Thermodynamic evaluation and optimization of the As–Co,As–Fe and As–Fe–S systems

A critical evaluation of all available phase diagram and thermodynamic data for the As–Co and As–Fe binary systems as well as the As–Fe–S ternary system has been performed and thermodynamic assessments over the whole composition ranges are presented using the CALPHAD method. To predict thermodynamic properties and phase equilibria for these systems, the Modified Quasichemical Model (MQM) for short range ordering was used for the liquid phases. The Compound Energy Formalism (CEF) was used for the solid solutions. Since Co and Fe are ferromagnetic, magnetic contributions were added to describe the Gibbs energy of cobalt and iron rich solid solutions. Important uncertainties remain for the liquidus of As-rich regions in the binary subsystems.     

Phase transition,microstructure and solidification of Ce–La–Fe and Ce–Nd–Fe alloys: Experimental investigation and thermodynamic calculation

In this work, phase transition temperatures of La–Fe and Ce–Fe alloys were determined using differential thermal analysis (DTA), while phase transition temperatures, microstructure, and phase compositions of La–Ce–Fe and Ce-Nd-Fe alloys were studied using DTA and scanning electron microscopy with energy dispersive spectroscopy (SEM-EDS). Based on the available experimental data reported in the literature and the experimental results determined in this work, the La–Fe and Ce–Fe systems were re-assessed thermodynamically using the CALPHAD (CALcuation of PHAse Diagrams) method, and then the Ce–La–Fe and Ce-Nd-Fe systems were calculated by combining the re-assessed La–Fe and Ce–Fe systems with the previously assessed Nd–Fe, Ce–La, and Ce–Nd systems. The calculated phase diagrams and thermodynamic properties of the La–Fe and Ce–Fe systems are consistent with the experimental data. The calculated isothermal sections and vertical sections in the Ce–La–Fe and Ce-Nd-Fe systems are in good agreement with the experimental results. The solidification behaviors of Ce–La–Fe and Ce-Nd-Fe as-cast alloys were analyzed through the experimental examination and thermodynamic calculation with Scheil-Gulliver non-equilibrium model. The simulated results agree well with the experimental results. It indicates that the reasonable thermodynamic parameters of the Ce–La–Fe and Ce-Nd-Fe systems were obtained finally, which would be fundamental to developing a thermodynamic database of the multi-component Nd-RE-Fe-B alloy systems and then to designing novel Nd-Fe-B permanent magnets with light rare-earth metals La and Ce.     

Quantum teleportation and Birman–Murakami–Wenzl algebra

In this paper, we investigate the relationship of quantum teleportation in quantum information science and the Birman–Murakami–Wenzl (BMW) algebra in low-dimensional topology. For simplicity, we focus on the two spin-1/2 representation of the BMW algebra, which is generated by both the Temperley–Lieb projector and the Yang–Baxter gate. We describe quantum teleportation using the Temperley–Lieb projector and the Yang–Baxter gate, respectively, and study teleportation-based quantum computation using the Yang–Baxter gate. On the other hand, we exploit the extended Temperley–Lieb diagrammatical approach to clearly show that the tangle relations of the BMW algebra have a natural interpretation of quantum teleportation. Inspired by this interpretation, we construct a general representation of the tangle relations of the BMW algebra and obtain interesting representations of the BMW algebra. Therefore, our research sheds a light on a link between quantum information science and low-dimensional topology.     

Max–plus matrix method and cycle time assignability and feedback stabilizability for min–max–plus systems

A variety of problems arising in nonlinear systems with timing constraints such as manufacturing plants, digital circuits, scheduling managements, etc., can be modeled as min–max–plus systems described by the expressions in which the operations minimum, maximum and addition appear. This paper applies the max–plus matrix method to analyze the cycle time assignability and feedback stabilizability of min–max–plus systems with min–max–plus inputs and max–plus outputs, which are nonlinear extensions of the systems studied in recent years. The max–plus projection matrix representation of closed-loop systems is introduced to establish some structural and quantitative relationships between reachability, observability, cycle time assignability and feedback stabilizability. The necessary and sufficient conditions for the cycle time assignability with respect to a state feedback and an output feedback, respectively, and the sufficient condition for the feedback stabilizability with respect to an output feedback are derived. Furthermore, one output feedback stabilization policy is designed so that the closed-loop systems take the maximal Lyapunov exponent as an eigenvalue. The max–plus matrix method based on max–plus algebra and directed graph is constructive and intuitive, and several numerical examples are given to illustrate this method.     

5–6–7 Meshes: Remeshing and analysis

We introduce a new type of meshes called 5–6–7 meshes. For many mesh processing tasks, low- or high-valence vertices are undesirable. At the same time, it is not always possible to achieve complete vertex valence regularity, i.e. to only have valence-6 vertices. A 5–6–7 mesh is a closed triangle mesh where each vertex has valence 5, 6, or 7. An intriguing question is whether it is always possible to convert an arbitrary mesh into a 5–6–7 mesh. In this paper, we answer the question in the positive. We present a 5–6–7 remeshing algorithm which converts a closed triangle mesh with arbitrary genus into a 5–6–7 mesh which (a) closely approximates the original mesh geometrically, e.g. in terms of feature preservation and (b) has a comparable vertex count as the original mesh. We demonstrate the results of our remeshing algorithm on meshes with sharp features and different topology and complexity.     

