Boltzmann-Grad limit of a hard sphere system in a box with isotropic boundary conditions

<p style='text-indent:20px;'>In this paper we present a rigorous derivation of the Boltzmann equation in a compact domain with {isotropic} boundary conditions. We consider a system of <inline-formula><tex-math id="M1">\begin{document}$ N $\end{document}</tex-math></inline-formula> hard spheres of diameter <inline-formula><tex-math id="M2">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula> in a box <inline-formula><tex-math id="M3">\begin{document}$ \Lambda : = [0, 1]\times(\mathbb{R}/\mathbb{Z})^2 $\end{document}</tex-math></inline-formula>. When a particle meets the boundary of the domain, it is instantaneously reinjected into the box with a random direction, {but} conserving kinetic energy. We prove that the first marginal of the process converges in the scaling <inline-formula><tex-math id="M4">\begin{document}$ N\epsilon^2 = 1 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ \epsilon\rightarrow 0 $\end{document}</tex-math></inline-formula> to the solution of the Boltzmann equation, with the same short time restriction of Lanford's classical theorem.</p>

Damage Constitutive Model of Microcrack Rock under Tension

To investigate the tensile properties of brittle rock with microdamage, an indirect tensile test was conducted. High-speed image acquisition and acoustic emission (AE) were applied to record the process. After the tests, the images were analysed using the digital image correlation (DIC) method to obtain the stress and strain development of the rock under tension. The damage constitutive model was also developed in this study. Based on known and assumed statistical distributions for microcracks and the theory of fracture and statistical damage, the mechanical properties and failure mechanisms of brittle rock under tension were analysed. The basic statistical parameters of the main cracks in the elements were described, and the damage variable was defined to develop the effective modulus. A constitutive model for microdamage brittle rock-like materials was established based on the effective modulus. Additionally, to describe the crack propagation, a random-direction crack under tension was analysed to calculate the crack-tip stress intensity factor. After applying the basic parameters of the sandstone to the analytical model, the results showed that the analytical model agreed with the experimental results.

Tracking Area Boundary-aware Protocol for Pseudo Stochastic Mobility Prediction in LTE Networks

Accurate mobility prediction enables efficient and faster paging services in these networks. This in turn facilitates the attainment of higher bandwidths and execution of activities such as handovers at low latencies. The conventional mobility prediction models operate on unrealistic assumptions that make them unsuitable for cellular network mobile station tracking. For instance, the Feynman-Verlet, first order kinetic model and Random Waypoint assume that mobile phones move with constant velocity while Manhattan, Freeway, city area, street unit, obstacle mobility, and pathway mobility postulate that mobile station movement is restricted along certain paths. In addition, obstacle mobility model speculate that the mobile station signal is completely absorbed by an obstacle while random walk, random waypoint, Markovian random walk, random direction, shortest path model, normal walk, and smooth random assume that a mobile station can move in any direction. Moreover, the greatest challenge of the random direction model is the requirement that a border behavior model be specified for the reaction of mobile stations reaching the simulation area boundary. In this paper, a protocol that addresses the border behavior problem is developed. This protocol is shown to detect when the subscriber has moved out of the current tracking area, which is crucial during handovers.

Localizing and quantifying structural damage by means of a beetle swarm optimization algorithm

An efficient meta-heuristic algorithm, named beetle swarm optimization (BSO), is proposed to localize and quantify structural damage using limited vibration measurement data. The beetle antennae search (BAS) algorithm that imitats a random walking mechanism in nature was recently developed to solve the optimization problem. However, the ratio of convergence of this algorithm significantly relys on the random direction and deviation for high-dimensional problems. To overcome this shortcoming, the BSO inspired by the swarm intelligence strategy is proposed. In the iterative search process of the BSO, each beetle swarm moves in a random direction like the BAS and the swarm of beetles is cognitive with the optimal one for the searching behavior. Consequently, the optimal one is updated step by step until a better beetle appears. To demonstrate the capability and robustness of the BSO, numerical and experimental studies using limited vibration measurement data of an offshore wind turbine structure are carried out for structural damage identification. An novel objective function is established by combining natural frequencies with mode shapes of the structure. The numerical results show that the BSO can accurately localize and quantify various types of damage even in a noise and temperature variations polluted environment. Moreover, it has higher accuracy and faster convergence speed than the BAS and the particle swarm optimization (PSO) algorithms. These promising performances could contribute to establishing a structural monitoring system for safety assurance of wind turbine structures.

