The mechanics of reinforcement of polymers by graphene nanoplatelets

A detailed study has been undertaken of the mechanisms of stress transfer in polymeric matrices with different values of Young's modulus, Em, reinforced by graphene nanoplatelets (GNPs). For each material, the Young's modulus of the graphene filler, Ef, has been determined using the rule of mixtures and it is found to scale with the value of Em. Additionally stress-induced Raman bands shifts for the different polymer matrices show different levels of stress transfer from the polymer matrix to the GNPs, which again scale with Em. A theory has been developed to predict the stiffness of the bulk nanocomposites from the mechanics of stress transfer from the matrix to the GNP reinforcement based upon the shear-lag deformation of individual graphene nanoplatelets. Overall it is found that it is only possible to realise the theoretical Young's modulus of graphene of 1.05 TPa for discontinuous nanoplatelets as Em approaches 1 TPa; the effective modulus of the reinforcement will always be less for lower values of Em. For flexible polymeric matrices the level of reinforcement is independent of the graphene Young's modulus and, in general, the best reinforcement will be obtained in nanocomposites with strong graphene-polymer interfaces and aligned nanoplatelets with high aspect ratios

Pricing and Hedging Asian Basket Options with Quasi-Monte Carlo Simulations

In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by the aid of the Malliavin Calculus, extending the procedure employed by Montero and Kohatsu-Higa (2003). Efficient path-generation algorithms, such as Linear Transformation and Principal Component Analysis, exhibit a high computational cost in a market with time-dependent volatilities. We present a new and fast Cholesky algorithm for block matrices that makes the Linear Transformation even more convenient. Moreover, we propose a new-path generation technique based on a Kronecker Product Approximation. This construction returns the same accuracy of the Linear Transformation used for the computation of the deltas and the prices in the case of correlated asset returns while requiring a lower computational time. All these techniques can be easily employed for stochastic volatility models based on the mixture of multi-dimensional dynamics introduced by Brigo et al. (2004).Comment: 16 page

The Two Fluid Drop Snap-off Problem: Experiments and Theory

We address the dynamics of a drop with viscosity $\lambda \eta$ breaking up inside another fluid of viscosity $\eta$. For $\lambda=1$, a scaling theory predicts the time evolution of the drop shape near the point of snap-off which is in excellent agreement with experiment and previous simulations of Lister and Stone. We also investigate the $\lambda$ dependence of the shape and breaking rate.Comment: 4 pages, 3 figure

Iterative algorithm and estimation of solution for a fractional order differential equation

In this paper, we establish an iterative algorithm and estimation of solutions for a fractional turbulent flow model in a porous medium under a suitable growth condition. Our main tool is the monotone iterative technique

Sub-Doppler spectroscopy of Rb atoms in a sub-micron vapor cell in the presence of a magnetic field

We report the first use of an extremely thin vapor cell (thickness ~ 400 nm) to study the magnetic-field dependence of laser-induced-fluorescence excitation spectra of alkali atoms. This thin cell allows for sub-Doppler resolution without the complexity of atomic beam or laser cooling techniques. This technique is used to study the laser-induced-fluorescence excitation spectra of Rb in a 50 G magnetic field. At this field strength the electronic angular momentum J and nuclear angular momentum I are only partially decoupled. As a result of the mixing of wavefunctions of different hyperfine states, we observe a nonlinear Zeeman effect for each sublevel, a substantial modification of the transition probabilities between different magnetic sublevels, and the appearance of transitions that are strictly forbidden in the absence of the magnetic field. For the case of right- and left- handed circularly polarized laser excitation, the fluorescence spectra differs qualitatively. Well pronounced magnetic field induced circular dichroism is observed. These observations are explained with a standard approach that describes the partial decoupling of I and J states

Dynamics of fully nonlinear capillary–gravity solitary waves under normal electric fields

Two-dimensional capillary–gravity waves travelling under the effect of a vertical electric field are considered. The fluid is assumed to be a dielectric of infinite depth. It is bounded above by another fluid which is hydrodynamically passive and perfectly conducting. The problem is solved numerically by time-dependent conformal mapping methods. Fully nonlinear waves are presented, and their stability and dynamics are studied