Probabilistic interpretation of a system of quasilinear parabolic PDEs

Using a forward–backward stochastic differential equations (FBSDE) associated to a transmutation process driven by a finite sequence of Poisson processes, we obtain a probabilistic interpretation for a non-degenerate system of quasilinear parabolic partial differential equations (PDEs). The novetly is that the linear second order differential operator is different on each line of the system.     

Effect of boundary layer losses on 2D detonation cellular structures

We evaluate the effect of boundary layer losses on two-dimensional H2/O2/Ar cellular detonations obtained in narrow channels. The experiments provide the details of the cellular structure and the detonation speed deficits from the ideal CJ speed. We model the effect of the boundary layer losses by incorporating the flow divergence in the third dimension due to the negative boundary layer displacement thickness, modeled using Mirels’ theory. The cellular structures obtained numerically with the resulting quasi-2D formulation of the reactive Euler equations with two-step chain-branching chemistry are found in excellent agreement with experiment, both in terms of cell dynamics and velocity deficits, provided the boundary layer constant of Mirels is modified by a factor of 2. A significant increase in the cell size is found with increasing velocity deficit. This is found to be very well captured by the induction zone increase in slower detonations due to the lower temperatures in the induction zone.     

Computational Study of the One‐ and Two‐Dimensional Infrared Spectra of a Proton‐Transfer Mode in a Hydrogen‐Bonded Complex Dissolved in a Polar Nanocluster

The signatures of nanosolvation on the one‐ and two‐dimensional (1D and 2D) IR spectra of a proton‐transfer mode in a hydrogen‐bonded complex dissolved in polar solvent molecule nanoclusters of varying size are elucidated by using mixed quantum–classical molecular dynamics simulations. For this particular system, increasing the number of solvent molecules successively from N=7 to N=9 initiates the transition of the system from a cluster state to a bulk‐like state. Both the 1D and 2D IR spectra reflect this transition through pronounced changes in their peak intensities and numbers, but the time‐resolved 2D IR spectra also manifest spectral features that uniquely identify the onset of the cluster‐to‐bulk transition. In particular, it is observed that in the 1D IR spectra, the relative intensities of the peaks change such that the number of peaks decreases from three to two as the size of the cluster increases from N=7 to N=9. In the 2D IR spectra, off‐diagonal peaks are observed in the N=7 and N=8 cases at zero waiting time, but not in the N=9 case. It is known that there are no off‐diagonal peaks in the 2D IR spectrum of the bulk version of this system at zero waiting time, so the disappearance of these peaks is a unique signature of the onset of bulk‐like behavior. Through an examination of the trajectories of various properties of the complex and solvent, it is possible to relate the emergence of these off‐diagonal peaks to an interplay between the vibrations of the complex and the solvent polarization dynamics.     

Synthesis,characterization and electrical properties of hybrid Zn2GeO4–ZnO beaded nanowire arrays

We report the syntheses of vertically aligned, beaded zinc germinate (Zn₂GeO₄)/zinc oxide (ZnO) hybrid nanowire arrays via a catalyst-free approach. Vertically aligned ZnO nanowire is used as a lattice matching reactive template for the growth of Zn₂GeO₄/ZnO nanowire. The morphology and structure of the as-prepared samples were characterized using X-ray diffractometry (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and energy-dispersive X-ray spectroscopy (EDS). TEM studies revealed the beaded microstructures of the Zn₂GeO₄/ZnO nanowire. The thickness and microstructures of crystalline beads could be easily controlled by tuning the growth duration and temperature. The photoluminescence spectrum of the Zn₂GeO₄/ZnO nanowires is composed of two peaks, i.e., the ultraviolet (UV) peak and the defect peak. For longer treatment duration of the samples, both the UV and defect peak intensities decrease dramatically. One application of the as-prepared Zn₂GeO₄/ZnO nanowire is to use the nanowire as template for the growth of three-dimensionally (3D) aligned, high-density ZnO nanobranches en route to hierarchical structure. The study of field emission properties of the as-prepared samples revealed the low turn-on voltage and high current density electron emission from the 3D ZnO nanobranches as compared to the ZnO nanowires and Zn₂GeO₄/ZnO nanowires. Furthermore, the electrical transport behavior of single hybrid nanowire device indicates the formation of back-to-back Schottky barriers (SBs) formation at the contacts and its application in white-light response has been demonstrated.     

