Marginal relevance of disorder for pinning models

The effect of disorder on pinning and wetting models has attracted much attention in theoretical physics. In particular, it has been predicted on the basis of the Harris criterion that disorder is relevant (annealed and quenched models have different critical points and critical exponents) if the return probability exponent α, a positive number that characterizes the model, is larger than ½. Weak disorder has been predicted to be irrelevant (i.e., coinciding critical points and exponents) if α < ½. Recent mathematical work has put these predictions on firm ground. In renormalization group terms, the case α = ½ is a marginal case, and there is no agreement in the literature as to whether one should expect disorder relevance or irrelevance at marginality. The question is also particularly intriguing because the case α = ½ includes the classical models of two‐dimensional wetting of a rough substrate, of pinning of directed polymers on a defect line in dimension (3 + 1) or (1 + 1), and of pinning of an heteropolymer by a point potential in three‐dimensional space. Here we prove disorder relevance both for the general α = ½ pinning model and for the hierarchical pinning model proposed by Derrida, Hakim, and Vannimenus, in the sense that we prove a shift of the quenched critical point with respect to the annealed one. In both cases we work with Gaussian disorder and we show that the shift is at least of order exp(?1/β⁴) for β small, if β² is the disorder variance. © 2009 Wiley Periodicals, Inc.     

Scanning tunnelling microscopy of charge-density waves in transition metal chalcogenides

We have used scanning tunnelling microscopes (STMs) operating at liquid helium and liquid nitrogen temperatures to image the charge-density waves (CDWs) in transition metal chalcogenides. The layer structure dichalcogenides TaSe₂, TaS₂, NbSe₂, VSe₂, TiSe₂ and TiS₂ have been studied including representative polytype phases such as 1T, 2H and 4Hb. Experimental results are presented for the complete range of CDW amplitudes and structures observed in these materials. In most cases both the CDW and the surface atomic structure have been simultaneously imaged. Results on the trichalcogenide NbSe₃ are also included.

The formation of the CDW along with the associated periodic lattice distortion gaps the Fermi surface (FS) and modifies the local density-of-states (LDOS) detected by the tunnelling process. The tunnelling microscopes have been operated mostly in the constant current mode which maps the LDOS at the position of the tunnelling tip. The relative amplitudes and profiles of the CDW superlattice and the atomic lattice have been measured and confirm on an atomic scale the CDW structures predicted by X-ray, electron and neutron diffraction. The absolute STM deflections are larger than expected for the CDW induced modifications of the LDOS above the surface and possible enhancement mechanisms are reviewed.

In the 2H trigonal prismatic coordination phases the CDWs involve a relatively small charge transfer and the atomic structure dominates the STM images. In the 1T octahedral coordination phases the charge transfer is large and the CDW structure dominates the STM image with an anomalously large enhancement of the STM profile. Systematic comparison of the STM profiles with band structure and FS information is included.

In the case of the 4Hb mixed coordination phases at the lowest temperatures two nearly independent CDWs form in alternate sandwiches. STM studies on 4Hb crystals with both octahedral and trigonal prismatic surface sandwiches have been carried out. The STM scans detect the relative strengths of the two CDWs as well as the interactions between the two types of CDW structure.

The STM scans are also able to detect defects and domain structure in the CDW image. Several examples will be given demonstrating the potential of the STM to detect these local variations in LDOS on an atomic scale. In contrast to the layer structure crystals the linear chain compound NbSe₃ shows a complex surface atomic structure as well as the formation of two CDWs. The surface atomic structure is resolved in the STM scans and profiles have detected the presence of the CDW modulation at 77K and 4.2K. These results demonstrate the feasibility of detecting CDW structure in the presence of complex atomic structure and using materials where dynamical CDW effects can also be studied by STM.

The range of STM results presented here show that the STM scans are extremely sensitive to the detail of the CDW structure and its effect on the LDOS. Although much of this structure has been deduced from diffraction studies, the ability to examine the CDW structure on an atomic scale with the STM is new. The sensitivity of the STM method suggests potential applications to a wide range of electronic structures in materials.     

Optical saturation driven by exciton confinement in molecular chains: a time-dependent density-functional theory approach

We identify excitonic confinement in one-dimensional molecular chains (i.e., polyacetylene and H2) as the main driving force for the saturation of the chain polarizability as a function of the number of molecular units. This conclusion is based on first principles time-dependent density-functional theory calculations using a recently developed exchange-correlation kernel that accounts for excitonic effects. The failure of simple local and semilocal functionals is shown to be linked to the lack of memory effects, spatial ultranonlocality, and self-interaction corrections. These effects get smaller as the gap reduces, in which case such simple approximations do perform better.     

Synthesis of potential HIV integrase inhibitors inspired by natural polyphenol structures

Drawing inspiration from the structural features of some natural polyphenols, the synthesis of two different model compounds as potential inhibitors of HIV integrase (IN) has been described. The former was characterised by a diketo acid (DKA) bioisostere, such as a β-hydroxycarbonyl moiety, between two fragments containing aromatic groups, while in the latter an epoxide linked two polyoxygenated aromatic residues. The moieties present in the structures are thought to function by chelating divalent metal ions on the enzyme catalytic site. Overall, 10 compounds were prepared and some of that submitted to molecular modelling studies (to investigate their interactions with the active site of IN), to metal titration studies (to detect their chelating capability) and to biological assays.     

A domino approach to pyrazino- indoles and pyrroles using vinyl selenones

Herein we disclose an efficient and flexible approach to biologically relevant 3,4-dihydropyrazino[1,2-a]indol-1(2H)ones and 3,4-dihydropyrrolo[1,2-a]pyrazin-1(2H)ones through a domino Michael/intramolecular nucleophilic substitution pathway using potassium hydroxide in dichloromethane. Variously substituted vinyl selenones and 1H-indole-2-carboxamides or 1H-pyrrole-2-carboxamides have been employed with success in chemo and regio-selective processes. The introduction of an amino acid portion on the amidic function is well tolerated without racemization.     

Some properties of third order differential operators

Consider the third order differential operator L given by and the related linear differential equation L(x)(t) + x(t) = 0. We study the relations between L, its adjoint operator, the canonical representation of L, the operator obtained by a cyclic permutation of coefficients a _i , i = 1,2,3, in L and the relations between the corresponding equations.We give the commutative diagrams for such equations and show some applications (oscillation, property A).     

Kinetic investigation of porphyrin interaction with chiral templates reveals unexpected features of the induction and self-propagation mechanism of chiral memory

Kinetics of the porphyrin aggregation leading to a chiral memory system shows a remarkable "catalytic" effect of the noncovalent templates explaining their self-replication ability.     

Equivalency for Disconjugate Operators

The solutions of the dfferential equation L_nx + a₀(t)x = 0, where L_n is a disconjugate operator and a₀ is of one sign, are studied according to their behavior as t → ∞. We prove equivalence theorems between solutions of this equation and its adjoint in terms of property A and property B. These theorems generalize the results known for n = 3 and for odd order binomial equations. Some applications are given too.