scholarly journals Small deviations for time-changed Brownian motions and applications to second-order chaos

2014 ◽  
Vol 19 (0) ◽  
Author(s):  
Daniel Dobbs ◽  
Tai Melcher
2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Yamin Wang ◽  
Ziqiao Huang ◽  
Fuad E. Alsaadi ◽  
Stanislao Lauria ◽  
Yurong Liu

This paper is concerned with the random attractors for a class of second-order stochastic lattice dynamical systems. We first prove the uniqueness and existence of the solutions of second-order stochastic lattice dynamical systems in the spaceF=lλ2×l2. Then, by proving the asymptotic compactness of the random dynamical systems, we establish the existence of the global random attractor. The system under consideration is quite general, and many existing results can be regarded as the special case of our results.


Author(s):  
W. L. Bell

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.


Author(s):  
W. T. Donlon ◽  
S. Shinozaki ◽  
E. M. Logothetis ◽  
W. Kaizer

Since point defects have a limited solubility in the rutile (TiO2) lattice, small deviations from stoichiometry are known to produce crystallographic shear (CS) planes which accomodate local variations in composition. The material used in this study was porous polycrystalline TiO2 (60% dense), in the form of 3mm. diameter disks, 1mm thick. Samples were mechanically polished, ion-milled by conventional techniques, and initially examined with the use of a Siemens EM102. The electron transparent thin foils were then heat-treated under controlled atmospheres of CO/CO2 and H2 and reexamined in the same manner.The “as-received” material contained mostly TiO2 grains (∼5μm diameter) which had no extended defects. Several grains however, aid exhibit a structure similar to micro-twinned grains observed in reduced rutile. Lattice fringe images (Fig. 1) of these grains reveal that the adjoining layers are not simply twin related variants of a single TinO2n-1 compound. Rather these layers (100 - 250 Å wide) are alternately comprised of stoichiometric TiO2 (rutile) and reduced TiO2 in the form of Ti8O15, with the Ti8O15 layers on either side of the TiO2 being twin related.


1996 ◽  
Vol 43 (9) ◽  
pp. 1765-1771 ◽  
Author(s):  
M. W. HAMILTON and D. S. ELLIOTT

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