Raman Scattering of Nanocrystalline δ-TiNx Synthesized by Mechanical Milling

Introduction Raman scattering is a powerful nondestructive technique that gives vibrational information about organic and inorganic materials. Raman scattering features, such as intensity, frequency and width, are strongly dependent on compositions, defects, short-range orders, crystal structures, and internal stresses of materials. Therefore, it has been widely used to obtain detailed information about the structural properties of semiconductors, high-Tc superconductors, ceramics, catalysts, carbon based materials, and Ⅲ-Ⅴ valent metallic nitride materials, including lattice perfection, strain, crystalline, interface, and compositional uniformity[1].     

Study of spin sum rules (and the strong coupling constant at large distances)

We present recent results from Jefferson Lab on sum rules related to the spin structure of the nucleon. We then discuss how the Bjorken sum rule with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an effective coupling for the strong force at all distances.     

Multiscale simulation of flow and heat transfer of nanofluid with lattice Boltzmann method

Based on the lattice Boltzmann (LB) approach, a novel hybrid method has been proposed for getting insight into the microscale characteristics of the multicomponent flow of nanofluid. In this method, the whole computational domain is divided into two regions in which different-sized meshes are involved for simulation (fine mesh and coarse mesh). The multicomponent LB method is adopted in the fine mesh region, and the single-component LB approach is applied to the coarse mesh region where the nanofluid is treated as a mixed single-component fluid. The conservation principles of mass, momentum and energy are used to derive a hybrid scheme across the different scaled regions. Numerical simulation is carried out for the Couette flow and convective heat transfer in a parallel plate channel to validate the hybrid method. The computational results indicate that by means of the present method, not only the microscopic characteristics of the nanofluid flow can be simulated, but also the computational efficiency can be remarkably improved compared with the pure multicomponent LB method.     

Lattice Boltzmann method for simulating particle–fluid interactions

The lattice Boltzmann method （LBM） has gained increasing popularity in the last two decades as an alternative numerical approach for solving fluid flow problems. One of the most active research areas in the LBM is its application in particle-fluid systems, where the advantage of the LBM in efficiency and parallel scalability has made it superior to many other direct numerical simulation （DNS） techniques. This article intends to provide a brief review of the application of the LBM in particle-fluid systems. The numerical techniques in the LBM pertaining to simulations of particles are discussed, with emphasis on the advanced treatment for boundary conditions on the particle-fluid interface. Other numerical issues, such as the effect of the internal fluid, are also briefly described. Additionally, recent efforts in using the LBM to obtain closures for particle-fluid drag force are also reviewed.     

Provide a suitable range to include the thermal creeping effect on slip velocity and temperature jump of an air flow in a nanochannel by lattice Boltzmann method

The thermal creeping effect on slip velocity of air forced convection through a nanochannel is studied for the first time by using a lattice Boltzmann method. The nanochannel side walls are kept hot while the cold inlet air streams along them. The computations are presented for the wide range of Reynolds number, Knudsen number and Eckert number while slip velocity and temperature jump effects are involved. Moreover appropriate validations are performed versus previous works concerned the micro–nanoflows.The achieved results are shown as the velocity and temperature profiles at different cross sections, streamlines and isotherms and also the values of slip velocity and temperature jump along the nanochannel walls. The ability of the lattice Boltzmann method to simulate the thermal creeping effects on hydrodynamic and thermal domains of flow is shown at this study; so that its effects should be involved at lower values of Eckert number and higher values of Reynolds number especially at entrance region where the most temperature gradient exists.     

Simulation of phase separation with large component ratio for oil-in-water emulsion in ultrasound field

