Variational approximations for renormalization group transformations

Approximate recursion relations which give upper and lower bounds on the free energy are described. Optimal calculations of the free energy can then be obtained by treating parameters within the renormalization equations variationally. As an example, a particularly simple lower bound approximation which preserves the symmetry of the Hamiltonian (the one-hypercube approximation) is described. The approximation is applied to both the Ising model and the Wilson-Fisher model. At the fixed point a parameter is set variationally and critical indices are calculated. For the Ising model the agreement with the exact results atd = 2 is surprisingly good, 0.1%, and is good atd=3 and evend=4. For the Wilson-Fisher model the recursion relation is reduced to a one-dimensional integral equation which can be solved numerically givingv=0.652 atd=3, or by expansion in agreement with the results of Wilson and Fisher to leading order in . The method is also used to calculate thermodynamic functions for thed = 2 Ising model; excellent agreement with the Onsager solution is found.Supported in part by the National Science Foundation under Grants Nos. MPS73-04886A01 and GH-41512 and by the Brown University Materials Research Laboratory supported by the National Science Foundation. M.C.Y. was supported by a grant from the Scientific and Technical Research Council of Turkey.     

Double Diastereoselection Operative During π-Facially Selective Addition of Chiral 1-Cyclopentenyllithium Reagents to (7R)-7-Methyl-7-Vinylbicyclo[3.2.0]Hept-2-En-6-One

Reaction of the title cyclobutanone with chiral cyclopentenyllithium reagents occurs exclusively from the convex face with low diastereoselectivity. Nonetheless, polycyclic networks with as many as nine stereogenic centers can be elaborated in very few steps.     

Weak Liouville-Arnol′d Theorems and Their Implications

This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion and obtain two theorems reminiscent of the Liouville-Arnol′d theorem. Moreover, we also obtain results on the structure of the configuration spaces of such systems that are reminiscent of results on the configuration space of completely integrable Tonelli Hamiltonians.     

Adamantyl ferrocene derivatives: Antioxidant abilities and effects on model lipid membranes

A series of homoannularly and heteroannularly substituted adamantyl ferrocene derivatives has been synthesized and their effects on membrane fluidity were investigated using liposomes as the membrane models. The liposome formulations of adamantyl ferrocene derivatives were characterized by using dynamic light scattering, differential scanning calorimetry and fluorescence anisotropy measurements. It was demonstrated that adamantyl ferrocene derivatives incorporated into the liposome significantly affect the structure of the lipid bilayer. The results of the study have revealed that adamantyl ferrocene derivatives, compounds 9 – 12, partition into the hydrophobic/hydrophilic interface of the membrane, causing a significant decrease in membrane fluidity. The antioxidant potential of synthesized compounds was assessed with DPPH method and it was shown that the examined compounds possess certain antioxidant activity.     

Orientation and conformation of two [6]carbohelicenes in stretched polystyrene and a thermoresponsive polyaspartate

Two functionalized [6]carbohelicenes, one of which was also available in its two enantiomeric pure forms, were oriented in stretched polystyrene in CDCl₃, and in a recently introduced chiral thermoresponsive lyotropic polyaspartate (poly(benzyl)_0.5(phenethyl)_0.5-L-aspartate) in C₂D₂Cl₄. From the resulting ¹H,¹³C residual dipolar couplings, the helical pitch of a methylated [6]carbohelicene was determined and found to be in agreement with theoretical predictions and existing crystal structures (d(C2,C2′) ≈ 4.3 Å). For a second [6]carbohelicene with para-methoxyphenyl substituents, a clear conformational preference of the substituents was observed. The orientational properties of the two helicene enantiomers in the chiral polyaspartate are very similar, but both drastically change around 306 K. We suggest this behavior is due to an unusual phase transition in the liquid crystal.     

Kinematics of layered reinforced-concrete planar beam finite elements with embedded transversal cracking

In this work crack formation and development is addressed and implemented in a planar layered reinforced-concrete beam element. The crack initiation and growth is described using the strength criterion in conjunction with exact kinematics of the interlayer connection. In this way a novel embedded-discontinuity beam finite element is derived in which the tensile stresses in concrete at the crack position reaching the tensile strength will trigger a crack to open. Since the element is multi-layered, in this way the crack is allowed to propagate through the depth of the beam. The cracked layer(s) will involve discontinuity in the cross-sectional rotation equal to the crack-profile angle, as well as a discontinuity in the position vector of the layer’s reference line. A bond–slip relationship is superimposed onto this model in a kinematically consistent manner with reinforcement being treated as an additional layer of zero thickness with its own material parameters and a constitutive law implemented in the multi-layered beam element.