The Complete Jamming Landscape of Confined Hard Discs

An exact description of the complete jamming landscape is developed for a system of hard discs of diameter $\sigma$, confined between two lines separated by a distance $1+\sqrt{3/4} < H/\sigma < 2$. By considering all possible local packing arrangements, the generalized ensemble partition function of jammed states is obtained using the transfer matrix method, which allows us to calculate the configurational entropy and the equation of state for the packings. Exploring the relationship between structural order and packing density, we find that the geometric frustration between local packing environments plays an important role in determining the density distribution of jammed states and that structural "randomness" is a non-monotonic function of packing density. Molecular dynamics simulations show that the properties of the equilibrium liquid are closely related to those of the landscape.Comment: 5 Pages, 4 figure

Advances in cataract surgery

Cataract surgery is a technique described since recorded history, yet it has greatly evolved only in the latter half of the past century. The development of the intraocular lens and phacoemulsification as a technique for cataract removal could be considered as the two most significant strides that have been made in this surgical field. This review takes a comprehensive look at all aspects of cataract surgery, starting from patient selection through the process of consent, anaesthesia, biometry, lens power calculation, refractive targeting, phacoemulsification, choice of intraocular lens and management of complications, such as posterior capsular opacification, as well as future developments. As the most common ophthalmic surgery and with the expanding range of intraocular lens options, optometrists have an important and growing role in managing patients with cataract

The formation of high number density InSb quantum dots, resulting from direct InSb/GaSb (001) heteroepitaxy

We report the direct deposition of indium antimonide, by molecular beam epitaxy (MBE) on gallium antimonide, resulting in the formation of quantum dots (QDs) with a maximum density of ~5.3×1010 cm−2. Using reflection high energy electron diffraction (RHEED) and atomic force microscopy (AFM) for the analysis of samples with InSb depositions of 1–6 ML equivalent thickness, we observe an apparent value for the critical thickness for InSb/GaSb (001) deposition of 2.3±0.3 ML, for the growth temperatures of 275 °C and 320 °C

Transverse instability for non-normal parameters

We consider the behaviour of attractors near invariant subspaces on varying a parameter that does not preserve the dynamics in the invariant subspace but is otherwise generic, in a smooth dynamical system. We refer to such a parameter as ``non-normal''. If there is chaos in the invariant subspace that is not structurally stable, this has the effect of ``blurring out'' blowout bifurcations over a range of parameter values that we show can have positive measure in parameter space. Associated with such blowout bifurcations are bifurcations to attractors displaying a new type of intermittency that is phenomenologically similar to on-off intermittency, but where the intersection of the attractor by the invariant subspace is larger than a minimal attractor. The presence of distinct repelling and attracting invariant sets leads us to refer to this as ``in-out'' intermittency. Such behaviour cannot appear in systems where the transverse dynamics is a skew product over the system on the invariant subspace. We characterise in-out intermittency in terms of its structure in phase space and in terms of invariants of the dynamics obtained from a Markov model of the attractor. This model predicts a scaling of the length of laminar phases that is similar to that for on-off intermittency but which has some differences.Comment: 15 figures, submitted to Nonlinearity, the full paper available at http://www.maths.qmw.ac.uk/~eo

Effect of natural convection on oscillating flow in a pipe with cryogenic temperature difference across the ends

The effect of natural convection on the oscillatory flow in an open-ended pipe driven by a timewise sinusoidally varying pressure at one end and subjected to an ambient-to-cryogenic temperature difference across the ends, is numerically studied. Conjugate effects arising out of the interaction of oscillatory flow with heat conduction in the pipe wall are taken into account by considering a finite thickness wall with an insulated exterior surface. Two cases, namely, one with natural convection acting downwards and the other, with natural convection acting upwards, are considered. The full set of compressible flow equations with axissymmetry are solved using a pressure correction algorithm. Parametric studies are conducted with frequencies in the range 5–15 Hz for an end-to-end temperature difference of 200 and 50 K. Results are obtained for the variation of velocity, temperature, Nusselt number and the phase relationship between mass flow rate and temperature. It is found that the Rayleigh number has a minimal effect on the time averaged Nusselt number and phase angle. However, it does influence the local variation of velocity and Nusselt number over one cycle. The natural convection and pressure amplitude have influence on the energy flow through the gas and solid

