Neutral Boundaries Research Articles

Radiologic Assessment of Knee Phenotypes Based on the Coronal Plane Alignment of the Knee Classification in a Korean Population.

The Coronal Plane Alignment of the Knee (CPAK) classification system has been developed as a comprehensive system that describes 9 coronal plane phenotypes based on constitutional limb alignment and joint line obliquity (JLO). Due to the characteristics of Asian populations, which show more varus and wider distribution in lower limb alignment than other populations, modification of the boundaries of the arithmetic hip-knee-ankle angle (aHKA) and JLO should be considered. The purpose of this study was to determine the knee phenotype in a Korean population based on the original CPAK and modified CPAK classification systems. We reviewed prospectively collected data of 500 healthy and 500 osteoarthritic knees between 2021 and 2023 using radiographic analysis and divided them based on the modified CPAK classification system by widening the neutral boundaries of the aHKA to 0° ± 3° and using the actual JLO as a new variable. Using long-leg standing weight-bearing radiographs, 6 radiographic parameters were measured to evaluate the CPAK type: the mechanical HKA angle, medial proximal tibial angle (MPTA), lateral distal femoral angle (LDFA), aHKA, JLO, and actual JLO. From 2 cohorts of 1,000 knees, the frequency distribution representing all CPAK types was different between the healthy and arthritic groups. The most common categories were type II (38.2%) in the healthy group and type I (53.8%) in the arthritic group based on the original CPAK classification. The left and upward shift in the distribution of knee phenotypes in the original classification was corrected evenly after re-establishing the boundaries of a neutral aHKA and the actual JLO. According to the modified CPAK classification system, the most common categories were type II (35.2%) in the healthy group and type I (38.0%) in the arthritic group. Although the modified CPAK classification corrected the uneven distribution seen when applying the original classification system in a Korean population, the most common category was type I in Korean patients with osteoarthritic knees in both classification systems. Furthermore, there were different frequencies of knee phenotypes among healthy and arthritic knees.

Hot cracking susceptibility prediction from quantitative multi-phase field simulations with grain boundary effects

Hot cracks are notorious defects in casting, welding, and additive manufacturing. Grain boundaries play a key role in hot cracking formation. Still, their effects are often neglected in hot cracking susceptibility predictions, and thus a quantitative picture of hot cracking susceptibility and liquid fracture is still lacking. In this work, we construct a multi-order parameter phase-field model for binary alloy solidification to simulate attractive, neutral, and repulsive grain boundaries in the thin-interface limit. Phase-field simulations of different combinations of grain boundary and bi-crystal growth types are used to obtain solidification path data, which is then used as the input into the Rappaz, Drezet and Gremaud (RDG) model (Rappaz et al., 1999). We study the so-called Λ-shape variation of hot cracking susceptibility as a function of solute concentration, showing that the magnitude of the Λ curve peak shifts to higher values and to lower concentrations as grain boundary energy increases. Meanwhile, the peak magnitude becomes higher and shifts to a higher value and higher concentrations when convergent grain growth is applied. Furthermore, in all cases examined, the corresponding pressure drops predicted for hot cracking exceed the theoretical liquid rupture stress, consistent with experimental observations. These results demonstrate that quantitative phase-field simulations, when coupled with the RDG model, are capable of relatively accurately predicting liquid rapture states relevant to hot cracking since the large disparity between the predicted pressure drop and critical stress of liquid film is eliminated through the consideration of grain boundary effects in the solidification path calculation.

Defining the lumbar and trunk-thigh neutral zone from the passive stiffness curve: application to hybrid sit-stand postures and chair design