Optical travelator: transport and dynamic sorting of colloidal microspheres with an asymmetrical line optical tweezers

We report the transport, funnelling and dynamic sorting of colloidal microspheres in an aqueous suspension using line optical tweezers with asymmetrical intensity profiles. The line tweezers readily trapped and propelled the microspheres along the length of the line tweezers. Using this simple technique, transporting and funnelling of microspheres within a microscopic region were demonstrated. To illustrate the dynamic particle-sorting capability of the line tweezers, a binary colloidal system comprising of microspheres with diameters of 1.1 μm and 3.2 μm were driven past the line tweezers by electrophoresis. As the optical trapping force is dependent on the size of the microspheres, the line tweezers was able to change the path of the larger spheres while exerting little influence on the smaller spheres thus sorting the two types of microspheres. At optimized laser power and flow rate of microspheres, sorting efficiency greater than 90% has been achieved. PACS 42.15.Eq; 87.80.Cc; 87.80.Fe; 82.70.Dd     

Surface modification studies of edge-oriented molybdenum sulfide nanosheets

We have synthesized edge-oriented MoS2 nanosheets by the evaporation of a single source precursor based on Mo(IV)-tetrakis(diethylaminodithiocarbomato). The surface chemistry of the MoS2 nanosheets has been studied in order to evaluate the chemical reactivities of the basal planes and edges. By irradiating the MoS2 nanosheet with a scanning infrared laser, micron-scale lithographical structures can be created due to laser-induced oxidation of MoS2 to form nanocrystalline MoO3. Preferential reactivities of the MoS2 basal edges in an electrochemical environment and during vapor phase deposition have been demonstrated. Functionalization of the basal plane with 1-pyrene acetic acid allows the immobilization of DNA and immunoglobins on the MoS2 basal plane.     

Scanning mirror on a vibrating membrane for dynamic optical trapping

A study of the variation of the spectral shape and the harmonic distribution of the high-order harmonics generated from silver plasma on the frequency chirp of the driving laser radiation (793 nm 48 fs) is reported. The results of the systematic study of the harmonic generation from the 21st order up to the 61st order (λ=13 nm) are presented. A tuning of the harmonic wavelength up to 0.8 nm can be accomplished by variation of the laser chirp. PACS 42.65.Ky; 42.79.Nv; 52.38.Mf     

Tail Behavior of a Threshold Autoregressive Stochastic Volatility Model

We consider a threshold autoregressive stochastic volatility model where the driving noises are sequences of iid regularly random variables. We prove that both the right and the left tails of the marginal distribution of the log-volatility process (α_t)_t are regularly varying with tail exponent −α with α > 0. We also determine the exact values of the coefficients in the tail behaviour of the process (α_t)_t. AMS 2000 Subject Classification. Primary—62G32, 62PO5     

Fabrication of size-tunable gold nanoparticles array with nanosphere lithography, reactive ion etching, and thermal annealing

Two-dimensional ordered arrays of gold (Au) nanoparticles were fabricated using two different variants of the nanosphere lithography technique. First, ordered arrays of polystyrene nanospheres on Si substrate were used as deposition masks through which gold films were deposited by electron beam evaporation. After the removal of the nanospheres, an array of triangular Au nanodisks was left on the Si substrate. After thermal annealing at increasing temperature, systematic shape transition of the nanostructures from original triangular Au nanodisks to rounded nanoparticles was observed. This approach allows us to systematically vary the size and morphology of the particles. In the second and novel technique, we made use of reactive ion etching to simultaneously reduce the dimension of the masking nanospheres and create arrays of nanopores on the substrate prior to the deposition of the Au films. These samples were subsequently annealed, which resulted in size-tunable and ordered Au nanoparticle arrays with the nanoparticles nested in the nanopores of the templated substrate. With the nanoparticles anchored in the nanopores, the substrate could be useful as a template for growth of other nanomaterials.     

Critical Homogenization of SDEs Driven by a Levy Process in Random Medium

We are concerned with homogenization of stochastic differential equations (SDE) with stationary coefficients driven by Poisson random measures and Brownian motions in the critical case, that is, when the limiting equation admits both a Brownian part as well as a pure jump part. We state an annealed convergence theorem. This problem is deeply connected with homogenization of integral partial differential equations.