Converging shocks in elastic-plastic solids

We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy e = e_(s)(I_1)+e_(h)(ρ,ς), where e_(s) accounts for shear through the first invariant of the Cauchy–Green tensor, and e_(h) represents the hydrostatic contribution as a function of the density ρ and entropy ς. In the strong-shock limit, reached as the shock approaches the axis or origin r=0, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., e_(h) = e_(h)(ρ), with a power-law dependence e_(h) ∝ ρ_(α), shock dynamics predicts that for a converging shock located at r=R(t) at time t, the Mach number increases as M ∝ [log(1/R)]^α, independently of the space index s, where s=2 in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with p(ρ) of the arctanh type, which enforces a finite density in the strong-shock limit, leads to M ∝ R^(−(s−1)) for strong shocks. A nonisothermal constitutive law, whose hydrostatic part eh is that of an ideal gas, is also tested, recovering the strong-shock limit M∝R^(−(s−1)/n(γ)) originally derived by Whitham for perfect gases, where γ is inherently related to the maximum compression ratio that the material can reach, (γ+1)/(γ−1). From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the hydrostatic part of the energy essentially commands the strong-shock behavior, the shear modulus and yield stress modify the compression ratio and velocity of the shock far from the axis or origin. A characterization of the elastic-plastic transition in converging shocks, which involves an elastic precursor and a plastic compression region, is finally exposed

Regularity of solutions to a fractional elliptic problem with mixed Dirichlet-Neumann boundary data

In this work we study regularity properties of solutions to fractional elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with the Spectral Fractional Laplacian

The Hardcore Scorecard: Defining, Quantifying and Understanding “Hardcore” Video Game Culture

ABSTRACT The goal of the current study is to further conceptualize and define the term “hardcore” as it relates to video game culture. Past research indicates that members of cultural subdivisions favor their own group versus others due to perceived commonalities (Durkheim, 1915; Tajfel, 1970). In gaming culture, the subdivisions of “hardcore” and “casual” games/gamers have become especially salient in recent years. However, the definition of what constitutes “hardcore” and “casual” is inconsistent (Adams, 2000; Alexandre, 2012; Jacobs & Ip, 2003; Juul, 2010; Kim, 2001; Kuittinen, Kultima, Niemelä & Paavilainen, 2007; Wallace & Robbins, 2006). Therefore, it is beneficial to better understand these terms considering the implications: less audience infighting, more accurately tailored game design/marketing, and less ambiguous/sensationalist gaming journalism/media. A sample of 109 undergraduate students from a large university (19,000 undergraduates) in an upstate New York city (metropolitan population of 1.1 million) completed an online survey, reporting their perceptions of hardcore gaming. Values were then attributed to certain video game criteria based on the survey results and applied to popular games. The sum of these values produced a hardcore index for the “scorecard.” To assess the scorecard’s validity, correlations were run between our final values and an independently collected hardcore percentage publicly available on the Wii’s Nintendo Channel (327,818.45 average respondents per game). Results suggest hardcore gaming is perceived as a harsh subculture consisting of long play times, challenging play, anti-social behavior, and content not suitable for children. The index produced by the resulting “hardcore scorecard” was significantly correlated (r = .765, p \u3c .01) with the independently collected data on the Nintendo Channel. Thus, the current research provides tools the gaming industry (users, developers, journalists) can use to their advantage by better understanding and defining the term “hardcore,” as well as a valuable blueprint for future research to continue refining and improving

Complex, Dynamic Combination of Physical, Chemical and Nutritional Variables Controls Spatio-Temporal Variation of Sandy Beach Community Structure

Sandy beach ecological theory states that physical features of the beach control macrobenthic community structure on all but the most dissipative beaches. However, few studies have simultaneously evaluated the relative importance of physical, chemical and biological factors as potential explanatory variables for meso-scale spatio-temporal patterns of intertidal community structure in these systems. Here, we investigate macroinfaunal community structure of a micro-tidal sandy beach that is located on an oligotrophic subtropical coast and is influenced by seasonal estuarine input. We repeatedly sampled biological and environmental variables at a series of beach transects arranged at increasing distances from the estuary mouth. Sampling took place over a period of five months, corresponding with the transition between the dry and wet season. This allowed assessment of biological-physical relationships across chemical and nutritional gradients associated with a range of estuarine inputs. Physical, chemical, and biological response variables, as well as measures of community structure, showed significant spatio-temporal patterns. In general, bivariate relationships between biological and environmental variables were rare and weak. However, multivariate correlation approaches identified a variety of environmental variables (i.e., sampling session, the C:N ratio of particulate organic matter, dissolved inorganic nutrient concentrations, various size fractions of photopigment concentrations, salinity and, to a lesser extent, beach width and sediment kurtosis) that either alone or combined provided significant explanatory power for spatio-temporal patterns of macroinfaunal community structure. Overall, these results showed that the macrobenthic community on Mtunzini Beach was not structured primarily by physical factors, but instead by a complex and dynamic blend of nutritional, chemical and physical drivers. This emphasises the need to recognise ocean-exposed sandy beaches as functional ecosystems in their own right