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At least 703 records · Page 39Linked to original sources
PubMed2006

Fracture spacing in layered materials and pattern transition from parallel to polygonal fractures.

We perform three-dimensional simulations of fracture growth in a three-layered plate model with an embedded heterogeneous layer under horizontal biaxial stretch (representing stretch from directional to isotropic) by the finite element approach. The fractures develop under a quasistatical, slowly increasing biaxial strain. The material inhomogeneities are accounted for by assigning each element a failure threshold that is defined by a given statistical distribution. A universal scale law of fracture spacing to biaxial strain in terms of principal stress ratio is well demonstrated in a three-dimensional fashion. The numerically obtained fracture patterns show a continuous pattern transition from parallel fractures, laddering fracture to polygonal fractures, which depends strongly on the far-field loading conditions in terms of principal stress ratio lambda = sigma(2)/sigma(1), from uniaxial (lambda = 0), anisotropic (0 < lambda < 1) to isotropic stretch (lambda = 1). We find that, except for further opening of existing fractures after they are well-developed (saturation), new fractures may also initiate and propagate along the interface between layers, which may serve as another mechanism to accommodate additional strain for fracture saturated layers.

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PubMed2006

Spatial wave intensity correlations in quasi-one-dimensional wires.

Spatial intensity correlations between waves transmitted through random media are analyzed within the framework of the random matrix theory of transport. Assuming that the statistical distribution of transfer matrices is isotropic, we found that the spatial correlation function can be expressed as the sum of three terms, with distinctive spatial dependences. This result coincides with the one obtained in the diffusive regime from perturbative calculations, but holds all the way from quasiballistic transport to localization. While correlations are positive in the diffusive regime, we predict a transition to negative correlations as the length of the system decreases.

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PubMed2000

Fluctuating spin g-tensor in small metal grains

In the presence of spin-orbit scattering, the splitting of an energy level varepsilon(&mgr;) in a generic small metal grain due to the Zeeman coupling to a magnetic field B--> depends on the direction of B-->, as a result of mesoscopic fluctuations. The anisotropy is described by the eigenvalues g(2)(j) ( j = 1,2,3) of a tensor G, corresponding to the (squares of) g-factors along three principal axes. We consider the statistical distribution of G and find that the anisotropy is enhanced by eigenvalue repulsion between the g(j).

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PubMed2002

Structure, properties, and dynamics of oxygen vacancies in amorphous SiO2.

Oxygen vacancies in SiO2 have long been regarded as bistable, forming a Si-Si dimer when neutral and a puckered configuration when positively charged. We report first-principles calculations of O vacancies in amorphous SiO2 supercells that unveil significantly more complex behavior. We find that the vast majority of O vacancies do not pucker after capture of a hole, but are shallow traps. The remaining vacancies exhibit two distinct types of puckering. Upon capturing an electron, one type forms a metastable dipole, while the other collapses to a dimer. A statistical distribution of O vacancies is obtained, and the implications for charge transport and trapping in SiO2 are discussed.

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PubMed2003

Nonaxisymmetric energy deposition pattern on ASDEX upgrade divertor target plates during type-I edge-localized modes.

In the ASDEX Upgrade tokamak, complex power deposition structures on the divertor target plates during type-I edge-localized modes (ELMs) have been discovered by fast (few microseconds), two-dimensional (40 x 40 cm(2)) infrared thermography. In addition to the usual axisymmetric power deposition line near the separatrix, there appear, statistically distributed, several laterally displaced and inclined stripes, mostly well separated from each other and from the main strike zone. These structures are interpreted as footprints of approximately field aligned, helical perturbations at the low field side of the main plasma edge related to the nonlinear ELM evolution. Based on this picture, the ELM related mode structure can be derived from the target load pattern, yielding on average toroidal mode numbers in a range of 8-24.

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PubMed2004

Quantum chaos of bogoliubov waves for a bose-einstein condensate in stadium billiards.

We investigate the possibility of quantum (or wave) chaos for the Bogoliubov excitations of a Bose-Einstein condensate in billiards. Because of the mean field interaction in the condensate, the Bogoliubov excitations are very different from the single particle excitations in a noninteracting system. Nevertheless, we predict that the statistical distribution of level spacings is unchanged by mapping the non-Hermitian Bogoliubov operator to a real symmetric matrix. We numerically test our prediction by using a phase shift method for calculating the excitation energies.

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PubMed2005

Crossover behavior in burst avalanches: signature of imminent failure.

The statistics of damage avalanches during a failure process typically follows a power law. When these avalanches are recorded only near the point at which the system fails catastrophically, one finds that the power law has an exponent which is different from that one finds if the recording of events starts away from the vicinity of catastrophic failure. We demonstrate this analytically for bundles of many fibers, with statistically distributed breakdown thresholds for the individual fibers and where the load is uniformly distributed among the surviving fibers. In this case the distribution D(Delta) of the avalanches (Delta) follows the power law Delta-xi with xi=3/2 near catastrophic failure and xi=5/2 away from it. We also study numerically square networks of electrical fuses and find xi=2.0 near catastrophic failure and xi=3.0 away from it. We propose that this crossover in xi may be used as a signal of imminent failure.