This paper presents an exploration for separation of oil-in-water and coalescence of oil droplets in ultrasound field via lattice Boltzmann method. Simulations were conducted by the ultrasound traveling and standing waves to enhance oil separation and trap oil droplets. The focus was to the effect of ultrasound irradiation on oil-in-water emulsion properties in the standing wave field, such as oil drop radius, morphology and growth kinetics of phase separation. Ultrasound fields were applied to irradiate the oil-in-water emulsion for getting flocculation of the oil droplets in 420 kHz case, and larger dispersed oil droplets and continuous phases in 2 MHz and 10 MHz cases, respectively. The separated phases started to rise along the direction of sound propagation after several periods. The rising rate of the flocks was significantly greater in ultrasound case than that of oil droplets in the original emulsion, indicating that ultrasound irradiation caused a rapid increase of oil droplet quantity in the progress of the separation. The separation degree was also significantly improved with increasing frequency or irradiation time. The dataset was rearranged for growth kinetics of ultrasonic phase separation in a plot by spherically averaged structure factor and the ratio of oil and emulsion phases. The analyses recovered the two different temporal regimes: the spinodal decomposition and domain growth stages, which further quantified the morphology results. These numerical results provide guidance for setting the optimum condition for the separation of oil-in-water emulsion in the ultrasound field.     

An efficient and accurate lattice for pricing derivatives under a jump-diffusion process

Derivatives are popular financial instruments whose values depend on other more fundamental financial assets (called the underlying assets). As they play essential roles in financial markets, evaluating them efficiently and accurately is critical. Most derivatives have no simple valuation formulas; as a result, they must be priced by numerical methods such as lattice methods. In a lattice, the prices of the derivatives converge to theoretical values when the number of time steps increases. Unfortunately, the nonlinearity error introduced by the nonlinearity of the option value function may cause the pricing results to converge slowly or even oscillate significantly. The lognormal diffusion process, which has been widely used to model the underlying asset’s price dynamics, does not capture the empirical findings satisfactorily. Therefore, many alternative processes have been proposed, and a very popular one is the jump-diffusion process. This paper proposes an accurate and efficient lattice for the jump-diffusion process. Our lattice is accurate because its structure can suit the derivatives’ specifications so that the pricing results converge smoothly. To our knowledge, no other lattices for the jump-diffusion process have successfully solved the oscillation problem. In addition, the time complexity of our lattice is lower than those of existing lattice methods by at least half an order. Numerous numerical calculations confirm the superior performance of our lattice to existing methods in terms of accuracy, speed, and generality.     

On the structure of digital explicit nonlinear and inversive pseudorandom number generators

We analyze the lattice structure and distribution of the digital explicit inversive pseudorandom number generator introduced by Niederreiter and Winterhof as well as of a general digital explicit nonlinear generator. In particular, we extend a lattice test designed for this class of pseudorandom number generators to parts of the period and arbitrary lags and prove that these generators pass this test up to very high dimensions. We also analyze the behavior of digital explicit inversive and nonlinear generators under another very strong lattice test which in its easiest form can be traced back to Marsaglia and provides a complexity measure essentially equivalent to linear complexity.     

Lattice based extended formulations for integer linear equality systems

We study different extended formulations for the set with in order to tackle the feasibility problem for the set Pursuing the work of Aardal, Lenstra et al. using the reformulation , our aim is to derive reformulations of the form with 0  ≤  s ≤ n − m where preferably all the coefficients of P are small compared to the coefficients of A and T. In such cases the new variables μ appear to be good branching directions, and in certain circumstances permit one to deduce rapidly that the instance is infeasible. We give a polynomial time algorithm for identifying such P, T if possible, and for the case that A has one row a we analyze the reformulation when s = 1, that is, one μ-variable is introduced. In particular, we determine the integer width of the extended formulations in the direction of the μ-variable, and derive a lower bound on the Frobenius number of a. We conclude with some preliminary tests to see if the reformulations are effective when the number s of additional constraints and variables is limited. This work was partly carried out within the framework of ADONET, a European network in Algorithmic Discrete Optimization, contract no. MRTN-CT-2003-504438. The first author is financed in part by the Dutch BSIK/BRICKS project. The research was carried out in part while the second author visited CWI, Amsterdam with the support of the NWO visitor grant number B 61-556.     

On the combinatorics of Galois numbers

We define interval decompositions of the lattice of subspaces of a finite-dimensional vector space. We show that such a decomposition exists if and only if there exists a family of linear forms with certain properties. As applications we prove that all finite-dimensional real vector spaces admit an interval decomposition, while GF(2)ⁿ has an interval decomposition if and only if n≤4. On the other hand, we present an interval decomposition of GF(3)⁵. This partially answers a question of Faigle and Kruse (2004) [1] and [4].