Step-by-step first order antiferroelectric-paraelectric transition induced by frustration and electric field

We show analytically that even not too strong frustrating next neighbor interaction strongly affects first order antiferroelectric-paraelectric transition in an external electric field. We apply mean-field Landau theory. In the electric field a single phase transition at T ₀ splits into a step-by-step staircase with a series of intermediate phases. Unexpectedly enough we found that the equilibrium structures of the phases differ substantially from structures formed at low temperature both without field and in field. Polarization of intermediate structures decreases with temperature in a stepwise manner. Similar step-by-step transitions can occur also in magnetic materials with frustrating interaction.     

Relationship between the nucleation and precrystallization liquid phase during homogeneous crystallization of metals

A comparative estimation of the size parameters of clusters of precrystallization liquid phase (PLP) of metals and critical crystalline nuclei has revealed the sizes of critical crystalline nuclei to be smaller than those of PLP clusters. Based on the results of estimation of the radii of critical crystalline nucleus by the methods of classical theory and molecular dynamics, it has been found for the first time that the radius of critical crystalline nucleus is about 0.2–0.4 of the PLP cluster radius. This fact confirmed the hypothesis of Ubellode et al. about the formation of a transition layer with a partially ordered structure between the solid and liquid phases. A scheme of the nucleation and growth of a crystalline nucleus under conditions of transition layer formation is proposed.

     

A multi-moment vortex method for 2D viscous fluids

In this paper we introduce simplified, exact, combinatorial formulas that arise in the vortex interaction model found in [33]. These combinatorial formulas allow for the efficient implementation and development of a new multi-moment vortex method (MMVM) using a Hermite expansion to simulate 2D vorticity. The method naturally allows the particles to deform and become highly anisotropic as they evolve without the added cost of computing the non-local Biot–Savart integral. We present three examples using MMVM. We first focus our attention on the implementation of a single particle, large number of Hermite moments case, in the context of quadrupole perturbations of the Lamb–Oseen vortex. At smaller perturbation values, we show the method captures the shear diffusion mechanism and the rapid relaxation (on Re^1/3 time scale) to an axisymmetric state. We then present two more examples of the full multi-moment vortex method and discuss the results in the context of classic vortex methods. We perform numerical tests of convergence of the single particle method and show that at least in simple cases the method exhibits the exponential convergence typical of spectral methods. Lastly, we numerically investigate the spatial accuracy improvement from the inclusion of higher Hermite moments in the full MMVM.     

The Cauchy Transform of Certain Distributions with Application

We study boundary properties of the Cauchy transform of certain distributions with supports on non-rectifiable curves and apply these results for solution of the Riemann boundary value problem.     

Bayesian knowledge base tuning

For a knowledge-based system that fails to provide the correct answer, it is important to be able to tune the system while minimizing overall change in the knowledge-base. There are a variety of reasons why the answer is incorrect ranging from incorrect knowledge to information vagueness to incompleteness. Still, in all these situations, it is typically the case that most of the knowledge in the system is likely to be correct as specified by the expert (s) and/or knowledge engineer (s). In this paper, we propose a method to identify the possible changes by understanding the contribution of parameters on the outputs of concern. Our approach is based on Bayesian Knowledge Bases for modeling uncertainties. We start with single parameter changes and then extend to multiple parameters. In order to identify the optimal solution that can minimize the change to the model as specified by the domain experts, we define and evaluate the sensitivity values of the results with respect to the parameters. We discuss the computational complexities of determining the solution and show that the problem of multiple parameters changes can be transformed into Linear Programming problems, and thus, efficiently solvable. Our work can also be applied towards validating the knowledge base such that the updated model can satisfy all test-cases collected from the domain experts.     

Synthesis of 7-Alkoxyquinolines,Coumarins, and Resorufins

Synthesis of the title compounds by treatment of the sodium salts of 7-quinolinol, 7-hydroxycoumarin, and resorufin with alkyl halides is described.     

Addendum to: Capillary Floating and The Billiard Ball Problem

We compare the results of our earlier paper on the floating in neutral equilibrium at arbitrary orientation in the sense of Finn-Young with the literature on its counterpart in the sense of Archimedes. We add a few remarks of personal and social-historical character.