Hybrid basis scheme for computing electrostatic fields exterior to close-to-touching discs

This paper presents a simple and effective new numerical scheme for the computation of electrostatic fields exterior to a collection of close-to-touching discs. The method is presented in detail for the two-disc case. The key idea is to represent the required complex potential using a hybrid set of basis functions comprising the usual Fourier–Laurent expansion about each circle centre complemented by a subsidiary expansion in a variable associated with conformal mapping of the physical domain to a concentric annulus domain. We also rigorously prove that there is a representation of the solution in the hybrid basis with a faster decay rate of coefficients than is obtained by using a nonhybrid basis, thereby providing a rationalization for the success of the method. The numerical scheme is easy to implement and adaptable to the case of multiple close-to-touching cylinders

Financial Stability of Islamic Versus Conventional Banks in Pakistan

This study aims to analyze and compare the financial stability of Pakistani banks covering a timeframe of 5 years from 2012 to 2016. This study employs the financial soundness indicators of the International Monetary Funds and State Bank of Pakistan and the z-score index. The comparative analysis through average scores is performed using 3 indicators of financial stability namely Z-Score, Capital Adequacy Ratio (CAR) and Equity to Total Assets Ratio. The findings of the research reveal that (i) conventional banks are more financially stable than Islamic banks; (ii) large conventional banks are more financially stable than large Islamic banks; (iii) small Islamic banks are less stable than small conventional bank. The implication of this paper is that conventional banks have the potential of absorbing financial stability shock as compare to Islamic banks on the basis of stated financial soundness indicators and Z-Score specifically.DOI: 10.15408/aiq.v10i2.650

Numerical modeling of quasiplanar giant water waves

In this work we present a further analytical development and a numerical implementation of the recently suggested theoretical model for highly nonlinear potential long-crested water waves, where weak three-dimensional effects are included as small corrections to exact two-dimensional equations written in the conformal variables [V.P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Numerical experiments based on this theory describe the spontaneous formation of a single weakly three-dimensional large-amplitude wave (alternatively called freak, killer, rogue or giant wave) on the deep water.Comment: revtex4, 8 pages, 7 figure

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A 343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419 (1996)] as well as direct numerical computation, following the numerical scheme of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (non-singular) zero surface tension solutions. The effect is present even when the relevant zero surface tension solution has asymptotic behavior consistent with selection theory.Such singular effects therefore cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structually unstable flow, restoring the hyperbolicity of multifinger fixed points.Comment: 16 pages, 15 figures, submitted to Phys. Rev

Distal radius fractures: a prospective study of the clinical and radiological outcomes in surgically managed patients

Background: Objective of the research was to evaluate radiological and functional outcome in fractures of the distal radius treated by various surgical methods.Methods: 89 patients with distal radius fractures were randomly divided into three groups according to a computer-generated table of randomization. 40 patients were managed by K wire fixation. 22 patients were managed by external fixator. 27 patients were managed by volar plating technique. Anatomical restoration was evaluated by posterior-anterior and lateral radiographs obtained preoperatively and at 09 months of follow up to evaluate radial height (RH), radial inclination (RI) and volar tilt (VT). Functional outcome was evaluated using Mayo scoring system.Results: According to Mayo score, in K-wire group 72.5% (n=29) patients had excellent to good outcome, 17.5% (n=7) had fair outcome while as 10% (n=4) patients had poor outcome. In external fixator group 72.7% (n=16) patients had excellent to good outcome while as 27.3% (n=6) had fair outcome. In volar plating group 81.5% (n=22) patients had excellent to good outcome while as 18.5% (n=5) had fair outcome.Conclusions: In our study we found that volar locked plating provides advantage in dorsally or volarly displaced intra-articular fractures with excellent to good radiological outcome. However, in type B (partial intra-articular fractures) fractures, volar locking compression plate (LCP) and external fixator provide almost equivocal results. Percutaneous pinning can be recommended for extra-articular or simple intra-articular fracture patterns, with a loss of volar and/or RI but without significant radial shortening

Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition

Successful applications of the Kruskal-Segur approach to interfacial pattern formation have remained limited due to the necessity of an integral formulation of the problem. This excludes nonlinear bulk equations, rendering convection intractable. Combining the method with Zauderer's asymptotic decomposition scheme, we are able to strongly extend its scope of applicability and solve selection problems based on free boundary formulations in terms of partial differential equations alone. To demonstrate the technique, we give the first analytic solution of the problem of velocity selection for dendritic growth in a forced potential flow.Comment: Submitted to Europhys. Letters, No figures, 5 page

An Insight into the Application of Gradations of Circularity in the Food Packaging Industry: A Systematic Literature Review and a Multiple Case Study

This is the final version. Available on open access from MDPI via the DOI in this recordData Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to primary data collection and to protect the identities of the participants (interviews were conducted and transcribed).Given its unsustainable growth, the food packaging industry (FPI) has become a priority industry in the circular economy. Given the academic significance attributed to the gradations of circularity in maximising resource efficiency in the food packaging industry, this paper aims to identify the current state of the application of those gradations of circularity in the FPI by finding the least and most commonly used circular strategies in the FPI. Moreover, it aims to identify the drivers of and barriers to the implementation of the gradations of circularity and the levers for overcoming such barriers through SLR using multiple case studies, namely five small-medium enterprises (SMEs) in the FPI that each represent one of the five least implemented circular strategies. The research identified that the efforts of the FPI toward adopting circular strategies were not aligned with the gradations of circularity. Based on the research findings, a lever–barrier matrix is proposed as a toolkit for SMEs planning a transition toward the circular economy or are in the transition phase

Semiclassical low energy scattering for one-dimensional Schr\"odinger operators with exponentially decaying potentials

We consider semiclassical Schr\"odinger operators on the real line of the form $$H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)$$ with $\hbar>0$ small. The potential $V$ is assumed to be smooth, positive and exponentially decaying towards infinity. We establish semiclassical global representations of Jost solutions $f_\pm(\cdot,E;\hbar)$ with error terms that are uniformly controlled for small $E$ and $\hbar$, and construct the scattering matrix as well as the semiclassical spectral measure associated to $H(\hbar)$. This is crucial in order to obtain decay bounds for the corresponding wave and Schr\"odinger flows. As an application we consider the wave equation on a Schwarzschild background for large angular momenta $\ell$ where the role of the small parameter $\hbar$ is played by $\ell^{-1}$. It follows from the results in this paper and \cite{DSS2}, that the decay bounds obtained in \cite{DSS1}, \cite{DS} for individual angular momenta $\ell$ can be summed to yield the sharp $t^{-3}$ decay for data without symmetry assumptions.Comment: 44 pages, minor modifications in order to match the published version, will appear in Annales Henri Poincar