Critical evaluation and thermodynamic optimization of the Al–Ce,Al–Y,Al–Sc and Mg–Sc binary systems

New critical evaluations and optimizations of the Al–Ce, Al–Y, Al–Sc and Mg–Sc systems are presented. The Modified Quasichemical Model is used for the liquid phases which exhibit a high degree of short-range ordering. A number of solid solutions in the binary systems are modelled using the Compound Energy Formalism. All available and reliable experimental data such as enthalpies of mixing in liquid alloys, heats of formation of intermetallic phases, phase diagrams, etc. are reproduced within experimental error limits. It is shown that the Modified Quasichemical Model reproduces the partial enthalpy of mixing data in the liquid alloys better than the Bragg–Williams random mixing model which does not take short-range ordering into account.     

Thermodynamic optimization of the Mn–P and Fe–Mn–P systems

Thermodynamic modeling of the Mn–P and Fe–Mn–P systems in the full composition was carried out using the CALculation of PHAse Diagrams (CALPHAD) method based on the critical evaluation of all available phase equilibria and thermodynamic data. The liquid and solid solutions were described using the Modified Quasichemical Model and Compound Energy Formalism, respectively. The Gibbs energies of the binary stoichiometric iron and manganese phosphides were determined based on reliable experimental data. The ternary (Fe,Mn)₃P, (Fe,Mn)₂P and (Fe,Mn)P phosphides were modeled as solid solutions with mutual substitution between Fe and Mn atoms. The Gibbs energy of the liquid solution was predicted using the Toop interpolation technique with P as an asymmetric component, without any ternary parameters. The thermodynamic properties of P in the entire composition region and the liquidus of the ternary system were well reproduced. Based on the thermodynamic models with optimized parameters, unexplored phase diagrams and thermodynamic properties of the Fe–Mn–P system were predicted.     

Thermodynamic assessment of the Si–Zn,Mn–Si,Mg–Si–Zn and Mg–Mn–Si systems

The binary Si–Zn and Mn–Si systems have been critically evaluated based upon available phase equilibrium and thermodynamic data, and optimized model parameters have been obtained giving the Gibbs energies of all phases as functions of temperature and composition. The liquid solution has been modeled with the Modified Quasichemical Model (MQM) to account for the short-range-ordering. The results have been combined with those of our previous optimizations of the Mg–Si, Mg–Zn and Mg–Mn systems to predict the phase diagrams of the Mg–Si–Zn and Mg–Mn–Si systems. The predictions have been compared with available data.     

Critical assessment and thermodynamic modeling of the Cu–Fe–O–Si system

The present study is the first Calphad-type assessment of the Cu–Fe–O–Si system. All relevant thermodynamic and phase equilibrium data have been critically evaluated to produce a thermodynamic database describing the Gibbs energies of all phases in the system. The predictive range of the database covers all conditions of pyrometallurgical production of copper in terms of temperature and oxygen partial pressure. Liquid oxide slag and liquid metal phases have been described using two separate solution models, both developed within the framework of the Modified Quasichemical Formalism. Slag model is expressed as [Cu⁺, Fe²⁺, Fe³⁺, Si⁴⁺][O^2-] and metal model is expressed as (Cu^I, Fe^II, O^II). They are internally consistent with the models for fcc–Cu, fcc–Fe, bcc–Fe, spinel, wüstite, CuFeO₂, Cu₂O, Fe₂SiO₄, Fe₂O₃ and SiO₂ obtained in the previous optimizations of the Cu–O, Fe–O, Cu–Fe, Cu–Fe–O, Cu–O–Si, Fe–O–Si sub-systems.     

Thermodynamic modeling of the Al–Bi,Al–Sb,Mg–Al–Bi and Mg–Al–Sb systems

All available thermodynamic and phase diagram data of the binary Al–Bi and Al–Sb systems and ternary Mg–Al–Bi and Mg–Al–Sb systems were critically evaluated, and all reliable data were used simultaneously to obtain the best set of the model parameters for each ternary system. The Modified Quasichemical Model used for the liquid solution shows a high predictive capacity for the ternary systems. The ternary liquid miscibility gaps in the Mg–Al–Bi and Mg–Al–Sb systems resulting from the ordering behaviour of the liquid solutions can be well reproduced with one additional ternary parameter. Using the optimized model parameters, the experimentally unexplored portions of the Mg–Al–Bi and Mg–Al–Sb ternary phase diagrams were more reasonably predicted. All calculations were performed using the FactSage thermochemical software package.     

On Unitary and Forward–Backward MODE

A new unitary (real-valued) formulation of the popular MODE direction-of-arrival (DOA) estimator is considered. Our unitary MODE algorithm has a reduced computational complexity because it is based on the eigendecomposition of a real-valued covariance matrix. We prove its exact equivalence to the forward-backward MODE (FB-MODE) estimator derived by Stoica and Jansson. This property sheds a new light on the usefulness of FB-MODE.     

Experimental investigations and thermodynamic modelling of the Cr–Nb–Sn–Zr system

This work reports the Calphad modelling of the Cr–Nb–Sn–Zr quaternary system. In a previous paper, the thermodynamic modelling of the Cr–Nb–Sn system was presented. Since no experimental data were available for the Cr–Sn–Zr ternary system, new experimental data are provided, within this study, on the isothermal section at 900 °C. A ternary C14 phase has been identified on the Sn-poor side of the phase diagram. In addition to these experimental data, Density Functional Theory (DFT) calculations are carried out in order to determine formation enthalpies of the stable and metastable compounds. At last, the Special Quasirandom Structures (SQS) method is jointly used with DFT calculations in order to estimate the mixing enthalpies of the A2 and A3 binary solid solutions. Finally, these experimental and calculated data in addition to those from the literature, are used as input data for the Calphad modelling of the Cr–Zr, Nb–Zr and Sn–Zr binary systems and the Cr–Nb–Zr, Cr–Sn–Zr and Nb–Sn–Zr ternary systems. A complete database for the Cr–Nb–Sn–Zr quaternary system is provided.