Quantitative Phase Field Model of Alloy Solidification

We present a detailed derivation and thin interface analysis of a phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy. This advance with respect to previous phase-field models is achieved by the addition of a phenomenological "antitrapping" solute current in the mass conservation relation [A. Karma, Phys. Rev. Lett 87, 115701 (2001)]. This antitrapping current counterbalances the physical, albeit artificially large, solute trapping effect generated when a mesoscopic interface thickness is used to simulate the interface evolution on experimental length and time scales. Furthermore, it provides additional freedom in the model to suppress other spurious effects that scale with this thickness when the diffusivity is unequal in solid and liquid [R. F. Almgren, SIAM J. Appl. Math 59, 2086 (1999)], which include surface diffusion and a curvature correction to the Stefan condition. This freedom can also be exploited to make the kinetic undercooling of the interface arbitrarily small even for mesoscopic values of both the interface thickness and the phase-field relaxation time, as for the solidification of pure melts [A. Karma and W.-J. Rappel, Phys. Rev. E 53, R3017 (1996)]. The performance of the model is demonstrated by calculating accurately for the first time within a phase-field approach the Mullins-Sekerka stability spectrum of a planar interface and nonlinear cellular shapes for realistic alloy parameters and growth conditions.Comment: 51 pages RevTeX, 5 figures; expanded introduction and discussion; one table and one reference added; various small correction

Women’s Experiences with Prenatal Care: A Mixed-Methods Study Exploring the Influence of the Social Determinants of Health

Background & Purpose: Racial and ethnic disparities pervade birth outcomes in the United States and the state of Connecticut. While Connecticut’s infant mortality rate is less than the national average, rates for the state’s Black/African American and Hispanic/Latino communities exceed it. This study explored how prenatal care in Connecticut may be enhanced to address these disparities. Methods: In spring 2013, seven focus groups and two semi-structured interviews were conducted (n=47). Participants also self-administered brief surveys. Recruited by local service providers, participants were 18 or older, pregnant and/or in the first year post-partum at the time. Most self-identified as non-white. Results: Even when care was perceived as strong quality, participants perceived a lack of patient-centeredness. Participants knew the importance of prenatal care and actively prioritized it even when experiencing challenges accessing healthcare services or barriers to broader conditions needed to be healthy. Participants also reported experiencing discrimination in healthcare. Conclusions & Implications: The women esteemed providers’ clinical advice, but felt unheard in their prenatal care experiences and faced structural challenges which may be addressed by changing institutional policies and procedures

Vector chiral order in frustrated spin chains

By means of a numerical analysis using a non-Abelian symmetry realization of the density matrix renormalization group, we study the behavior of vector chirality correlations in isotropic frustrated chains of spin S=1 and S=1/2, subject to a strong external magnetic field. It is shown that the field induces a phase with spontaneously broken chiral symmetry, in line with earlier theoretical predictions. We present results on the field dependence of the order parameter and the critical exponents.Comment: 8 pages, 9 figure

A Carleman type estimate for the Mindlin-Timoshenko plate model

This thesis focuses on results concerning providing a Carleman type estimate for the Mindlin-Timoshenko plate equations. The main approach is to provide an estimate for each of the three equations in the model then present these estimates in totality as a singular Carleman estimate for the entire model. The initial equation in the model is a simple two dimensional hyperbolic partial differential equation known as the wave equation. Prior research has been done for this type of equation and will be applied to provide the Carleman estimate for the first equation in the model. The estimate for the second and third equations will be derived by first establishing a point-wise inequality for the principal part of the equation multiplied by an exponential weight. After establishing a suitable pseudo-convex function for the exponential weight factor, specifications will be applied to the established point-wise estimates which will lead to the Carleman type estimates and their corresponding integral inequalities

Death in the Medical Social System: An Analysis of Deviance

A thesis presented to the faculty of the School of Social Sciences at Morehead State University in partial fulfillment of the requirements for the Degree of Master of Arts in Sociology by Christine A. Larson-Kurz in December of 1977

Transparent conducting films in the Zn-Sn-O tie line

Coatings were obtained on borosilicate glass and fused silica substrates with thicknesses of up to 230 nm from solutions with compositions along the Zn-Sn-O tie line. The preparation of the sols was accomplished by combinatorial chemistry with a robotic sample processor using different Zn-II, Sn-II and Sn-IV salts and alkoxides, as well as salts of different doping agents ( e. g. Sb-V, Ta-V, In-III) dissolved in various solvents and additives. The films were made by spin- coating followed by a thermal treatment in air, inert or reducing atmosphere at temperatures up to 1000°C. Except for a few cases, mixed crystalline phases of ZnO, SnO2 and ZnSnO3 or Zn2SnO4 are usually observed within the range 0.4 < [Zn]/([ Zn] + [ Sn]) < 0.75. Pure Zn2SnO4 and ZnSnO3 coatings exhibit good optical properties with a haze < 0.2% and a transmission in the visible range > 85%. In contrast to literature, results obtained for similar coatings by sputtering and pulsed laser deposition, all the sol - gel coatings showed a high resistivity of rho > 3 &Omega;cm even after a forming gas treatment and/ or doping

Light-by-light-type corrections to the muon anomalous magnetic moment at four-loop order

The numerically dominant QED contributions to the anomalous magnetic moment of the muon stem from Feynman diagrams with internal electron loops. We consider such corrections and present a calculation of the four-loop light-by-light-type corrections where the external photon couples to a closed electron or muon loop. We perform an asymptotic expansion in the ratio of electron and muon mass and reduce the resulting integrals to master integrals which we evaluate using analytical and numerical methods. We confirm the results present in the literature which are based on different computational methods.Comment: 16 page

Feedback control of unstable cellular solidification fronts

We present a numerical and experimental study of feedback control of unstable cellular patterns in directional solidification (DS). The sample, a dilute binary alloy, solidifies in a 2D geometry under a control scheme which applies local heating close to the cell tips which protrude ahead of the other. For the experiments, we use a real-time image processing algorithm to track cell tips, coupled with a movable laser spot array device, to heat locally. We show, numerically and experimentally, that spacings well below the threshold for a period-doubling instability can be stabilized. As predicted by the numerical calculations, cellular arrays become stable, and the spacing becomes uniform through feedback control which is maintained with minimal heating.Comment: 4 pages, 4 figures, 1 tabl

Intraframe Sequential Picture Coding

This Paper Generalizes Time-Discrete Autoregressive Source Coding Results of Rate-Distortion Theory to Two Dimensions. a 2-D Discrete Autoregressive Source is Defined and Shown to Produce a 2-D Wide-Sense Markovian Field. the Rate Distortion Function of the Source is Then Obtained under Assumption of Gaussian Field Statistics and a Squared Error Fidelity Criterion. a Procedure for Generating an Ensemble of 2-D Codewords Whose Statistics Satisfy the Variational Equations for R(D) is Given. These 2-D Codewords Are, by Space-Time Mappings, 1-D Tree Codes, and It is Noted that a Tree Coding Theorem of Jelinek, Berger, Davis and Hellman Applies. the Problem of Instrumenting Nearly Optimum 2-D Sequential Encoding is Discussed Briefly. the Paper Stresses Potential Application to Image Coder Design. Copyright © 1977 by the Institute of Electrical and Electronics Engineers, Inc