Regularization of a Mathematical Model of the Wheatley Heart Valve.

This note considers the mathematical model published in the Journal of Biomechanical Engineering by McKee et al. [McKee, S., Cuminato, J. A., Stewart, I. W., and Wheatley, D. J., 2021, "A Mathematical Representation of the Wheatley Heart Valve," ASME J. Biomech. Eng., 143(8), p. 081006]. The model presented there suffers from the fact that there is a line discontinuity in the first derivative producing what appears to be a kink in each of the leaflets. This note is concerned with regularizing the shape of the valve while holding to Wheatley's essential idea [Wheatley, D. J., 2016, "Heart Valve," U.S. Patent No. 9,259,313, UK Patent No. 2,982,340 (2017), European Patent No. 2,979,666 (2017)].

A Mathematical Representation of the Wheatley Heart Valve.

Starting from a hand-drawn contour plot, this note develops a set of intersecting and contiguous circles whose perimeter, upon extending appropriately to three dimensions, can be seen to be a natural mathematical representation of the Wheatley heart valve.

Two-dimensional flow and linear stability properties of smectic A liquid crystals.

We examine some leading-order flow and stability properties of smectic A (SmA) liquid crystals (LCs) in two spatial dimensions by analysing a fully nonlinear continuum theory of these materials. We derive a system of equations for the dynamic variables describing the flow velocity and orientation of the material under suitable assumptions upon these quantities. This system can provide insight into the leading-order behaviour under quite general circumstances, and we provide an example of utilising this system to determine the flow induced by a constant pressure gradient applied normally to the smectic layers. We then consider the effect of oscillatory perturbations on a relaxed, stationary sample of SmA, and provide criteria under which one would expect to see the onset of instability in the form of inequalities between the material parameters and perturbative wave number. We find that instability occurs for physically realisable values of these quantities, and, in particular, that certain viscosities characterising the SmA phase can act as 'destabilising agents' such that one could, for a given sample with known parameter values, manipulate the behaviour of that sample.

Nonlinearities in tilt and layer displacements of planar lipid bilayers.

A novel continuum model is proposed to describe the deformations of a planar lipid bilayer suspended across a circular pore. The model is derived within a new theoretical framework for smectic A liquid crystals in which the usual director n, which defines the average orientation of the molecules, is not constrained to be normal to the layers. The free energy is defined by considering the elastic splay of the director, the bending and compression of the lipid bilayer, the cost of tilting the director with respect to the layer normal, the surface tension, and the weak anchoring of the director. Variational methods are used to derive the equilibrium equations and boundary conditions. The resulting boundary value problem is then solved numerically to compute the fully nonlinear displacement of the layers and tilt of the lipid molecules. A parametric study shows that an increase in surface tension produces a decrease in the deformation of the lipid bilayers while an opposite effect is obtained when increasing the anchoring strength.

Couette flow of a smectic A liquid crystal.

This paper considers the dynamics of cylindrically arranged parallel layers of smectic A liquid crystal subjected to Couette flow. Governing equations are constructed using a recently developed dynamic theory for smectic A (Stewart 2007 Contin. Mech. Thermodyn. 18 343-60). These equations are solved to provide analytical solutions for the smectic layer undulations and velocity profiles. Results show the dependence of the response time of the smectic layers upon the permeation constant and the layer compression modulus. The relaxation times for the flow profiles are shown to depend upon two viscosities; estimates for these times are shown to be shorter than that for a typical approximation to the relaxation time of the smectic layer undulations.

Configuration of a smectic A liquid crystal due to an isolated edge dislocation.

We discuss the static configuration of a smectic A liquid crystal subject to an edge dislocation under the assumption that the director and layer normal fields ([Formula: see text] and [Formula: see text], respectively) defining the smectic arrangement are not, in general, equivalent. After constructing the free energy for the smectic, we obtain exact solutions to the equilibrium equations which result from its minimisation at quadratic order in the variables which describe the distortion, and hence a complete description of the smectic configuration across the domain of the sample. We also examine the effect of relaxing the constraint [Formula: see text] for different values of the constants which characterise the response of the material to distortions, and compare these results with the 'classical' case considered by previous authors, in which equivalence of [Formula: see text] and [Formula: see text] is enforced.

