Macrosegregation During Dendritic Arrayed Growth of Hypoeutectic Pb-Sn Alloys: Influence of Primary Arm Spacing and Mushy Zone Length

Thermosolutal convection in the dendritic mushy zone occurs during directional solidification of hypoeutectic lead tin alloys in a positive thermal gradient, with the melt on the top and the solid below. This results in macrosegregation along the length of the solidified samples. The extent of macrosegregation increases with increasing primary dendrite spacings for constant mushy zone length. For constant primary spacings, the macrosegregation increases with decreasing mushy zone length. Presence of convection reduces the primary dendrite spacings. However, convection in the interdendritic melt has significantly more influence on the spacings as compared with that in the overlying melt, which is caused by the solutal buildup at the dendrite tips

Toward a 21st-century health care system: Recommendations for health care reform

The coverage, cost, and quality problems of the U.S. health care system are evident. Sustainable health care reform must go beyond financing expanded access to care to substantially changing the organization and delivery of care. The FRESH-Thinking Project (www.fresh-thinking.org) held a series of workshops during which physicians, health policy experts, health insurance executives, business leaders, hospital administrators, economists, and others who represent diverse perspectives came together. This group agreed that the following 8 recommendations are fundamental to successful reform: 1. Replace the current fee-for-service payment system with a payment system that encourages and rewards innovation in the efficient delivery of quality care. The new payment system should invest in the development of outcome measures to guide payment. 2. Establish a securely funded, independent agency to sponsor and evaluate research on the comparative effectiveness of drugs, devices, and other medical interventions. 3. Simplify and rationalize federal and state laws and regulations to facilitate organizational innovation, support care coordination, and streamline financial and administrative functions. 4. Develop a health information technology infrastructure with national standards of interoperability to promote data exchange. 5. Create a national health database with the participation of all payers, delivery systems, and others who own health care data. Agree on methods to make de-identified information from this database on clinical interventions, patient outcomes, and costs available to researchers. 6. Identify revenue sources, including a cap on the tax exclusion of employer-based health insurance, to subsidize health care coverage with the goal of insuring all Americans. 7. Create state or regional insurance exchanges to pool risk, so that Americans without access to employer-based or other group insurance could obtain a standard benefits package through these exchanges. Employers should also be allowed to participate in these exchanges for their employees' coverage. 8. Create a health coverage board with broad stakeholder representation to determine and periodically update the affordable standard benefit package available through state or regional insurance exchanges

Prevalence of Frailty in European Emergency Departments (FEED): an international flash mob study

Introduction Current emergency care systems are not optimized to respond to multiple and complex problems associated with frailty. Services may require reconfiguration to effectively deliver comprehensive frailty care, yet its prevalence and variation are poorly understood. This study primarily determined the prevalence of frailty among older people attending emergency care. Methods This cross-sectional study used a flash mob approach to collect observational European emergency care data over a 24-h period (04 July 2023). Sites were identified through the European Task Force for Geriatric Emergency Medicine collaboration and social media. Data were collected for all individuals aged 65 + who attended emergency care, and for all adults aged 18 + at a subset of sites. Variables included demographics, Clinical Frailty Scale (CFS), vital signs, and disposition. European and national frailty prevalence was determined with proportions with each CFS level and with dichotomized CFS 5 + (mild or more severe frailty). Results Sixty-two sites in fourteen European countries recruited five thousand seven hundred eighty-five individuals. 40% of 3479 older people had at least mild frailty, with countries ranging from 26 to 51%. They had median age 77 (IQR, 13) years and 53% were female. Across 22 sites observing all adult attenders, older people living with frailty comprised 14%. Conclusion 40% of older people using European emergency care had CFS 5 + . Frailty prevalence varied widely among European care systems. These differences likely reflected entrance selection and provide windows of opportunity for system configuration and workforce planning

On the Gibbs adsorption equation and diffuse interface models

In this paper we discuss some applications of the classical Gibbs adsorption equation to specific diffuse interface models that are based on conserved and non-conserved order parameters. Such models are natural examples of the general methodology developed by J. W. Gibbs in his treatment of the thermodynamics of surfaces. We employ the methodology of J. W. Cahn, which avoids the use of conventional dividing surfaces to define surface excess quantities. We show that the Gibbs adsorption equation holds for systems with gradient energy coefficients, provided the appropriate definitions of surface excess quantities are used. We consider, in particular, the phase-field model of a binary alloy with gradient energy coefficients for solute and the phase field. We derive a solute surface excess quantity that is independent of a dividing surface convention, and find that the adsorption in this model is influenced by the surface free energies of the pure components of the binary alloy as well as the solute gradient energy coefficient. We present one-dimensional numerical solutions for this model corresponding to a stationary planar interface and show the consistency of the numerical results with the Gibbs adsorption equation. We also discuss the Gibbs adsorption equation in the context of other diffuse interface models that arise in spinodal decomposition and order-disorder transitions

Thin interface asymptotics for an energy/entropy approach to phase-field models with unequal conductivities

