Optimal search strategies of space-time coupled random walkers with finite lifetimes

We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers "mortal creepers". A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate $\omega_m$. While still alive, the creeper has a finite mean frequency $\omega$ of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an $\omega_m$-dependent optimal frequency $\omega=\omega_{opt}$ that maximizes the probability of eventual target detection. We work primarily in one-dimensional ($d=1$) domains and examine the role of initial conditions and of finite domain sizes. Numerical results in $d=2$ domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the $d=1$ case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard "target problem" in which many creepers start at random locations at the same time.Comment: 18 pages, 7 figures. The title has been changed with respect to the one in the previous versio

Wheel Design and Tension Analysis for the Tethered Axel Rover on Extreme Terrain

As the Mars Exploration rovers have reaffirmed, some of the most interesting sites for scientists to explore on planetary surfaces lie in terrains that are currently inaccessible to state-of-the art rovers. We have been developing the Axel rover as a robotic platform to access steep and challenging terrain. We will summarize the recent mechanical upgrades since we introduced the tethered Axel concept last year

Dipolar condensates confined in a toroidal trap: ground state and vortices

We study a Bose-Einstein condensate of 52Cr atoms confined in a toroidal trap with a variable strength of s-wave contact interactions. We analyze the effects of the anisotropic nature of the dipolar interaction by considering the magnetization axis to be perpendicular to the trap symmetry axis. In the absence of a central repulsive barrier, when the trap is purely harmonic, the effect of reducing the scattering length is a tuning of the geometry of the system: from a pancake-shaped condensate when it is large, to a cigar-shaped condensate for small scattering lengths. For a condensate in a toroidal trap, the interaction in combination with the central repulsive Gaussian barrier produces an azimuthal dependence of the particle density for a fixed radial distance. We find that along the magnetization direction the density decreases as the scattering length is reduced but presents two symmetric density peaks in the perpendicular axis. For even lower values of the scattering length we observe that the system undergoes a dipolar-induced symmetry breaking phenomenon. The whole density becomes concentrated in one of the peaks, resembling an origin-displaced cigar-shaped condensate. In this context we also analyze stationary vortex states and their associated velocity field, finding that this latter also shows a strong azimuthal dependence for small scattering lengths. The expectation value of the angular momentum along the z direction provides a qualitative measure of the difference between the velocity in the different density peaks.Comment: 9 pages, 12 figure

Three-dimensional flow structure and bed morphology in large elongate meander loops with different outer bank roughness characteristics

© 2016. American Geophysical Union. All Rights Reserved. Few studies have examined the three-dimensional flow structure and bed morphology within elongate loops of large meandering channels. The present study focuses on the spatial patterns of three-dimensional flow structure and bed morphology within two elongate meander loops and examines how differences in outer bank roughness influence near-bank flow characteristics. Three-dimensional velocities were measured during two different events—a near-bankfull flow and an overbank event. Detailed data on channel bathymetry and bed form geometry were obtained during a near-bankfull event. Flow structure within the loops is characterized by strong topographic steering by the point bar, by the development of helical motion associated with flow curvature, and by acceleration of flow where bedrock is exposed along the outer bank. Near-bank velocities during the overbank event are less than those for the near-bankfull flow, highlighting the strong influence of the point bar on redistribution of mass and momentum of the flow at subbankfull stages. Multiple outer bank pools are evident within the elongate meander loop with low outer bank roughness, but are not present in the loop with high outer bank roughness, which may reflect the influence of abundant large woody debris on near-bank velocity characteristics. The positions of pools within both loops can be linked to spatial variations in planform curvature. The findings indicate that flow structure and bed morphology in these large elongate loops is similar to that in small elongate loops, but differs somewhat from flow structure and bed morphology reported for experimental elongate loops