Simple model of bouncing ball dynamics. Displacement of the limiter assumed as a cubic function of time

Nonlinear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered and the Poincare map, describing evolution from an impact to the next impact, is described. Displacement of the limiter is assumed as periodic, cubic function of time. Due to simplicity of this function analytical computations are possible. Several dynamical modes, such as fixed points, 2 - cycles and chaotic bands are studied analytically and numerically. It is shown that chaotic bands are created from fixed points after first period doubling in a corner-type bifurcation. Equation for the time of the next impact is solved exactly for the case of two subsequent impacts occurring in the same period of limiter's motion making analysis of chattering possible.Comment: 8 pages, 1 figure, presented at the DSTA 2011 conference, Lodz, Polan

Simple model of bouncing ball dynamics: displacement of the table assumed as quadratic function of time

Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles and chaotic bands are studied analytically and numerically. It is shown that chaotic bands appear due to homoclinic structures created from unstable 2 - cycles in a corner-type bifurcation.Comment: 11 pages, 6 figure

Quality assessment of bituminous binders based on the viscoelastic properties: Polish experience

Construction of modern and durable bituminous pavements requires high quality bituminous binder, aggregates and additives. The main objective of this paper was to analyse and compare viscoelastic properties of unmodified and polymer modified bitumens produced in Poland, Europe, in order to assess their quality. In this paper there are presented results of bituminous binder European classification tests (penetration, softening point and Fraass breaking point) as well as rheological test results conducted over a wide range of temperatures. In addition, image analysis of the microstructure of selected polymer modified bitumens is also presented. Based on the analysis it was concluded that although bituminous binders complies with European specification requirements, they are significantly different in terms of their rheological properties. It was found that regardless of binder producer, bituminous binder within the same hardness group exhibit different low and high temperature properties

Probing the photoreactivity of aryl chlorides with oxygen

Molecular oxygen was used to probe the mechanism of the phototransformation of chlorobenzene and 4-chloroanisole in organic solvents. Laser. ash photolysis, electron paramagnetic resonance and product distribution studies clarified the reaction mechanisms of these compounds under a wide range of conditions. The main primary photochemical reaction step is the homolytic cleavage of the C-Cl bond to produce a triplet radical pair in the solvent cage. In non-polar solvents hydrogen abstraction, after radical diffusion, leads to reduction. In polar solvents, in addition to H-abstraction, electron transfer within the caged radical pair occurs and leads to an ion pair (phenyl cation and Cl(-)). In the presence of oxygen, phenyl radicals can form phenylperoxyl radicals which have a bathochromically shifted absorption, thus making the homolytic cleavage visible by. ash photolysis. The peroxyl radicals can couple, leading to more polar compounds, or undergo back reaction to the phenyl radical. For concentrations of the aryl chlorides of higher than 10(-3) M, dimerization becomes an important transformation process and occurs after reaction of the transients with ground state molecules. In addition, excimer formation is postulated to be involved in the dimerization process

Triple immunofluorescence labeling of atherosclerotic plaque components in apoE/LDLR -/- mice.

This paper presents a simple and reliable method of triple immunofluorescence staining that allows simultaneous detection of various cell types present in atherosclerotic plaque of apolipoprotein E and LDL receptor-double knockout (apoE/LDLR -/-) mice. We used combined direct and indirect procedures applying commercially available primary antibodies raised in different species to detect smooth muscle cells (Cy3-conjugated mouse anti-smooth muscle actin, SMA), macrophages (rat anti-CD68) and T lymphocytes (rabbit anti-CD3). Fixation of the material in acetone and modified incubation protocol employing nonfat dry milk in preincubation and incubation media significantly increased the intensity of labeling and effectively quenched the background. Our method offers an efficient way to detect qualitative as well as quantitative changes of macrophages, T lymphocytes and smooth muscle cells in atherosclerotic plaque of apoE/LDLR -/- mice during atherosclerosis development or in response to pharmacological treatment

A Search for High-Frequency Coronal Brightness Variations in the 21 August 2017 Total Solar Eclipse

We report on a search for short-period intensity variations in the green-line FeXIV 530.3 nm emission from the solar corona during the 21 August 2017 total eclipse viewed from Idaho in the United States. Our experiment was performed with a much more sensitive detection system, and with better spatial resolution, than on previous occasions (1999 and 2001 eclipses), allowing fine details of quiet coronal loops and an active-region loop system to be seen. A guided 200-mm-aperture Schmidt-Cassegrain telescope was used with a state-of-the-art CCD camera having 16-bit intensity discrimination and a field-of-view 0.43 degree x 0.43 degree that encompassed approximately one third of the visible corona. The camera pixel size was 1.55 arcseconds, while the seeing during the eclipse enabled features of approx. 2 arcseconds (1450 km on the Sun) to be resolved. A total of 429 images were recorded during a 122.9 second portion of the totality at a frame rate of 3.49 images per second. In the analysis, we searched particularly for short-period intensity oscillations and travelling waves, since theory predicts fast-mode magneto-hydrodynamic (MHD) waves with short periods may be important in quiet coronal and active-region heating. Allowing first for various instrumental and photometric effects, we used a wavelet technique to search for periodicities in some 404 000 pixels in the frequency range 0.5-1.6 Hz (periods: 2 second to 0.6 second). We also searched for travelling waves along some 65 coronal structures. However, we found no statistically significant evidence in either. This negative result considerably refines the limit that we obtained from our previous analyses, and it indicates that future searches for short-period coronal waves may be better directed towards Doppler shifts as well as intensity oscillations