Ballistic Annihilation Kinetics: The Case of Discrete Velocity Distributions

The kinetics of the annihilation process, $A+A\to 0$, with ballistic particle motion is investigated when the distribution of particle velocities is {\it discrete}. This discreteness is the source of many intriguing phenomena. In the mean field limit, the densities of different velocity species decay in time with different power law rates for many initial conditions. For a one-dimensional symmetric system containing particles with velocity 0 and $\pm 1$, there is a particular initial state for which the concentrations of all three species as decay as $t^{-2/3}$. For the case of a fast ``impurity'' in a symmetric background of $+$ and $-$ particles, the impurity survival probability decays as $\exp(-{\rm const.}\times \ln^2t)$. In a symmetric 4-velocity system in which there are particles with velocities $\pm v_1$ and $\pm v_2$, there again is a special initial condition where the two species decay at the same rate, t^{-\a}, with \a\cong 0.72. Efficient algorithms are introduced to perform the large-scale simulations necessary to observe these unusual phenomena clearly.Comment: 18 text pages, macro file included, hardcopy of 9 figures available by email request to S

Fundamentals of microcrack nucleation mechanics

A foundation for ultrasonic evaluation of microcrack nucleation mechanics is identified in order to establish a basis for correlations between plane strain fracture toughness and ultrasonic factors through the interaction of elastic waves with material microstructures. Since microcracking is the origin of (brittle) fracture, it is appropriate to consider the role of stress waves in the dynamics of microcracking. Therefore, the following topics are discussed: (1) microstress distributions with typical microstructural defects located in the stress field; (2) elastic wave scattering from various idealized defects; and (3) dynamic effective-properties of media with randomly distributed inhomogeneities

The first products made in space: Monodisperse latex particles

The preparation of large particle size 3 to 30 micrometer monodisperse latexes in space confirmed that original rationale unequivocally. The flight polymerizations formed negligible amounts of coagulum as compared to increasing amounts for the ground-based polymerizations. The number of offsize large particles in the flight latexes was smaller than in the ground-based latexes. The particle size distribution broadened and more larger offsize particles were formed when the polymerizations of the partially converted STS-4 latexes were completed on Earth. Polymerization in space also showed other unanticipated advantages. The flight latexes had narrower particle size distributions than the ground-based latexes. The particles of the flight latexes were more perfect spheres than those of the ground-based latexes. The superior uniformity of the flight latexes was confirmed by the National Bureau of Standards acceptance of the 10 micrometer STS-6 latex and the 30 micrometer STS-11 latexes as Standard Reference Materials, the first products made in space for sale on Earth. The polymerization rates in space were the same as those on Earth within experimental error. Further development of the ground-based polymerization recipes gave monodisperse particles as large as 100 micrometer with tolerable levels of coagulum, but their uniformity was significantly poorer than the flight latexes. Careful control of the polymerization parameters gave uniform nonspherical particles: symmetrical and asymmetrical doublets, ellipsoids, egg-shaped, ice cream cone-shaped, and popcorn-shaped particles

Sodium vacancy ordering and the co-existence of localized spins and itinerant charges in NaxCoO2

The sodium cobaltate family (NaxCoO2) is unique among transition metal oxides because the Co sits on a triangular lattice and its valence can be tuned over a wide range by varying the Na concentration x. Up to now detailed modeling of the rich phenomenology (which ranges from unconventional superconductivity to enhanced thermopower) has been hampered by the difficulty of controlling pure phases. We discovered that certain Na concentrations are specially stable and are associated with superlattice ordering of the Na clusters. This leads naturally to a picture of co-existence of localized spins and itinerant charge carriers. For x = 0.84 we found a remarkably small Fermi energy of 87 K. Our picture brings coherence to a variety of measurements ranging from NMR to optical to thermal transport. Our results also allow us to take the first step towards modeling the mysterious ``Curie-Weiss'' metal state at x = 0.71. We suggest the local moments may form a quantum spin liquid state and we propose experimental test of our hypothesis.Comment: 16 pages, 5 figure

Preferential loss of a polymorphic RIZ allele in human hepatocellular carcinoma

The RIZ (PRDM2) locus commonly undergoes loss of heterozygosity (LOH) and maps within the minimal deleted region on 1p36 in hepatocellular carcinoma (HCC). Although peptide-altering mutations of RIZ are rare in HCC, the RIZ1 product is commonly lost in HCC and has tumour suppressive activities. Here, we analysed RIZ gene mutations and LOH in HCC, breast cancer, familial melanoma, colon cancer, and stomach cancer. We found 7 polymorphisms but no mutations. By analysing the Pro704-deletion polymorphism, we detected LOH of RIZ in 31 of 79 (39%) informative HCC cases, 11 of 47 (23%) colon cancer cases, 8 of 43 (19%) breast cancer cases, 8 of 66 (12%) stomach cancer cases. Importantly, loss of the Pro704+allele was found in 74% of the 31 LOH positive HCC cases (P< 0.01), indicating a preferential loss and hence a stronger tumour suppressor role for this allele compared to the P704−allele. In addition, the Pro704+allele was found to be more common in Asians (0.61) than Caucasians (0.42) (P = 0.0000), suggesting an interesting link between gene polymorphisms and potential differences in tumour incidence between racial groups. © 2001 Cancer Research Campaign http://www.bjcancer.co

Multiscale mechanisms of nutritionally induced property variation in spider silks.