Functional outcomes of arthroscopic capsular release of the elbow.

PURPOSE: Elbow contracture is a common and difficult problem to manage. The purpose of this study was to determine the functional outcomes of arthroscopic capsular release in the management of elbow contractures. METHODS: A total of 22 patients (14 males, 8 females; mean age, 42 years) undergoing arthroscopic contracture release were retrospectively reviewed at a minimum follow-up of 1 year (mean, 25 months). In all, 20 patients had a capsulectomy, and 2 underwent capsulotomy. Patient-rated questionnaires (Disability of the Arm, Shoulder, and Hand questionnaire [DASH], American Shoulder and Elbow Surgeons Elbow Form [ASES-e], and Short Form-36 [SF-36]) and clinical, radiographic, and objective evaluations were used to assess outcomes. Motion and strength were measured by independent evaluators through standard goniometry and the LIDO Isokinetic System (Loredan Biomedical, West Sacramento, CA). RESULTS: Mean flexion significantly improved from 122 degrees +/- 15 degrees to 141 degrees +/- 12 degrees (P < .001). Mean extension significantly improved from 38 degrees +/- 18 degrees to 19 degrees +/- 13 degrees (P < .001). Mean arc improvement was 38 degrees +/- 23 degrees (P < .001). None of the patients had instability, and no major neurovascular complications were reported. All patients had improved elbow function with a mean ASES-e score of 31 out of 36. Most patients were satisfied with their surgery, experienced minimal pain, and exhibited minimal impairment on the DASH. CONCLUSIONS: Arthroscopic debridement and capsulectomy of the contracted elbow is effective. Results are comparable with those of other reports in the literature in which both arthroscopic and open methods were used. LEVEL OF EVIDENCE: Level IV.

Surface anchoring and dynamics of jump-wise director reorientations in planar cholesteric layers.

A theoretical investigation is made into the dynamics of pitch jumps in cholesteric liquid-crystal layers having finite strength surface-anchoring conditions. A presentation is given of general formulations which connect the dynamics of pitch jumps with the key material parameters such as the viscosity, the specific form of the anchoring potential, and the dimensionless parameter S(d)=K(22)/Wd , where K22 is the elastic modulus, W is the depth of the anchoring potential, and d is the layer thickness. To illustrate the dependence of the pitch jump dynamics upon the shape and strength of the anchoring potential, we investigate two sets of different model surface-anchoring potentials for a jump mechanism that is connected with the slipping of the director at a surface over the barrier of the anchoring potential. Two types of "narrow" well potentials that are natural extensions of the more familiar "wide" potentials are considered: one type is based upon the well-known Rapini-Papoular potential and the other upon the B potential, introduced in Belyakov, Stewart, and Osipov, JETP 99, 73 (2004). Calculations for the unwinding (winding) of the helix in the process of the jump were performed to investigate the case of infinitely strong anchoring on one surface and finite anchoring on the other, which is important in applications. The results show that an experimental investigation of the dynamics of the pitch jumps will allow one to distinguish different shapes of the finite strength anchoring potential, and will, in particular, provide a means for determining whether or not the well-known Rapini-Papoular anchoring potential is the best suited potential relevant to the dynamics of pitch jumps in cholesteric layers with finite surface-anchoring strength.

Traveling waves in ferroelectric smectic-C liquid crystals.

This article investigates, by means of Lie point symmetries, traveling wave solutions to a dynamic equation that frequently arises in the theory of ferroelectric smectic- C liquid crystals under the influence of an electric field. The equation considered has three sinusoidal nonlinearities and possible time-dependent solutions are discussed in the context of minima and maxima of the electric energy density for these liquid crystals: solutions travel between such constant equilibrium states. Implicit solutions to an approximation of the governing dynamic equation are determined. Nondimensional control parameters that characterize changes in the availability of equilibrium states as the magnitude of the field increases are also identified.

Iowa's pediatric low-vision services.