Edwards entropy and compactivity in a model of granular matter

Formulating a statistical mechanics for granular matter remains a significant challenge, in part, due to the difficulty associated with a complete characterization of the systems under study. We present a fully characterized model of a granular material consisting of $N$ two-dimensional, frictionless, hard discs, confined between hard walls, including a complete enumeration of all possible jammed structures. We show the properties of the jammed packings are independent of the distribution of defects within the system and that all the packings are isostatic. This suggests the assumption of equal probability for states of equal volume, which provides one possible way of constructing the equivalent of a microcanonical ensemble, is likely to be vaild for our model. An application of the second law of thermodynamics involving two subsystems in contact shows that the expected spontaneous equilibration of defects between the two is accompanied by an increase in entropy and that the equilibirum, obtained by entropy maximization, is characterized by the equality of compactivities. Finally, we explore the properties of the equivalent to the canonical ensemble for this system.Comment: Accepted PR

CFD analysis of high frequency miniature pulse tube refrigerators for space applications with thermal non-equilibrium model

High frequency, miniature, pulse tube cryocoolers are extensively used in space applications because of their simplicity. Parametric studies of inertance type pulse tube cooler are performed with different length-to-diameter ratios of the pulse tube with the help of the FLUENT® package. The local thermal non-equilibrium of the gas and the matrix is taken into account for the modeling of porous zones, in addition to the wall thickness of the components. Dynamic characteristics and the actual mechanism of energy transfer in pulse are examined with the help of the pulse tube wall time constant. The heat interaction between pulse tube wall and the oscillating gas, leading to surface heat pumping, is quantified. The axial heat conduction is found to reduce the performance of the pulse tube refrigerator. The thermal non-equilibrium predicts a higher cold heat exchanger temperature compared to thermal equilibrium. The pressure drop through the porous medium has a strong non-linear effect due to the dominating influence of Forchheimer term over that of the linear Darcy term at high operating frequencies. The phase angle relationships among the pressure, temperature and the mass flow rate in the porous zones are also important in determining the performance of pulse tube refrigerator

The c(4×4)–a(1×3) surface reconstruction transition on InSb(001) : static versus dynamic conditions

The transition between the a(1 × 3) and c(4 × 4) surface reconstructions of InSb(0 0 1) has been carefully monitored by reflection high energy electron diffraction as a function of temperature and Sb2 flux, without incident In flux. Arrhenius-like behaviour is observed across the whole range of Sb2 fluxes and temperatures, allowing accurate internal calibration of substrate temperature. This behaviour is in contrast to aggregated data obtained under dynamic molecular beam epitaxy conditions, which show two regimes rather than a single Arrhenius-like phase boundary. The results are explained qualitatively by the atomistic kinetics in static versus dynamic conditions

A prospective comparative study of functional outcome of distal extra articular tibia fracture fixed with intramedullary nail versus locking compression plate

Background: Distal tibia fractures are one of the most common long bone fractures and their management presents with a series of problems due to the soft tissue surroundings and even more at risk due to their proximity to ankle joint. In our paper we showed functional outcome of distal extra articular tibia fracture while comparing its management between intramedullary nailing and locking compression plate.Methods: There were 40 patients from November 2019 to November 2020 with distal extra articular tibia fracture. Patients were divided into 2 groups, first group included 20 patients managed with intramedullary nail and the second group included 20 patients managed with locking compression plate. Patients were followed preoperatively, intraoperatively and postoperatively for functional outcome and assessed clinically using AOFAS score and radiologically using X-ray.Results: Out of the 40 cases treated in this manner, all cases were available for the follow up for a period of 1 year. Overall results by 1 year follow up showed excellent in 7 cases (35%) good in 13 cases (65%) in nailing group and in plating group showed excellent in 4 cases (20%), good in 12 cases (60%), fair in 3 cases (15%) and poor in 1 case (5%).Conclusions: All fractures united well. Complications were encountered in 4 patients, 2 patients had superficial wound infections,1 patient had deep infection and another had persistent ankle pain in plating group and 2 patients had superficial wound infection in nailing group. No cases showed malunion or nonunion in both plating as well as nailing group