Multi‐asset barrier options and occupation time derivatives

A general framework is formulated to price various forms of European style multi‐asset barrier options and occupation time derivatives with one state variable having the barrier feature. Based on the lognormal assumption of asset price processes, the splitting direction technique is developed for deriving the joint density functions of multi‐variate terminal asset prices with provision for single or double barriers on one of the state variables. A systematic procedure is illustrated whereby multi‐asset option price formulas can be deduced in a systematic manner as extensions from those of their one‐asset counterparts. The formulation has been applied successfully to derive the analytic price formulas of multi‐asset options with external two‐sided barriers and sequential barriers, multi‐asset step options and delayed barrier options. The successful numerical implementation of these price formulas is demonstrated.     

Integro-differential equation for joint probability density in phase space associated with continuous-time random walk

We derive an integro-differential equation for the joint probability density function in phase space associated with the continuous-time random walk, with generic waiting time probability density function and external force. This equation permits us to investigate whole diffusion processes covering initial-, intermediate-, and long-time ranges, which can distinguish the evolution details for systems having the same behavior in the long-time limit with different initial- and intermediate-time behaviors. Moreover, we obtained analytic solutions for probability density functions both in velocity and phase spaces, and interesting dynamic behaviors are discovered.     

Delayed saturation controller for vibration suppression in a stainless-steel beam

This paper considers the effect of time delays on the saturation control of first-mode vibration of a stainless-steel beam. Time delay is commonly caused by measurements of the system states, transport delay, on-line computation, filtering and processing of data, calculating and executing of control forces as required in control processing. The method of multiple scales is employed to obtain the analytical solutions of limit cycles and their stability and to investigate the bifurcations of the system under consideration. All the predictions from analytical solutions are in agreement with the numerical simulation. The analytical results show that a delay can change the range of the saturation control, either widening or shrinking the effective frequency bandwidth. Thus, vibration control of a beam can be achieved using an appropriate choice of the delay in a self-feedback signal. From the examples illustrated, this paper provides a positive example that time delay can also be utilized to suppress vibration in systems when time delay cannot be neglected.     

Depth‐integrated,non‐hydrostatic model with grid nesting for tsunami generation,propagation, and run‐up

Tsunamis generated by earthquakes involve physical processes of different temporal and spatial scales that extend across the ocean to the shore. This paper presents a shock‐capturing dispersive wave model in the spherical coordinate system for basin‐wide evolution and coastal run‐up of tsunamis and discusses the implementation of a two‐way grid‐nesting scheme to describe the wave dynamics at resolution compatible to the physical processes. The depth‐integrated model describes dispersive waves through the non‐hydrostatic pressure and vertical velocity, which also account for tsunami generation from dynamic seafloor deformation. The semi‐implicit, finite difference model captures flow discontinuities associated with bores or hydraulic jumps through the momentum‐conserved advection scheme with an upwind flux approximation. The two‐way grid‐nesting scheme utilizes the Dirichlet condition of the non‐hydrostatic pressure and both the horizontal velocity and surface elevation at the inter‐grid boundary to ensure propagation of dispersive waves and discontinuities across computational grids of different resolution. The inter‐grid boundary can adapt to bathymetric features to model nearshore wave transformation processes at optimal resolution and computational efficiency. A coordinate transformation enables application of the model to small geographic regions or laboratory experiments with a Cartesian grid. A depth‐dependent Gaussian function smoothes localized bottom features in relation to the water depth while retaining the bathymetry important for modeling of tsunami transformation and run‐up. Numerical experiments of solitary wave propagation and N‐wave run‐up verify the implementation of the grid‐nesting scheme. The 2009 Samoa Tsunami provides a case study to confirm the validity and effectiveness of the modeling approach for tsunami research and impact assessment. Copyright © 2010 John Wiley & Sons, Ltd.     

Plasma-immersion ion implantation of the interior surface of asmall cylindrical bore using an auxiliary electrode for finite rise-timevoltage pulses

Plasma-immersion ion implantation (PIII) can be used to process the interior surfaces of odd-shape specimens such as a cylindrical bore. The temporal evolution of the plasma sheath in a small cylindrical bore in the presence of a grounded coaxial auxiliary electrode is derived for voltage pulses of different rise times by solving Poisson's equation and the equations of ion continuity, and motion numerically using the appropriate boundary conditions. It is found that the maximum ion impact energy and the average impact energy are improved for finite rise-time voltage pulses, and shorter rise times yield better results. Our results allow the selection of a suitable auxiliary electrode radius to improve the average impact energy for a given rise time     

Enhancement effect of high-frequency noise of injection lasers with reflected waves due to direct modulation

It is found experimentally that the high-frequency noise of an injection laser associated with wave injection due to external reflection is significantly increased when the direct modulation is applied. It is clarified that the noise enhancement effect is caused by the increasing of the quantum shot noise of the injection laser due to the current modulation. The high- frequency noise of the narrow stripe laser is smaller than that of the wide stripe laser.     