BACKGROUND: Reports in the literature concerning best practice for the evaluation and management of children with visual impairments are limited, with a resulting lack of information concerning the potential for optimizing vision to enhance general development and assist with the educational needs of this population. METHOD: The development of a multidisciplinary approach to provide low-vision services for children with visual impairment has occurred over the past 18 years in Iowa. In that time, 1,348 children from around the state of Iowa have been evaluated through an itinerant low-vision service program, coordinated by the Iowa Braille School. RESULTS: A low-vision clinic model--designed to provide services (primarily) for academic students--was not meeting the needs of the pediatric low-vision population in the state. After a statewide review of the program, changes were made that have resulted in low-vision services being provided to a greater and more diverse number of students. The roles of the various members of the multidisciplinary team will be reviewed. Changes in large-print orders and use by special education teachers in the state as a direct result of the low-vision services will also be discussed. CONCLUSION: Ongoing, comprehensive multidisciplinary low-vision services--including optometric low-vision care as a key component--are necessary to help children with visual impairments meet their educational, vocational, and avocational needs. With ongoing low-vision services, unnecessary costs such as those associated with large-print materials can be reduced, thereby creating significant savings to local, state, and federal special educational services.

Acoustic waves in compressible planar layered smectic liquid crystals.

A dynamic theory for compressible smectic C (SmC) liquid crystals is postulated following previous work by Leslie et al (1991 Mol. Cryst. Liq. Cryst. 198 443-54), Nakagawa (1996 J. Phys. Soc. Japan 65 100-6; 2004 J. Non-Newtonian Fluid Mech. 119 123-9) and de Gennes and Prost (1993 The Physics of Liquid Crystals 2nd edn (Oxford: Oxford University Press)). This theory is then implemented with a constructed bulk elastic energy and asymmetric stress tensor to describe a system of planar layered SmC liquid crystals undergoing various modes of undulation. We show that previous work on smectic A (SmA) liquid crystals by de Gennes and Prost (1993 The Physics of Liquid Crystals 2nd edn (Oxford: Oxford University Press)) can be expanded for SmC and consolidated. Novel and confirming estimates for SmC material parameter values are produced by considering the dependence of the system on these parameters.

Shear flow in smectic A liquid crystals.

This paper considers the onset of a shear-induced instability in a sample of smectic A liquid crystal. Unlike many previous models, the usual director n need not necessarily coincide with the local smectic layer normal a; the traditional Oseen constraint ([Formula: see text]) is not imposed when flow is present. A recent dynamic theory for smectic A (Stewart 2007 Contin. Mech. Thermodyn. 18 343-60) will be used to examine a stationary instability in a simple model when the director reorientation and smectic layer distortions are, firstly, assumed not to be coupled to the velocity and, secondly, are supposed coupled to the velocity. A critical shear rate at which the onset of the instability occurs will be identified, together with an accompanying critical director tilt angle and critical wavenumber for the associated smectic layer undulations. Despite some critical phenomena being largely unaffected by any coupling to the flow, it will be shown that the influence of some material parameters, especially the smectic layer compression constant B(0) and the coupling constant B(1), upon the critical shear rate and critical tilt angle can be greatly affected by flow.

Layer undulations induced by a magnetic or electric field in concentric cylindrical layers of smectic-A liquid crystals.

This paper derives theoretical results for the onset of Helfrich-Hurault-type transitions in samples of smectic-A liquid crystals arranged in concentric cylindrical layers [J. Chem. Phys. 55, 839 (1971); 59, 2068 (1973)]. A magnetic field is applied in the azimuthal direction, parallel to the layers. The governing equilibrium equation is solved in order to derive the critical magnitude H(c) of the magnetic field above which the onset of periodic smectic layer distortions is expected. The distortion solution is shown to be energetically favorable for H>H(c). Some examples of critical thresholds are given, by means of figures, for relevant physical parameters. The qualitative features of the solution at H(c) are displayed via the plot of a typical variable solution to the equilibrium equation in a particular case. The consequences of the results, especially the relationship between H(c) and the radial depth, are explored, and comparisons are drawn with known results for infinite planar aligned smectic-A samples. The results are also interpreted for the case of an electric field which follows the plane of the layers in the usual wedge geometry. Critical applied voltage magnitudes U(c) are derived for various radial sample depths and wedge angles.

