Construction of the Hill48 and Yld89 for Auto-body Steel Sheets considering the Strain Rate

This paper deals with the anisotropic material properties and the initial yield locus considering the strain rate. Uni-axial tensile tests are performed with variation of the strain rate in order to obtain flow stress curves and the tensile properties. The R-values have been measured with a high speed camera by analyzing the deformation history during the tensile test. Anisotropy of auto-body steel sheets have been described by using Hill48 and Yld89 (Barlat89) yield functions according to the strain rate ranged from 0.001/sec to 100/sec. Hill48 and Yld89 yield loci of auto-body steel sheets at various strain rates have been constructed in order to visualize the initial yield state. The performance of two yield criteria is evaluated by comparing yield loci constructed in the principal stress plane. The initial yield locus becomes different from the static one when the strain rate is considered to describe the anisotropy of the steel sheets

Modulated structures in electroconvection in nematic liquid crystals

Motivated by experiments in electroconvection in nematic liquid crystals with homeotropic alignment we study the coupled amplitude equations describing the formation of a stationary roll pattern in the presence of a weakly-damped mode that breaks isotropy. The equations can be generalized to describe the planarly aligned case if the orienting effect of the boundaries is small, which can be achieved by a destabilizing magnetic field. The slow mode represents the in-plane director at the center of the cell. The simplest uniform states are normal rolls which may undergo a pitchfork bifurcation to abnormal rolls with a misaligned in-plane director.We present a new class of defect-free solutions with spatial modulations perpendicular to the rolls. In a parameter range where the zig-zag instability is not relevant these solutions are stable attractors, as observed in experiments. We also present two-dimensionally modulated states with and without defects which result from the destabilization of the one-dimensionally modulated structures. Finally, for no (or very small) damping, and away from the rotationally symmetric case, we find static chevrons made up of a periodic arrangement of defect chains (or bands of defects) separating homogeneous regions of oblique rolls with very small amplitude. These states may provide a model for a class of poorly understood stationary structures observed in various highly-conducting materials ("prechevrons" or "broad domains").Comment: 13 pages, 13 figure

Likelihood Geometry

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its maximum likelihood degree. We present an introduction to this theory and its statistical motivations. Many favorite objects from combinatorial algebraic geometry are featured: toric varieties, A-discriminants, hyperplane arrangements, Grassmannians, and determinantal varieties. Several new results are included, especially on the likelihood correspondence and its bidegree. These notes were written for the second author's lectures at the CIME-CIRM summer course on Combinatorial Algebraic Geometry at Levico Terme in June 2013.Comment: 45 pages; minor changes and addition

Outcomes of concomitant aortic valve replacement and coronary artery bypass grafting at teaching hospitals versus nonteaching hospitals

ObjectiveHospitals with a high volume and academic status produce better patient outcomes than other hospitals after complex surgical procedures. Risk models show that concomitant aortic valve replacement and coronary artery bypass grafting pose a greater risk than isolated coronary artery bypass grafting or aortic valve replacement. We examined the relationship of hospital teaching status and the presence of a thoracic surgery residency program with aortic valve replacement/coronary artery bypass grafting outcomes.MethodsBy using the Nationwide Inpatient Sample database, we identified patients who underwent concomitant aortic valve replacement/coronary artery bypass grafting from 1998 to 2007 at nonteaching hospitals, teaching hospitals without a thoracic surgery residency program, and teaching hospitals with a thoracic surgery residency program. Multivariate analysis was performed to identify intergroup differences. Risk-adjusted multivariable logistic regression analysis was used to assess independent predictors of in-hospital mortality and complication rates.ResultsThe 3 groups of patients did not differ significantly in their baseline characteristics. Patients who underwent aortic valve replacement/coronary artery bypass grafting had higher overall risk-adjusted complication rates in nonteaching hospitals (odds ratio 1.58; 95% confidence interval, 1.39–1.80; P < .0001) and teaching hospitals without a thoracic surgery residency program (odds ratio 1.42; 95% confidence interval, 1.26–1.60; P < .0001) than in thoracic surgery residency program hospitals. However, no difference was observed in the adjusted mortality rate for nonteaching hospitals (odds ratio 0.95; 95% confidence interval, 0.87–1.04; P = .25) or teaching hospitals without a thoracic surgery residency program (odds ratio 1.00; 95% confidence interval, 0.92–1.08; P = .98) when compared with thoracic surgery residency program hospitals. Robust statistical models were used for analysis, with c-statistics of 0.98 (complications) and 0.82 (mortality).ConclusionPatients who require complex cardiac operations may have better outcomes when treated at teaching hospitals with a thoracic surgery residency program

Thermodynamic properties of excess-oxygen-doped La2CuO4.11 near a simultaneous transition to superconductivity and long-range magnetic order

We have measured the specific heat and magnetization {\it versus} temperature in a single crystal sample of superconducting La$_{2}$CuO$_{4.11}$ and in a sample of the same material after removing the excess oxygen, in magnetic fields up to 15 T. Using the deoxygenated sample to subtract the phonon contribution, we find a broad peak in the specific heat, centered at 50 K. This excess specific heat is attributed to fluctuations of the Cu spins possibly enhanced by an interplay with the charge degrees of freedom, and appears to be independent of magnetic field, up to 15 T. Near the superconducting transition $T_{c}$($H$=0)= 43 K, we find a sharp feature that is strongly suppressed when the magnetic field is applied parallel to the crystallographic c-axis. A model for 3D vortex fluctuations is used to scale magnetization measured at several magnetic fields. When the magnetic field is applied perpendicular to the c-axis, the only observed effect is a slight shift in the superconducting transition temperature.Comment: 8 pages, 8 figure

Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection

Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes ($\approx$ hydrodynamic modes) of the underlying physical system, much more than quasi one- and two-dimensional patterns are. The reason is the lack of damping boundaries. This paper compares two analytic techniques to derive the patten dynamics from hydrodynamics, which are usually equivalent but lead to different results when applied to multiple homogeneous soft modes. Dielectric electroconvection in nematic liquid crystals is introduced as a model for three-dimensional pattern formation. The 3D pattern dynamics including soft modes are derived. For slabs of large but finite thickness the description is reduced further to a two-dimensional one. It is argued that the range of validity of 2D descriptions is limited to a very small region above threshold. The transition from 2D to 3D pattern dynamics is discussed. Experimentally testable predictions for the stable range of ideal patterns and the electric Nusselt numbers are made. For most results analytic approximations in terms of material parameters are given.Comment: 29 pages, 2 figure