Comment on ``Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets"

In a recent Letter (PRL 83, 3297 (1999)), Hida presented numerical results indicating that the Haldane phase of the Heisenberg antiferromagnetic spin-1 chain is stable against bond randomness, for box distributions of the bond strength, even when the box distribution stretches to zero bond strength. The author thus concluded that the Haldane phase is stable against bond randomness for any distribution of the bond strength, no matter how broad. In this Comment, we (i) point out that the randomness distributions studied in this Letter do not represent the broadest possible distributions, and therefore these numerical results do not lead to the conclusion that the Haldane phase is stable against any randomness; and (ii) provide a semiquantitative estimate of the critical randomness beyond which the Haldane phase yields to the Random Singlet phase, in a specific class of random distribution functions for the bond strength.Comment: A comment on PRL 83, 3297 (1999). One pag

A study of children learning multicolumn addition with microcomputer software support.

Three computer-aided tutoring procedures were devised to teach multicolumn addition according to the standard school algorithm, one procedure to each of three groups of 2nd-grade children. The key differences between groups were the demands placed on short term memory and the amount of conceptual understanding the procedures attempted to teach. Each child solved a sequence of two-digit problems on a computer screen by touching each digit with a light pen in the correct sequence. The control group did not receive on-screen number-fact assistance. One treatment ( assisted ) group did receive on-screen number-fact assistance, testing the hypothesis that the algorithm is learned more effectively when learned first as a sequence of procedural steps alone, without subjects\u27 need to recall number-facts. A second treatment ( simulation ) group received the same on-screen assistance along with an additional display of simulated blocks which, like concrete manipulative materials, represented symbol manipulations. The simulation group tested a second hypothesis that a concurrent display of the meaning of procedural steps contributes to even more effective algorithmic learning. T-tests (one-tailed, 5% level) applied pair-wise to pretest/posttest difference scores indicated support for the first hypothesis but not for the second, an indication that 2nd-grade children learn the addition algorithm more effectively if demand on short term memory is temporarily lifted. A descriptive framework called superposition of frames is proposed to account for anomalies in findings and for the rich diversity of errors generally manifested by children in multidigit addition. Drawing on current concepts in cognitive psychology and mathematics education, this description suggests that children\u27s mathematical knowledge is fragmented into isolated, unstable, and sometimes entrenched frames of knowledge. When a child finds appropriate correspondences between frames and initiates a superposition of frames, the child\u27s procedural and conceptual knowledge, previously in disarray, may then become integrated. Implications for elementary mathematics instruction are discussed

Hydrogen thermal conductivity at temperatures from 2000 to 4000 deg F Final report

Hydrogen thermal conductivity at temperatures from 2000 to 4600 deg

Additive noise effects in active nonlinear spatially extended systems

We examine the effects of pure additive noise on spatially extended systems with quadratic nonlinearities. We develop a general multiscale theory for such systems and apply it to the Kuramoto-Sivashinsky equation as a case study. We first focus on a regime close to the instability onset (primary bifurcation), where the system can be described by a single dominant mode. We show analytically that the resulting noise in the equation describing the amplitude of the dominant mode largely depends on the nature of the stochastic forcing. For a highly degenerate noise, in the sense that it is acting on the first stable mode only, the amplitude equation is dominated by a pure multiplicative noise, which in turn induces the dominant mode to undergo several critical state transitions and complex phenomena, including intermittency and stabilisation, as the noise strength is increased. The intermittent behaviour is characterised by a power-law probability density and the corresponding critical exponent is calculated rigorously by making use of the first-passage properties of the amplitude equation. On the other hand, when the noise is acting on the whole subspace of stable modes, the multiplicative noise is corrected by an additive-like term, with the eventual loss of any stabilised state. We also show that the stochastic forcing has no effect on the dominant mode dynamics when it is acting on the second stable mode. Finally, in a regime which is relatively far from the instability onset, so that there are two unstable modes, we observe numerically that when the noise is acting on the first stable mode, both dominant modes show noise-induced complex phenomena similar to the single-mode case

Gene flow risk assessment in centres of crop origin and diversity

Poster presented at Plant Biology & Botany Join Congress. Chicago (USA), 7-11 Jul 200

Ground State and Magnetization Process of the Mixture of Bond-Alternating and Uniform S=1/2 Antiferromagnetic Heisenberg Chains

The mixture of bond-alternating and uniform S=1/2 antiferromagnetic Heisenberg chains is investigated by the density matrix renormalization group method. The ground state magnetization curve is calculated and the exchange parameters are determined by fitting to the experimentally measured magnetization curve of \CuCl$_{2x}$Br$_{2(1-x)}$($\gamma$-pic)$_2$. The low field behavior of the magnetization curve and low temperature behavior of the magnetic susceptibility are found to be sensitive to whether the bond-alternation pattern (parity) is fixed all over the sample or randomly distributed. The both quantities are compatible with the numerical results for the random parity model.Comment: 5 pages, 7 figures. Final and enlarged version accepted for publication in J. Phys. Soc. Jp