Minimal surfaces in S(3) with constant contact angle

We provide a characterization of the Clifford Torus in S(3) via moving frames and contact structure equations. More precisely, we prove that minimal surfaces in S(3) with constant contact angle must be the Clifford Torus. Some applications of this result are then given, and some examples are discussed.

A Skyrme-like model with an exact BPS bound

We propose a new Skyrme-like model with fields taking values on the sphere S3 or, equivalently, on the group SU(2). The action of the model contains a quadratic kinetic term plus a quartic term which is the same as that of the Skyrme-Faddeev model. The novelty of the model is that it possess a first order Bogomolny type equation whose solutions automatically satisfy the second order Euler-Lagrange equations. It also possesses a lower bound on the static energy which is saturated by the Bogomolny solutions. Such Bogomolny equation is equivalent to the so-called force free equation used in plasma and solar Physics, and which possesses large classes of solutions. An old result due to Chandrasekhar prevents the existence of finite energy solutions for the force free equation on the entire three- dimensional space R3. We construct new exact finite energy solutions to the Bogomolny equations for the case where the space is the three-sphere S3, using toroidal like coordinates.

Three-dimensional analysis of budding sites and released virus suggests a revised model for HIV-1 morphogenesis

Current models of HIV-1 morphogenesis hold that newly synthesized viral Gag polyproteins traffic to and assemble at the cell membrane into spherical protein shells. The resulting late-budding structure is thought to be released by the cellular ESCRT machinery severing the membrane tether connecting it to the producer cell. Using electron tomography and scanning transmission electron microscopy, we find that virions have a morphology and composition distinct from late-budding sites. Gag is arranged as a continuous but incomplete sphere in the released virion. In contrast, late-budding sites lacking functional ESCRT exhibited a nearly closed Gag sphere. The results lead us to propose that budding is initiated by Gag assembly, but is completed in an ESCRT-dependent manner before the Gag sphere is complete. This suggests that ESCRT functions early in HIV-1 release-akin to its role in vesicle formation-and is not restricted to severing the thin membrane tether.

Formation of the three-dimensional geometry of the red blood cell membrane

Red blood cells (RBCs) are nonnucleated liquid capsules, enclosed in deformable viscoelastic membranes with complex three dimensional geometrical structures. Generally, RBC membranes are highly incompressible and resistant to areal changes. However, RBC membranes show a planar shear deformation and out of plane bending deformation. The behaviour of RBCs in blood vessels is investigated using numerical models. All the characteristics of RBC membranes should be addressed to develop a more accurate and stable model. This article presents an effective methodology to model the three dimensional geometry of the RBC membrane with the aid of commercial software COMSOL Multiphysics 4.2a and Fortran programming. Initially, a mesh is generated for a sphere using the COMSOL Multiphysics software to represent the RBC membrane. The elastic energy of the membrane is considered to determine a stable membrane shape. Then, the actual biconcave shape of the membrane is obtained based on the principle of virtual work, when the total energy is minimised. The geometry of the RBC membrane could be used with meshfree particle methods to simulate motion and deformation of RBCs in micro-capillaries

Unsteady mixed convection with double diffusion over a horizontal cylinder and a sphere within a porous medium

The combined effects of the permeability of the medium, magnetic field, buoyancy forces and dissipation on the unsteady mixed convection flow over a horizontal cylinder and a sphere embedded in a porous medium have been studied. The nonlinear coupled partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The skin friction, heat transfer and mass transfer increase with the permeability of the medium, magnetic field and buoyancy parameter. The heat and mass transfer continuously decrease with the stream-wise distance, whereas the skin friction increases from zero, attains a maximum and then decreases to zero. The skin friction, heat transfer and mass transfer are significantly affected by the free stream velocity distribution. The effect of dissipation parameter is found to be more pronounced on the heat transfer than on the skin friction and mass transfer

Boundary perturbations and the Helmholtz equation in three dimensions

We propose an analytic perturbative scheme in the spirit of Lord Rayleigh's work for determining the eigenvalues of the Helmholtz equation in three dimensions inside an arbitrary boundary where the eigenfunction satisfies either the Dirichlet boundary condition or the Neumann boundary condition. Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to the best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schrodinger perturbation theory. The efficacy of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.

