A note on modular forms and generalized anomaly cancellation formulas

By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formula

Multiple positive solutions of singular nonlinear Sturm-Liouville problems with caratheodory perturbed term

By employing a well-known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth-order singular differential equation Lu=p(t)f(t,u(t),u′′(t))-g(t,u(t),u′′(t)),0<t<1,α1u(0)-β1u'(0)=0,γ1u(1)+δ1u'(1)=0,α2u′′(0)-β2u′′′(0)=0,γ2u′′(1)+δ2u′′′(1)=0, with αi,βi,γi,δi≥0 and βiγi+αiγi+αiδi>0,    i=1,2, where L denotes the linear operator Lu:=(ru′′′)'-qu′′,r∈C1([0,1],(0,+∞)), and q∈C([0,1],[0,+∞)). This equation is viewed as a perturbation of the fourth-order Sturm-Liouville problem, where the perturbed term g:(0,1)×[0,+∞)×(-∞,+∞)→(-∞,+∞) only satisfies the global Carathéodory conditions, which implies that the perturbed effect of g on f is quite large so that the nonlinearity can tend to negative infinity at some singular points

Exact solution of gyration radius of individual's trajectory for a simplified human mobility model

Gyration radius of individual's trajectory plays a key role in quantifying human mobility patterns. Of particular interests, empirical analyses suggest that the growth of gyration radius is slow versus time except the very early stage and may eventually arrive to a steady value. However, up to now, the underlying mechanism leading to such a possibly steady value has not been well understood. In this Letter, we propose a simplified human mobility model to simulate individual's daily travel with three sequential activities: commuting to workplace, going to do leisure activities and returning home. With the assumption that individual has constant travel speed and inferior limit of time at home and work, we prove that the daily moving area of an individual is an ellipse, and finally get an exact solution of the gyration radius. The analytical solution well captures the empirical observation reported in [M. C. Gonz`alez et al., Nature, 453 (2008) 779]. We also find that, in spite of the heterogeneous displacement distribution in the population level, individuals in our model have characteristic displacements, indicating a completely different mechanism to the one proposed by Song et al. [Nat. Phys. 6 (2010) 818].Comment: 4 pages, 4 figure

Calculation of nanowire thermal conductivity using complete phonon dispersion relations

The lattice thermal conductivity of crystalline Si nanowires is calculated. The calculation uses complete phonon dispersions, and does not require any externally imposed frequency cutoffs. No adjustment to nanowire thermal conductivity measurements is required. Good agreement with experimental results for nanowires wider than 35 nm is obtained. A formulation in terms of the transmission function is given. Also, the use of a simpler, nondispersive "Callaway formula", is discussed from the complete dispersions perspective.Comment: 4 pages, 3 figures. Accepted in Phys. Rev.

A general type of twisted anomaly cancellation formulas

For even dimensional manifolds, we prove some twisted anomaly cancellation formulas which generalize some well-known cancellation formulas. For odd dimensional manifolds, we obtain some modularly invariant characteristic forms by the Chern-Simons transgression and we also get some twisted anomaly cancellation formulas

Observation of pinning mode in Wigner solid of 1/3 fractional quantum Hall excitations

We report the observation of a resonance in the microwave spectra of the real diagonal conductivities of a two-dimensional electron system within a range of ~ +- .0.015 $from filling factor$\nu=1/3$. The resonance is remarkably similar to resonances previously observed near integer$\nu$, and is interpreted as the collective pinning mode of a disorder-pinned Wigner solid phase of$e/3$-charged carriers .Comment: version with edits for clarity, improved Figure 3 and added referenc

Optical conductivity in the normal state fullerene superconductors

We calculate the optical conductivity, $\sigma(\omega)$, in the normal state fullerene superconductors by self-consistently including the impurity scatterings, the electron-phonon and electron-electron Coulomb interactions. The finite bandwidth of the fullerenes is explicitely considered, and the vertex corection is included $a$ $la$ Nambu in calculating the renormalized Green's function. $\sigma(\omega)$ is obtained by calculating the current-current correlation function with the renormalized Green's function in the Matsubara frequency and then performing analytic continuation to the real frequency at finite temperature. The Drude weight in $\sigma(\omega)$ is strongly suppressed due to the interactions and transfered to the mid-infrared region around and above 0.06 eV which is somewhat less pronounced and much broader compared with the expermental observation by DeGiorgi $et$ $al$.Comment: 6 pages, 4 figures. To be published in Physical Review B, July 1

Directing Anisotropic Assembly of Metallic Nanoclusters by Exploiting Linear Trio Interactions and Quantum Size Effects: Au Chains on Ag(100) Thin Films

Discovery and understanding of mechanisms for kinetically controlled growth of metal nanoclusters can be enabled by realistic atomistic-level modeling with ab initio kinetics. KMC simulation of such a model for Au deposition on Ag(100) films reveals the formation of single-atom-wide Au chains below 275 K, even though 2D islands are thermodynamically preferred. Chain formation is shown to reflect a combination of strong linear trio attractions guiding assembly and a weak driving force and slow rate of transformation of 1D chains to 2D islands (or sometimes irreversible rounding of adatoms from chain sides to ends). Behavior can also be tuned by quantum size effects: chain formation predominates on 2-monolayer Ag(100) films supported on NiAl(100) at 250 K for low coverages but not on 1- or 3-monolayer films, and longer chains form than on bulk Ag(100). Our predictive kinetic modeling shows the potential for simulation-guided discovery and analysis of novel self-assembly processes