Iowa's pediatric low vision services.

BACKGROUND: Reports in the literature concerning the evaluation and low vision management of visually impaired children are limited, resulting in a lack of information about the characteristics and needs of this population. METHODS: A review was performed of 762 children evaluated over a 14-year period in a low vision clinic program coordinated by the Iowa Braille and Sight Saving School. RESULTS: The age, sex, ocular condition, best corrected visual acuity, habitual near point working distance, and optical devices recommended for use by these children were analyzed. CONCLUSIONS: Ongoing, comprehensive multidisciplinary low vision services are necessary to help children with visual impairments meet their educational, vocational and avocational needs. With ongoing low vision care unnecessary costs-such as those for large print material-can be avoided, therefore creating a significant savings to local or state educational services.

Proof of factorization for B --> D pi.

We prove that the matrix elements of four fermion operators mediating the decays B macro (0)-->D(+)pi(-) and B--->D(0)pi(-) factor into the product of a form factor describing the B-->D transition and a convolution of a short distance coefficient with the nonperturbative pion light-cone wave function. This is shown to all orders in alpha(s), with corrections suppressed by factors of 1/m(b), 1/m(c), and 1/E(pi). It is not necessary to assume that the pion state is dominated by the qq macro Fock state.

Dynamics of solitary waves in smectic-C* liquid crystals.

The dynamics of solitary waves in ferroelectric liquid crystals is considered in the context of an overdamped double sine-Gordon model. Various possible types of single waves are studied. The dependence of wave velocity and scale on the system parameters and initial conditions is found. Sharp initial profiles lead to waves with a universal form. The parameters of the wave arising from smooth profiles are determined also by the scale of the initial conditions. Numerical calculations show good agreement with analytical results. The possibility of using such waves to improve the characteristics of liquid crystal devices is also discussed.

Self-organized periodic photonic structure in a nonchiral liquid crystal.

A hybrid-aligned cell of the smectic A liquid material 8CB gives two stable director configurations, one of which is periodic and gives strong diffraction of light. This photonic lattice director profile arises from "frustration" caused by conflicting constraints imposed by the boundary conditions and the constant amplitude smectic density wave. A model is proposed which accords well with the experiment results, predicting correctly the dependence of the periodicity on the cell thickness and reproducing optical polarization microscopy results.

Renormalization-group improved calculation of top-quark production near threshold.

The top-quark cross section close to threshold in e(+)e(-) annihilation is computed including the summation of logarithms of the velocity at next-to-next-to-leading-logarithmic order in QCD. The remaining theoretical uncertainty in the normalization of the total cross section is at the few-percent level, an order of magnitude smaller than in previous next-to-next-to-leading order calculations. This uncertainty is smaller than the effects of a light standard-model Higgs boson.

The adaptation of existing personal inhalable aerosol samplers for bioaerosol sampling.

Health-related monitoring of bioaerosol exposures in the workplace should ideally be carried out using size-selective personal samplers that separate the aerosol into biologically relevant size fractions and allow both quantification and identification of the microorganisms present in each fraction. As a first stage in the development of personal bioaerosol samplers a number of collection substrates were assessed for their ability to maintain the viability of the collected microorganisms, so that subsequent culturing and species identification may be carried out. The substrates were tested with bioaerosols of varying robustness, consisting of Saccharomyces cerevisiae cells, Escherichia coli cells, and Penicillium expansum spores, aerosolized under controlled environmental conditions. The survival of microorganisms on each test substrate, assessed on the basis of the culturable fractions of cells recovered, was compared with that of microorganisms collected in a reference glass cyclone sampler. These bioefficiency tests identified the substrate combinations with the potential to fulfill personal sampler design criteria. The substrates were then subjected to further development to evaluate and optimize their particle size selection characteristics. The outcome of this work is two prototype personal bioaerosol samplers in which size-selective substrates are adapted for use in existing designs of personal inhalable sampler. This offers an effective and low-cost solution to personal monitoring of bioaerosol exposures in the workplace.