Finite-size corrections in the Ising model with special boundary conditions

The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz (BK) is analyzed. We derive exact finite-size corrections for the free energy F   of the critical ferromagnetic Ising model on the M×N$M\times N$ square lattice with Brascamp–Kunz boundary conditions [H.J. Brascamp, H. Kunz, J. Math. Phys. 15 (1974) 66]. We show that finite-size corrections strongly depend not only on the boundary conditions but also on the shape and pattern of the lattice. In the limit N→∞$N\to \infty$ we obtain the expansion of the free energy and the inverse correlation lengths for infinitely long strip with BK boundary conditions. Our results are consistent with the conformal field theory prediction for the mixed boundary conditions.     

Single-sided mobile NMR apparatus using the transverse flux of a single permanent magnet

This study presents a simple design for a mobile, single-sided nuclear magnetic resonance (NMR) apparatus which uses the magnetic flux parallel to the magnetization direction of a single, disc-shaped permanent magnet polarized in radial direction. The stray magnetic field above the magnet is approximately parallel to the magnetization direction of the magnet and is utilized as the B₀ magnetic field of the apparatus. The apparatus weighs 1.8 kg, has a compact structure and can be held in one's palm. The apparatus generates a B₀ field strength of about 0.279 T at the center of apparatus surface and can acquire a clear Hahn echo signal of a pencil eraser block lying on the RF coil in one shot. Moreover, a strong static magnetic field gradient exists in the direction perpendicular to the apparatus surface. The strength of the static magnetic field gradient near the center of the apparatus surface is about 10.2 T/m; one-dimensional imaging of thin objects and liquid self-diffusion coefficient measurements can be performed therein. The available spatial resolution of the one-dimensional imaging experiments using a 5×5 mm horizontal sample area is about 200 μm. Several nondestructive inspection applications of the apparatus, including distinguishing between polyethylene grains of different densities, characterizing epoxy putties of distinct set times and evaluating the fat content percentages of milk powders, are also demonstrated. Compared with many previously published designs, the proposed design bears a simple structure and generates a B₀ magnetic field parallel to the apparatus surface, simplifying apparatus construction and simultaneously rendering the selection of the radiofrequency coil relatively flexible.     

Efficient pricing of discrete Asian options

Asian options are popular path-dependent financial derivatives. This paper uses lattices to price fixed-strike European-style Asian options that are discretely monitored. The algorithm proposed can also be applied to floating-strike Asian options as well because fixed-strike and floating-strike Asian options are related through an equation. The discretely monitored version is usually found in practice instead of the continuously monitored version usually encountered in the literature. This paper presents the first provably quadratic-time convergent lattice algorithm for pricing fixed-strike European-style discretely monitored Asian options. It is the most efficient lattice algorithm with convergence guarantees. The algorithm relies on the Lagrange multipliers to choose the number of states for each node of the lattice. Extensive numerical experiments and comparisons with many existing numerical methods confirm the performance claims and the competitiveness of our algorithm. This result places fixed-strike European-style discretely monitored Asian options in the same complexity class as vanilla options.     

A note on the Sarmanov bivariate distributions

We investigate the maximum correlation for Sarmanov bivariate distributions with fixed marginals and strengthen the existing results in the literature. The improvement in the maximum correlation is significant. A characterization of the Sarmanov distribution via chi-square divergence is also given. This extends Nelsen [13] result about the Farlie-Gumbel-Morgenstern (FGM) distribution.     

Effects on the polarizability of mesoscopic metallic nanoparticles

The effects of temperature variation on the electric polarizability of mesoscopic metallic nanoparticles is studied via a theoretical model in which the temperature dependence of the electron–phonon and electron–electron scattering rates are taken into account. Furthermore, the nonlocal response of the metal, which is significant for particles of mesoscopic dimensions, is also included. It is found that the significance of the nonlocal effects can be very different with different metals, for the same smallness in size of the nanoparticles. In addition, while the imaginary part of the polarizability in general increases with temperature, the real part can both decrease or increase as temperature rises—in contrast to the case with the static polarizability of atomic clusters, which most of the time increases with temperature.     

A note on a Wiener process with measurement error

In this paper we give a closed form for the determinant and the inverse matrix of the covariance matrix of a Wiener process with measurement error. We will discuss its application in the analysis of degradation data for highly-reliable products.     

Tens of GHz Tantalum pentoxide‐based micro‐ring all‐optical modulator for Si photonics

A tantalum pentoxide‐based (Ta₂O₅‐based) micro‐ring all‐optical modulator was fabricated. The refractive index inside the micro‐ring cavity was modified using the Kerr effect by injecting a pumped pulse. The transmittance of the ring resonator was controlled to achieve all‐optical modulation at the wavelength of the injected probe. When 12 GHz pulses with a peak power of 1.2 W were coupled in the ring cavity, the transmission spectrum of the Ta₂O₅ resonator was red‐shifted by 0.04 nm because of the Kerr effect. The relationship between the modulation depth and gap of the Ta₂O₅ directional coupler is discussed. An optimized gap of 1100 nm was obtained, and a maximum buildup factor of 11.7 with 84% modulation depth was achieved. The nonlinear refractive index of Ta₂O₅ at 1.55 μm was estimated as 3.4 × 10^?14 cm²/W based on the Kerr effect, which is almost an order of magnitude higher than that of Si₃N₄. All results indicate that Ta₂O₅ has potential for use in nonlinear waveguide applications with modulation speeds as high as tens of GHz.

     

The anharmonic effect study of coupled Morse oscillators for the unimolecular reaction

The importance of anharmonic effect in dissociation of molecular systems especially clusters has been noted. In this paper, we shall study the effect of coupled anharmonic oscillator of the standard bilinear form (SBF) Morse oscillator (MO) potential on unimolecular reaction. We shall use the systematic theoretical approach, YL method, proposed by Yao and Lin (YAO L, et. al. J Phys Chem A, 2007, 111(29): 6722-6729), which can evaluate anharmonic effects on the rate constants based on the transition state theory. In treating the anharmonic effect with the Morse oscillator potential on unimolecular reactions under collision-free conditions by using the RRKM (Rice-Ramsperger-Kassel-Marcus) theory, the in-verse Laplace transformation of the partition functions was used to obtain the total amount of state and density of state by using the first-order and the second-order approximations of the saddle-point method. To demonstrate the anharmonic effect of the SBF Morse model, we choose some model systems and a real reaction as examples.     

Analyticity and Dynamic Behavior of a Damped Three-Layer Sandwich Beam

Using the Riesz basis approach, we study a sandwich beam that is composed of an outer stiff layer and a compliant middle layer. The dynamic behavior and analyticity of the system are obtained based on a detailed spectral analysis and Riesz basis generation. As a consequence, the analyticity of the solution and the exponential stability of the system are concluded. This work was supported by the National Natural Science Foundation of China, Program for New Century Excellent Talents in the Universities of China and by the National Research Foundation of South Africa.     

Adaptive finite element methods for the identification of distributed parameters in elliptic equation

In this paper, adaptive finite element method is developed for the estimation of distributed parameter in elliptic equation. Both upper and lower error bound are derived and used to improve the accuracy by appropriate mesh refinement. An efficient preconditioned project gradient algorithm is employed to solve the nonlinear least-squares problem arising in the context of parameter identification problem. The efficiency of our error estimators is demonstrated by some numerical experiments.