A Cop and Drunken Robber Game on n-DimensionalInfinite-Grid Graphs

A Cop and Drunken Robber (CDR) game is one variation of a famous combinatorial game, called Cops and Robbers, which has been extensively studied and applied in the area of theoretical and computer science as demonstrated by several conferences and publications. In this paper, for a natural number n, we present two strategies for a single cop to chase a drunken robber on n-dimensional infinite-grid graphs. Both strategies show that if the initial distance between the cop and the drunken robber is s, then the expected capture time is s+o(s).

Numerical Study of the Interaction between a Collapsing Bubble and a Movable Particle in a Free Field

This study numerically investigates the interactions between a collapsing bubble and a movable particle with a comparable size in a free field, which is associated with the microscopic mechanisms of the synergetic effects of cavitation erosion and particle abrasion on the damages of materials in fluid machineries. A new solver on OpenFOAM based on direct numerical simulations with the volume of fluid (VOF) method capturing the interface of a bubble and with the overset grid method handling the motion of the particle was developed to achieve the fluid–structure interaction (FSI). The results show that bubbles in cases with stand-off parameter χ (defined as (d0−Rp)/R0), where d0 is the initial distance between the centers of the bubble and particle, and Rp,R0 are the particle’s radius and the initial radius of the bubble respectively >1, experience spherical-shaped collapse under the influence of the approaching particle, which is attracted by the collapsing bubble. The bubbles in these cases no longer present non-spherical collapse. Additionally, a force balance model to account for the particle dynamics was established, in which the particle velocity inversely depends on the size of the particle, and approximately on the second power of the initial distance from the bubble. This analytical result accords with the numerical results and is valid for cases with χ>1 only, since it is based on the theory of spherical bubbles. These conclusions are important for further study of the interactions between a bubble and a movable particle near a rigid wall.

Influence of initial distance and heating rate on the aggregation of Cu and Au nanoparticles: a MD study

This paper investigates the effects of interparticle distance and heating rate on the aggregation characteristics of Cu/Au nanoparticles using molecular dynamics (MD) simulations, and focuses on discussing the effects of the two above-mentioned factors on the entire system. Our results suggested that the reduction in heating rate and increasing the initial distance of the particles would both contribute to raising the initial sintering temperature. However, when the particles’ initial distance was greater than the cut-off radius of the system, the initial sintering temperature was not increased any longer, but fluctuated within a certain range. Furthermore, the sintering force of the nanoparticles at the initial sintering temperature was investigated, and it was found that the heating rate made no obvious difference to it. Nonetheless, the sintering force varied under different initial distance of the particles (at the same heating rate) due to system energy changes.

A Novel Method to Calculate Objects’ Apparent Size

The angular diameter is the angle subtended by a generic object – an apple or a star – to the eye of an observer, and it describes how large the object appears from a given viewpoint. The angular diameter represents a powerful tool for distance calculations starting from directly measurable information and it finds application in several contexts varying from cosmography to architecture. In this article, the author proposes a novel equation to calculate the apparent diameter of whatever object. This equation defines a relation between the initial distance R0 at which the observed object is located and the object’s apparent diameter. Based on the preliminary tests conducted, the model seems to faithfully portrait this relation with respect to measured values, also at the astronomical scale, thus considering the Earth-Moon distance, where, the absolute error detected is about 0.56%. The tests highlighted also a dependency between the results accuracy and the measurement conditions suggesting a high level of sensibility linked to the initial magnification effect produced by the retina or the artificial lens employed.

Experimental investigations on the partner-finding behaviour of Isohypsibius dastychi (Isohypsibiidae: Tardigrada)

The present study gives the first detailed results on the partner-finding behaviour of tardigrades. We investigated whether the finding of mating partners by Isohypsibius dastychi followed certain criteria that are expected if pheromone signals are involved. For this purpose, tardigrade pairs were positioned in an arena, at a range of distances from each other. Only those females that were ready for mating attracted the male. The smaller the initial distance between them, the more directly the male headed for the female. The route travelled and time taken increased exponentially with increasing initial distance between partners, which means that the male lost orientation with respect to the female the larger the distance between the pair became. The findings indirectly suggest a yet undetermined female pheromone, which produces a concentration gradient in the water and loses strength quickly in terms of distance. Our assumption is supported by rare observations of sperm release without direct contact between partners that nevertheless resulted in fertile offspring. The observation that the female partners in this no-contact mating behaviour then deposited their eggs (a behaviour that was never seen when males were absent) suggests that they, likewise, can sense a fresh ejaculate of spermatozoa in their direct vicinity.

Effects of Initial Starting Distance and Gap Characteristics on Children’s and Young Adults’ Velocity Regulation When Intercepting Moving Gaps

Objective This study investigated how children and young adults regulate their velocity when crossing roads under varying traffic conditions. Background To cross roads safely, pedestrians must adapt their movements to the moving vehicles around them while tightly coupling their movement to visual information. Method Using an Oculus Rift, 16 children and 16 young adults walked on a treadmill and intercepted gaps between two simulated moving vehicles in an immersive virtual environment. We varied the participants’ initial distance from the curb to the interception point, as well as gap characteristics, including gap size and vehicle size. Results Varying the initial distance led to systematic adjustments in participants’ approach velocities. The inter-vehicle gap and the vehicle size affected the crossing position induced by the initial distance. However, participants did not systematically scale their positions according to the initial distance in narrow gap. Notably, children did not finely tune their movements when they approached wide gap from a closer distance or when they approached the large vehicle from closer distance. Conclusion Children were less precise in coupling their movements to the moving vehicle in complex traffic environments. In particular, large moving vehicles approaching at closer distances can pose risks when children cross roads. Application These findings suggest the need for an intervention program to improve children’s skill in perceiving larger vehicles and timing their movements when crossing roads. We suggest using an interactive virtual reality system to practice this skill.