A new time evolving Gaussian series representation of the imaginary time propagator

Frantsuzov and Mandelshtam [J. Chem. Phys. 121, 9247 (2004)] have recently demonstrated that a time evolving Gaussian approximation (TEGA) to the imaginary time propagator exp(-betaH) is useful for numerical computations of anharmonically coupled systems with many degrees of freedom. In this paper we derive a new exact series representation for the imaginary time propagator whose leading order term is the TEGA. One can thus use the TEGA not only as an approximation but also to obtain the exact imaginary time propagator. We also show how the TEGA may be generalized to provide a family of TEGA's. Finally, we find that the equations of motion governing the evolution of the center and width of the Gaussian may be thought of as introducing a quantum friction term to the classical evolution equations.     

Fluid in a closed narrow slit

The behavior of a fluid inside a closed narrow slit between solid walls is examined on the basis of the density functional theory. It is shown that the constraint of constant number of molecules leads to interesting effects which are absent when the slit is open and in contact with a reservoir. If the slit walls are identical, the density profiles at low temperatures or at high average densities rhoav of the fluid molecules in the slit have a sharp maximum in the middle of the slit, the value of the density at maximum being comparable to that of a liquid. The density of fluid at the walls is in this case comparable to the density of a vapor phase. At high temperatures or at low rhoav the fluid density in the middle of the slit is of the same order of magnitude as at the walls. For nonidentical walls the density maximum is shifted towards the wall with a stronger wall-fluid interaction. The transition between the two types (with and without the sharp maximum) of density profiles with the change of temperature in the slit occurs in a narrow range of temperatures, this range being larger for narrower slits. The pressures which the fluid exerts on the walls as well as the forces per unit area arising due to stresses in the sidewalls of the system can decrease with increasing rhoav. Such a behavior is not possible for homogeneous systems and can be explained by analyzing the fluid density at the walls when rhoav increases. The normal and transversal components of the pressure tensor were calculated as functions of the distance from the wall using the equation of hydrostatic equilibrium and direct calculation of the forces between molecules, respectively. The normal component decreases with increasing distance near the wall in contrast to the normal component near the liquid-vapor interface reported previously in the literature. The behavior of the transverse component does not depend on the fluid-solid interaction and is comparable to that for a liquid-vapor interface.     

Non-covalent monolayer-piercing anchoring of lipophilic nucleic acids: preparation, characterization, and sensing applications

Functional interfaces of biomolecules and inorganic substrates like semiconductor materials are of utmost importance for the development of highly sensitive biosensors and microarray technology. However, there is still a lot of room for improving the techniques for immobilization of biomolecules, in particular nucleic acids and proteins. Conventional anchoring strategies rely on attaching biomacromolecules via complementary functional groups, appropriate bifunctional linker molecules, or non-covalent immobilization via electrostatic interactions. In this work, we demonstrate a facile, new, and general method for the reversible non-covalent attachment of amphiphilic DNA probes containing hydrophobic units attached to the nucleobases (lipid-DNA) onto SAM-modified gold electrodes, silicon semiconductor surfaces, and glass substrates. We show the anchoring of well-defined amounts of lipid-DNA onto the surface by insertion of their lipid tails into the hydrophobic monolayer structure. The surface coverage of DNA molecules can be conveniently controlled by modulating the initial concentration and incubation time. Further control over the DNA layer is afforded by the additional external stimulus of temperature. Heating the DNA-modified surfaces at temperatures >80 °C leads to the release of the lipid-DNA structures from the surface without harming the integrity of the hydrophobic SAMs. These supramolecular DNA layers can be further tuned by anchoring onto a mixed SAM containing hydrophobic molecules of different lengths, rather than a homogeneous SAM. Immobilization of lipid-DNA on such SAMs has revealed that the surface density of DNA probes is highly dependent on the composition of the surface layer and the structure of the lipid-DNA. The formation of the lipid-DNA sensing layers was monitored and characterized by numerous techniques including X-ray photoelectron spectroscopy, quartz crystal microbalance, ellipsometry, contact angle measurements, atomic force microscopy, and confocal fluorescence imaging. Finally, this new DNA modification strategy was applied for the sensing of target DNAs using silicon-nanowire field-effect transistor device arrays, showing a high degree of specificity toward the complementary DNA target, as well as single-base mismatch selectivity.     

