Mixing by Cutting and Shuffling a Line Segment: The Effect of Incorporating Diffusion

Dynamical systems are commonly used to model mixing in fluid and granular flows. We consider a one-dimensional discontinuous dynamical system model (termed “cutting and shuffling” of a line segment), and we present a comprehensive computational study of finite-time mixing. The properties of the system depend on several parameters in a sensitive way, and the effect of each parameter is examined. Space-time and waterfall plots are introduced to visualize the mixing process with different mixing protocols without diffusion, showing a variety of distinct and complex behaviors in this “simple” dynamical system. To improve the mixing efficiency and avoid pathological cases, we incorporate diffusion into this model dynamical system. We show that diffusion can be quite effective at homogenizing a “mixture.” To make this effect clear, we compare cases without diffusion to those with “small” diffusivity and “large” diffusivity. Illustrative examples also show how to adapt mixing metrics from the literature, namely the number of cutting interfaces and a mixing norm, to quantify the degree of mixing in our cutting and shuffling system. To study the evolution of mixing through a large set of possible cutting and shuffling parameters, we introduce fit functions for the number of cutting interfaces and the mixing norm. These fits allow us to determined time constants of mixing for each different system considered, thereby quantifying the “speed” of mixing. Systems with various different permutations (shuffling protocols) are considered, then average properties can be computed, which hold true (on average) for all allowed permutations. The relationship between the fit parameters and the system parameters is also investigated through scatter plots in the fit parameter space. Next, universal mixing behaviors are identified by specifically introducing a critical half-mixing time, which must be found computationally. Using the latter, a rescaling of different dynamical regimes (decay curves of the mixing norm) fall onto a universal profile valid across all parameters of the cutting and shuffling dynamical system. Then, a prediction for this critical half-mixing time is made on the basis of the evolution of the number of subsegments of continuous color (unmixed subsegments). This prediction, which is called a stopping time in the finite Markov chain literature, must also be found numerically. The latter compares well with the previously computed half-mixing time, which provides an approach to determine when a system has become uniform. Finally, we examine the dependence of the half-mixing times on the characteristic P´eclet number of the system (an inverse dimensionless diffusivity), and we show that as the P´eclet number becomes large, the system transitions more sharply from an unmixed initial state to a mixed final state. This phenomenon, which is know as a “cut-off” in the finite Markov chain literature thus appears to be well substantiated by our numerical investigation of cutting and shuffling a line segment in the presence of diffusion

Team Queue: A mobile application which provides a third party stage for an E-Sports service provider

E-Sports, known as electronic sports, professional video gaming or pro gaming, refers to the use of video games for sports. In today’s a growing economy, there is a continuous strengthening of the E-Sports industry; E-Sports has officially become a kind of sports. Believe or not, E-Sports has an incredible market share in the gaming market. In 2017, E-Sport the grew of 41.3 % over last year, which equates up the value of $696 million (NewZoo, 2017). According to 2017 Global E-Sports Market Report (NewZoo, 2017), day, worldwide, there are E-Sports games held every day. It also reported that 67 million people playing every month, 27 million playing every day, and over 7.5 million playing concurrently during each day’s peak play time. Also, the E-Sports enthusiast audience is made up of mostly young people and males, with half of them aged between 21-35 and 71% males. The purpose of this project, through interactive design, is to create a mobile application that helps ordinary players find teammates and join a team faster and more convenient than ever

Channel Estimation for Frequency Division Duplexing Multi-user Massive MIMO Systems via Tensor Compressive Sensing

To make full use of space multiplexing gains for the multi-user massive multiple-input multiple-output, accurate channel state information at the transmitter (CSIT) is required. However, the large number of users and antennas make CSIT a higher-order data representation. Tensor-based compressive sensing (TCS) is a promising method that is suitable for high-dimensional data processing; it can reduce training pilot and feedback overhead during channel estimation. In this paper, we consider the channel estimation in frequency division duplexing (FDD) multi-user massive MIMO system. A novel estimation framework for three dimensional CSIT is presented, in which the modes include the number of transmitting antennas, receiving antennas, and users. The TCS technique is employed to complete the reconstruction of three dimensional CSIT. The simulation results are given to demonstrate that the proposed estimation approach outperforms existing algorithms