Stability of Relativistic Matter with Magnetic Fields for Nuclear Charges up to the Critical Value

We give a proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge $Z\alpha=2/\pi$.Comment: LaTeX2e, 12 page

On the Order of Plates Providing the Maximum Ballistic Limit Velocity of a Layered Armor

Abstract The high-velocity impact of a three-dimensional rigid sharp impactor penetrating into a ductile layered armor is studied using a simpli"ed model for an impactor}armor interaction. The goal of the study is to determine the order of the plates in the armor that provides the maximum ballistic limit velocity. It is found that the ratio of the distortion pressure to the density of the plate is the parameter that determines the order of the plates in the multi-layered armor that provides the maximum ballistic limit velocity, namely, the plates must be placed in the order of increasing this parameter, regardless of their thickness. The right order of the plates can be of prime importance if the values of this parameter vary strongly for di!erent plates. Numerical simulation is performed in order to verify the theoretical "ndings and to obtain a quantitative estimate for the increase in the ballistic limit that results from changing the order of the plates in the armor

Estimating specific surface area of fine stream bed sediments from geochemistry

Specific surface area (SSA) of headwater stream bed sediments is a fundamental property which determines the nature of sediment surface reactions and influences ecosystem-level, biological processes. Measurements of SSA – commonly undertaken by BET nitrogen adsorption – are relatively costly in terms of instrumentation and operator time. A novel approach is presented for estimating fine (2.5 mg kg−1), four elements were identified as significant predictors of SSA (ordered by decreasing predictive power): V > Ca > Al > Rb. The optimum model from these four elements accounted for 73% of the variation in bed sediment SSA (range 6–46 m2 g−1) with a root mean squared error of prediction – based on leave-one-out cross-validation – of 6.3 m2 g−1. It is believed that V is the most significant predictor because its concentration is strongly correlated both with the quantity of Fe-oxides and clay minerals in the stream bed sediments, which dominate sediment SSA. Sample heterogeneity in SSA – based on triplicate measurements of sub-samples – was a substantial source of variation (standard error = 2.2 m2 g−1) which cannot be accounted for in the regression model. The model was used to estimate bed sediment SSA at the other 1792 sites and at 30 duplicate sites where an extra sediment sample had been collected, 25 m from the original site. By delineating sub-catchments for the headwater sediment sites only those sub-catchments were selected with a dominant (>50% of the sub-catchment area) bedrock formation and land use type; the bedrock and land use classes accounted for 39% and 7% of the variation in bed sediment SSA, respectively. Variation in estimated, fine bed sediment SSA from the paired, duplicate sediment sites was small (2.7 m2 g−1), showing that local variation in SSA at stream sites is modest when compared to that between catchments. How the approach might be applied in other environments and its potential limitations are discussed

Local Guarantees in Graph Cuts and Clustering

Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$ or $-$ and the goal is to produce a clustering that agrees with the labels as much as possible: $+$ edges within clusters and $-$ edges across clusters. The classical approach towards Correlation Clustering (and other graph cut problems) is to optimize a global objective. We depart from this and study local objectives: minimizing the maximum number of disagreements for edges incident on a single node, and the analogous max min agreements objective. This naturally gives rise to a family of basic min-max graph cut problems. A prototypical representative is Min Max $s-t$ Cut: find an $s-t$ cut minimizing the largest number of cut edges incident on any node. We present the following results: $(1)$ an $O(\sqrt{n})$-approximation for the problem of minimizing the maximum total weight of disagreement edges incident on any node (thus providing the first known approximation for the above family of min-max graph cut problems), $(2)$ a remarkably simple $7$-approximation for minimizing local disagreements in complete graphs (improving upon the previous best known approximation of $48$), and $(3)$ a $1/(2+\varepsilon)$-approximation for maximizing the minimum total weight of agreement edges incident on any node, hence improving upon the $1/(4+\varepsilon)$-approximation that follows from the study of approximate pure Nash equilibria in cut and party affiliation games

Compressible flow structures interaction with a two-dimensional ejector: a cold-flow study

An experimental study has been conducted to examine the interaction of compressible flow structures such as shocks and vortices with a two-dimensional ejector geometry using a shock-tube facility. Three diaphragm pressure ratios ofP4 =P1 = 4, 8, and 12 have been employed, whereP4 is the driver gas pressure andP1 is the pressure within the driven compartment of the shock tube. These lead to incident shock Mach numbers of Ms = 1:34, 1.54, and 1.66, respectively. The length of the driver section of the shock tube was 700 mm. Air was used for both the driver and driven gases. High-speed shadowgraphy was employed to visualize the induced flowfield. Pressure measurements were taken at different locations along the test section to study theflow quantitatively. The induced flow is unsteady and dependent on the degree of compressibility of the initial shock wave generated by the rupture of the diaphragm