arXiv subjects

James E. McClure

Publications and source records attributed to James E. McClure.

25 records · Page 2Linked to original sources

arXiv2018

A geometric state function for two-fluid flow in porous media

Models that describe two-fluid flow in porous media suffer from a widely-recognized problem that the constitutive relationships used to predict capillary pressure as a function of the fluid saturation are non-unique, thus requiring a hysteretic description. As an alternative to the traditional perspec- tive, we consider a geometrical description of the capillary pressure, which relates the average mean curvature, the fluid saturation, the interfacial area between fluids, and the Euler characteristic. The state equation is formulated using notions from algebraic topology and cast in terms of measures of the macroscale state. Synchrotron-based X-ray micro-computed tomography (μCT) and high- resolution pore-scale simulation is applied to examine the uniqueness of the proposed relationship for six different porous media. We show that the geometric state function is able to characterize the microscopic fluid configurations that result from a wide range of simulated flow conditions in an averaged sense. The geometric state function can serve as a closure relationship within macroscale models to effectively remove hysteretic behavior attributed to the arrangement of fluids within a porous medium. This provides a critical missing component needed to enable a new generation of higher fidelity models to describe two-fluid flow in porous media.

physics.flu-dyn↗

arXiv2012

On semisimplicial sets satisfying the Kan condition

A semisimplicial set has face maps but not degeneracies. A basic fact, due to Rourke and Sanderson, is that a semisimplicial set satisfying the Kan condition can be given a simplicial structure. The present paper gives a combinatorial proof of this fact and a generalization to multisemisimplicial sets.

math.AT↗

arXiv2011

Multiplicative properties of Quinn spectra

We give a simple sufficient condition for Quinn's "bordism-type spectra" to be weakly equivalent to strictly associative ring spectra. We also show that Poincare bordism and symmetric L-theory are naturally weakly equivalent to monoidal functors. Part of the proof of these statements involves showing that Quinn's functor from bordism-type theories to spectra lifts to the category of symmetric spectra. We also give a new account of the foundations.

math.AT↗

arXiv2004

Cosimplicial Objects and little n-cubes. I

In this paper we show that if a cosimplicial space or spectrum $X^\bullet$ has a certain kind of combinatorial structure (we call it a $Ξ^n$-structure) then the total space of $X^\b$ has an action of a certain operad which is weakly equivalent to the little n-cubes operad. The $n\leq 2$ case was proved by a more complicated argument in our earlier paper A Solution of Deligne's Hochschild Cohomology Conjecture (http://front.math.ucdavis.edu/math.QA/9910126). In the special case $n=\infty$, we define a symmetric monoidal structure $\boxtimes$ on cosimplicial spaces and show that if $X^\b$ is a commutative $\boxtimes$-monoid then the total space of $\X^\b$ is an $E_\infty$ space.

math.QA↗

arXiv2004

Operads and cosimplicial objects: an introduction

This paper is an introduction to a series of papers in which we give combinatorial models for certain important operads (including A-infinity and E-infinity operads, the little n-cubes operads, and the framed little disks operad) and combinatorial conditions for them to act on a given space or chain complex. The paper does not assume any prior knowledge of operads--Sections 2, 6 and 9, which can be read independently, are an introduction to the theory of operads.

math.QA↗

arXiv2002

Multivariable cochain operations and little n-cubes

This is a revision of a paper first posted June 4, 2001. It will appear in the Journal of the AMS. In this paper we construct a small $E_\infty$ chain operad $§$ which acts naturally on the normalized cochains $S^*X$ of a topological space. We also construct, for each $n$, a suboperad $§_n$ which is quasi-isomorphic to the normalized singular chains of the little $n$-cubes operad. The case $n=2$ leads to a substantial simplification of our earlier proof of Deligne's Hochschild cohomology conjecture.

math.QA↗

arXiv2001

A solution of Deligne's conjecture

Deligne asked in 1993 whether the Hochschild cochain complex of an associative ring has a natural action by the singular chains of the little 2-cubes operad. In this paper we give an affirmative answer to this question. We also show that the topological Hochschild cohomology spectrum of an associative ring spectrum has an action of an operad equivalent to the little 2-cubes.

math.QA↗