Karma and Rappel [Phys. Rev. E 57 (1998) 4342] recently developed a new sharp interface asymptotic analysis of the phase-field equations that is especially appropriate for modeling dendritic growth at low undercoolings. Their approach relieves a stringent restriction on the interface thickness that applies in the conventional asymptotic analysis, and has the added advantage that interfacial kinetic effects can also be eliminated. However, their analysis focussed on the case of equal thermal conductivities in the solid and liquid phases; when applied to a standard phase-field model with unequal conductivities, anomalous terms arise in the limiting forms of the boundary conditions for the interfacial temperature that are not present in conventional sharp interface solidification models, as discussed further by Almgren [SIAM J. Appl. Math. 59 (1999) 2086]. In this paper we apply their asymptotic methodology to a generalized phase-field model which is derived using a thermodynamically consistent approach that is based on independent entropy and internal energy gradient functionals that include double wells in both the entropy and internal energy densities. The additional degrees of freedom associated with the generalized phase-field equations can be used to eliminate the anomalous terms that arise for unequal conductivities

Phase-field model for solidification of a eutectic alloy

In this paper we discuss two phase-field models for solidification of a eutectic alloy, a situation in which a liquid may transform into two distinct solid phases. The first is based on a regular solution model for the solid with a chemical miscibility gap. This model suffers from the deficiency that, in the sharp interface limit, it approximates a free-boundary problem in which the surface energy of the solid-solid interface is zero and consequently mechanical equilibrium at a trijunction requires that the solid-solid interface has zero dihedral angle (locally planar). We propose a second model which uses two order parameters to distinguish the liquid phase and the two solid phases. We provide a thermodynamically consistent derivation of this phase-field model which ensures that the local entropy production is positive. We conduct a sharp interface asymptotic analysis of the liquid-solid phase transition and show it is governed by a free-boundary problem in which both surface energy and interface kinetics are present. Finally, we consider a sharp interface asymptotic analysis of a stationary trijunction between the two solid phases and the liquid phase, from which we recover the condition that the interfacial surface tensions are in mechanical equilibrium (Young's equation). This sharp interface analysis compares favourably with numerical solutions of the phase-field model appropriate to a trijunction

Diffuse-Interface methods in fluid mechanics

We review the development of diffuse-interface models of hydrodynamics and their application to a wide variety of interfacial phenomena. These models have been applied successfully to situations in which the physical phenomena of interest have a length scale commensurate with the thickness of the interfacial region (e.g. near-critical interfacial phenomena or small-scale flows such as those occurring near contact lines) and fluid flows involving large interface deformations and/or topological changes (e.g. breakup and coalescence events associated with fluid jets, droplets, and large-deformation waves). We discuss the issues involved in formulating diffuse-interface models for single-component and binary fluids. Recent applications and computations using these models are discussed in each case. Further, we address issues including sharp-interface analyses that relate these models to the classical free-boundary problem, computational approaches to describe interfacial phenomena, and models of fully miscible fluids

A xi-Vector Formulation of Anisotropic Phase-Field Models: 3-D Asymptotics

In this paper we present a new formulation of a large class of phase-field models, which describe solidification of a pure material and allow for both surface energy and interface kinetic anisotropy, in terms of the Hoffman-Cahn ¸-vector. The ¸-vector has previously been used in the context of sharp interface models, where it provides an elegant tool for the representation and analysis of interfaces with anisotropic surface energy. We show that the usual gradient-energy formulations of anisotropic phasefield models are expressed in a natural way in terms of the ¸-vector when appropriately interpreted. We use this new formulation of the phase-field equations to provide a concise derivation of the GibbsThomson -Herring equation in the sharp-interface limit in three dimensions. PHASE-FIELD ¸-VECTOR June 15, 1995 1. Introduction The presence of surface energy anisotropy in the solidification of a pure material is a phenomenon of both practical and theoretical importance. In practice it ..

Convective stability in the Rayleigh-Benard and directional solidification problems - high-frequency gravity modulation

The effect of vertical, sinusoidal, time-dependent gravitational acceleration on the onset of solutal convection during directional solidification is analyzed in the limit of large modulation frequency-OMEGA. When the unmodulated state is unstable, the modulation amplitude required to stabilize the system is determined by the method of averaging, and is O(OMEGA). Comparison of the results from the averaged equations with numerical solutions of the full linear stability equations (based on Floquet theory) show that the difference is O(OMEGA-1/2). When the unmodulated state is stable, resonant modes of instability occur at large modulation amplitude. These are analyzed using matched asymptotic expansions to elucidate the boundary-layer structure for both the Rayleigh-Benard and directional solidification configurations. The leading-order term for the modulation amplitude is of O(OMEGA-2); the first-order correction of O(OMEGA-3/2) is calculated, and the results are compared with numerical solutions of the full linear stability equations. Based on these analyses, a thorough examination of the dependence of the stability criteria on the unmodulated Rayleigh number, Schmidt number, and distribution coefficient, is carried out

A phase-field/fluid motion model of solidification: Investigation of flow effects during directional solidification and dendritic growth

The phase-field model of solidification is extended to include the effects of fluid flow in the melt. The phase-field model is based on coupling the nist-equations for heat flow in the liquid and solid phases with an auxiliary nist-equation that describes the evolution of the phase-field variable, which is a non-conserved order parameter indicating the local phase, solid or liquid, at each point of the material. The solid-liquid interface is then represented by a diffuse transition layer in which the phase-field variable changes rapidly between its values in the bulk phases. The model is extended to include fluid flow by a further coupling to the Navier-Stokes nist-equations. Preliminary studies have been performed for a model in which the solid phase is treated as a liquid of high viscosity compared to the liquid phase. The main coupling in the Navier-Stokes nist-equations is then through an additional term in the stress tensor that depends on the gradients of the phase-field variable, representing the effects of capillary forces within the diffuse interface