Sphere to ring morphological transformation in drying nanofluid droplets in a contact-free environment

Understanding the transients of buckling in drying colloidal suspensions is pivotal for producing new functional microstructures with tunable morphologies. Here, we report first observations and elucidate the buckling instability induced morphological transition (sphere to ring structure) in an acoustically levitated, heated nanosuspension droplet using dynamic energy balance. Droplet deformation featuring the formation of symmetric cavities is initiated by capillary pressure that is two to three orders of magnitude greater than the acoustic radiation pressure, thus indicating that the standing pressure field has no influence on the buckling front kinetics. With an increase in heat flux, the growth rate of surface cavities and their post-buckled volume increase while the buckling time period reduces, thereby altering the buckling pathway and resulting in distinct precipitate structures. However, irrespective of the heating rate, the volumetric droplet deformation exhibits a linear time dependence and the droplet vaporization is observed to deviate from the classical D-2-law.

Pressure Controlled Self-Assembly of High Quality Three-Dimensional Colloidal Photonic Crystals

A concise pressure controlled isothermal heating vertical deposition (PCIHVD) method is developed, which provides an optimal growing condition with better stability and reproducibility for fabricating photonic crystals (PCs) without the limitation of colloidal sphere materials and sizes. High quality PCs are fabricated with PCIHVD from polystyrene spheres with diameters ranging from 200 nm to 1 mu m. The deep photonic band gap and steep photonic band edge of the samples are most favorable for realizing ultrafast optical devices, photonic chips, and communications. This method makes a meaningful advance in the quality and diversity of PCs and greatly promotes their wide applications.

Three-dimensional superconformal field theory, Chern-Simons theory, and their correspondence

In this thesis, we discuss 3d-3d correspondence between Chern-Simons theory and three-dimensional N = 2 superconformal field theory. In the 3d-3d correspondence proposed by Dimofte-Gaiotto-Gukov information of abelian flat connection in Chern-Simons theory was not captured. However, considering M-theory configuration giving the 3d-3d correspondence and also other several developments, the abelian flat connection should be taken into account in 3d-3d correspondence. With help of the homological knot invariants, we construct 3d N = 2 theories on knot complement in 3-sphere for several simple knots. Previous theories obtained by Dimofte-Gaiotto-Gukov can be obtained by Higgsing of the full theories. We also discuss the importance of all flat connections in the 3d-3d correspondence by considering boundary conditions in 3d N = 2 theories and 3-manifold.

The geometry and the number of contacts of monodisperse sphere packs using X-ray tomography

The three-dimensional structure of very large samples of monodisperse bead packs is studied by means of X-Ray Computed Tomography. We retrieve the coordinatesofeach bead inthe pack and wecalculate the average coordination number by using the tomographic images to single out the neighbors in contact. The results are compared with the average coordination number obtained in Aste et al. (2005) by using a deconvolution technique. We show that the coordination number increases with the packing fraction, varying between 6.9 and 8.2 for packing fractions between 0.59 and 0.64. © 2005 Taylor & Francis Group.

Exact analytical expressions for the potential of electrical double layer interactions for a sphere-plate system.

Exact, closed-form analytical expressions are presented for evaluating the potential energy of electrical double layer (EDL) interactions between a sphere and an infinite flat plate for three different types of interactions: constant potential, constant charge, and an intermediate case as given by the linear superposition approximation (LSA). By taking advantage of the simpler sphere-plate geometry, simplifying assumptions used in the original Derjaguin approximation (DA) for sphere-sphere interaction are avoided, yielding expressions that are more accurate and applicable over the full range of κa. These analytical expressions are significant improvements over the existing equations in the literature that are valid only for large κa because the new equations facilitate the modeling of EDL interactions between nanoscale particles and surfaces over a wide range of ionic strength.

