Intramolecular diels-alder/1,3-dipolar cycloaddition cascade of 1,3,4-oxadiazoles

Full details of a systematic exploration of the intramolecular [4 + 2]/[3 + 2] cycloaddition cascade of 1,3,4-oxadiazoles are disclosed in which the scope and utility of the reaction are defined.     

Random walks on lattices. IV. Continuous-time walks and influence of absorbing boundaries

The general study of random walks on a lattice is developed further with emphasis on continuous-time walks with an asymmetric bias. Continuous time walks are characterized by random pauses between jumps, with a common pausing time distribution(t). An analytic solution in the form of an inverse Laplace transform for P(l, t), the probability of a walker being atl at timet if it started atl _o att=0, is obtained in the presence of completely absorbing boundaries. Numerical results for P(l, t) are presented for characteristically different (t), including one which leads to a non-Gaussian behavior for P(l, t) even for larget. Asymptotic results are obtained for the number of surviving walkers and the mean l showing the effect of the absorption at the boundary.This study was partially supported by ARPA and monitored by ONR(N00014-17-0308).     

Intramolecular Diels-Alder and tandem intramolecular Diels-Alder/1,3-dipolar cycloaddition reactions of 1,3,4-oxadiazoles

The scope of intramolecular Diels-Alder and a novel tandem Diels-Alder/1,3-dipolar cycloaddition cascade of 1,3,4-oxadiazoles is disclosed. In the cases examined, the tandem cycloadditions construct three new rings with formation of four new C-C bonds and set all six stereocenters about a central six-membered ring in a single step including three contiguous and four total quaternary centers without a trace of a second diastereomer.     

Evaluating perturbation contributions in SAFT models by comparing to molecular simulation of n-alkanes

SAFT models are generally written as a perturbation series of the Helmholtz energy with reciprocal temperature as the argument. The perturbation coefficients are then functions of density and molecular size. The variation of the perturbation coefficients with molecular size is given primarily by Wertheim's theory [6], [7], [8] and [9], but there may be additional variations as in the PC-SAFT model. In the present work, we compare the characterization of perturbation coefficients inferred from PC-SAFT to those derived from molecular simulations.The molecular simulations are based on Discontinuous Molecular Dynamics (DMD) and second order Thermodynamic Perturbation Theory (TPT). DMD simulation is applied to the repulsive part of the potential model with molecular details like fused hard spheres for the interaction sites and 110° bond angles. The thermodynamic effects of disperse attractions are treated by rigorous application of TPT. The present work re-examines the related work of Elliott and Gray [35] in the low density and critical regions, focusing on n-alkanes with carbon numbers ranging from 3 to 80.We find that SAFT theory overestimates the repulsive contribution (A₀) and underestimates the first order contribution (A₁) of Helmholtz energy relative to simulation. Nevertheless, the correlations are qualitatively reasonable. Significant inconsistencies arise when considering the second order contribution (A₂). For example, the PC-SAFT characterization of A₂ becomes larger than A₁ in the low density, long chain limit, raising concerns about the convergence of the series. Furthermore, fluctuations are underestimated in the critical region and overestimated in the liquid region. In each case, we can suggest improved characterizations. Altogether, these results suggest ways to modify the SAFT formalism to achieve greater consistency between atomistic and coarse-grained models.     

The Chemistry of the Noncrystalline State

This article sets out to describe and account for the chemical and physical consequences of the presence of gross disorder in solids. Knowledge of the structure of such disordered materials is an obvious prerequisite to a further understanding of other properties and behavior, and our current knowledge of the structure of various noncrystalline systems is discussed together with the experimental techniques which need to be employed in order to obtain such information. The so-called glass transition, which takes place as a liquid is supercooled below the crystallization temperature, is discussed in terms of the various models which have been proposed to account for this phenomenon. The effect of noncrystallinity on electronic properties is also discussed, and we highlight new developments in the understanding of electron localization and transport processes. Finally, two applications of amorphous solids are considered in some detail: optical fibers for use in communication networks and “superionic” glasses for possible use in solid-state batteries.     