Minimal data exist on the neutral position for the lumbar spine, trunk, and thighs when adopting a hybrid posture. This study examined sex differences in the neutral zone lumbar stiffness and the lumbar and trunk-thigh angle boundaries of the neutral zone, and determined if the standing lumbar angle fell within the neutral zone. Passive lumbar flexion and extension moment-angle curves were generated for 31 participants (13 M, 18 F), pooled from two datasets, with trunk-thigh angles available for 10 participants. The neutral zone was defined as the low stiffness zone from both the flexion and extension curves. Males demonstrated significantly greater extensor stiffness. Neutral lumbar and trunk-thigh angles ranged on average −22.2 to 0.2° and 124.2 to 159.6° for males and −17.8 to −1.3° and 143.2 to 159.5° for females, respectively. Standing lumbar angles fell outside the neutral zone for 44% of participants. These neutral zone boundaries may inform kinematics for hybrid chair designs. Practitioner summary: Adoption of a neutral spinal posture may be achieved through hybrid chair design, yet minimal data exists on a physiologically defined neutral zone. Using measures of in vivo lumbar stiffness, the lumbar and trunk-thigh angular boundaries of the neutral zone were defined for both males and females. Abbreviations: EMG: electromyography; MVC: maximal voluntary contraction

Linear stability of a rotating channel flow subjected to a static magnetic field

Magnetohydrodynamics is effective to control the instabilities of fluid flows. This control process is cost-effective and compact because it does not require extra mechanical components. In the present study, the effect of a constant uniform magnetic field on the linear stability of a rotating channel flow is investigated. The electromagnetic field is applied in the spanwise direction alongside the axis of rotation. The Hartmann and rotation numbers characterize the magnetic and rotational effects. The axial flow is governed by the centrifugal force, and the Coriolis force due to rotation makes the flow unstable at relatively low Reynolds numbers concerning spanwise disturbances. The modal instabilities of the flow are captured by solving the Orr–Sommerfeld–Squire eigenvalue problem. Numerical results confirm that the employed magnetic force has a prominent stabilizing role on the linear instabilities of the rotating channel flow. Notably, the higher Hartmann numbers suppress the temporal growth of the most unstable mode and decrease the area of neutral stability boundaries. The onset of rotational instability occurs at a higher critical Reynolds number for a stronger magnetic field. Further, the presence of Lorentz force restricts the co-existence of multiple unstable modes and the mode competition phenomenon, which results in structure modification of roll-cells and tardy secondary flow. The findings of this investigation would be useful in designing bio-medical and mechanical tools where the rotational instabilities are harmful. Furthermore, it is hoped that the obtained results will motivate the experimental verification and look for worthy applications.

Validation and modification of the Coronal Plane Alignment of the Knee classification in the Asian population.

AimsThe Coronal Plane Alignment of the Knee (CPAK) classification is a simple and comprehensive system for predicting pre-arthritic knee alignment. However, when the CPAK classification is applied in the Asian population, which is characterized by more varus and wider distribution in lower limb alignment, modifications in the boundaries of arithmetic hip-knee-ankle angle (aHKA) and joint line obliquity (JLO) should be considered. The purposes of this study were as follows: first, to propose a modified CPAK classification based on the actual joint line obliquity (aJLO) and wider range of aHKA in the Asian population; second, to test this classification in a cohort of Asians with healthy knees; third, to propose individualized alignment targets for different CPAK types in kinematically aligned (KA) total knee arthroplasty (TKA).MethodsThe CPAK classification was modified by changing the neutral boundaries of aHKA to 0° ± 3° and using aJLO as a new variable. Radiological analysis of 214 healthy knees in 214 Asian individuals was used to assess the distribution and mean value of alignment angles of each phenotype among different classifications based on the coronal plane. Individualized alignment targets were set according to the mean lateral distal femoral angle (LDFA) and medial proximal tibial angle (MPTA) of different knee types.ResultsA very high concentration, 191 from 214 individuals (89.3%), were found in knee types with apex distal JLO when the CPAK classification was applied in the Asian population. By using aJLO as a new variable, the high distribution percentage in knee types with apex distal JLO decreased to 125 from 214 individuals (58.4%). The most common types in order were Type II (n = 70; 32.7%), Type V (n = 55; 25.7%), and Type I (n = 46; 21.5%) in the modified CPAK classification.ConclusionThe modified CPAK classification corrected the uneven distribution when applying the CPAK classification in the Asian population. Setting individualized TKA alignment targets according to CPAK type may be a practical method to recreate optimal LDFA and MPTA in KA-TKA.Cite this article: Bone Jt Open 2022;3(3):211–217.

