Emergent <Emphasis Type=Italic>SO</Emphasis>(3) Symmetry of the Frictionless Shear Jamming Transition

We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actually have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor.     

A solution for the narrow rectangular punch

This paper considers the problem of a rectangular flat ended punch acting on an elastic half-space. An approximate solution is generated through application of the elastic line integral equations. The results produced by this method are then compared with another approximate solution already available.

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Zusammenfassung Dieser Aufsatz behandelt das Problem eines starren, flachen Stempels mit rechteckigen Grundriss, der in einen elastischen Halbraum gepresst wird. Eine Näherungslösung wird erzeugt mittels der Integralgleichung des elastischen Linienkontakts. Die auf dieser Weise gewonnene Ergebnisse werden mit einer schon bekannten Näherungslösung verglichen.

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Résumé Dans ce rapport, on considère le problème d'un cachet rigide à base plane rectangulaire qui est poussée dans une semi-espace élastique. Une solution approximative est générée par application de l'équation integrale du contact élastique de ligne. Les résultats produits par cette méthode sont comparés à une solution approximative déjà connue.

     

Shale-Gas Permeability and Diffusivity Inferred by Improved Formulation of Relevant Retention and Transport Mechanisms

A theoretically improved model incorporating the relevant mechanisms of gas retention and transport in gas-bearing shale formations is presented for determination of intrinsic gas permeability and diffusivity. This is accomplished by considering the various flow regimes according to a unified Hagen–Poiseuille-type equation, fully compressible treatment of gas and shale properties, and numerical solution of the non-linear pressure equation. The present model can accommodate a wide range of fundamental flow mechanisms, such as continuum, slip, transition, and free molecular flow, depending on the prevailing flow conditions characterized by the Knudsen number. The model indicates that rigorous determination of shale-gas permeability and diffusivity requires the characterization of various important parameters included in the present phenomenological modeling approach, many of which are not considered in previous studies. It is demonstrated that the improved model matches a set of experimental data better than a previous attempt. It is concluded that the improved model provides a more accurate means of analysis and interpretation of the pressure-pulse decay tests than the previous models which inherently consider a Darcian flow and neglect the variation of parameters with pressure.     

Nonlinear limit for a system of diffusing particles which alternate between two states

We study a system of particles and the nonlinear McKean-Vlasov diffusion that is its limit for weak interactions. Each particle switches between two states, both with their own diffusion dynamics. There is interaction, in particular, in the rates of the switches. We show existence and uniqueness for the system of particles by stopping-time techniques. For the nonlinear martingale problem, we use a time-change that allows us to return to a strong pathwise representation, and then we use a contraction argument for an appropriate metric. Finally, we show propagation of chaos.     

A connection between Strassen's and Donsker-Varadhan's laws of the iterated logarithm

Summary A connection is given between various functional laws of the iterated logarithm for Brownian motion due to Donsker and Varadhan, Csáki, Chung, Strassen, and the author.Supported by an NSF grant