Ring structures on groups of arithmetic functions

Using the theory of Witt vectors, we define ring structures on several well-known groups of arithmetic functions, which in another guise are formal Dirichlet series. The set of multiplicative arithmetic functions over a commutative ring R is shown to have a unique functorial ring structure for which the operation of addition is Dirichlet convolution and the operation of multiplication restricted to the completely multiplicative functions coincides with point-wise multiplication. The group of additive arithmetic functions over R also has a functorial ring structure. In analogy with the ghost homomorphism of Witt vectors, there is a functorial ring homomorphism from the ring of multiplicative functions to the ring of additive functions that is an isomorphism if R is a Q-algebra. The group of rational arithmetic functions, that is, the group generated by the completely multiplicative functions, forms a subring of the ring of multiplicative functions. The latter ring has the structure of a Bin(R)-algebra, where Bin(R) is the universal binomial ring equipped with a ring homomorphism to R. We use this algebra structure to study the order of a rational arithmetic function, as well the powersfα for α∈Bin(R) of a multiplicative arithmetic function f. For example, we prove new results about the powers of a given multiplicative arithmetic function that are rational. Finally, we apply our theory to the study of the zeta function of a scheme of finite type over Z.     

On tracial approximation

Let C be a class of unital C*-algebras. The class TAC of C*-algebras which can be tracially approximated (in the Egorov-like sense first considered by Lin) by the C*-algebras in C is studied (Lin considered the case that C consists of finite-dimensional C*-algebras or the tensor products of such with C([0,1])). In particular, the question is considered whether, for any simple separable A∈TAC, there is a C*-algebra B which is a simple inductive limit of certain basic homogeneous C*-algebras together with C*-algebras in C, such that the Elliott invariant of A is isomorphic to the Elliott invariant of B. An interesting case of this question is answered. In the final part of the paper, the question is also considered which properties of C*-algebras are inherited by tracial approximation. (Results of this kind are obtained which are used in the proof of the main theorem of the paper, and also in the proof of the classification theorem of the second author given in [Z. Niu, A classification of tracially approximately splitting tree algebra, in preparation] and [Z. Niu, A classification of certain tracially approximately subhomogeneous C*-algebras, PhD thesis, University of Toronto, 2005]—which also uses the main result of the present paper.)     

Finite element approximation of the Dirichlet problem using the boundary penalty method

Numerische Mathematik - This paper considers a finite element approximation of the Dirichlet problem for a second order self-adjoint elliptic equation,Au=f, in a region Ω ⊂ ℝn (n=2...     

Mixed convection boundary-layer flow over a vertical surface embedded in a porous medium

In this paper we have numerically investigated the existence and uniqueness of a vertically flowing fluid passed a model of a thin vertical fin in a saturated porous media. We have assumed the two-dimensional mixed convection from a fin, which is modelled as a fixed, semi-infinite vertical surface, embedded in a fluid-saturated porous media under the boundary-layer approximation. We have taken the temperature, in excess of the constant temperature in the ambient fluid on the fin, to vary as  , where is measured from the leading edge of the plate and λ is a fixed constant. The Rayleigh number is assumed to be large so that the boundary-layer approximation may be made and the fluid velocity at the edge of the boundary-layer is assumed to vary as . The problem then depends on two parameters, namely λ and , the ratio of the Rayleigh to Péclet numbers. It is found that when λ>0 (<0) there are (is) dual (unique) solution(s) when is grater than some negative values of (which depends on λ). When λ<0 there is a range of negative value of (which depends on λ) for which dual solutions exist and for both λ>0 and λ<0 there is a negative value of (which depends on λ) for which there is no solution. Finally, solutions for 0<1 and 1 have been obtained.