The SPHERE Study: Secondary prevention of heart disease in general practice: protocol of a randomised controlled trial of tailored practice and patient care plans with parallel qualitative, economic and policy analyses. [ISRCTN24081411]

Background: The aim of the SPHERE study is to design, implement and evaluate tailored practice and personal care plans to improve the process of care and objective clinical outcomes for patients with established coronary heart disease (CHD) in general practice across two different health systems on the island of Ireland.CHD is a common cause of death and a significant cause of morbidity in Ireland. Secondary prevention has been recommended as a key strategy for reducing levels of CHD mortality and general practice has been highlighted as an ideal setting for secondary prevention initiatives. Current indications suggest that there is considerable room for improvement in the provision of secondary prevention for patients with established heart disease on the island of Ireland. The review literature recommends structured programmes with continued support and follow-up of patients; the provision of training, tailored to practice needs of access to evidence of effectiveness of secondary prevention; structured recall programmes that also take account of individual practice needs; and patient-centred consultations accompanied by attention to disease management guidelines.

Methods: SPHERE is a cluster randomised controlled trial, with practice-level randomisation to intervention and control groups, recruiting 960 patients from 48 practices in three study centres (Belfast, Dublin and Galway). Primary outcomes are blood pressure, total cholesterol, physical and mental health status (SF-12) and hospital re-admissions. The intervention takes place over two years and data is collected at baseline, one-year and two-year follow-up. Data is obtained from medical charts, consultations with practitioners, and patient postal questionnaires. The SPHERE intervention involves the implementation of a structured systematic programme of care for patients with CHD attending general practice. It is a multi-faceted intervention that has been developed to respond to barriers and solutions to optimal secondary prevention identified in preliminary qualitative research with practitioners and patients. General practitioners and practice nurses attend training sessions in facilitating behaviour change and medication prescribing guidelines for secondary prevention of CHD. Patients are invited to attend regular four-monthly consultations over two years, during which targets and goals for secondary prevention are set and reviewed. The analysis will be strengthened by economic, policy and qualitative components.

Religion, Human Rights, Equality and the Public Sphere

This article distinguishes three different conceptions of the relationship between religion and the public sphere. The reconciliation of these different aspects of freedom of religion can be seen to give rise to considerable difficulties in practice, and the legal and political systems of several Western European countries are struggling to cope. Four recurring issues that arise in this context are identified and considered: what is a 'religion' and what are 'religious' beliefs and practices for the purposes of the protection of 'freedom of religion', together with the closely related issue of who decides these questions; what justification there is for a provision guaranteeing freedom of religion at all; which manifestations of religious association are so unacceptable as to take the association outside the protection of freedom of religion altogether; and what weight should be given to freedom of religion when this freedom stands opposed to other values. It is argued that the scope and meaning of human rights in this context is anything but settled and that this gives an opportunity to those who support a role for religion in public life to intervene.

Crime, justice and the legitimacy of military power in the international sphere

This article examines how a discourse of crime and justice is beginning to play a significant role in justifying international military operations. It suggests that although the coupling of war with crime and justice is not a new phenomenon, its present manifestations invite careful consideration of the connection between crime and political theory. It starts by reviewing the notion of sovereignty to look then at the history of the criminalisation of war and the emergence of new norms to constrain sovereign states. In this context, it examines the three ways in which military force has recently been authorised: in Iraq, in Libya and through drones in Yemen, Pakistan and Somalia. It argues the contemporary coupling of military technology with notions of crime and justice allows the reiteration of the perpetration of crimes by the powerful and the representation of violence as pertaining to specific dangerous populations in the space of the international. It further suggests that this authorises new architectures of authority, fundamentally based on military power as a source of social power.