Variability in spider major ampullate (MA) silk properties at different scales has proven difficult to determine and remains an obstacle to the development of synthetic fibers mimicking MA silk performance. A multitude of techniques may be used to measure multiscale aspects of silk properties. Here we fed five species of Araneoid spider solutions that either contained protein or were protein deprived and performed silk tensile tests, small and wide-angle X-ray scattering (SAXS/WAXS), amino acid composition analyses, and silk gene expression analyses, to resolve persistent questions about how nutrient deprivation induces variations in MA silk mechanical properties across scales. Our analyses found that the properties of each spider's silk varied differently in response to variations in their protein intake. We found changes in the crystalline and non-crystalline nanostructures to play specific roles in inducing the property variations we found. Across treatment MaSp expression patterns differed in each of the five species. We found that in most species MaSp expression and amino acid composition variations did not conform with our predictions based on a traditional MaSp expression model. In general, changes to the silk's alanine and proline compositions influenced the alignment of the proteins within the silk's amorphous region, which influenced silk extensibility and toughness. Variations in structural alignment in the crystalline and non-crystalline regions influenced ultimate strength independent of genetic expression. Our study provides the deepest insights thus far into the mechanisms of how MA silk properties vary from gene expression to nanostructure formations to fiber mechanics. Such knowledge is imperative for promoting the production of synthetic silk fibers

Extensions and degenerations of spectral triples

For a unital C*-algebra A, which is equipped with a spectral triple and an extension T of A by the compacts, we construct a family of spectral triples associated to T and depending on the two positive parameters (s,t). Using Rieffel's notation of quantum Gromov-Hausdorff distance between compact quantum metric spaces it is possible to define a metric on this family of spectral triples, and we show that the distance between a pair of spectral triples varies continuously with respect to the parameters. It turns out that a spectral triple associated to the unitarization of the algebra of compact operators is obtained under the limit - in this metric - for (s,1) -> (0, 1), while the basic spectral triple, associated to A, is obtained from this family under a sort of a dual limiting process for (1, t) -> (1, 0). We show that our constructions will provide families of spectral triples for the unitarized compacts and for the Podles sphere. In the case of the compacts we investigate to which extent our proposed spectral triple satisfies Connes' 7 axioms for noncommutative geometry.Comment: 40 pages. Addedd in ver. 2: Examples for the compacts and the Podle`s sphere plus comments on the relations to matricial quantum metrics. In ver.3 the word "deformations" in the original title has changed to "degenerations" and some illustrative remarks on this aspect are adde

Sodium ion ordering of Na0.77CoO2 under competing multi-vacancy cluster, superlattice and domain formation

Hexagonal superlattice formed by sodium multi-vacancy cluster ordering in Na$_{0.77}$CoO$_2$ has been proposed based on synchrotron X-ray Laue diffraction study on electrochemically fine-tuned single crystals. The title compound sits closely to the proposed lower end of the miscibility gap of x ~ 0.77-0.82 phase separated range. The average sodium vacancy cluster size is estimated to be 4.5 Na vacancies per layer within a large superlattice size of sqrt{19}a*sqrt{19}a*3c. The exceptionally large Na vacancy cluster size favors large twinned simple hexagonal superlattice of sqrt{19}a, in competition with the smaller di-, tri- and quadri-vacancy clusters formed superlattices of sqrt{12}a and sqrt{13}a. Competing electronic correlations are revealed by the observed spin glass-like magnetic hysteresis below ~ 3K and the twin, triple and mono domain transformations during thermal cycling between 273-373K.Comment: 7 pages, 6 figure

A Computational Efficient Method For Hbt Intermodulation Distortions And Two-Tone Characteristics Simulation

In this paper, a new simulation method for two-tone characteristics calculations and the third-order intercept point (OIP3) of heterojunction bipolar transistor (HBT) in large-scale time domain is proposed. Base on waveform relaxation (WR) and monotone iterative (MI) methods, we solve a set of nonlinear ordinary differential equation (ODE) of equivalent circuit. With this approach, the two-tone characteristics in frequency domain for HBTs were directly computed from time domain result with fast Fourier transform (FFT). Simulation results on a realistic HBT are presented to show the accuracy and efficiency of the method.