Interference fracturing: Nonuniform distributions of perforation clusters that promote simultaneous growth of multiple hydraulic fractures

One of the important hurdles in horizontal-well stimulation is the generation of hydraulic fractures (HFs) from all perforation clusters within a given stage, despite the challenges posed by stress shadowing and reservoir variability. In this paper, we use a newly developed, fully coupled, parallel-planar 3D HF model to investigate the potential to minimize the negative impact of stress shadowing and thereby to promote more-uniform fracture growth across an array of HFs by adjusting the location of the perforation clusters. In this model, the HFs are assumed to evolve in an array of parallel planes with full 3D stress coupling while the constant fluid influx into the wellbore is dynamically partitioned to each fracture so that the wellbore pressure is the same throughout the array. The model confirms the phenomenon of inner-fracture suppression because of stress shadowing when the perforation clusters are uniformly distributed. Indeed, the localization of the fracture growth to the outer fractures is so dominant that the total fractured area generated by uniform arrays is largely independent of the number of perforation clusters. However, numerical experiments indicate that certain nonuniform cluster spacings promote a profound improvement in the even development of fracture growth. Identifying this effect relies on this new model's ability to capture the full hydrodynamical coupling between the simultaneously evolving HFs in their transition from radial to Perkins-Kern-Nordgren (PKN)-like geometries (Perkins and Kern 1961; Nordgren 1972)

Extremal Problems in Bergman Spaces and an Extension of Ryabykh's Theorem

We study linear extremal problems in the Bergman space $A^p$ of the unit disc for $p$ an even integer. Given a functional on the dual space of $A^p$ with representing kernel $k \in A^q$, where $1/p + 1/q = 1$, we show that if the Taylor coefficients of $k$ are sufficiently small, then the extremal function $F \in H^{\infty}$. We also show that if $q \le q_1 < \infty$, then $F \in H^{(p-1)q_1}$ if and only if $k \in H^{q_1}$. These results extend and provide a partial converse to a theorem of Ryabykh.Comment: 16 pages. To appear in the Illinois Journal of Mathematic

Meeting the challenge for foot health in rheumatic diseases

Background: National guidelines recommend that patients with rheumatic diseases should have access to podiatry services and evidence is emerging that podiatry interventions are effective in the management of foot problems in this patient group. Despite this recognition it is generally perceived that access to podiatry services appears to be varied or absent. Objectives: To identify the nature of foot health problems presenting in a rheumatology clinic and to ascertain the availability and suitability of foot care for these problems. Method: A convenience sample of 139 patients (100 female and 39 male) was recruited. An assessment of foot health, and footwear was carried out and patients completed the foot function index (FFI). Any unmet foot care needs were identified. Results: The majority of the 139 patients presented with symptomatic callus and toenail problems and over half with foot deformity. There was no clear difference between genders. There was evidence of the effects of foot pain caused by these problems but low prescription of foot orthoses and specialist footwear. Conclusion: Overall this study indicates that poor foot health and foot pain as being common in patients with rheumatic diseases. The lack of foot care could lead to reduction in mobility and in some cases serious complications. This paper recommends that a specialist and dedicated foot care service is provided for these patients

THE EFFECT OF THE STM TIP ON SI(100) RECONSTRUCTED SURFACES

We present a theoretical study of the effects of the STM tip on the geometry of Si(100) reconstructed surfaces. The energy barrier to switching between different reconstructions is also discussed. We use a molecular dynamics method and self-consistent forces to simulate the time-dependent behaviour of the surface atoms. The molecular orbital calculations are performed at the CNDO level using a cluster model. Our results indicate significant differences for positively and negatively biased tips. The thermally induced rocking of surface dimers is inhibited by the application of a positive bias to the tip and it is promoted by a negative bias. These bias-dependent effects may offer a plausible explanation for the bias dependence of STM images of this surface

EFFECTS OF THE STM TIP ON ADSORBATE IMAGE

Scanning tunnelling microscopy provides atomic scale information about surface topography and electronic structure. However, the way the tip affects the STM image cannot always be neglected. We present a theoretical study of the effect of the non-uniform electric field of the tip on STM image of adsorbed molecules using Bardeen's approach. Self-consistent geometry optimization and wave-function calculations have been carried out within the CNDO approximation in a cluster model. Our results indicate significant effects. Thus for adsorbed CO on metal, the molecules reorient because of the tip, and the image is changed qualitatively as well as quantitatively. This may explain the lack of observation of CO at low coverage by STM. Our results also suggest the STM might be used for molecular modification

Magnetic resonance imaging: a tool for pork pie development

The traditional British pork pie consists of roughly chopped pork cooked in a hot water pastry crust. Due to shrinkage of the meat during cooking, the gap formed around the meat is usually sealed using a gelatin based jelly to exclude air and thus help to preserve the pie. The properties of the jelly are such that it will ingress into the pastry crust causing undesirable softening. The jelly is traditionally produced by simmering pig trotters with seasoning for several hours. In this work we demonstrate the potential of magnetic resonance imaging (MRI) as a tool for investigating the conditions required for producing jellies with different properties and present two examples of this use. Firstly we demonstrate that MRI can determine the ability of water to diffuse through the jelly which is critical in minimizing the amount of moisture moving from the jelly to the crust. Secondly, the impact of jelly temperature on the penetration length into the crust is investigated. These examples highlight the power of MRI as a tool for food assessment

Covariant Quantum Fields on Noncommutative Spacetimes

A spinless covariant field $\phi$ on Minkowski spacetime \M^{d+1} obeys the relation $U(a,\Lambda)\phi(x)U(a,\Lambda)^{-1}=\phi(\Lambda x+a)$ where $(a,\Lambda)$ is an element of the Poincar\'e group \Pg and $U:(a,\Lambda)\to U(a,\Lambda)$ is its unitary representation on quantum vector states. It expresses the fact that Poincar\'e transformations are being unitary implemented. It has a classical analogy where field covariance shows that Poincar\'e transformations are canonically implemented. Covariance is self-reproducing: products of covariant fields are covariant. We recall these properties and use them to formulate the notion of covariant quantum fields on noncommutative spacetimes. In this way all our earlier results on dressing, statistics, etc. for Moyal spacetimes are derived transparently. For the Voros algebra, covariance and the *-operation are in conflict so that there are no covariant Voros fields compatible with *, a result we found earlier. The notion of Drinfel'd twist underlying much of the preceding discussion is extended to discrete abelian and nonabelian groups such as the mapping class groups of topological geons. For twists involving nonabelian groups the emergent spacetimes are nonassociative.Comment: 20 page

ELECTRONIC-STRUCTURE OF V- CENTER IN MGO

The authors have investigated in detail the two models of the V- centre, where a hole is trapped at a cation vacancy. These are the model of Bartram, Swenberg and Fourn (1965), where optical transitions occur within an O- ion, and the model of Schirmer, Koidl and Reik (1974), which involves a hole hopping from one oxygen ion to another. The calculations show (i) that the hole should be self-trapped on a single oxygen, as observed, (ii) that the predictions of ground-state ionization energy and of elastic and electrical dipole moments (apart from some uncertainties in local-field corrections) agree adequately with measurements, (iii) that the transitions within an O- ion appear to account for observed structure at around 1.5 eV, both in energy and oscillator strength, and (iv) that the observed 2.3 eV band corresponds to the transition suggested by Schirmer et al. Calculations are also given for some centres related to the V- centre, V0, V(Al)- and (Na)0, again predicting optical absorption in good agreement with experiment