Mixed principal eigenvalues in dimension one

This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the $L^{2}$-Poincar\'e inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue.Comment: 45 pages; Front. Math. China, 201

Enhanced and reduced solute transport and flow strength in salt finger convection in porous media

We report a pore-scale numerical study of salt finger convection in porous media, with a focus on the influence of the porosity in the non-Darcy regime, which has received little attention in previous research. The numerical model is based on the lattice Boltzmann method with a multiple-relaxation-time scheme and employs an immersed boundary method to describe the fluid-solid interaction. The simulations are conducted in a two-dimensional, horizontally-periodic domain with an aspect ratio of 4, and the porosity is varied from 0.7 to 1, while the solute Rayleigh number ranges from 4*10^6 to 4*10^9. Our results show that, for all explored Rayleigh number, solute transport first enhances unexpectedly with decreasing porosity, and then decreases when porosity is smaller than a Rayleigh number-dependent value. On the other hand, while the flow strength decreases significantly as porosity decreases at low Rayleigh number, it varies weakly with decreasing porosity at high Rayleigh number and even increases counterintuitively for some porosities at moderate Rayleigh number. Detailed analysis of the salinity and velocity fields reveals that the fingered structures are blocked by the porous structure and can even be destroyed when their widths are larger than the pore scale, but become more ordered and coherent with the presence of porous media. This combination of opposing effects explains the complex porosity-dependencies of solute transport and flow strength. The influence of porous structure arrangement is also examined, with stronger effects observed for smaller porosity and higher Rayleigh number. These findings have important implications for passive control of mass/solute transport in engineering applications

Determined to die! Ability to act following multiple self-inflicted gunshot wounds to the head. The cook county office of medical examiner experience (2005-2012) and review of literature

Cases of multiple (considered 2+) self-inflicted gunshot wounds are a rarity and require careful examination of the scene of occurrence; thorough consideration of the decedent’s psychiatric, medical, and social histories; and accurate postmortem documentation of the gunshot wounds. We present a series of four cases of multiple self-inflicted gunshot wounds to the head from the Cook County Medical Examiner’s Office between 2005 and 2012 including the first case report of suicide involving eight gunshot wounds to the head. In addition, a review of the literature concerning multiple self-inflicted gunshot wounds to the head is performed. The majority of reported cases document two gunshot entrance wound defects. Temporal regions are the most common affected regions (especially the right and left temples). Determining the capability to act following a gunshot wound to the head is necessary in crime scene reconstruction and in differentiation between homicide and suicide

A Sparse Smoothing Newton Method for Solving Discrete Optimal Transport Problems

The discrete optimal transport (OT) problem, which offers an effective computational tool for comparing two discrete probability distributions, has recently attracted much attention and played essential roles in many modern applications. This paper proposes to solve the discrete OT problem by applying a squared smoothing Newton method via the Huber smoothing function for solving the corresponding KKT system directly. The proposed algorithm admits appealing convergence properties and is able to take advantage of the solution sparsity to greatly reduce computational costs. Moreover, the algorithm can be extended to solve problems with similar structures including the Wasserstein barycenter (WB) problem with fixed supports. To verify the practical performance of the proposed method, we conduct extensive numerical experiments to solve a large set of discrete OT and WB benchmark problems. Our numerical results show that the proposed method is efficient compared to state-of-the-art linear programming (LP) solvers. Moreover, the proposed method consumes less memory than existing LP solvers, which demonstrates the potential usage of our algorithm for solving large-scale OT and WB problems.Comment: 29 pages, 17 figure

The RSU Access Problem Based on Evolutionary Game Theory for VANET

We identify some challenges in RSU access problem. There are two main problems in V2R communication. (1) It is difficult to maintain the end-to-end connection between vehicles and RSU due to the high mobility of vehicles. (2) The limited RSU bandwidth resources lead to the vehicles’ disorderly competition behavior, which will give rise to multiple RSUs having overlap area environment where RSU access becomes crucial for increasing vehicles’ throughput. Focusing on the problems mentioned above, the RSU access question in the paper is formulated as a dynamic evolutionary game for studying the competition of vehicles in the single community and among multiple communities to share the limited bandwidth in the available RSUs, and the evolutionary equilibrium evolutionary stable strategy (ESS) is considered to be the solution to this game. Simulation results based on a realistic vehicular traffic model demonstrate the evolution process of the game and how the ESS can affect the network performance