Classical theory of atom–surface scattering: The rainbow effect

The scattering of heavy atoms and molecules from surfaces is oftentimes dominated by classical mechanics. A large body of experiments have gathered data on the angular distributions of the scattered species, their energy loss distribution, sticking probability, dependence on surface temperature and more. For many years these phenomena have been considered theoretically in the framework of the “washboard model” in which the interaction of the incident particle with the surface is described in terms of hard wall potentials. Although this class of models has helped in elucidating some of the features it left open many questions such as: true potentials are clearly not hard wall potentials, it does not provide a realistic framework for phonon scattering, and it cannot explain the incident angle and incident energy dependence of rainbow scattering, nor can it provide a consistent theory for sticking. In recent years we have been developing a classical perturbation theory approach which has provided new insight into the dynamics of atom–surface scattering. The theory includes both surface corrugation as well as interaction with surface phonons in terms of harmonic baths which are linearly coupled to the system coordinates. This model has been successful in elucidating many new features of rainbow scattering in terms of frictions and bath fluctuations or noise. It has also given new insight into the origins of asymmetry in atomic scattering from surfaces. New phenomena deduced from the theory include friction induced rainbows, energy loss rainbows, a theory of super-rainbows, and more. In this review we present the classical theory of atom–surface scattering as well as extensions and implications for semiclassical scattering and the further development of a quantum theory of surface scattering. Special emphasis is given to the inversion of scattering data into information on the particle–surface interactions.     

Finite-deformation analysis of the elastostatic field near the tip of a crack: Reconsideration and higher-order results

Summary In this paper we return to the asymptotic analysis, within the nonlinear equilibrium theory of compressible elastic solids, of the deformations and stresses near the tip of a traction-free crack in a slab of all-around infinite extent under conditions of plane strain. As before, the loading at infinity is taken to be one of uniform uni-axial tension at right angles to the faces of the crack. We show that once a restrictive assumption introduced at the start of our earlier asymptotic treatment of the problem is relinquished, certain perplexing anomalies encountered in the previous analysis no longer arise. The present reconsideration of the problem leads to modifications in the dominant-order results for the secondary deformations and stresses, while those pertaining to the physical quantities of primary interest remain unaffected. Furthermore, this investigation encompasses some higher-order considerations, which supply an essential clarification and improvement of the lowest-order asymptotic solution.

---

Zusammenfassung In dieser Arbeit wird die asymptotische Ermittelung, im Rahmen der nichtlinearen Elastizitätstheorie ebener Verformungen, von dem elastostatischen Feld am Ende eines Risses in einer allseitig unendlichen Scheibe wieder aufgenommen und fortgesetzt. Wir zeigen hier, dass gewisse physikalisch unerklärbare Resultate in unserer früheren Behandlung des Problems beseitigt werden wenn man eine unserer ursprünglichen Annahmen über die asymptotische Struktur der Lösung verallgemeinert. Obwohl diese Verallgemeinerung keinen Einfluss auf die wichtigsten. vorher gefundenen Resultate hat, führt sie zu wesentlichen Änderungen in den sekundären Spannungen und in der sekundären Verschiebung. Die vorliegende Arbeit enthält überdies auch asymptotische Betrachtungen zweiter Ordnung die für das Verständnis der Lösung niedrigster Ordnung unentbehrlich sind.

---

---

The results communicated in this paper were obtained in the course of an investigation conducted under Contract N00014-67-A-0094-0020 of the California Institute of Technology with the Office of Naval Research in Washington, D. C.     

Membranes of block copolymer-poly(divinylbenzene) blends for the pervaporation of alcohol/water mixtures

Two hydrophobic ABA three block thermoplastic elastomers, namely styrene/butadiene/styrene (SBS) and styrene/ethylene—butylene/styrene (SEBS), have been employed to prepare membranes by their casting from toluene solutions. While they were expected to be permselective to alcohols from water—alcohol mixtures, they did not display the expected permselectivity. Their modification, by the inclusion of divinylbenzene (DVB) into the casting solutions followed by polymerization, generated increased alcohol permselectivity and permeation rate. There exists an optimum proportion of DVB for which the separation factor and the permeation rate became maximal. The permeation rate became higher with increasing operating temperature, whereas the separation factor decreased moderately. As expected, the pervaporation performance for alcohols from water—alcohol mixtures increases with an increase in the hydrophobicity of the alcohol.     

Finding hidden hamiltonian cycles

Consider a random graph G composed of a Hamiltonian cycle on n labeled vertices and dn random edges that “high” the cycle. Is it possible to unravel the structures, that is, to efficiently find a Himiltonian cycle in G? We describe an O(n³ log n)-step algorithm A for this purpose, and prove that it succeeds almost surely. Part one of A properly covers the “trouble spots” of G by a collection of disjoint paths. (This is the hard part to analyze). Part two of A extends this cover to a full cycle by the rotation-extension technique which is already classical for such problems. © 1994 John Wiley & Sons, Inc.