A class of convex functions Cr,a (x) symmetric about x = 1/2 and depending on two control parameters: 0 < r < 1 and 0 < a < 12 are considered as one-dimensional non-invertible maps, which map the interval [0,1] into itself. Some of them produce a sequence of periodic doublings culminating in chaos. New features are recorded. The behavior of the iterates and their bifurcations are analyzed. The universality of their behavior is discussed. M. Abou-Ghantous.
This project is in its initial exploratory stage. M. Abou-Ghantous.
The low frequency dielectric response of eastern white pine and redwood samples have been investigated using a computer-controlled low frequency Impedance Analyzer. The specimens were sectioned into tangent planes viewed in the relation to the longitudinal axis of the tree where the wavy appearance of the growing ring is clearly observed. Samples were measured in dry and humid conditions at a fixed thickness. Comparison is also made with different thicknesses. The results are presented in terms of complex capacitance plots. Two responses have been observed from the frequency spectrum: a shallow mid-frequency loss peak at f ª 10 Hz and low frequency dispersion at F < 1 Hz. The behavior is evidence of an anomalous transport process and has been analyzed in terms of constant phase angle (CPA) response. B. Bodakian. (Supported by URB.)
The dielectric response of sand samples from oil drilling core, taken from a range of depths from surface to 680 m deep, has been investigated with humidity and frequency as the principal variables. Comparison is made with black volcanic sand. The results are represented in terms of impedance and admittance plots. Two loss peaks have been observed at f £ 10 and f ~ 103 - 104 Hz. The low frequency peak is interpreted by a q - dc transport process. B. Bodakian. (Supported by URB.)
The study of the formation of sellinite, a body-centered cubic phase of Bismuth oxide stabilized by doping, and a semi-conductor with high optical activity. This work requires high-temperature x-ray diffraction and differential thermal analysis. S. Chehab, J. C. Boivin* and D. H. H. Quon*.
A coupled spin system is subjected to two resonant closely-spaced pump microwave frequencies, w1p and w2p. Multiple quantum (MQ) transitions cause the magnetization of the resonant line to oscillate at harmonics of the frequency difference w = w1p - w2p. The resulting oscillation is transferred, via relaxation, to other hyperfine lines. The transfer of oscillation can be observed by means of a third weak microwave field at a frequency wo, resonant with a coupled hyperfine line. This mode of detection of this oscillation constitutes a MQ ELDOR display. The frequencies wp and wo and the dc magnetic field are set such that one is sitting on a MQELDOR line. The system is then subjected to an rf field whose frequency is swept and the intensity of the MQELDOR line is monitored. The resulting spectrum is a hyperfine selective ENDOR display whose intensity depends on whether the induced rf transitions couple the observed and pumped hyperfine lines or not. T. Christidis, H. Mouchawrab* and J. S. Hyde*. (Supported by URB; National Institute of Health, USA.)
This project has the primary aim to test models of evolved stars of different masses by comparing the predicted surface abundance anomalies with the observed ones in red, yellow or blue giants/supergiants. In particular, the CNO and Na anomalies give insight into the internal structure of the evolved stars, since they result from the combined effect of nuclear reactions and convective mixing in their deep interiors. M. El Eid. (Supported by URB.)
Modeling of exploding supernovae envelopes including radiation transport to follow the optical evolution of the supernovae (light curves), and a detailed network of nuclear reaction to study the heavy element nucleosynthesis during the explosion. A special emphasis concerns the production of xenon isotopes in exploding massive stars. M. El Eid, B. Mayer* and L. The. (Supported by URB.)
Changes in the dielectric properties of a material can be used to characterize the effects produced by the application of an external stimulus, such as thermal stress. This method has recently been extended to living systems. McCrae and Esrick have shown that the electrical impedance of skeletal muscle changes during the application of hyperthermia treatments. The low-frequency b dispersion exhibited a two-stage decrease. A rapid, initial decrease was attributed to the shrinking of cells with a corresponding increase in extracellular space and to the leaking of intracellular fluid through the membrane. A subsequent, slower decrease was attributed to histolysis. In addition, an Arrhenius analysis identified two activation energies. F. X. Hart* and B. Bodakian. (Supported by URB.)
A model describing strong microphase segregation in polymeric brushes under change in temperature was proposed. The main features of the phase behavior are described by the temperature-anchoring density phase diagram. An analytical theory of globulization kinetics under abrupt temperature jump was developed and compared to the results of computer simulations. L. L. Klushin. (Supported by AUB BOBST start-up grant.)
The problem of the centrifugal distortion constants (CDC), Dv, Hv, ... for a diatomic molecule is considered. It is shown that a new formulation of the standard Rayleigh-Schrödinger perturbation theory can give simple and compact analytical expressions of the CDC (up to any order). The program uses one routine (the integration of the equation y” + fy = s) repeated for different s; it is quite simple and gives no difficulties at the boundaries and there is no need to use any mathematical or numerical artifices. H. Kobeissi* and C. H. Trad. (Supported by URB; LNCSR.)
Matric elements Mvv’ = < Fv |Q(r - re)| Fv’> for Morse oscillators are considered. A “local” approach to the determination of Mvv’ can be used for the rotating Morse oscillator as well as for other potential functions under certain specified conditions. The numerical application for a standard potential is presented; it shows that: (1) the results of the present method (PM) are the limits of those of an improved Cooley-Numerov method when the mesh-size h decreases; (2) PM results are compared to those obtained by the same method with constant f; when h varies the PM gives the ‘best’ results; (3) the orthogonality integral Mv*v obtained by PM is almost 10-14 or better for low and high levels. H. Kobeissi*, M. Kobeissi* and C. H. Trad. (Supported by URB; Lebanese University.)
An exact analytical solution was obtained for the problem of adsorption of an ideal polymer chain onto a planar surface in the presence of an external stretching field. The nature of the adsorption-stretching phase transition, and the details of the critical behavior were analyzed. A. M. Skvortsov*, A. A. Gorbunov* and L. L. Klushin. (Supported by URB; International Science Foundation: grant R1H000.)
Electron paramagnetic resonance was used to characterize the first use of a thiol-specific spin label in membranes. Procedures for use of the spin-label, 1-oxyl-2,5,5, tetramethyl-D3-pryyoline-3-methyl (methanethiosulfonate; MTS) covalently attached to membrane proteins in human erythrocyte membranes are reported. The major findings are: (1) MTS was found to be thiol-specific in membranes as it is for soluble proteins; (2) MTS labels ghost proteins in as few as 30 minutes at room temperature, providing a distinct advantage when sensitive or fragile membranes are to be used; (3) the distribution of the spin label suggest that the major cytoskeletal protein, spectrin, and the major transmembrane protein, Band 3, incorporate the highest percentage of spin label. This procedure expands the tools with which the researcher can investigate the physical state of membrane proteins and its alteration upon interaction of membrane perturbants or in pathological conditions. C. H Trad, W. James* and D. A. Butterfield*. (Supported by National Institute of Health, USA; National Science Foundation, USA.)