending on the density structure in the common gap. This is illustrated for the Kepler-46 system, for which we reproduce the period ratio of Kepler-46b and c.Comment: 15 pages, 11 figures, accepted for publication in Ap

Performance Dynamics and Termination Errors in Reinforcement Learning: A Unifying Perspective

In reinforcement learning, a decision needs to be made at some point as to whether it is worthwhile to carry on with the learning process or to terminate it. In many such situations, stochastic elements are often present which govern the occurrence of rewards, with the sequential occurrences of positive rewards randomly interleaved with negative rewards. For most practical learners, the learning is considered useful if the number of positive rewards always exceeds the negative ones. A situation that often calls for learning termination is when the number of negative rewards exceeds the number of positive rewards. However, while this seems reasonable, the error of premature termination, whereby termination is enacted along with the conclusion of learning failure despite the positive rewards eventually far outnumber the negative ones, can be significant. In this paper, using combinatorial analysis we study the error probability in wrongly terminating a reinforcement learning activity which undermines the effectiveness of an optimal policy, and we show that the resultant error can be quite high. Whilst we demonstrate mathematically that such errors can never be eliminated, we propose some practical mechanisms that can effectively reduce such errors. Simulation experiments have been carried out, the results of which are in close agreement with our theoretical findings.Comment: Short Paper in AIKE 201

Mineralogical, optical, geochemical, and particle size properties of four sediment samples for optical physics research

X-ray diffraction and spectroscopy were used to investigate the mineralogical and chemical properties of the Calvert, Ball Old Mine, Ball Martin, and Jordan Sediments. The particle size distribution and index of refraction of each sample were determined. The samples are composed primarily of quartz, kaolinite, and illite. The clay minerals are most abundant in the finer particle size fractions. The chemical properties of the four samples are similar. The Calvert sample is most notably different in that it contains a relatively high amount of iron. The dominant particle size fraction in each sample is silt, with lesser amounts of clay and sand. The indices of refraction of the sediments are the same with the exception of the Calvert sample which has a slightly higher value

Market Signals Transmitted by Grid Pricing

Grid pricing improves the flow of information to producers, but market signals sent by grids may not be clearly understood. This study uses a two-stage Coefficients of Separate Determination process, four sets of fed cattle carcass data, and sensitivity analyses to identify market signals sent by grid pricing. Weight sends a stronger market signal than carcass quality characteristics such as quality and yield grade. Although grids are shaping production, market signals indicate that lower quality carcasses are penalized more than higher quality carcasses are rewarded. Sensitivity analyses suggest changes in quality and yield grade discounts have the greatest impact on market signals.beef cattle, Coefficients of Separate Determination, grid pricing, market signals, value-based marketing, Demand and Price Analysis,

Limit Theorems For Quantum Walks Associated with Hadamard Matrices

We study a one-parameter family of discrete-time quantum walk models on the line and in the xy-plane associated with the Hadamard walk. Weak convergence in the long-time limit of all moments of the walker's pseudo-velocity on the line and in the xy-plane is proved. Symmetrization on the line and in the xy-plane is theoretically investigated, leading to the resolution of the Konno-Namiki-Soshi conjecture in the special case of symmetrization of the unbiased Hadamard walk on the line . A necessary condition for the existence of a phenomenon known as localization is given