Surface microscopic structure and electrochemical rectification of a branched alkanethiol self-assembled monolayer

The tert-butanethiol self-assembled monolayers (SAMs) on Au(111) surfaces were prepared from various solvents and investigated by a combination of scanning tunneling microscopy (STM) and electrochemistry in aqueous environments. High-resolution STM images reveal a (radical(7) x radical(7))R19 degrees surface lattice structure, in contrast with the conventional lattice (radical(3) x radical(3))R30 degrees structure for straight-chain alkanethiol SAMs. Interestingly, such a branched monolayer shows electrochemical rectification toward redox probes. We suggest that electrochemical rectification could be a general characteristic of short-chain branched alkanthiol SAMs, and originate in localized electronic effects.     

Internal concentration gradients of guest molecules in nanoporous host materials: measurement and microscopic analysis

Evolution of internal concentration profiles of methanol in 2-D pore structure of ferrierite crystal was measured in the pressure range of 0 to 80 mbar with the help of the recently developed interference microscopy technique. The measured profiles showed that both a surface barrier and internal diffusion controlled the kinetics of adsorption/desorption. Furthermore, they indicated that in the main part of the crystal, the z-directional 10-ring channels were not accessible to methanol and that the transport of methanol mainly occurred via 8-ring y-directional channels. The roof-like part of the crystal was almost instantaneously filled/emptied during adsorption/desorption, indicating accessible 10-ring channels in this section. The measured profiles were analyzed microscopically with the direct application of Fick's second law, and the transport diffusivity of methanol in ferrierite was determined as a function of adsorbed phase concentration. The transport diffusivity varied by more than 2 orders of magnitude over the investigated pressure range. Transport diffusivities, calculated from measured profiles from small and large pressure step changes, were all found to be consistent. Simulated concentration profiles obtained from the solution of Fick's second law with the calculated functional dependence of diffusivities on concentration compared very well with the measured concentration profiles, indicating validity and consistency of the measured data and the calculated diffusivities. The results indicate the importance of measuring the evolution of concentration profiles as this information is vital in determining (1) the direction of internal transport, (2) the presence of internal structural defects, and (3) surface/internal transport barriers. Such detailed information is available neither from common macroscopic methods since, they measure changes in macroscopic properties and use model assumptions to predict the concentration profiles inside, nor from microscopic methods, since they only provide information on average displacement of diffusing molecules.     

Analysis of data fusion methods in virtual screening: theoretical model

This paper presents a theoretical model of how data fusion can be used to combine the results of multiple similarity searches of chemical databases. The model is based on frequency distributions of similarity values that are fused using a multiple integration over regions defined by the particular fusion rule that is being applied. For pairwise fusion, the resulting double integrals are straightforward to evaluate for simple model distributions. Similarity values for recovered-active and recovered-nonactive frequency distributions are independently modeled using a constant background, linearly biased terms, and a first-order correlated term. The model shows that two standard fusion rules can give performance enhancements in some cases but that the results of fusion are dependent on many factors that, taken together, can lead to seemingly inconsistent levels of enhancement.     

Emerging chemical patterns: a new methodology for molecular classification and compound selection

A concept termed Emerging Chemical Patterns (ECPs) is introduced as a novel approach to molecular classification. The methodology makes it possible to extract key molecular features from very few known active compounds and classify molecules according to different potency levels. The approach was developed in light of the situation often faced during the early stages of lead optimization efforts: too few active reference molecules are available to build computational models for the prediction of potent compounds. The ECP method generates high-resolution signatures of active compounds. Predictive ECP models can be built based on the information provided by sets of only three molecules with potency in the nanomolar and micromolar range. In addition to individual compound predictions, an iterative ECP scheme has been designed. When applied to different sets of active molecules, iterative ECP classification produced compound selection sets with increases in average potency of up to 3 orders of magnitude.     

General entanglement scaling laws from time evolution

We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local Hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions violating this entanglement-boundary law. Implications for the classical simulatability are outlined.     

Lyapunov-Schmidt reduction for unfolding heteroclinic networks of equilibria and periodic orbits with tangencies

This article concerns arbitrary finite heteroclinic networks in any phase space dimension whose vertices can be a random mixture of equilibria and periodic orbits. In addition, tangencies in the intersection of un/stable manifolds are allowed. The main result is a reduction to algebraic equations of the problem to find all solutions that are close to the heteroclinic network for all time, and their parameter values. A leading order expansion is given in terms of the time spent near vertices and, if applicable, the location on the non-trivial tangent directions. The only difference between a periodic orbit and an equilibrium is that the time parameter is discrete for a periodic orbit. The essential assumptions are hyperbolicity of the vertices and transversality of parameters. Using the result, conjugacy to shift dynamics for a generic homoclinic orbit to a periodic orbit is proven. Finally, equilibrium-to-periodic orbit heteroclinic cycles of various types are considered.     

An implicit box scheme for subsonic compressible flow with dissipative source term

We investigate the stability and convergence of an implicit box scheme for subsonic flows modelled by scalar conservation laws with dissipative and possibly stiff source terms. The scheme is proposed for solving transient gas flow problems in pipeline networks. Such networks are operated in the subsonic flow region and are characterized by pressure losses due to dissipative friction terms. We verify the properties stated by Kru?kov’s theorem (Kru?kov, Math. USSR-Sb. 10:217–243, 1970) for the approximate solution and prove its convergence to the entropy solution.     

Determination of homogenized diffusion properties in micro-cracked porous materials

Methods of micromechanics [2, 3] are used to obtain homogenized diffusion properties for intact and micro-cracked porous materials. A two scale homogenization technique is proposed. A REV^uc that represents the porous microstructure is modelled as a spherical pore-space inclusion in a matrix, whose diffusion coefficient does not depend on the microstructure geometry but only on the porosity. For cracked porous materials, a REV^c is modelled with the diffusion coefficient for intact porous materials as the matrix phase with ellipsoidal inclusions representing micro-cracks. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computation of the Three-Dimensional Stress State in Composite Shell Structures with Mixed Finite Elements

Being able to compute the complete three-dimensional stress state in layered composite shell structures is essential in order to examine complicated interlaminar failure modes such as delamination. We lay out a mixed finite element formulation with independent displacements, rotations, stress resultants and shell strains. A mixed hybrid shell element with 4 nodes and 5 or 6 nodal degrees of freedom is developed, so that the element formulation can also be used for problems with shell intersections. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)