Modeling of thermodynamic properties of ABr-PrBr3 (A=Li-Cs ) systems

The thermodynamic properties of ABr-PrBr₃(A=Li-Cs) systems were assessed by the CALPHAD method. The liquid phase in the systems was described by the non-stoichiometric associate model. The entropies of mixing in the liquid were evaluated from experimental liquidus and enthalpy of mixing data. For the pseudobinary compounds A₃PrBr₆,APr₂Br₇, and A₂PrBr₅ (A=K,Rb) and Cs₃PrBr₆ and CsPr₂Br₇, the dependences of Gibbs energies of formation on temperature were calculated. The anomalies of sequences of thermodynamic properties in RbBr-PrBr₃ were observed and discussed. The nature of the liquid phase and precision of calculations of the Rb₂PrBr₅(s) compound were discussed.     

Experimental investigation and thermodynamic assessment of the Cu-Sn-Ti ternary system

The Cu-Sn-Ti ternary system has been studied via experiments and thermodynamic modelling. In the experimental section, the composition of the alloys was selected based on the preliminary calculations and available literature data. Metallography, scanning electron microscopy and electron probe microanalysis were employed to analyse alloy samples prepared by arc-melting after annealing at 800 °C for 760 h. Solid phase relations at 800 °C were established. In contrast to earlier reports, the CuSn₃Ti₅ phase was interpreted as a binary intermetallic compound (Sn₃Ti₅) with extended Cu solubility. In the modelling section, three binary sub-systems were critically evaluated and updated according to the new experimental data and theoretical calculations reported in literature. According to their crystal structures and homogeneity ranges, appropriate sublattice models were proposed for SnTi₃,SnTi₂,Sn₃Ti₅ and Sn₅Ti₆. A set of self-consistent thermodynamic parameters for the Cu-Sn-Ti ternary system was obtained by considering the present experimental results and reported experimental information. The calculated results compare with the available experimental data to validate the present thermodynamic assessment.     

Calculation of phase equilibria for an alloy nanoparticle in contact with a solid nanowire

Phase equilibria in a system constituted of an alloy nanoparticle in contact with a solid nanowire have been modelled based on the minimization of a Gibbs free energy function. The Gibbs free energy consists of a bulk, surface and interface contribution. The bulk contribution is taken from CALPHAD thermodynamic databases and the surface properties from the literature. The effect of particle size and surface and interfacial properties on the liquidus line of the Au-Ge and In-Si systems has been studied. The results are compared to the bulk phase diagram and phase equilibria calculated for nano-systems with different geometries.     

On global solutions to fractional functional differential equations with infinite delay in Fréchet spaces

In this paper, we investigate global uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces. We shall rely on a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. The results are obtained by using the α-resolvent family (S_α(t))_t≥0 on a complex Banach space X combined with the above-mentioned fixed point theorem. As an application, a controllability result with one parameter is also provided to illustrate the theory.     

Algorithms to Separate $\{0,\frac{1}{2}\}$ -Chvátal-Gomory Cuts

Chvátal-Gomory cuts are among the most well-known classes of cutting planes for general integer linear programs (ILPs). In case the constraint multipliers are either 0 or , such cuts are known as -cuts. It has been proven by Caprara and Fischetti (Math. Program. 74:221–235, 1996) that separation of -cuts is -hard. In this paper, we study ways to separate -cuts effectively in practice. We propose a range of preprocessing rules to reduce the size of the separation problem. The core of the preprocessing builds a Gaussian elimination-like procedure. To separate the most violated -cut, we formulate the (reduced) problem as integer linear program. Some simple heuristic separation routines complete the algorithmic framework. Computational experiments on benchmark instances show that the combination of preprocessing with exact and/or heuristic separation is a very vital idea to generate strong generic cutting planes for integer linear programs and to reduce the overall computation times of state-of-the-art ILP-solvers.     

In vivo interactive visualization of four-dimensional blood flow patterns

In this paper we give an overview over a series of experiments to visualize and measure flow fields in the human vascular system with respect to their diagnostic capabilities. The experiments utilize a selection of GPU-based sparse and dense flow visualization algorithms to show the diagnostic opportunities for volumetric cardiovascular phase contrast magnetic resonance imaging data sets. Besides classical hardware accelerated particle and line-based approaches, an extensible tublet-based visualization, a four-dimensional volumetric line integral convolution and a new two-dimensional cutting plane tool for three-dimensional velocity data sets have been implemented. To evaluate the results, several hearts of human subjects have been investigated and a flow phantom was built to artificially simulate distinctive flow features. Our results demonstrate that we are able to provide an interactive tool for cardiovascular diagnostics with complementary hardware accelerated visualizations. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.

Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability

Data reduction is a key technique in the study of fixed parameter algorithms. In the AI literature, pruning techniques based on simple and efficient-to-implement reduction rules also play a crucial role in the success of many industrial-strength solvers. Understanding the effectiveness and the applicability of data reduction as a technique for designing heuristics for intractable problems has been one of the main motivations in studying the phase transition of randomly-generated instances of NP-complete problems.In this paper, we take the initiative to study the power of data reductions in the context of random instances of a generic intractable parameterized problem, the weighted d-CNF satisfiability problem. We propose a non-trivial random model for the problem and study the probabilistic behavior of the random instances from the model. We design an algorithm based on data reduction and other algorithmic techniques and prove that the algorithm solves the random instances with high probability and in fixed-parameter polynomial time O(dknm) where n is the number of variables, m is the number of clauses, and k is the fixed parameter. We establish the exact threshold of the phase transition of the solution probability and show that in some region of the problem space, unsatisfiable random instances of the problem have parametric resolution proof of fixed-parameter polynomial size. Also discussed is a more general random model and the generalization of the results to the model.