Numerical Study on Plastic Strain Distributions and Mechanical Behaviour of a Tube under Bending

Tubular pipe structures have been used in various applications—domestic, aviation, marine, manufacturing and material testing. The applications of tubular pipes have been considered greatly in the installation of tubular pipes, marine risers and pipe bending. For the investigation of plastic strains and the mechanical behaviour of a tube under bending, considerations were made utilising an exponent model with assumptions on the plane strain. The bending moment, wall thickness effect, cross-sectional distribution, stresses during bending and neutral layer boundaries were all presented as necessary theoretical formulations on the physics of tubular pipe bending. This model was based on the analytical and numerical investigation. In principle, the application can be observed as the spooling of pipes, bending of pipes and reeling. Comparisons were made on two models developed on the finite element analysis in Simscale OpenFEA, namely the linear-elastic and the elasto-plastic models. This study presents visualization profiles using plastic strain to assess its effect on the tubular pipes. This can increase due to the limitation of plastic deformation on the composite materials selected.

Diffusive effects in local instabilities of a baroclinic axisymmetric vortex

We present a local stability analysis of an idealized model of the stratified vortices that appear in geophysical settings. The base flow comprises an axisymmetric vortex with background rotation and an out-of-plane stable stratification, and a radial stratification in the thermal wind balance with the out-of-plane momentum gradient. Solving the local stability equations along fluid particle trajectories in the base flow, the dependence of short-wavelength instabilities on the Schmidt number $Sc$ (ratio between momentum and mass diffusivities) is studied, in the presence of curvature effects. In the diffusion-free limit, the well-known symmetric instability is recovered. In the viscous, double-diffusive regime, instability characteristics are shown to depend on three non-dimensional parameters (including $Sc$ ), and two different instabilities are identified: (i) a monotonic instability (same as symmetric instability at $Sc = 1$ ), and (ii) an oscillatory instability (absent at $Sc = 1$ ). Separating the base flow and perturbation characteristics, two each of base flow and perturbation parameters (apart from $Sc$ ) are identified, and the entire parameter space is explored for the aforementioned instabilities. In comparison with $Sc = 1$ , monotonic and oscillatory instabilities are shown to significantly expand the instability region in the space of base flow parameters as $Sc$ moves away from unity. Neutral stability boundaries on the plane of $Sc$ and a modified gradient Richardson number are then identified for both these instabilities. In the absence of curvature effects, our results are shown to be consistent with previous studies based on normal mode analysis, thus establishing that the local stability approach is well suited to capturing symmetric and double-diffusive instabilities. The paper concludes with a discussion of curvature effects, and the likelihood of monotonic and oscillatory instabilities in typical oceanic settings.

Stability of two-layer flows past slippery surfaces. II. Inclined channels

In this paper, the linear stability characteristics of a two-layered liquid–liquid flow in an inclined channel with slippery walls are investigated. Previous studies on two-layered inclined channel flows have observed the presence of multiple base state flow profiles, two for countercurrent flow and up to three base states for co-current flow. The role of wall slip on the multiple base states associated with each holdup solution is analyzed here. Subsequently, a linear stability analysis, using a combination of a long-wave asymptotic analysis and finite wavenumber numerical calculation, is carried out with the slip boundary condition. Neutral stability boundaries are presented for each base state, with comparisons made with the previous results obtained for the no-slip boundary condition. It was found that the wall slip could have both stabilizing and destabilizing effects depending on the flow rates and the value of holdup—the location of an interface.

Long-Range Fluctuation-Induced Forces in Driven Electrolytes.

We study the stochastic dynamics of an electrolyte driven by a uniform external electric field and show that it exhibits generic scale invariance despite the presence of Debye screening. The resulting long-range correlations give rise to a Casimir-like fluctuation-induced force between neutral boundaries that confine the ions; this force is controlled by the external electric field, and it can be both attractive and repulsive with similar boundary conditions, unlike other long-range fluctuation-induced forces. This work highlights the importance of nonequilibrium correlations in electrolytes and shows how they can be used to tune interactions between uncharged biological or synthetic structures at large separations.