Numerical study on an isolated vortex of the type-II superconductor in the presence of a twin plane

Based on the Ginzburg-Landau theory and using the numerical relaxation approach, we have carried out a numerical analysis of an isolated vortex structure for a type-II superconductor in the presence of a twin plane (being a normal region) situated parallel to the external magnetic field. Meanwhile, the lower critical field is also calculated and is found to decrease as compared to the twin-free case, which is consistent with the intuitive theoretical understanding and the fact that twins are easy channels for the flux penetration.     

TEM investigation of nanophase aluminum powder.

Nanophase aluminum powder was characterized in a field-emission-gun transmission electron microscope (TEM). Different techniques were used to investigate the structure of the particles, including conventional bright-field and dark-field imaging, scanning transmission electron microscopy (STEM), high-resolution lattice imaging, diffraction studies, energy dispersive X-ray spectroscopy (EDS) analysis and mapping, and electron energy loss spectroscopy (EELS) analysis and mapping. It has been established that the particle cores consist of aluminum single crystals that sometimes contain crystal lattice defects. The core is covered by a passivating layer of aluminum oxide a few nanometers thick. The alumina is mostly amorphous, but evidences of partial crystallinity of the oxide were also found. The thickness of this layer was measured using different techniques, and the results are in good agreement with each other. The particles are agglomerated in two distinct ways. Some particles were apparently bonded together during processing before oxidation. These mostly form dumbbells covered by a joint oxide layer. Also, oxidized particles are loosely assembled into relatively large clusters.     

Surface charge spectroscopy and its applications

Surface Charge Spectroscopy (SCS) is a surface sensitive technique for measuring potential distributions across an ultrathin (<100Å) insulator/semiconductor structure. Although the applicability of the technique is rather narrowly confined to such a specific sample structure, SCS bears considerable industrial significance because insulator/semiconductor structures are the most commonly used functional elements in microelectronics, and because gate insulators used in the industry are indeed getting to a nanometer thickness scale. The basic SCS concept relies on the measurements of the potential energies of electronic states using the conventional photoemission spectroscopic method, energy data which bear the information of the electrical potential gradient across the probed surface region. Surface sensitivity of SCS is thus contained in the framework of photoemission spectroscopy. Unlike conventional photoemission studies, SCS always measures the potential gradients corresponding to a specific surface potential. In fact, its analytical power is only shown when the surface potential of a sample can be controlled, and coincidentally an insulator/semiconductor device structure in microelectronics is only functional when the potential gradient extending into the semiconductor region can be changed effectively by the surface potential of the insulator. When SCS data are examined beyond the simple space-charge model commonly employed by electrical characterisation techniques like capacitance-voltage measurements, they can give information other than the relationship between the insulator surface potential and semiconductor surface potential (and thus interface state distributions across the bandgap of the semiconductor). Rather, they also provide unique information on the depth distributions of various types of fixed charges in the sample structure at an atomic level, and on the insulator breakdown mechanisms.     

Unusual light-driven amplification through unexpected regioselective photogeneration of five-membered azaheterocyclic AIEgen

Developing versatile synthetic methodologies with merits of simplicity, efficiency, and environment friendliness for five-membered heterocycles is of incredible importance to pharmaceutical and material science, as well as a huge challenge to synthetic chemistry. Herein, an unexpected regioselective photoreaction to construct a fused five-membered azaheterocycle with an aggregation-induced emission (AIE) characteristic is developed under mild conditions. The formation of the five-membered ring is both thermodynamically and kinetically favored, as justified by theoretical calculation and experimental evidence. Markedly, a light-driven amplification strategy is proposed and applied in selective mitochondria-targeted cancer cell recognition and fluorescent photopattern fabrication with improved resolution. The work not only delivers the first report on efficiently generating a fused five-membered azaheterocyclic AIE luminogen under mild conditions via photoreaction, but also offers deep insight into the essence of the photosynthesis of fused five-membered azaheterocyclic compounds.

A multifunctional, AIE-based, fused five-membered azaheterocycle is photogenerated with light-driven amplification to combat the photobleaching issue and fabricate display materials.