Numerical experiments on billiards

We investigate decay properties of correlation functions in a class of chaotic billiards. First we consider the statistics of Poincaré recurrences (induced by a partition of the billiard): the results are in agreement with theoretical bounds by Bunimovich, Sinai, and Bleher, and are consistent with a purely exponential decay of correlations out of marginality. We then turn to the analysis of the velocity-velocity correlation function: except for intermittent situations, the decay is purely exponential, and the decay rates scale in a simple way with the (uniform) curvature of the dispersing arcs. A power-law decay is instead observed when the system is equivalent to an infinite-horizon Lorentz gas. Comments are given on the behaviour of other types of correlation functions, whose decay, during the observed time scale, appears slower than exponential.     

Axially symmetric,uniformly rotating neutron stars in general relativity: a non-perturbative approach

The equilibrium problem for an axially symmetric, uniformly rotating, elastic solid neutron star is considered within the framework of a new formulation of relativistic elasticity. The analysis is fully relativistic and free of any assumption about the existence of a globally relaxed state of the star. Static configurations may exist only for rigid motions, and for such motions a set of six Einstein equations for six variables is proposed. Due both to the importance of elastic-solid lattices for the structure of neutron stars crusts and to the lack, up to now, of satisfactory axially symmetric perfect fluid interior solutions matching an asimpotically flat exterior, the results seem to indicate the possibility of constructing physically valid models of axially symmetric astrophysical objects in general relativity. The particular case of non-rotating axially symmetric elastic sources is also discussed.     

The inelastic hard dimer gas: a nonspherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution alpha<1, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting nonequilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalize to inelastic systems a recently method introduced [G. Ciccotti and G. Kalibaeva, J. Stat. Phys. 115, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres held together by rigid bonds. Each dimer consists of two hard disks of diameter d, whose centers are separated by a fixed distance a. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event-driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law t(-2), describing how the kinetic energy of an inelastic hard-sphere system with a constant coefficient of restitution decreases in time, holds even in the case of these nonspherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.     

Treatment of Malignant Melanoma by High-Peak-Power 1064 nm Irradiation Followed by Photodynamic Therapy

Irradiation of B16 pigmented melanoma subcutaneously transplanted in C57 mice with a single 650 mj pulse (10 ns) of 1064 nm light from a Q-switched Nd: YAG laser caused instantaneous bleaching of the pigmented tissue. Visual and histological examination of the resulting gray-colored tumor revealed the breakdown of melanosomes with no detectable alteration of the normal and tumor-overlying skin. Histological examination of the irradiated tumor showed some degree of vascular damage; the depth of the photodamage was not affected by the successive delivery of three consecutive light pulses. The bleached tumor grew at a modestly slower rate but the high-peak-power (HPP) laser treatment did not affect the tumor concentration of a photodynamic sensitizer Si(IV)-naphthalocyanine (isoBO-SiNc) intravenously injected 24 h before Nd : YAG irradiation. Treatment of the B16 pigmented melanoma by photodynamic therapy (PDT: 1 mg/kg isoBO-SiNc, 300 mW/cm², 520 J/cm²) from a 774 nm diode laser immediately after the 1064 nm irradiation resulted in a 16 day delay of tumor regrowth, which was markedly longer than the delay (ca 6 days) obtained after PDT under identical conditions without the preirradia-tion. Thus, pretreatment of pigmented tumors with HPP 1064 nm light appears to enhance their susceptibility to conventional PDT. The tumor response was further enhanced by repeating the combined HPP/PDT treatment at an interval of 10 days (regrowth delay: 27 days), as well as by applying hyperthermia immediately after HPP/PDT (regrowth delay: ca 34 days).     

Inter-method comparison for the determination of antimony and arsenic in peat samples

