Scattering of a longitudinal wave by a circular crack in a fluid-saturated porous medium

Physical properties of many natural and man-made materials can be modelled using the concept of poroelasticity. Some porous materials, in addition to the network of pores, contain larger inhomogeneities such as inclusions, cavities, fractures or cracks. A common method of detecting such inhomogeneities is based on the use of elastic wave scattering. We consider interaction of a normally incident time-harmonic longitudinal plane wave with a circular crack imbedded in a porous medium governed by Biot's equations of dynamic poroelasticity. The problem is formulated in cylindrical co-ordinates as a system of dual integral equations for the Hankel transform of the wave field, which is then reduced to a single Fredholm integral equation of the second kind. It is found that the scattering that takes place is predominantly due to wave inducedfluid flow between the pores and the crack. The scattering magnitude depends on the size of the crack relative to the slow wave wavelength and has it's maximum value when they are of the same order

Enhacement in the dymanic response of a viscoelastic fluid flowing through a longitudinally vibrating tube

We analyzed effects of elasticity on the dynamics of fluids in porous media by studying a flow of a Maxwell fluid in a tube, which oscillates longitudinally and is subject to oscillatory pressure gradient. The present study investigates novelties brought about into the classic Biot's theory of propagation of elastic waves in a fluid-saturated porous solid by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. Using the time Fourier transform and transforming the problem into the frequency domain, we calculated: (A) the dynamic permeability and (B) the function $F(\kappa)$ that measures the deviation from Poiseuille flow friction as a function of frequency parameter $\kappa$. This provides a more complete theory of flow of Maxwell fluid through the longitudinally oscillating cylindrical tube with the oscillating pressure gradient, which has important practical applications. This study has clearly shown transition from dissipative to elastic regime in which sharp enhancements (resonances) of the flow are found

The Biot-Savart operator and electrodynamics on subdomains of the three-sphere

We study steady-state magnetic fields in the geometric setting of positive curvature on subdomains of the three-dimensional sphere. By generalizing the Biot-Savart law to an integral operator BS acting on all vector fields, we show that electrodynamics in such a setting behaves rather similarly to Euclidean electrodynamics. For instance, for current J and magnetic field BS(J), we show that Maxwell's equations naturally hold. In all instances, the formulas we give are geometrically meaningful: they are preserved by orientation-preserving isometries of the three-sphere. This article describes several properties of BS: we show it is self-adjoint, bounded, and extends to a compact operator on a Hilbert space. For vector fields that act like currents, we prove the curl operator is a left inverse to BS; thus the Biot-Savart operator is important in the study of curl eigenvalues, with applications to energy-minimization problems in geometry and physics. We conclude with two examples, which indicate our bounds are typically within an order of magnitude of being sharp.Comment: 24 pages (was 28 pages) Revised to include a new introduction, a detailed example, and results about helicity; other changes for readabilit

Analysis of coupled heat and moisture transfer in masonry structures

Evaluation of effective or macroscopic coefficients of thermal conductivity under coupled heat and moisture transfer is presented. The paper first gives a detailed summary on the solution of a simple steady state heat conduction problem with an emphasis on various types of boundary conditions applied to the representative volume element -- a periodic unit cell. Since the results essentially suggest no superiority of any type of boundary conditions, the paper proceeds with the coupled nonlinear heat and moisture problem subjecting the selected representative volume element to the prescribed macroscopically uniform heat flux. This allows for a direct use of the academic or commercially available codes. Here, the presented results are derived with the help of the SIFEL (SIimple Finite Elements) system.Comment: 23 pages, 11 figure

Theory of Sound Propagation in Superfluid Solutions Filled Porous Media

A theory of the propagation of acoustic waves in a porous medium filled with superfluid solution is developed. The elastic coefficients in the system of equations are expressed in terms of physically measurable quantities. The equations obtained describe all volume modes that can propagate in a porous medium saturated with superfluid solution. Finally, derived equations are applied to the most important particular case when the normal fluid component is locked inside a highly porous media (aerogel) by viscous forces and the velocities of two longitudinal sound modes are calculated.Comment: 13 pages, 0 figure

The Chagos Islands cases: the empire strikes back

Good governance requires the accommodation of multiple interests in the cause of decision making. However, undue regard for particular sectional interests can take their toll upon public faith in government administration. Historically, broad conceptions of the good of the commonwealth were employed to outweigh the interests of groups that resisted colonisation. In the decision making of the British Empire, the standard approach for justifying the marginalisation of the interests of colonised groups was that they were uncivilised and that particular hardships were the price to be paid for bringing to them the imperial dividend of industrial society. It is widely assumed that with the dismantling of the British Empire, such impulses and their accompanying jurisprudence became a thing of the past. Even as decolonisation proceeded apace after the Second World War, however, the United Kingdom maintained control of strategically important islands with a view towards sustaining its global role. In an infamous example from this twilight period of empire, in the 1960s imperial interests were used to justify the expulsion of the Chagos islanders from the British Indian Ocean Territory (BIOT). Into the twenty-first century, this forced elision of the UK’s interests with the imperial “common good” continues to take centre stage in courtroom battles over the islanders’ rights, being cited before domestic and international tribunals in order to maintain the Chagossians’ exclusion from their homeland. This article considers the new jurisprudence of imperialism which has emerged in a string of decisions which have continued to marginalise the Chagossians’ interests

Superconductors with Magnetic Impurities: Instantons and Sub-gap States

When subject to a weak magnetic impurity potential, the order parameter and quasi-particle energy gap of a bulk singlet superconductor are suppressed. According to the conventional mean-field theory of Abrikosov and Gor'kov, the integrity of the energy gap is maintained up to a critical concentration of magnetic impurities. In this paper, a field theoretic approach is developed to critically analyze the validity of the mean field theory. Using the supersymmetry technique we find a spatially homogeneous saddle-point that reproduces the Abrikosov-Gor'kov theory, and identify instanton contributions to the density of states that render the quasi-particle energy gap soft at any non-zero magnetic impurity concentration. The sub-gap states are associated with supersymmetry broken field configurations of the action. An analysis of fluctuations around these configurations shows how the underlying supersymmetry of the action is restored by zero modes. An estimate of the density of states is given for all dimensionalities. To illustrate the universality of the present scheme we apply the same method to study `gap fluctuations' in a normal quantum dot coupled to a superconducting terminal. Using the same instanton approach, we recover the universal result recently proposed by Vavilov et al. Finally, we emphasize the universality of the present scheme for the description of gap fluctuations in d-dimensional superconducting/normal structures.Comment: 18 pages, 9 eps figure

Espon-Interstrat. Espon in Integrated Territorial Strategies.

The INTERSTRAT project’s overall aim is “to encourage and facilitate the use of ESPON 2013 Programme findings in the creation and monitoring of Integrated Territorial Development Strategies (ITDS) and to support transnational learning about the actual and potential contribution of ESPON to integrated policy-making.” We defined integrated territorial development as ‘the process of shaping economic, social and environmental change through spatially sensitive policies and programmes’

Thermal conductivity through the nineteenth century

As a material property and as a metaphor, thermal conductivity occupies an important position in physical, biological and geological sciences. Yet, its precise measurement is dependent on using electricity as a proxy because flowing heat cannot directly be measured.Comment: Submitted to Physics Today. 4,500 words, 4 figure