The motion of a sphere freely rising or falling in a 5d (d is the diameter of the sphere) square tube was numerically studied for the sphere-to-fluid density ratio ranging from 0.1 to 2.3 (0.1 ≤ ρs/ρ ≤ 2.3, ρs is the density of spheres and ρ the fluid density) and Galileo number from 140 to 230 (140 ≤ Ga ≤ 230). We report that Hopf bifurcation occurs at Gacrit ≈ 157, where both the heavy and light spheres lose stability. The helical motion is widely seen for all spheres at Ga > 160 resulting from a double-threaded vortex interacting with the tube walls, which becomes irregular at Ga ≥ 190 where heavy spheres act differently from their counterparts; that is, heavy spheres change their helical directions alternately while light spheres exhibit helical trajectories with jaggedness in connection with the shedding of the double-threaded vortices. This is because of the difference in inertia between the heavy and light spheres. We also checked the oscillation periods for the helical motion of the spheres. They show opposite variations with ρs/ρ for the two types of spheres. Light spheres (ρs/ρ ≤ 0.7) reach a zigzagging regime at Ga ≥ 200 where a vortex loop (hairpin-like vortical structure) is formed which may develop into a vortex ring downstream at small ρs/ρ. This might be the first time a transition from the helical motion to the zigzagging motion for heavy spheres (ρs/ρ ≥ 1.8) has been reported. Finally, we examined the dependence of both the terminal Reynolds number and the drag coefficient of the spheres on the Galileo number.

Visual place recognition (VPR) in condition-varying environments is still an open problem. Popular solutions are convolutional neural network (CNN)-based image descriptors, which have been shown to outperform traditional image descriptors based on hand-crafted visual features. However, there are two drawbacks of current CNN-based descriptors: (a) their high dimension and (b) lack of generalization, leading to low efficiency and poor performance in real robotic applications. In this paper, we propose to use a convolutional autoencoder (CAE) to tackle this problem. We employ a high-level layer of a pre-trained CNN to generate features and train a CAE to map the features to a low-dimensional space to improve the condition invariance property of the descriptor and reduce its dimension at the same time. We verify our method in four challenging real-world datasets involving significant illumination changes, and our method is shown to be superior to the state-of-the-art. The code of our work is publicly available at https://github.com/MedlarTea/CAE-VPR.

We consider a queueing system where arriving customers join the queue at some random position. This constitutes an impolite arrival discipline because customers do not necessarily go to the end of the line upon arrival. Although mean performance measures like the average waiting time and average number of customers in the queue are the same for all such disciplines, we show that the variance of the waiting time increases as the arrival discipline becomes more impolite, in the sense that a customer is more likely to choose a position closer to the server. For the M/G/1 model, we also provide an iterative procedure for computing the moments of the waiting time distribution. Explicit computational formulas are derived for an interesting special model where a customer joins the queue either at the head or at the end of the line.

Recent developments in stochastic modeling show that enormous analytical advantages can be gained if a general cumulative distribution function (c.d.f.) can be approximated by generalized hyperexponential distributions. In this paper, we introduce a procedure to explicitly construct such approximations of an arbitrary c.d.f. Although our approach can be used in different types of stochastic models, the main motivation comes from queueing theory in obtaining approximations of the idle-period distribution and other performance measures in GI/G/1 queues.

We study a generalization of the GI/G/l queue in which the server is turned off at the end of each busy period and is reactivated only when the sum of the service times of all waiting customers exceeds a given threshold of size D. Using the concept of a “randomly selected” arriving customer, we obtain as our main result a relation that expresses the waiting-time distribution of customers in this model in terms of characteristics associated with a corresponding standard GI/G/1 queue, obtained by setting D = 0. If either the arrival process is Poisson or the service times are exponentially distributed, then this representation of the waiting-time distribution can be specialized to yield explicit, transform-free formulas; we also derive, in both of these cases, the expected customer waiting times. Our results are potentially useful, for example, for studying optimization models in which the threshold D can be controlled.

Ball milling of ammonothermally synthesized GaN powders was performed in an ethanol solution for a variety of durations, resulting in average particle sizes of nanometer. The ball milled powders showed an obviously brightened color and improved dispersability, indicating reduced levels of aggregation. X-ray diffraction (XRD) peaks of the ball milled GaN powders were significantly broadened compared to those of the as-synthesized powders. The broadening of the XRD peaks was partially attributed to the reduction in the average particle size, which was confirmed through SEM analyses. On the other hand, rare earth doping of commercial GaN powders was also achieved through a ball mill assisted solid state reaction process. Rare earth salts were mixed with GaN powder by ball milling. The as-milled powders were heat treated under different conditions to facilitate the dopant diffusion. Luminescence properties of the rare earth doped GaN powders at near infrared range were investigated and the results were discussed.

Vasicek (1977) proved that among all queueing disciplines that do not change the departure process of the queue, FIFO and LIFO yield, respectively, the smallest and the largest expectation of any given convex function of the service delay. In this note we further show that, if arriving customers join the queue stochastically ‘closer' to the server(s), then the expected value of any convex function of service delay is larger. As a more interesting result, we also show that if the function under consideration is concave, then the conclusion will be exactly the opposite. This result indicates that LIFO will be the best discipline if the delay cost is an increasing function but at a diminishing rate.

A variety of performance measures of a GI/G/1 queue are explicitly related to the idle-period distribution of the queue, suggesting that the system analysis can be accomplished by the analysis of the idle period. However, the ‘stand-alone' relationship for the idle-period distribution of the GI/G/1 queue (i.e. the counterpart of Lindley's equation) has not been found in the literature. In this paper we develop a non-linear integral equation for the idle period distribution of the GI/G/1 queue. We also show that this non-linear system defines a unique solution. This development makes possible the analysis of the GI/G/1 queue in a different perspective.