Dispersity effects on phase behavior and structural evolution in ultrathin films of a deuterated polystyrene-block-poly(methyl methacrylate) diblock copolymer

We report the unique phase behavior and structural transitions in thin films of a distorted network (DNW) nanostructure, which is an equilibrium phase contained in the bulk of a nearly-symmetric deuterated polystyrene-block-poly (methyl methacrylate), dPS-b-PMMA, block copolymer. The DNW is due to a broad dispersity for the PMMA block. Grazing incidence small-angle X-ray scattering, neutron reflectometry, atomic force microscopy and transmission electron microscopy techniques were used to characterize thermally-annealed dPS-b-PMMA ultrathin films with neutral boundaries at both the free surface and substrate interface. Brief thermal annealing imposed on the ultrathin films leads to perpendicular lamellae (L⊥). Upon increasing the duration of thermal annealing, the dPS-b-PMMA ultrathin films exhibit thickness dependence of phase transition kinetics and different irreversible routes of phase transition. As a result, the protracted thermal annealing of the thin films of various thicknesses produces either hexagonal arrays of perpendicular PMMA cylinders (HEX-C⊥) or disordered PMMA nanostructures (DIS). The phase transition routes and kinetics in ultrathin films suggest various possibilities to obtain diverse nanoscale patterns via thin film self-assembly.

Nonlocal Adhesion Models for Microorganisms on Bounded Domains

In 2006 Armstrong, Painter, and Sherratt formulated a nonlocal differential equation model for cell-cell adhesion. For the one-dimensional case on a bounded domain we derive various types of biological boundary conditions, describing adhesive, repulsive, and neutral boundaries. We prove local and global existence and uniqueness for the resulting integrodifferential equations. In numerical simulations we consider adhesive, repulsive, and neutral boundary conditions, and we show that the solutions mimic known behavior of fluid adhesion to boundaries. In addition, we observe interior pattern formation due to cell-cell adhesion.

Influence of micro-explosions on the stability of laminar premixed water-in-fuel emulsion spray flames

A model is presented for a one-dimensional laminar premixed flame, propagating into a rich, off-stoichiometric, fresh homogenous mixture of water-in-fuel emulsion spray, air and inert gas. Due to its relatively large latent heat of vaporisation, the water vapour acts to cool the flame that is sustained by the prior release of fuel vapour. To simplify the inherent complexity that characterises the analytic solution of multi-phase combustion processes, the analysis is restricted to fuel-rich laminar premixed water-in-fuel flames, and assumes a single-step global chemical reaction mechanism. The main purpose is to investigate the steady-state burning velocity and burnt temperature as functions of parameters such as initial water content in the emulsified droplet and total liquid droplet loading. In particular, the influence of micro-explosion of the spray’s droplets on the flame’s characteristics is highlighted for the first time. Steady-state analytical solutions are obtained and the sensitivity of the flame temperature and the flame propagating velocity to the initial water content of the micro-exploding emulsion droplets is established. A linear stability analysis is also performed and reveals the manner in which the micro-explosions influence the neutral stability boundaries of both cellular and pulsating instabilities.

Linear stability analysis of laminar premixed water-in-fuel emulsion spray flames

This paper considers the stability of a laminar water-in-fuel spray premixed flame. The droplets of the spray are comprised of two immiscible components viz. water and fuel, with the water being contained within an outer liquid shell of fuel. The fuel and water evaporate sequentially. Due to its relatively large latent heat of vaporization the water vapor acts to cool the flame that is sustained by prior release of fuel vapor. To simplify the inherent complexity that characterizes the analytic solution of multi-phase combustion processes, the analysis is restricted to fuel-rich laminar premixed water-in-fuel flames, and assumes a single-step global chemical reaction mechanism. Steady-state solutions are obtained and the sensitivity of the flame temperature and the flame propagating velocity to the initial water content of the emulsion droplets is established. The linear stability analysis revealed an increased proneness to cellular instability induced by the presence of increased water content of the emulsion droplets. A similar effect was noted for the neutral pulsating stability boundaries.