Four analytical approaches, based on different physical principles, for the determination of antimony (Sb) and arsenic (As) in ancient peat samples were critically evaluated: (a) open vessel digestion/hydride generation-atomic absorption spectrometry (HG-AAS), (b) closed-pressurized digestion in a microwave oven followed by sector field-inductively coupled plasma-mass spectrometry (SF-ICP-MS), (c) digestion in a microwave autoclave and subsequent quadrupole-inductively coupled plasma-mass spectrometry (Q-ICP-MS) measurements and (d) instrumental neutron activation analysis (INAA). The quality control scheme applied, always included the use of adequate plant reference materials to ensure the accuracy and precision of the analytical procedures. Additionally, two internal peat reference materials were analyzed using all four analytical approaches, generally showing good agreement for both elements. Method detection limits for As and Sb provided by all procedures were approximately 5 and 2 ng g⁻¹ which is sufficiently low for the reliable quantification of both elements in ancient, pre-anthropogenic peat samples. A comparison of As and Sb concentrations in a set of peat samples determined by INAA, HG-AAS and SF-ICP-MS revealed that INAA underestimated the values in a systematic manner, whereas HG-AAS and SF-ICP-MS data agreed very well. Best precision of the results was obtained by analytical procedures involving HG-AAS or Q-ICP-MS and varied from 3.6 to 4.3% and 7.1 to 7.5% for As (at about 0.5 μg g⁻¹) and Sb (at about 0.1 μg g⁻¹), respectively. The highest sample throughput (40 samples per run accomplished in 2 h) combined with low risk of sample contamination could be realized in the high-pressure microwave autoclave. The amount of sample required by all approaches was 200 mg, except for INAA which needed at least 25 times more sample mass to achieve comparable detection limits. For the quantification of As and Sb, inductively coupled plasma-mass spectrometry (ICP-MS) was preferred over INAA and HG-AAS, mainly because (a) less sample is needed and (b) As and Sb can be determined simultaneously. In addition, ICP-MS offers the possibility to measure concurrently a wide range of other elements which also are of environmental interest.     

Mass spectrometric identification of a candidate biomarker peptide from the in vitro interaction of epichlorohydrin with red blood cells

The reaction products of epichlorohydrin with human alpha- and beta- globins, obtained through in vitro incubation of these compounds and red blood cells, were determined by using reversed-phase high-performance liquid chromatography (RP-HPLC), electrospray ionization mass spectrometry and matrix-assisted laser desorption/ionization tandem mass spectrometry. The alpha-globin was much more reactive than the beta-globin. At low incubation ratios, approximating the order of magnitude of epichlorohydrin concentration as found in workplaces, the only modified peptide still detectable was the 62-90 belonging to the alpha-chain and carrying an incremental mass of 92 u on either His72 or His89. Given that the two peptides co-eluted in a single chromatographic peak during RP-HPLC separation, they could be chosen as suitable biomarkers for quantification in the setting up of a new methodology for the biological monitoring of persons occupationally exposed, replacing currently known procedures.     

ADRIAMYCIN RESISTANCE IN CHINESE HAMSTER FIBROBLASTS FOLLOWING OXIDATIVE STRESS INDUCED BY PHOTODYNAMIC THERAPY

Photodynamic therapy (PDT) generates reactive oxygen species that are responsible for the initial cytotoxic events produced by this treatment. An extended (16 h) porphyrin incubation prior to light irradiation increased expression of the 75, 78 and 94 kDa glucose-regulated stress proteins (GRP), as well as the cognate form of the 70 kDa heat shock protein. However, these stress proteins were not induced following isoeffective PDT doses using a short (1 h) porphyrin incubation protocol. In the current study, Chinese hamster fibroblasts were used to examine sensitivity to adjunctive PDT and adriamycin as previous reports indicate a correlation between stress protein synthesis and a decrease in adriamycin cytotoxicity. Treatments that either induced GRP ( i.e . PDT with an extended porphyrin incubation or exposure to the calcium ionophore A23187) or did not induce GRP ( i.e . PDT with a short porphyrin incubation or UV irradiation) were followed at increasing time intervals with a 1 h adriamycin incubation. A time-dependent decrease in adriamycin cytotoxicity was observed when cells were first exposed to either of the PDT protocols or to A23187. Alterations in intracellular drug levels did not account for the change in adriamycin sensitivity. Likewise, intracellular glutathione concentrations and antioxidant enzyme activities were not significantly altered following PDT or A23187. Parameters associated with altered adriamycin sensitivity included a decrease in the percentage of S phase cells following PDT and A23187 as well as a depletion of intracellular ATP after PDT using the extended porphyrin incubation. These results demonstrate that PDT can be added to the growing list of diverse stresses producing transient resistance to adriamycin and that stress protein induction is not universally associated with all oxidative treatments inducing this resistance.     

A regularity result for a class of non-uniformly elliptic operators

Archiv der Mathematik - We obtain an explicit Hölder regularity result for viscosity solutions of a class of second order fully nonlinear equations led by operators that are neither...