The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells

Digest and analysis of the organization of health councils in eight schools and communities in Massachusetts

Thesis (M.A.)--Boston University, 1946. This item was digitized by the Internet Archive

Remarks, Before the 82nd Annual Meeting of the American Institute of Certified Public Accountants, Los Angeles Hilton, October 8, 1969

https://egrove.olemiss.edu/aicpa_assoc/2073/thumbnail.jp

The non-local Lotka–Volterra system with a top hat kernel — Part 1:dynamics and steady states with small diffusivity

We study the dynamics of the nonlocal Lotka-Volterra system u t = Duuxx + u (1 − ϕ * u − αv), v t = Dvvxx + v (1 − ϕ * v − βu), where a star denotes the spatial convolution and the kernel ϕ is a top hat function. We initially focus on the case of small, equal diffusivities (D = Du = Dv ≪ 1) together with weak interspecies interaction (α, β ≪ 1), and specifically α, β ≪ D. This can then be extended to consider small, but unequal, diffusivities and weak interactions, with now α, β ≪ Du, Dv ≪ 1. Finally we are able to develop the theory for the situation when the diffusivities remain small, but the interactions become stronger.. In each case, we find that u and v independently develop into periodic spatial patterns that consist of separated humps on an O(1) timescale, and that these patterns become quasi-steady on a timescale proportional to the inverse diffusivity. These then interact on a longer timescale proportional to the inverse interaction scale, and approach a meta-stable state. Finally, a stable steady state is achieved on a much longer timescale, which is exponentially large relative to the preceding timescales. We are able to quantify this interaction process by determining a planar dynamical system that governs the temporal evolution of the separation between the two periodic arrays of humps on these sequentially algebraically and then exponentially long timescales. We find that, once the humps no longer overlap, the subsequent dynamics lead to a symmetric disposition of the humps, occurring on the exponentially-long timescale. Numerical solutions of the full evolution problem cannot access the behaviour on this final extreme timescale, but it can be fully explored through the dynamical system

The evolution problem for the 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 2. The Cauchy problem on a finite interval

In the second part of this series of papers, we address the same Cauchy problem that was considered in part 1, namely the nonlocal Fisher-KPP equation in one spatial dimension, $$u_t = D u_{xx} + u(1-\phi*u),$$ where $\phi*u$ is a spatial convolution with the top hat kernel, $\phi(y) \equiv H\left(\frac{1}{4}-y^2\right)$, except that now the spatial domain is the finite interval $[0,a]$ rather than the whole real line. Consequently boundary conditions are required at the interval end-points, and we address the situations when these boundary conditions are of either Dirichlet or Neumann type. This model forms a natural extension to the classical Fisher-KPP model, with the introduction of the simplest possible nonlocal effect into the saturation term. Nonlocal reaction-diffusion models arise naturally in a variety of (frequently biological or ecological) contexts, and as such it is of fundamental interest to examine its properties in detail, and to compare and contrast these with the well known properties of the classical Fisher-KPP model

Microstructural and Isotopic Constraints on WL Rim Formation

Coordinated microanalyses of Wark-Lovering (WL) rims are needed to best understand their origin and to decipher their subsequent evolution both in the nebular and parent body settings. Here we present the mineralogy, petrology, microstructures, O isotopic compositions, and Al-Mg systematics of a WL rim on a Type B CAI, Big Guy, from the reduced CV3 chondrite Vigarano [1]. Our SEM and TEM study reveals seven distinct mineral layers in the WL rim that include: (1) gehlenite with rare grossite, (2) hibonite, (3) spinel with minor hibonite and perovskite, (4) zoned melilite (k(sub ~0-10)), (5) anorthite, (6) zoned diopside grading outwards from Al,Ti-rich to Al,Tipoor, and (7) forsterite intergrown with diopside. We infer a two-stage history in which WL rim formation was initiated by flash melting and extensive evaporation of the original inclusion edge, followed by subsequent condensation under highly dynamic conditions. The outermost edge of the CAI mantle is mineralogically and texturally distinct compared to the underlying mantle that is composed of coarse, zoned melilite (k(sub ~10-60)) grains. The mantle edge contains finegrained gehlenite with hibonite and rare grossite that likely formed by rapid crystallization from a Ca,Al-rich melt produced during a flash vaporization event [2]. These gehlenite and hibonite layers are surrounded by successive layers of spinel, melilite, diopside, and forsterite, indicating their sequential gas-solid reactions onto hibonite. Anorthite occurs as a discontinuous layer that corrodes adjacent melilite and Al-diopside, and appears to have replaced them [3,4], probably even later than the forsterite layer formation. All the WL rim minerals analyzed using the JSC NanoSIMS 50L are 16O-rich (17O 23), indicating their formation in an 16O-rich gas reservoir. Our data are in contrast with many CV CAIs that show heterogeneous 17O values across their WL rims [5]. Our Al-Mg data obtained using the UCLA ims-1290 ion microprobe of the CAI interior and the WL rim define a well-correlated isochron with (26Al/27Al)(sub 0) = 4.94 10(exp 5), indicating their synchronous formation 5 10(exp 4) years after the canonical CAI value. In contrast, no 26Mg excesses are observed in the WL rim anorthite, which suggests its later formation or later isotopic resetting in an 16O-rich gas reservoir, after 26Al had decayed

Performance of the track matching

The procedure and the performance of the track matching algorithm at the time of DC'06 is described. The event-weighted efficiency is 79.3 % for all long tracks increasing to 86 % for tracks with p>5 GeV. An approach to tune the matching algorithm with real data is presented and a discussion on future improvements to the algorithm given