Proximity-interference wake-induced vibration at subcritical Re: Mechanism analysis using a linear dynamic model

Wake-induced vibration (WIV) contains rich and complex phenomena due to the flow interference between cylinders. The aim of the present study is to gain physical insight into the intrinsic dynamics of WIV via linear stability analysis (LSA) of the fluid-structure interaction (FSI) system. A reduced-order-model-based linear dynamic model, combined with the direct computational fluid dynamics/computational structural dynamics simulation method, is adopted to investigate WIV in two identical tandem cylinders at low Re. The spacing ratio L/D, with L as the center-to-center distance and D as the diameter of cylinders, is selected as 2.0 to consider the effect of proximity flow interference. Results show that extensive WIV along with the vortex shedding could occur at subcritical Re conditions due to the instability of one coupled mode (i.e., coupled mode I, CM-I) of the FSI system. The eigenfrequency of CM-I transfers smoothly from close to the reduced natural frequency of structure to the eigenfrequency of uncoupled wake mode as the reduced velocity U* increases. Thus, CM-I characterizes as the structure mode (SM) at low U*, while it characterizes as the wake mode (WM) at large U*. Mode conversion of CM-I is the primary cause of the “frequency transition” phenomenon observed in WIV responses. Furthermore, LSA indicates that there exists a critical mass ratio mcr*, below which no upper instability boundary of CM-I exists (Uupper*→∞). The unbounded instability of CM-I ultimately leads to the “infinite WIV” phenomenon. The neutral stability boundaries for WIV in the (Re, U*) plane are determined through LSA. It is shown that the lowest Re possible for WIV regarding the present configuration is Relowest≈34. LSA accurately captures the dynamics of WIV at subcritical Re and reveals that it is essentially a fluid-elastic instability problem. This work lays a good foundation for the investigation of WIV at supercritical high Re and gives enlightenment to the understanding of more complex WIV phenomena therein.

Effect of Low Rotation Rate on Steady Convection During the Solidification of a Ternary Alloy

We consider the problem of steady convective flow during the directional solidification of a horizontal ternary alloy system rotating at a constant and low rate about a vertical axis. Under the limit of large far-field temperature, the flow region is modeled to be composed of two horizontal mushy layers, which are referred to here as a primary layer over a secondary layer. We first determine the basic state solution and then carry out linear stability analysis to calculate the neutral stability boundary and the critical conditions at the onset of motion. We find, in particular, that there are two flow solutions and each solution exhibits two neutral stability boundaries, and the flow can be multi-modal in the low rotating rate case with local minima on each neutral boundary. The critical Rayleigh number and the wave number as well as the vertical volume flux increase with the rotation rate, but the flow is found to be less stabilizing as compared to the binary alloy counterpart flow. The effects of low rotation rate increase the solid fraction and the liquid fraction at certain vertically oriented fluid lines, and the highest value of such increase is at a horizontal level close to the interface between the two mushy layers.

On the Yih–Marangoni instability of a two-phase plane Poiseuille flow in a hydrophobic channel

The linear stability analysis of a plane Poiseuille flow of two immiscible, incompressible fluids of different viscosities and densities in a hydrophobic channel, in the presence of an insoluble surfactant at the interface is examined, within the framework of Orr–Sommerfeld system. The walls of the channel are modeled as walls with velocity slip/no-slip. The equations governing the flow system are solved numerically by a Chebyshev collocation method for a wide range of dimensionless parameters describing the flow system. The effects of slip on the neutral stability boundaries for the interface modes in the presence/absence of an insoluble surfactant at the interface are examined for different thickness ratios of the two layers, with density and/or viscosity stratification. Slip conditions at the wall show a promise for control of the Yih–Marangoni instability of the corresponding flow system in a rigid channel. The influence of the parameters on the critical Reynolds number for the shear mode is assessed. The study reveals that it is possible to control instabilities in interface dominated rigid channel flows by designing the walls of the channel as hydrophobic/rough/porous or undulated surfaces as these can be modeled as one with slip at the substrates.

