Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces

ABSTRACT

The theory of calculus of variations is a mathematical tool which is widely used in different scientific areas in particular in physics and chemistry. This theory is strongly related with optimisation. In fact the former seeks to optimise an integral related with some physical magnitude over some space to an extremum by varying a function of the coordinates. On the other hand, reaction paths and potential energy surfaces, in particular their stationary points, are the basis of many chemical theories, in particular reactions rate theories. We present a review where it is gathered together the variational nature of many types of reaction paths: steepest descent, Newton trajectories, artificial force induced reaction (AFIR) paths, gradient extremals, and gentlest ascent dynamics (GAD) curves. The variational basis permits to select the best optimisation technique in order to locate important theoretical objects on a potential energy surface.     

On the kinetic theory of a dense gas of rough spheres

The revised Enskog equation for a dense gas of rough spheres is considered. TheH theorem and the conservation equations are discussed.     

Hydrodynamic equations for attractive particle systems on ℤ

Hydrodynamic properties for a class of nondiffusive particle systems are investigated. The method allows one to study local equilibria for a class of asymmetric zero-range processes, and applies as well to other models, such as asymmetric simple exclusion and misanthropes. Attractiveness is an essential ingredient. The hydrodynamic equations present shock wave phenomena. Preservation of local equilibrium is proven to hold away from the shocks. The problem of breakdown of local ergodicity at the shocks, which was investigated by D. Wick in a particular model, remains open in this more general setup.     

An independent component analysis-based approach on ballistocardiogram artifact removing

Interest about simultaneous electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data acquisition has rapidly increased during the last years because of the possibility that the combined method offers to join temporal and spatial resolution, providing in this way a powerful tool to investigate spontaneous and evoked brain activities. However, several intrinsic features of MRI scanning become sources of artifacts on EEG data. Noise sources of a highly predictable nature such as those related to the pulse MRI sequence and those determined by magnetic gradient switching during scanning do not represent a major problem and can be easily removed. On the contrary, the ballistocardiogram (BCG) artifact, a large signal visible on all EEG traces and related to cardiac activity inside the magnetic field, is determined by sources that are not fully stereotyped and causing important limitations in the use of artifact-removing strategies. Recently, it has been proposed to use independent component analysis (ICA) to remove BCG artifact from EEG signals. ICA is a statistical algorithm that allows blind separation of statistically independent sources when the only available information is represented by their linear combination. An important drawback with most ICA algorithms is that they exhibit a stochastic behavior: each run yields slightly different results such that the reliability of the estimated sources is difficult to assess. In this preliminary report, we present a method based on running the FastICA algorithm many times with slightly different initial conditions. Clustering structure in the signal space of the obtained components provides us with a new way to assess the reliability of the estimated sources.     

Synthesis,characterization, and cytotoxicity evaluation of high-magnetization multifunctional nanoclusters

The paper presents the synthesis, characterization, and in vitro cytotoxicity tests of Fe₃O₄ magnetic nanoclusters coated with ethylenediaminetetraacetic acid disodium salt (EDTA). Electron microscopy analysis (SEM) evidences that magnetite nanoparticles are closely packed into the clusters stabilized with EDTA with well-defined near spherical shapes and sizes in the range 100–200 nm. From XRD measurements, we determined the mean size of the crystallites inside the magnetic cluster about 36 nm. The saturation magnetization determined for the magnetic clusters stabilized with EDTA has high value, about 81.7 emu/g at 300 K. X-ray photoelectron spectroscopy has been used to determine both the elemental and chemical structure of the magnetic cluster surface. In vitro studies have shown that the magnetic clusters at low doses did not induce toxicity on human umbilical vein endothelial cells or lesions of the cell membrane. In contrast, at high doses, the magnetic clusters increased the lipid peroxidation and reduced the leakage of a cytoplasmic enzyme, lactate dehydrogenase (LDH), in parallel with increasing the antioxidant defense.

Open image in new window

Graphical abstract SEM images of EDTA-coated magnetic clusters (MCs) and the HUVEC viability at different MC doses

     

Intensity-related dynamics of femtosecond frequency combs

We have performed systematic studies of intensity-related dynamics of the pulse repetition and carrier-envelope offset frequencies in mode-locked Ti:sapphire lasers. We compared the results far two laser systems that have different intracavity dispersion-compensation schemes. We found that the carrier-envelope phase noise and its dynamic response depend critically on the mode-locking conditions. An intensity-related shift of the laser spectrum was found to be instrumental in interpretations.