Failure Inference and Optimization for Step Stress Model Based on Bivariate Wiener Model

In this paper, we consider the situation under a life test, in which the failure time of the test units are not related deterministically to an observable stochastic time varying covariate. In such a case, the joint distribution of failure time and a marker value would be useful for modeling the step stress life test. The problem of accelerating such an experiment is considered as the main aim of this paper. We present a step stress accelerated model based on a bivariate Wiener process with one component as the latent (unobservable) degradation process, which determines the failure times and the other as a marker process, the degradation values of which are recorded at times of failure. Parametric inference based on the proposed model is discussed and the optimization procedure for obtaining the optimal time for changing the stress level is presented. The optimization criterion is to minimize the approximate variance of the maximum likelihood estimator of a percentile of the products' lifetime distribution

3GPP-inspired Stochastic Geometry-based Mobility Model for a Drone Cellular Network

This paper deals with the stochastic geometry-based characterization of the time-varying performance of a drone cellular network in which the initial locations of drone base stations (DBSs) are modeled as a Poisson point process (PPP) and each DBS is assumed to move on a straight line in a random direction. This drone placement and trajectory model closely emulates the one used by the third generation partnership project (3GPP) for drone-related studies. Assuming the nearest neighbor association policy for a typical user equipment (UE) on the ground, we consider two models for the mobility of the serving DBS: (i) UE independent model, and (ii) UE dependent model. Using displacement theorem from stochastic geometry, we characterize the time-varying interference field as seen by the typical UE, using which we derive the time-varying coverage probability and data rate at the typical UE. We also compare our model with more sophisticated mobility models where the DBSs may move in nonlinear trajectories and demonstrate that the coverage probability and rate estimated by our model act as lower bounds to these more general models. To the best of our knowledge, this is the first work to perform a rigorous analysis of the 3GPP-inspired drone mobility model and establish connection between this model and the more general non-linear mobility models

Impulsive gravitational waves of massless particles in extended theories of gravity

We investigate the vacuum pp-wave and Aichelburg-Sexl-type solutions in f(R) and the modified Gauss-Bonnet theories of gravity with both minimal and nonminimal couplings between matter and geometry. In each case, we obtain the necessary condition for the theory to admit the solution and examine it for several specific models. We show that the wave profiles are the same or proportional to the general relativistic one

The formation number of vortex rings formed in uniform background co-flow

The formation of vortex rings generated by an impulsively started jet in the presence of uniform background co-flow is studied experimentally to extend previous results. A piston–cylinder mechanism is used to generate the vortex rings and the co-flow is supplied through a transparent shroud surrounding the cylinder. Digital particle image velocimetry (DPIV) is used to measure the development of the ring vorticity and its eventual pinch off from the generating jet for ratios of the co-flow to jet velocity ($R_{v})$ in the range 0 – 0.85. The formation time scale for the ring to obtain maximal circulation and pinch off from the generating jet, called the formation number ($F$), is determined as a function of $R_{v}$ using DPIV measurements of circulation and a generalized definition of dimensionless discharge time or ‘formation time’. Both simultaneous initiation and delayed initiation of co-flow are considered. In all cases, a sharp drop in $F$ (taking place over a range of 0.1 in $R_{v}$) is centred around a critical velocity ratio ($R_{crit}$). As the initiation of co-flow was delayed, the magnitude of the drop in $F$ and the value of $R_{crit}$ decreased. A kinematic model based on the relative velocities of the forming ring and jet shear layer is formulated and correctly predicts vortex ring pinch off for $R_{v} \,{>}\, R_{crit}$. The results of the model indicate the reduction in $F$ at large $R_{v}$ is directly related to the increased convective velocity provided to the ring by the co-flow