The Geometry of Systems of Third Order Differential Equations Induced by Second Order Regular Lagrangians

A system of third order differential equations, whose coefficients do not depend explicitly on time, can be viewed as a third order vector field, which is called a semispray, and lives on the second order tangent bundle. We prove that a regular second order Lagrangian induces such a semispray, which is uniquely determined by two associated Poincaré-Cartan one-forms. To study the geometry of this semispray, we construct a horizontal distribution, which is a Lagrangian subbundle for an associated Poincaré-Cartan two-form. Using this semispray and the associated nonlinear connection we define dynamical covariant derivatives of first and second order. With respect to this, the second order dynamical derivative of the Lagrangian metric tensor vanishes.     

Orbital picture of ionization and its breakdown in nanoarrays of quantum dots

We present exact numerical results indicating that ionization could be a useful tool to study electron correlations in artificial molecules and nanoarrays of metallic quantum dots. For nanorings consisting of Ag quantum dots of the type already fabricated, we demonstrate that the molecular orbital picture breaks down even for lowest energy ionization processes, in contrast to ordinary molecules. Our ionization results yield a transition point between localization and delocalization regimes in good agreement with various experimental data.     

Surface photovoltage spectroscopy and surface piezoelectric effect in GaAs

“Real” (111) surfaces of n-type GaAs were investigated employing surface photovoltage spectroscopy and the surface piezoelectric effect. Surface states at the energy position E_c ? E_t ? 0.72 eV were found on both the Ga and the As surfaces. Both types of surfaces exhibited a barrier of about 0.55 V. No variations in the surface barrier or the energy position of the surface states were observed in various ambients at atmospheric pressure (dry air, wet air, ammonia and ozone). However, the capture cross-section of the surface states for electrons, as determined from the surface piezoelectric effect transients (of the order of 10^?13 cm²), was found to be sensitive to the ambient. It decreased in wet air and increased in ozone. This effect was more pronounced on the As than on the Ga surfaces. Additional surface states were found to be present in the energy region of 0.9 to 1.0 eV, below the bottom of the conduction band. However, their exact energy positions could not be determined due to interference caused by the carrier trapping of the surface states at E_c ? E_t ? 0.72 eV.     

Fluctuation-driven molecular transport through an asymmetric membrane channel

Channel proteins that selectively conduct molecules across cell membranes often exhibit an asymmetric structure. By means of a stochastic model, we argue that channel asymmetry in the presence of nonequilibrium fluctuations, fueled by the cell's metabolism as observed recently, can dramatically influence the transport through such channels by a ratchetlike mechanism. For an aquaglyceroporin that conducts water and glycerol, we show that a previously determined asymmetric glycerol potential leads to enhanced inward transport of glycerol, but for unfavorably high glycerol concentrations also to enhanced outward transport that protects a cell against poisoning.     

Effect of Alkyl Side Chain on the Conformational Properties of Polysulfones with Quaternary Groups

Modification of intrinsic viscosity, temperature coefficient, and preferential adsorption coefficient of polysulfones with different alkyl side groups in N,N-dimethylformamide/methanol and N,N-dimethylformamide/water was investigated at different compositions and temperatures. The specific interactions, such as hydrogen bonding and polyelectrolyte effect induced by an enhanced dissociation of the ionizable groups, determine both the modification of the solvation power of the polymer coil and the difference in the composition of the mixed solvent inside and outside the coil.     

A Bound of the Finslerian Ricci Scalar

In the Riemannian as well as in the Finslerian geometry, certain conditions on the Ricci scalar or the Ricci tensor provide obstructions on the topology of the base manifold and so on the configuration of cut points by limitations of the injectivity radius, see the Bonnet–Myers theorem and its variants and generalizations. In this paper, we show that conversely, prescribing the injectivity radius of a Finsler manifold, some limitations of the Ricci scalar are obtained. Some consequences of the condition that the Ricci tensor is h-parallel with respect to the Chern–Rund connection are found. In addition, some classes of examples are provided.     

Antiproliferative and Antimicrobial Effects of Rosmarinus officinalis L. Loaded Liposomes

Rosmarinus officinalis L. is a species that is widely known for its culinary and medicinal uses. The purpose of the present study consisted of the evaluation of the antiproliferative and antimicrobial effects of R. officinalis-loaded liposomes (L-R). Characterization of the liposomes was performed by establishing specific parameters. The load of the obtained liposomes was analyzed using an LC-MS method, and antiproliferative assays evaluated the cell viability on a liver adenocarcinoma cell line and on a human hepatic stellate cell line. Antimicrobial assays were performed by agar–well diffusion and by broth microdilution assays. The obtained liposomes showed high encapsulation efficiency, suitable particle size, and good stability. High amounts of caffeic (81.07 ± 0.76), chlorogenic (14.10 ± 0.12), carnosic (20.03 ± 0.16), rosmarinic (39.81 ± 0.35), and ellagic (880.02 ± 0.14) acids were found in their composition, together with other polyphenols. Viability and apoptosis assays showed an intense effect on the cancerous cell line and a totally different pattern on the normal cells, indicating a selective toxicity towards the cancerous ones and an anti-proliferative mechanism. Antimicrobial potential was noticed against all tested bacteria, with a better efficacy towards Gram-positive species. These results further confirm the biological activities of R. officinalis leaf extract, and proposes and characterizes novel delivery systems for their encapsulation, enhancing the biological activities of polyphenols, and overcoming their limitations.     

Surface influence on the rotational and translational dynamics of molecules confined inside a mesoporous carbon xerogel

Low-field nuclear magnetic resonance techniques are employed to extract information about the effects introduced by the interaction with the surface on the rotational and translational dynamics of molecules confined inside a mesoporous carbon xerogel. The molecules under study were water, cyclohexane, and hexane. They were chosen due to their different interaction strength with the carbonaceous matrix. Frequency dependent longitudinal relaxation measurements, using the fast field cycling technique, allowed extraction of the fractal dimension of the carbon xerogel surface. It was observed that the measured value is influenced by the molecule affinity to the surface. Diffusion measurements, using the pulse field gradient technique, have revealed that the stronger interaction with the surface of cyclohexane and hexane molecules leads to an increased diffusive tortuosity, as compared with water.     

Global optimization using bad derivatives: Derivative-free method for molecular energy minimization

A general method designed to isolate the global minimum of a multidimensional objective function with multiple minima is presented. The algorithm exploits an integral “coarse-graining” transformation of the objective function, U, into a smoothed function with few minima. When the coarse-graining is defined over a cubic neighborhood of length scale ϵ, the exact gradient of the smoothed function, 𝒰_ϵ, is a simple three-point finite difference of U. When ϵ is very large, the gradient of 𝒰_ϵ appears to be a “bad derivative” of U. Because the gradient of 𝒰_ϵ is a simple function of U, minimization on the smoothed surface requires no explicit calculation or differentiation of 𝒰_ϵ. The minimization method is “derivative-free” and may be applied to optimization problems involving functions that are not smooth or differentiable. Generalization to functions in high-dimensional space is straightforward. In the context of molecular conformational optimization, the method may be used to minimize the potential energy or, preferably, to maximize the Boltzmann probability function. The algorithm is applied to conformational optimization of a model potential, Lennard–Jones atomic clusters, and a tetrapeptide. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1445–1455, 1998