Winding Clusters in Percolation on the Torus and the Möbius Strip

Using a simulation technique introduced recently, we study winding clusters in percolation on the torus and the Möbius strip for different aspect ratios. The asynchronous parallelization of the simulation makes very large system and sample sizes possible. Our high accuracy results are fully consistent with predictions from conformal field theory. The numerical results for the Möbius strip and the number distribution of winding clusters on the torus await theoretical explanation. To our knowledge, this study is the first of its kind.     

Chemical and thermal stability of alkanethiol and sulfur passivated InP(100)

InP(100) surfaces treated with Na2Sx9H20 and CnH(2n+1)SH are examined by contact angle measurement, X-ray photoelectron spectroscopy, and atomic force microscopy to determine the chemical and thermal behavior of these passivated surfaces. The surfaces coated by octadecanethiol (n = 18) self-assembled monolayers (SAMs) are found to be more stable toward oxidation than the S-passivated surface. The chemical stability of octadecanethiol SAMs in various environments is examined. The thiol monolayer is found to be stable in 0.1 M HCl but degrades in 0.1 M NaOH, boiling chloroform, and water. The behavior of these surfaces at elevated temperatures under a vacuum is also investigated. The octadecanethiol-coated InP(100) is stable up to 473 K, above which the films begin to degrade. Unlike other substrates on which the entire molecule including the sulfur headgroup desorbs together, on InP, the sulfur headgroup remains on the surface even after annealing to 673 K. These observations suggest that the desorption occurs by S-C bond cleavage as well as In-S bond cleavage. The sulfur of S-passivated InP is found to be more thermally stable than that of the octadecanethiol monolayer, perhaps due to their different bonding geometries and hence energies.     

“One dimensional” double layer. The effect of size asymmetry of cations and anions on charge-storage in ultranarrow nanopores—an Ising model theory

We develop a statistical mechanical theory of charge storage in quasi-single-file ionophilic nanopores with pure room temperature ionic liquid cations and anions of different size. The theory is mapped to an extension of the Ising model exploited earlier for the case of cations and anions of the same size. We calculate the differential capacitance and the stored energy density per unit surface area of the pore. Both show asymmetry in the dependence on electrode potential with respect to the potential of zero charge, related to the difference in the size of the ions, which will be interesting to investigate experimentally. It also approves the increase of charge storage capacity via obstructed charging, which in these systems emerges for charging nanopores with smaller ions.     

Anisotropy and universality: the Oslo model, the rice pile experiment, and the quenched Edwards-Wilkinson equation

We show that any amount of anisotropy moves the Oslo model to another known universality class, the exponents of which can be derived exactly. This amounts to an exact solution of the quenched Edwards-Wilkinson equation with a drift term. We argue that anisotropy is likely to be experimentally relevant and may explain why consistent exponents have not been extracted in the rice pile experiments.     

Entropy Production in Exactly Solvable Systems

The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms.     

Interionic Interactions in Conducting Nanoconfinement

Interionic interactions in conducting nanopores determine how counterions may be packed in the pores subject to the applied voltage. In ideal metals, interactions are exponentially screened by metallic electrons. However, modern nanoporous electrodes are predominantly made of carbon materials. To what extent is this screening affected by a different mode of dielectric response in such materials? To answer this question we study Coulomb interaction of charges in cylindrical and slit pores that allow finite electric field penetration into the pore walls, as well as the Coulomb interaction in a nanogap between two thin walls of graphene modeled by a non‐local dielectric function. In all cases studied the screening was found to be subtly different than in metallic nanopores, but still strong enough to support realization of the so called superionic state in such pores.     

Demonstration of a mode-conversion cavity add-drop filter

We experimentally demonstrate a new type of add-drop filter incorporating an asymmetric Y-branch waveguide coupler and a shifted-grating mode-conversion cavity. The device relies on mode separation in the asymmetric Y-branch and wavelength-selective mode conversion upon reflection from the shifted-grating cavity. Add-drop functionality is demonstrated in a three-port integrated silicon-on-insulator device.     

Integrated waveguide Fabry-Perot microcavities with silicon/air Bragg mirrors

We demonstrate in-plane microfabricated Fabry-Perot cavities with cryogenically etched silicon/air distributed Bragg reflector (DBR) mirrors and integrated silicon-on-insulator rib waveguides. Several DBR configurations and cavity lengths were measured. Various devices exhibit Q=26963, FWHM=0.060 nm, finesse F=489, free spectral range FSR=81.7 nm, and DBR mirror reflectance R=99.4%. Thermo-optic tuning over 6.7 nm is also demonstrated.     

ZnO/cubic (Mg,Zn)O radial nanowire heterostructures

The formation and properties of radial heteroepitaxial ZnO/(Mg,Zn)O nanowires is reported in which the (Mg,Zn)O is cubic. Synthesis is achieved via a catalyst-driven molecular beam epitaxy technique. The nanowires were grown on Ag-coated Si substrates at growth temperatures ranging from T_g=300 to 500 °C, using Zn, Mg, and O₃/O₂ as the reactive flux. Structural and compositional analyses indicate that the core of the nanowire is ZnO possessing the hexagonal wurtzite structure, with the (Mg,Zn)O sheath assuming the cubic rock salt structure. Since (Mg,Zn)O has a larger band-gap energy (up to 7.8 eV) than that of ZnO (3.37 eV), these radial heterostructure nanorods provide an interesting system for quantum confinement and one-dimensional nanoscale device studies. PACS 81.05.Dz; 81.07.Vb