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PubMed2005

Role of embedded clustering in dilute magnetic semiconductors: Cr doped GaN.

Results of extensive density-functional studies provide direct evidence that Cr atoms in Cr:GaN have a strong tendency to form embedded clusters, occupying Ga sites. Significantly, for larger than 2-Cr-atom clusters, states containing antiferromagnetic coupling with net spin in the range 0.06-1.47 muB/Cr are favored. We propose a picture where various configurations coexist and the statistical distribution and associated magnetism will depend sensitively on the growth details. Such a view may elucidate many puzzling observations related to the structural and magnetic properties of III-N and other dilute semiconductors.

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PubMed2006

Thermally activated depinning of a narrow domain wall from a single defect.

We describe the field induced depinning process of a magnetic domain wall (DW) from a single bidimensional nanometric defect. The DW propagates in a wire lithographed on a film with strong perpendicular anisotropy. We observe a statistical distribution of the relaxation time consistent with a Néel-Brown picture of magnetization reversal. This indicates that the nanometric DW can be considered as an ideal monodomain particle switching over a single energy barrier. Such a stochastic character of DW depinning has to be taken into account for spintronic applications.

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PubMed2006

What is in a pebble shape?

We propose to characterize the shapes of flat pebbles in terms of the statistical distribution of curvatures measured along the pebble contour. This is demonstrated for the erosion of clay pebbles in a controlled laboratory apparatus. Photographs at various stages of erosion are analyzed, and compared with two models. We find that the curvature distribution complements the usual measurement of aspect ratio, and connects naturally to erosion processes that are typically faster at protruding regions of high curvature.

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PubMed2006

Coulomb blockade and transport in a chain of one-dimensional quantum dots.

A long one-dimensional wire with a finite density of strong random impurities is modeled as a chain of weakly coupled quantum dots. At low temperature T and applied voltage V its resistance is limited by breaks: randomly occurring clusters of quantum dots with a special length distribution pattern that inhibit the transport. Because of the interplay of interaction and disorder effects the resistance can exhibit T and V dependences that can be approximated by power laws. The corresponding two exponents differ greatly from each other and depend not only on the intrinsic electronic parameters but also on the impurity distribution statistics.

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PubMed1971

The photosynthetic unit in chlorella measured by repetitive short flashes.

Apparent size of the photosynthetic unit in Chlorella pyrenoidosa was estimated by the method of Emerson and Arnold: rate of oxygen evolution was measured under repetitive saturating flashes of about 10-microsecond duration separated by dark periods of 0.033 to 0.100 second. Cells used were taken from six steady state cultures maintained at different light intensities. Cell characteristics included a variation in chlorophyll content from 1 to 5%. Apparent size of the photosynthetic unit varied systematically with chlorophyll content in the range of 1560 to 2350 chlorophylls per O(2) per flash. Values for unit size showed no unusual statistical distribution and were not changed significantly by addition of low level background light at 645 or 705 nanometers. Maximal rate of unit turnover, calculated from light-saturated rate and unit size, varied inversely with chlorophyll content in the range of 70 to 180 per second.

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PubMed2001

Trigonal sodium calcium germanate, Na(2.54)Ca(1.73)Ge(3)O(9).

Single crystals of a new germanate, Na(2.54)Ca(1.73)Ge(3)O(9), have been synthesized. The structure has a six-membered ring of GeO(4) tetrahedra, which is similar to the rings of the silicate analogue Na(2)Ca(2)Si(3)O(9), and both structures contain pseudo-cubic subcells with an edge length of 3.8 A. The details of the two compounds are slightly different, however. For example, two O atoms are statistically distributed about twofold axes in the title compound, while the silicate analogue has no such O-atom distributions. In addition, the title germanate has an extra partially populated metal site containing 54 (4)% Na, with no equivalent site in the silicate analogue.

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PubMed2005

New triple molybdates Cs3LiCo2(MoO4)4 and Rb3LiZn2(MoO4)4, filled derivatives of the Cs6Zn5(MoO4)8 type.

