Asymmetric Properties of Heat Conduction in a One-Dimensional Frenkel-Kontorova Model

In this Letter, we show numerically that the rectifying effect of heat flux in a one-dimensional two-segment Frenkel-Kontorova chain demonstrated in recent literature is merely available under the limit of the weak coupling between the two constituent segments. Surprisingly, the rectifying effect will be reversed when the properties of the interface and the system size change. The two types of asymmetric heat conduction are dominated by different mechanisms, which are all induced by the nonlinearity. We further discuss the possibility of the experimental realization of thermal diode or rectifier devices.Comment: 4 Pages, 4 figure

Ergodic property of Markovian semigroups on standard forms of von Neumann algebras

We give sufficient conditions for ergodicity of the Markovian semigroups associated to Dirichlet forms on standard forms of von Neumann algebras constructed by the method proposed in Refs. [Par1,Par2]. We apply our result to show that the diffusion type Markovian semigroups for quantum spin systems are ergodic in the region of high temperatures where the uniqueness of the KMS-state holds.Comment: 25 page

Lattice Boltzmann Approach to High-Speed Compressible Flows

We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara [Phys. Rev. E \textbf{69}, 056702 (2004)] and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number up to 30 (or higher), which is validated by well-known benchmark tests. Simulations on Riemann problems with very high ratios ($1000:1$) of pressure and density also show good accuracy and stability. Successful recovering of regular and double Mach shock reflections shows the potential application of the lattice Boltzmann model to fluid systems where non-equilibrium processes are intrinsic. The new scheme for stability can be easily extended to other lattice Boltzmann models.Comment: Figs.11 and 12 in JPEG format. Int. J. Mod. Phys. C (to appear

Biocompatible Mesoporous Hollow Carbon Nanocapsules for High Performance Supercapacitors.

A facile and general method for the controllable synthesis of N-doped hollow mesoporous carbon nanocapsules (NHCNCs) with four different geometries has been developed. The spheres (NHCNC-1), low-concaves (NHCNC-2), semi-concaves (NHCNC-3) and wrinkles (NHCNC-4) shaped samples were prepared and systematically investigated to understand the structural effects of hollow particles on their supercapacitor performances. Compared with the other three different shaped samples (NHCNC-1, NHCNC-2, and NHCNC-4), the as-synthesized semi-concave structured NHCNC-3 demonstrated excellent performance with high gravimetric capacitance of 326 F g-1 (419 F cm-3) and ultra-stable cycling stability (96.6% after 5000 cycles). The outstanding performances achieved are attributed to the unique semi-concave structure, high specific surface area (1400 m2 g-1), hierarchical porosity, high packing density (1.41 g cm-3) and high nitrogen (N) content (up to 3.73%) of the new materials. These carbon nanocapsules with tailorable structures and properties enable them as outstanding carriers and platforms for various emerging applications, such as nanoscale chemical reactors, catalysis, batteries, solar energy harvest, gas storage and so on. In addition, these novel carbons have negligible cytotoxicity and high biocompatibility for human cells, promising a wide range of bio applications, such as biomaterials, drug delivery, biomedicine, biotherapy and bioelectronic devices

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

Rotation and Macroturbulence in Metal-poor Field Red Giant and Red Horizontal Branch Stars

We report the results for rotational velocities, Vrot sin i, and macroturbulence dispersion, zeta(RT), for 12 metal-poor field red giant branch stars and 7 metal-poor field red horizontal branch stars. The results are based on Fourier transform analyses of absorption line profiles from high-resolution (R ~ 120,000), high-S/N (~ 215 per pixel) spectra obtained with the Gecko spectrograph at CFHT. We find that the zeta(RT) values for the metal-poor RGB stars are very similar to those for metal-rich disk giants studied earlier by Gray and his collaborators. Six of the RGB stars have small rotational values, less than 2.0 km/sec, while five show significant rotation, over 3 km/sec. The fraction of rapidly rotating RHB stars is somewhat lower than found among BHB stars. We devise two empirical methods to translate the line-broadening results obtained by Carney et al. (2003, 2008) into Vrot sin i for all the RGB and RHB stars they studied. Binning the RGB stars by luminosity, we find that most metal-poor field RGB stars show no detectable sign, on average, of rotation. However, the most luminous stars, with M(V) <= -1.5, do show net rotation, with mean values of 2 to 4 km/sec, depending on the algorithm employed, and these stars also show signs of radial velocity jitter and mass loss.Comment: accepted for publication in the Astronomical Journa

Large Electronic Anisotropy and Enhanced Chemical Activity of Highly Rippled Phosphorene

We investigate the electronic structure and chemical activity of rippled phosphorene induced by large compressive strains via first-principles calculation. It is found that phosphorene is extraordinarily bendable, enabling the accommodation of ripples with large curvatures. Such highly rippled phosphorene shows a strong anisotropy in electronic properties. For ripples along the armchair direction, the band gap changes from 0.84 to 0.51 eV for the compressive strain up to -20% and further compression shows no significant effect, for ripples along the zigzag direction, semiconductor to metal transition occurs. Within the rippled phosphorene, the local electronic properties, such as the modulated band gap and the alignments of frontier orbitals, are found to be highly spatially dependent, which may be used for modulating the injection and confinement of carriers for optical and photovoltaic applications. The examination of the interaction of a physisorbed NO molecule with the rippled phosphorene under different compressive strains shows that the chemical activities of the phosphorene are significantly enhanced at the top and bottom peaks of the ripples, indicated by the enhanced adsorption and charge transfer between them. All these features can be ascribed to the effect of curvatures, which modifies the orbital coupling between atoms at the ripple peaks

All exact traveling wave solutions of the combined KdV-mKdV equation

In this article, we employ the complex method to obtain all meromorphic solutions of complex combined Korteweg-de Vries-modified Korteweg-de Vries equation (KdV-mKdV equation) at first, then we find all exact traveling wave solutions of the combined KdV-mKdV equation. The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic exact traveling wave solutions of the combined KdV-mKdV equation are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions wr,2(z)wr,2(z) and simply periodic solutions ws,2(z)ws,2(z) such that they are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role in finding exact solutions in mathematical physics. We also give some computer simulations to illustrate our main results

Path integrals and symmetry breaking for optimal control theory

This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a linear equation. The transformation is similar to the transformation used to relate the classical Hamilton-Jacobi equation to the Schr\"odinger equation. As a result of the linearity, the usual backward computation can be replaced by a forward diffusion process, that can be computed by stochastic integration or by the evaluation of a path integral. It is shown, how in the deterministic limit the PMP formalism is recovered. The significance of the path integral approach is that it forms the basis for a number of efficient computational methods, such as MC sampling, the Laplace approximation and the variational approximation. We show the effectiveness of the first two methods in number of examples. Examples are given that show the qualitative difference between stochastic and deterministic control and the occurrence of symmetry breaking as a function of the noise.Comment: 21 pages, 6 figures, submitted to JSTA