Embedology

Mathematical formulations of the embedding methods commonly used for the reconstruction of attractors from data series are discussed. Embedding theorems, based on previous work by H. Whitney and F. Takens, are established for compact subsetsA of Euclidean space R^k. Ifn is an integer larger than twice the box-counting dimension ofA, then almost every map fromR ^k toR ⁿ , in the sense of prevalence, is one-to-one onA, and moreover is an embedding on smooth manifolds contained withinA. IfA is a chaotic attractor of a typical dynamical system, then the same is true for almost everydelay-coordinate map fromR ^k toR ⁿ . These results are extended in two other directions. Similar results are proved in the more general case of reconstructions which use moving averages of delay coordinates. Second, information is given on the self-intersection set that exists whenn is less than or equal to twice the box-counting dimension ofA.  

分子动力学模拟纳米晶体银的结构和性能

通过分子动力学方法，采用以局域密度（ＬＤＡ）氨似和二阶动量矩（ＳＭＡ）近似为基础的多体热函数，模拟了纳米面心立方晶体银的结构，对模拟的结果进了不同尺寸的纳米晶体的能量分布，弹性表面能及熔点等计算，并与相应的实验结果进行了比较，结果表明采用此多体势函数模拟纳米晶体的结构和性能，比用其它势函数更精确，与实验结果更吻合。  

Stylized facts from a threshold-based heterogeneous agent model

A class of heterogeneous agent models is investigated where investors switch trading position whenever their motivation to do so exceeds some critical threshold. These motivations can be psychological in nature or reflect behaviour suggested by the efficient market hypothesis (EMH). By introducing different propensities into a baseline model that displays EMH behaviour, one can attempt to isolate their effects upon the market dynamics. The simulation results indicate that the introduction of a herding propensity results in excess kurtosis and power-law decay consistent with those observed in actual return distributions, but not in significant long-term volatility correlations. Possible alternatives for introducing such long-term volatility correlations are then identified and discussed.  

Atmospheric channel effects on free-space laser communication

Free-space laser communication offers an attractive alternative for transferring high-bandwidth data when fiber optic cable is neither practical nor feasible. However, there are a variety of deleterious features of the atmospheric channel that may lead to serious signal fading, and even the complete loss of signal altogether. Physical obstructions—such as birds, insects, tree limbs, or other factors—can temporarily or permanently block the laser line-of-sight. Platform/building motion due to wind, differential heating and cooling, or ground motion over time can result in serious misalignment of fixed-position laser communication systems. But most importantly of all, absorption and scattering due to particulate matter in the atmosphere may significantly decrease the transmitted optical signal, while random atmospheric distortions due to optical turbulence can severely degrade the wave-front quality of a signal-carrying laser beam, causing intensity fading and random signal losses at the receiver.  

Search for up-down quark mass differences via isospin symmetry breaking

We performed a series of experiments employing the two pion production reactions p + d → ³He + π⁰ and p + d → ³H + π⁺. The two isopin related reactions differ by a Clebsch Gordan coefficient of 2. We searched for deviations in this ratio in complete angular distributions in the range of the Δ excitation as well as in the vicinity of the η production threshold.  

Simultaneous measurements of the p+d→(A=3)+π reactions

A stack of annular detectors made of high-purity germanium was used to measure simultaneously pd → ³H π⁺ and pd → ³He π⁰ differential cross sections at beam momenta of 750 MeV/c, 800 MeV/c, and 850 MeV/c over a large angular range. The extracted total cross sections for the pd → ³He π⁰ reactions bridge a gap between near threshold data and those in the resonance region. The ratio of the cross sections for the two reaction channels taken at the same η=p^cm_π/m_π yields 2.11±0.08 indicating that a deviation from isospin symmetry is very small.  