Two new isotypic triple molybdates, namely tricesium lithium dicobalt tetrakis(tetraoxomolybdate), Cs3LiCo2(MoO4)4, and trirubidium lithium dizinc tetrakis(tetraoxomolybdate), Rb3LiZn2(MoO4)4, crystallize in the non-centrosymmetric cubic space group I-43d and adopt the Cs6Zn5(MoO4)8 structure type. In the parent structure, the Zn positions have 5/6 occupancy, while they are fully occupied by statistically distributed M2+ and Li+ cations in the title compounds. In both structures, all corners of the (M(2/3)Li(1/3))O4 tetrahedra (M = Co and Zn), having point symmetry -4, are shared with the MoO4 tetrahedra, which lie on threefold axes and share corners with three (M,Li)O4 tetrahedra to form open mixed frameworks. Large alkaline cations occupy distorted cuboctahedral cavities with -4 symmetry. The mixed tetrahedral frameworks in the structures are close to those of mayenite (12CaO.7Al2O3) and the related compounds 11CaO.7Al2O3.CaF2, wadalite (Ca6Al5Si2O16Cl3) and Na6Zn3(AsO4)4.3H2O, but the terminal vertices of the MoO4 tetrahedra are directed in opposite directions along the threefold axes compared with the configurations of Al(Si)O4 or AsO4 tetrahedra. The cation arrangements in Cs3LiCo2(MoO4)4, Rb3LiZn2(MoO4)4 and Cs6Zn5(MoO4)8 repeat the structure of Y3Au3Sb4, being stuffed derivatives of the Th3P4 type.

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PubMed2002

Average unit cell for Penrose tiling and its Gaussian approximation.

In this paper, the average unit cell for a quasicrystal is constructed by a statistical approach. For the Penrose tiling, it is shown that such a unit cell is fully equivalent to the oblique projection of the atomic surface onto physical space. The obtained statistical distributions can be easily extended to imperfect structures by using a Gaussian approximation. This leads to simple analytical expressions for diffraction intensities, which can be very useful in structure refinement.

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PubMed2000

Statistical dynamical theory of X-ray diffraction in the Bragg case: application to triple-crystal diffractometry

The statistical dynamical theory of X-ray diffraction is developed for a crystal containing statistically distributed microdefects. Fourier-component equations for coherent and diffuse (incoherent) scattered waves have been obtained in the case of so-called triple-crystal diffractometry. New correlation lengths and areas are introduced for characterization of the scattered volume.

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PubMed2001

A novel perovskite-like Ta-bronze KTa1+zO3: preparation, stoichiometry, conductivity and crystal structure studies.

A new cubic Ta-bronze (1) KTa(1+z)(+(5-delta))O(3) [z approximately 0.107 (3)] was obtained on a cathode by molten salt electrolysis of the system K(2)TaOF(5)-K(3)TaO(2)F(4)-(KF + NaF + LiF)(eutectic). Black, metallic cubic crystals of (1) are formed together with tetragonal beta-Ta. The perovskite-like crystal structure of (1) [a = 4.005 (1) A, space group Pm3m] was refined with anharmonic displacement parameters for Ta and K atoms and anisotropic displacement parameters for a split O-atom position [KM4CCD diffractometer; lambda(Mo Kalpha); 3320 measured reflections with I > 3sigma(I); R = 0.0095, wR = 0.0065, Deltarho(min) = -0.91 e A(-3), Deltarho(max) = 0.65 e A(-3)]. Defects in the O and K atomic positions were found. (1) is a semiconductor in the temperature range 4-300 K, whereas the well studied and closely related colourless transparent crystals KTa(+5)O(3) (2) are dielectric. Differences in the properties of (1) and (2) are assumed to be connected with the existence of Ta dumb-bells statistically distributed into the KTaO(3) matrix.

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PubMed2001

Structures of copper(II) and manganese(II) di(hydrogen malonate) dihydrate; effects of intensity profile truncation and background modelling on structure models.

The crystal structures of the title compounds were determined with net intensities I derived via the background-peak-background procedure. Least-squares optimizations reveal differences between the low-order (0 < s < 0.7 A(-1)) and high-order (0.7 < s < 1.0 A(-1)) structure models. The scale factors indicate discrepancies of up to 10% between the low-order and high-order reflection intensities. This observation is compound independent. It reflects the scan-angle-induced truncation error, because the applied scan angle (0.8 + 2.0 tan theta) degrees underestimates the wavelength dispersion in the monochromated X-ray beam. The observed crystal structures show pseudo-I-centred sublattices for three of its non-H atoms in the asymmetric unit. Our selection of observed intensities (I > 3 sigma) stresses that pseudo-symmetry. Model refinements on individual data sets with (h + k + l) = 2n and (h + k + l) = 2n + 1 illustrate the lack of model robustness caused by that pseudo-symmetry. To obtain a better balanced data set and thus a more robust structure we decided to exploit background modelling. We described the background intensities B(H-->) with an 11th degree polynomial in straight theta. This function predicts the local background b at each position H--> and defines the counting statistical distribution P(B), in which b serves as average and variance. The observation R defines P(R). This leads to P(I) = P(R)/P(B) and thus I = R - b and sigma(2)(I) = I so that the error sigma(I) is background independent. Within this framework we reanalysed the structure of the copper(II) derivative. Background modelling resulted in a structure model with an improved internal consistency. At the same time the unweighted R value based on all observations decreased from 10.6 to 8.4%. A redetermination of the structure at 120 K concluded the analysis.

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