Control of lasing in fully chaotic open microcavities by tailoring the shape factor

We demonstrate experimentally that lasing in a semiconductor microstadium can be optimized by controlling its shape. Under spatially uniform optical pumping, the first lasing mode in a GaAs microstadium with large major-to-minor-axis ratio usually corresponds to a high-quality scar mode consisting of several unstable periodic orbits. Interference of waves propagating along the constituent orbits may minimize light leakage at particular major-to-minor-axis ratio. By making stadium of the optimum shape, we are able to maximize the mode quality factor and align the mode frequency to the peak of the gain spectrum, thus minimizing the lasing threshold. This work opens the door to control chaotic microcavity lasers by tailoring the shape factor

The influence of compact and ordered carbon coating on solid-state behaviors of silicon during electrochemical processes

To address the issues of large volume change and low conductivity of silicon (Si) materials, carbon coatings have been widely employed as surface protection agent and conductive medium to encapsulate the Si materials, which can improve the electrochemical performance of Si-based electrodes. There has been a strong demand to gain a deeper understanding of the impact of efficient carbon coating over the lithiation and delithiation process of Si materials. Here, we report the first observation of the extended two-phase transformation of carbon-coated Si nanoparticles (Si/C) during electrochemical processes. The Si/C nanoparticles were prepared by sintering Si nanoparticles with polyvinylidene chloride precursor. The Si/C electrode underwent a two-phase transition during the first 20 cycles at 0.2 C, but started to engage in solid solution reaction when the ordered compact carbon coating began to crack. Under higher current density conditions, the electrode was also found to be involved in solid solution reaction, which, however, was due to the overwhelming demand of kinetic property rather than the breaking of the carbon coating. In comparison, the Si/C composites prepared with sucrose possessed more disordered and porous carbon structures, and presented solid solution reaction throughout the entire cycling process

Information of Structures in Galaxy Distribution

We introduce an information-theoretic measure, the Renyi information, to describe the galaxy distribution in space. We discuss properties of the information measure, and demonstrate its relationship with the probability distribution function and multifractal descriptions. Using the First Look Survey galaxy samples observed by the Infrared Array Camera onboard Spitzer Space Telescope, we present measurements of the Renyi information, as well as the counts-in-cells distribution and multifractal properties of galaxies in mid-infrared wavelengths. Guided by multiplicative cascade simulation based on a binomial model, we verify our measurements, and discuss the spatial selection effects on measuring information of the spatial structures. We derive structure scan functions at scales where selection effects are small for the Spitzer samples. We discuss the results, and the potential of applying the Renyi information to measuring other spatial structures.Comment: 25 pages, 8 figures, submitted to ApJ; To appear in The Astrophysical Journal 2006, 644, 678 (June 20th

Equivalence of robust stabilization and robust performance via feedback

One approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying (LPV) plants (where the controller has on-line access to the varying plant parameters) is through linear-fractional-transformation (LFT) models. Control issues to be addressed by controller design in this formalism include robust stability and robust performance. Here robust performance is defined as the achievement of a uniform specified $L^{2}$-gain tolerance for a disturbance-to-error map combined with robust stability. By setting the disturbance and error channels equal to zero, it is clear that any criterion for robust performance also produces a criterion for robust stability. Counter-intuitively, as a consequence of the so-called Main Loop Theorem, application of a result on robust stability to a feedback configuration with an artificial full-block uncertainty operator added in feedback connection between the error and disturbance signals produces a result on robust performance. The main result here is that this performance-to-stabilization reduction principle must be handled with care for the case of dynamic feedback compensation: casual application of this principle leads to the solution of a physically uninteresting problem, where the controller is assumed to have access to the states in the artificially-added feedback loop. Application of the principle using a known more refined dynamic-control robust stability criterion, where the user is allowed to specify controller partial-state dimensions, leads to correct robust-performance results. These latter results involve rank conditions in addition to Linear Matrix Inequality (LMI) conditions.Comment: 20 page

Resonant States in the Electronic Structure of the High Performance Thermoelectrics AgPbmSbTe_{m}SbTe_{2+m}$ ; The Role of Ag-Sb Microstructures

Ab initio electronic structure calculations based on gradient corrected density functional theory were performed on a class of novel quaternary compounds AgPb$_{m}SbTe$_{2+m}$, which were found to be excellent high temperature thermoelctrics with large figure of merit ZT ~2.2 at 800K. We find that resonant states appear near the top of the valence and bottom of the conduction bands of bulk PbTe when Ag and Sb replace Pb. These states can be understood in terms of modified Te-Ag(Sb) bonds. Electronic structure near the gap depends sensitively on the microstructural arrangements of Ag-Sb atoms, suggesting that large ZT values may originate from the nature of these ordering arrangements.Comment: Accepted in Physical Review Letter

Pinning control of fractional-order weighted complex networks

In this paper, we consider the pinning control problem of fractional-order weighted complex dynamical networks. The well-studied integer-order complex networks are the special cases of the fractional-order ones. The network model considered can represent both directed and undirected weighted networks. First, based on the eigenvalue analysis and fractional-order stability theory, some local stability properties of such pinned fractional-order networks are derived and the valid stability regions are estimated. A surprising finding is that the fractional-order complex networks can stabilize itself by reducing the fractional-order q without pinning any node. Second, numerical algorithms for fractional-order complex networks are introduced in detail. Finally, numerical simulations in scale-free complex networks are provided to show that the smaller fractional-order q, the larger control gain matrix D, the larger tunable weight parameter , the larger overall coupling strength c, the more capacity that the pinning scheme may possess to enhance the control performance of fractional-order complex networks

Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients

In this paper we give an affirmative answer to an open question mentioned in [Le Bris and Lions, Comm. Partial Differential Equations 33 (2008), 1272--1317], that is, we prove the well-posedness of the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.Comment: 11 pages. The proof has been modifie

Orbital Dependent Phase Control in Ca2-xSrxRuO4

We present first-principles studies on the orbital states of the layered perovskites Ca$_{2-x}$Sr$_x$RuO$_4$. The crossover from antiferromagnetic (AF) Mott insulator for $x < 0.2$ to nearly ferromagnetic (FM) metal at $x=0.5$ is characterized by the systematic change of the $xy$ orbital occupation. For the AF side ($x < 0.2$), we present firm evidence for the $xy$ ferro-orbital ordering. It is found that the degeneracy of $t_{2g}$ (or $e_g$) states is lifted robustly due to the two-dimensional (2D) crystal-structure, even without the Jahn-Teller distortion of RuO$_6$. This effect dominates, and the cooperative occupation of $xy$ orbital is concluded. In contrast to recent proposals, the resulting electronic structure explains well both the observed X-ray absorption spectra and the double peak structure of optical conductivity. For the FM side ($x=0.5$), however, the $xy$ orbital with half filling opens a pseudo-gap in the FM state and contributes to the spin $S$=1/2 moment (rather than $S$=1 for $x$=0.0 case) dominantly, while $yz,zx$ states are itinerant with very small spin polarization, explaining the recent neutron data consistently.Comment: 17 pages, 5 figure