Noise correlations of fermions and hard core bosons in a quasi-periodic potential

We use Hanbury-Brown-Twiss interferometry (HBTI) to study various quantum phases of hard core bosons (HCBs) and ideal fermions confined in a one-dimensional quasi-periodic (QP) potential. For HCBs, the QP potential induces a cascade of Mott-like band-insulator phases in the extended regime, in addition to the Mott insulator, Bose glass, and superfluid phases. At critical filling factors, the appearance of these insulating phases is heralded by a peak to dip transition in the interferogram, which reflects the fermionic aspect of HCBs. On the other hand, ideal fermions in the extended phase display various complexities of incommensurate structures such as devil’s staircases and Arnold tongues. In the localized phase, the HCB and the fermion correlations are identical except for the sign of the peaks. Finally, we demonstrate that HBTI provides an effective method to distinguish Mott and glassy phases. Original Text ? Astro, Ltd., 2007.  

Depth-resolved X-ray determination of surface strain in free-standing films of HVPE-grown GaN and 71Ga NMR characterization

Free-standing GaN films grown by hydride vapor phase epitaxy (HVPE) on c-plane sapphire have been studied for in-plane anisotropic strain. Lattice parameters are obtained from high-resolution X-ray diffraction data and the film quality is determined by measuring the rocking curves and by ⁷¹Ga nuclear magnetic resonance (NMR). The in-plane strain was determined using grazing incidence X-ray diffraction and conventional X-ray measurements. It is found that the in-plane lattice parameter varies with depth and has estimated surface strain anisotropy of 4.0791×10^-3 up to a thickness of 0.3 μm. The ⁷¹Ga NMR experiments reveal different degrees of inhomogeneity amongst the three samples. This is shown by the appearance of an additional broad central-transition peak shifted to higher frequency by a Knight shift from conduction electrons in sample regions having high carrier concentrations. PACS 72.80.Ey; 61.10.-i; 61.72.Hh  

Structural and electronic properties of V, Nb and Ta nanoclusters by tight-binding molecular dynamics simulations

We present tight-binding molecular dynamics (TBMD) calculations on V, Nb and Ta nanoclusters with N = 15, 65, 175 and 369 atoms. We found that rhombic dodecahedra are energetically favoured over rhombic hexahedra and icosahedra, with V forming the most compact cluster with the gyration radius increasing with the cluster size. In addition, from the calculated electronic density of states we found that the cluster size plays an important role in the HOMO-LUMO gap and that an increase in cluster size results in enhancement of the electronic density around the Fermi level. Furthermore, we found that the small clusters (N = 15, 65) exhibit energy gap that persists even at 900 K. These findings originate from charge transfer occurring between the inner and outer cluster atoms; interestingly, we found that in the small N = 15, 65 clusters electronic charge accumulates at each surface site at the expense of the inner cluster atoms, while in the larger clusters, N = 175 and 369, charge is gathered on the central particles of the cluster, suggesting different sub-surface character of the clusters. These findings are in agreement with available experimental and theoretical data and promise to offer important information for creating nanostructured materials with improved properties suitable for multiple technological applications.  

Pseudopotentials, correlations, and hierarchy states in quantum hall systems: When the composite Fermion picture works and why

A system of Fermions in a shell of angular momentum l can form a set of multiplets of total angular momentum L. The composite Fermion (CF) picture picks out the lowest lying energy multiplets by selecting from this set a subset that is “Laughlin correlated”, i.e. which maximally avoids pair orbits with the largest pair angular momentum L^′ (or smallest relative angular momentum R=2l−L^′). We demonstrate that Laughlin correlations occur only when the pseudopotential V(L^′) (the interaction energy of a pair as a function of L^′) increases with L^′ more rapidly, than the eigenvalue of L^′2 at the value of L^′ (or R) avoided in the Laughlin correlated state. This requirement is not satisfied for QEs and QHs of the Laughlin ν=1/3 and ν=1/5 states at R=1 and R=3 respectively. At and , clustering of QPs gives lower energy than Laughlin correlations. Novel spin polarized incompressible states at ν=4/11 and ν=4/13 cannot be explained as a second generation in the CF hierarchy.