Optimizing the accuracy and precision of the single‐pulse Laue technique for synchrotron photo‐crystallography

The accuracy that can be achieved in single‐pulse pump‐probe Laue experiments is discussed. It is shown that with careful tuning of the experimental conditions a reproducibility of the intensity ratios of equivalent intensities obtained in different measurements of 3–4% can be achieved. The single‐pulse experiments maximize the time resolution that can be achieved and, unlike stroboscopic techniques in which the pump‐probe cycle is rapidly repeated, minimize the temperature increase due to the laser exposure of the sample.     

A hybrid stochastic model of retinal angiogenesis

Understanding the biological principles that govern blood vessel growth in the retina has important clinical implications, for the prevention of possible retinopathies, which may eventually lead to blindness. The availability of a realistic mathematical model of the relevant phenomenon may support the medical community in both issues, diagnosis being related to inverse problems, and therapy to optimal control strategies. The mathematical modeling of retinal angiogenesis leads to an highly complex problem, because of dimension, nonlinearity, and intrinsic randomness. In this paper, we propose a reduced model which leads to numerical simulations that somehow reproduce normal vascularization and predict possible pathologies. We call our model hybrid because it includes the coupling of a fully stochastic model for the construction of a vessel network in the retina, with continuum underlying fields describing relevant factors, such as growth factors and oxygen. We perform numerical simulations of a stochastic particle system coupled with partial differential equations (PDEs)' so to obtain images of vessel structure resembling real retina vasculatures. We then derive a possible mean field approximation of the stochastic vessel network, so to obtain a fully deterministic PDE system for the evolution of the underlying fields. Actually, in order to reproduce the geometric structure of the retina vessel network, we have to keep a stochastic model (though simplified) for its construction. Future investigations may concern the use of such a mean field approximation in the numerical simulations of the retina vasculature. Inverse and optimal control problems being the final goal of our research plan.     

Decomposition of two functions in the orthogonality equation

The aim of this paper is to solve the orthogonality equation with two unknown functions. This problem was posed by J. Chmieliński during two international conferences.     

Molecular dynamics of zigzag single walled carbon nanotube immersion in water

The results of enthalpy of immersion in water for finite single-walled carbon nanotubes are reported. Using molecular dynamics simulation, we discuss the relation between the value of this enthalpy and tube diameters showing that the obtained plot can be divided into three regions. The structure of water inside tubes in all three regions is discussed and it is shown that the existence of the strong maximum of enthalpy observed for tube diameter ca. 1.17 nm is due to freezing of water under confinement. The calculations of hydrogen bond statistics and water density profiles inside tubes are additionally reported to confirm the obtained results. Next, we show the results of calculation for the same tubes but containing surface carbonyl oxygen groups at pore entrances. A remarkable rise in the value of enthalpy of immersion in comparison to the initial tubes is observed. We also discuss the influence of charge distribution between oxygen and carbon atom forming surface carbonyls on the structure of confined water. It is concluded for the first time that the presence of surface oxygen atoms at the pore entrances remarkably influences the structure and stability of ice created inside nanotubes, and surface carbonyls appear to be chaotropic (i.e. structure breaking) for confined water. This effect is explained by the pore blocking leading to a decrease (compared to initial structure) in the number of confined water molecules after introduction of surface oxygen groups at pore entrances.     

On self-similar solutions of semilinear wave equations in higher space dimensions

In this paper we analyze self-similar solutions of the semilinear wave equation Φ_tt − ΔΦ − Φ^p = 0 for n > 3 space dimensions. We found several classes of analytic solutions labeled by a single parameter, the form of which differ in the vicinity of the light cone. We also propose suitable numerical methods to study them.     

Eigenchannel method in quantum potential scattering

The eigenchannel method, generalizing the familiar phaseshift method, is formulated for scattering from a Hermitian short range potential. Scattering eigenchannels are defined as eigenstates of some generalized (weighted) operator spectral problem. Eigenvalues of that problem define eigenphaseshifts, the former being the negative of cotangents of the latter. Eigenchannel representations of generalized scattering states, transition operators, and Green operators are constructed. A variational approach to the method is also presented. The general theory is illustrated by applications to scattering of Schrödinger and Dirac particles.     

Thermal effectiveness of different IR radiators employed in rheumatoid hand therapy as assessed by thermovisual examination

We conducted a thermovisual comparison of mean hand surface temperature changes upon local heating with two different IR sources. Sixty-six patients with rheumatoid arthritis (47 women and 19 men; average age, 56.1 ± 8.6 years) were subjected to topical heat therapy for one hand with either the standard IR radiator (SIR) or the water filter IRA (wIRA). The surface temperature of the dorsal side of both hands was measured, and thermal images were taken before and up to 2 h after treatment. At 1 min after treatment, SIR application increased the surface skin temperature of the heated hand from 31.5 ± 1.9 to 35.0 ± 1.9 °C (P<0.05), while wIRA increased it from 32.1 ± 1.6 to 34.2 ± 1.1 °C (P<0.05). Constant decline in temperature was observed immediately after treatment, with the temperatures reaching baseline in about 30 and 120 min after wIRA and SIR treatment, respectively. Similar temperature changes were observed in the heated hands for wIRA and SIR, except at 1 min after treatment. Changes in the untreated hands indicated contralateral reaction. The temperature of the warmed hand showed a correlation to the body mass index.