Critical parameters for coarse coal underground slurry haulage systems

Factors are identified which must be considered in meeting the requirements of a transportation system for conveying, in a pipeline, the coal mined by a continuous mining machine to a storage location neat the mine entrance or to a coal preparation plant located near the surface. For successful operation, the slurry haulage the system should be designed to operated in the turbulent flow regime at a flow rate at least 30% greater than the deposition velocity (slurry flow rate at which the solid particles tend to settle in the pipe). The capacity of the haulage system should be compatible with the projected coal output. Partical size, solid concentration, density, and viscosity of the suspension are if importance as well as the selection of the pumps, pipes, and valves. The parameters with the greatest effect on system performance ar flow velocity, pressure coal particle size, and solids concentration

On limit points of the sequence of normalized prime gaps

Let $p_n$ denote the $n$th smallest prime number, and let $\boldsymbol{L}$ denote the set of limit points of the sequence $\{(p_{n+1} - p_n)/\log p_n\}_{n = 1}^{\infty}$ of normalized differences between consecutive primes. We show that for $k = 9$ and for any sequence of $k$ nonnegative real numbers $\beta_1 \le \beta_2 \le ... \le \beta_k$, at least one of the numbers $\beta_j - \beta_i$ ($1 \le i < j \le k$) belongs to $\boldsymbol{L}$. It follows at least $12.5$ of all nonnegative real numbers belong to $\boldsymbol{L}$.Comment: Revised and improve

The Need for an Independent Federal Judiciary: Prison Reform Litigation Spurs Structural Change – The California Penal Crisis

This Article examines Madrid V. Gomez, 889 F.Supp. 1146, the last case before the passage of the PLRA in which a federal court broadly intervened in a state prison system through structural reform litigation. Part II outlines the historical and jurisprudential foundations that legitimate federal judicial intervention in state prisons. Part III examines the California prison system through the lens of the Madrid litigation and the ongoing social and political problems caused by the prison crisis. Part IV concludes that judicial intervention remains the only viable tool to remedy constitutional deficiencies in state prisons when majoritarian political processes fail to produce serious reform. Therefore, it is essential that the power and independence of the federal judiciary be preserved to ensure the rights of the politically powerless and mitigate Constitutional harms

Mobility, fitness collection, and the breakdown of cooperation

The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters, they might share the benefit of cooperation while being more protected against noncooperating individuals, who benefit from cooperation but save the cost of cooperation. This is paradigmatically shown by the spatial prisoner's dilemma model. Here, we study this model in one and two spatial dimensions, but explicitly take into account that in biological setups, fitness collection and selection are separated processes occurring mostly on vastly different time scales. This separation is particularly important to understand the impact of mobility on the evolution of cooperation. We find that even small diffusive mobility strongly restricts cooperation since it enables noncooperative individuals to invade cooperative clusters. Thus, in most biological scenarios, where the mobility of competing individuals is an irrefutable fact, the spatial prisoner's dilemma alone cannot explain stable cooperation, but additional mechanisms are necessary for spatial structure to promote the evolution of cooperation. The breakdown of cooperation is analyzed in detail. We confirm the existence of a phase transition, here controlled by mobility and costs, which distinguishes between purely cooperative and noncooperative absorbing states. While in one dimension the model is in the class of the voter model, it belongs to the directed percolation universality class in two dimensions. DOI: 10.1103/PhysRevE.87.04271