In‐plane and out‐of‐plane defectivity in thin films of lamellar block copolymers

ABSTRACTWe investigate the ordering of poly(styrene‐b‐methyl methacrylate) (PS‐PMMA) lamellar copolymers (periodicityL0 = 46 nm) confined between a free surface and brushed poly(styrene‐r‐methyl methacrylate) silicon substrate. The processing temperature was selected to eliminate wetting layers at the top and bottom interfaces, producing approximately neutral boundaries that stabilize perpendicular domain orientations. The PS‐PMMA film thickness (t = 0.5L0 − 2.5L0) and brush grafting density (Σ = 0.2–0.6 nm−2) were systematically varied to examine their impacts on in‐plane and out‐of‐plane ordering. Samples were characterized with a combination of high‐resolution microscopy, X‐ray reflectivity, and grazing‐incidence small‐angle X‐ray scattering. In‐plane order at the top of the film (quantified through calculation of orientational correlation lengths) improved withtn, where the exponentnincreased from 0.75 to 1 as Σ decreased from 0.6 to 0.2 nm−2. Out‐of‐plane defects such as tilted domains were detected in all films, and the distribution of domain tilt angles was nearly independent oftand Σ. These studies demonstrate that defectivity in perpendicular lamellar phases is three‐dimensional, comprised of in‐plane topological defects and out‐of‐plane domain tilt, with little or no correlation between these two types of disorder. Strong interactions between the block copolymer and underlying substrate may trap both kinds of thermally generated defects. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 339–352

Effects of velocity slip on the inertialess instability of a contaminated two-layer film flow

This manuscript provides a theoretical stability analysis for the configuration of two-layer immiscible flow down an inclined plane with velocity slip along the incline in the limit of zero Reynolds number. Surfactants may be present at the air–liquid interface, liquid–liquid interface, or both. In addition to an Orr–Sommerfeld analysis (again at zero Reynolds number), a long wavelength stability analysis is performed and the results are shown to be consistent. The interface mode, namely the mode of instability that arises because of viscosity stratification, is examined. Stability results (growth rates as a function of slip parameter and neutral stability boundaries) for various configurations of viscosity, surfactant placement, and layer thickness are compared with those of the previous literature and found to agree. It is found that velocity slip along the inclined plane reduces the maximum growth rate of instabilities in configurations where they occur, and the range of unstable wave numbers shrinks as well, indicating that slip has a promise for stabilization. This suggests that there is a possibility of using this favourably as a control option for two-layer flows in the absence or presence of surfactants, in relevant applications by designing the substrate to be a porous substrate with small permeability or a slippery substrate or a rough substrate or a hydrophobic substrate which can be modelled as substrates with velocity slip.

Linear Stability Analysis of Laminar Premixed Fuel-Rich Double-Spray Flames

This paper considers the stability of a double-spray premixed flame formed when both fuel and oxidizer are initially present in the form of sprays of evaporating liquid droplets. To simplify the inherent complexity that characterizes the analytic solution of multi-phase combustion processes, the analysis is restricted to fuel-rich laminar premixed double-spray flames, and assumes a single-step global chemical reaction mechanism. Steady-state solutions are obtained and the sensitivity of the flame temperature and the flame propagating velocity to the initial liquid fuel and/or oxidizer loads are established. The stability analysis revealed an increased proneness to cellular instability induced by the presence of the two sprays, and for the fuel-rich case considered here the influence of the liquid oxidizer was found to be more pronounced than that of the liquid fuel. Similar effects were noted for the neutral pulsating stability boundaries. The impact of unequal latent heats of vaporization is also investigated and found to be in keeping with the destabilizing influence of heat loss due to droplet evaporation. It should be noted that as far as the authors are aware no experimental evidence is available for (at least) validation of the predictions. However, they do concur in a general and reasonable fashion with independent experimental evidence in the literature of the behavior of single fuel spray laminar premixed flames.

Nonhomogeneous-Nonequilibrium Two-Phase-Flow Model for Nuclear Reactor Single-Channel Stability Analysis

The effects of two-phase-flow modeling on nuclear reactor single-channel stability analysis are investigated with four two-phase-flow models, namely, the homogeneous-equilibrium model, the homogeneous-nonequilibrium model, the nonhomogeneous-equilibrium model, and the nonhomogeneous-nonequilibrium model. The models are applied to hot-channel analyses of a proposed typical supercritical-water-cooled-reactor (SCWR) design. The neutral stability boundaries derived by using the four models are compared and plotted on the traditional subcooling number versus phase change number plane. To ensure proper development of the models, they are benchmarked to the experimental data. It is found that the homogeneous models predict more conservative stability boundaries than the nonhomogeneous models and that the differences of the stability boundaries predicted by all four two-phase-flow models are reduced under higher-pressure conditions.