Albatrosses can memorize locations of predictable fishing boats but favour natural foraging

Human activities generate food attracting many animals worldwide, causing major conservation issues. The spatio-temporal predictability of anthropogenic resources could reduce search costs for animals and mediate their attractiveness. We investigated this through GPS tracking in breeding black-browed albatrosses attracted to fishing boats. We tested for answers to the following questions. (i) Can future boat locations be anticipated from cues available to birds? (ii) Are birds able to appropriately use these cues to increase encounters? (iii) How frequently do birds use these cues? Boats were spatially persistent: birds searching in the direction where they previously attended boats would encounter twice as many boats compared with following a random direction strategy. A large proportion of birds did not use this cue: across pairs of consecutive trips ( n = 85), 51% of birds switched their foraging direction irrespective of previous boat encounters. Still, 15 birds (27%) were observed to closely approach (approx. 0.1–1 km) where they previously attended a boat while boats were no longer there. This is less than the distance expected by chance (approx. 10–100 km), based on permutation control procedures accounting for individual-specific spatial consistency, suggesting individuals could memorize where they encountered boats across consecutive trips. We conclude albatrosses were able to exploit predictive cues from recent boat encounters but most favoured alternative resources.

Ethics and Best Practices for Mapping Archaeological Sites

Archaeologists are tasked with balancing a call to open data and the need to maintain confidentiality of sensitive archaeological site locations. Low-resolution mapping and data aggregation are the methods most commonly used to hide site locations; however, we understand little of the effectiveness of these practices. Trends in geomasking, obscuring observed geographic points, to anonymize public health data are suggested as a source of methods for sharing archaeological site data. Archaeologists have available to them a number of geomasking methods that balance open data and site security in different ways. Low-resolution mapping at several scales and random direction with fixed radius, random perturbation donut, and Gaussian donut techniques are tested on a set of archaeological site locations. Random perturbation donuts resulted in the best balance between obscuring archaeological locations and conveying observed spatial patterning. Researchers should carefully consider how they convey archaeological location data, as commonly used low-resolution scales may not provide the desired level of obscurity. Researchers should also be explicit as to how and why their methods of site visualization are chosen.

Effect of Time and Direction Preparation on Ankle Muscle Response During Backward Translation of a Support Surface in Stance

This study investigated the effect of the time and direction preparation on the electromyographic (EMG) response of the ankle extensor to the backward translation of the support surface in stance. Fifteen healthy adult males aged 35.9 ± 6.2 years participated in this study. In the constant session, the interval between the warning cue and the onset of the backward support surface translation was constant. In the random time session, the interval was randomly assigned in each trial, but the direction was backward across the trials. In the random direction session, the direction was randomly assigned in each trial, but the interval was constant. The EMG amplitude in the time epochs 100–175 ms after translation onset in the random time session was significantly greater than that in the constant session in the soleus, gastrocnemius, and tibialis anterior muscles. The EMG amplitude in the time epochs 120–185 ms after translation onset in the random direction session was significantly greater than that in the constant session in the gastrocnemius and tibialis anterior muscles. This finding indicates that time and direction preparation reduces the late component of the ankle EMG response to backward translation of the support surface. This finding is explained by the supposed process through which uncertainty of the upcoming event causes disinhibition of response or by how time and direction preparation optimizes the magnitude of the long-latency response mediated by the transcortical pathway.