Anticipating Stochastic 2D Navier-Stokes Equations

In this article, we consider the two-dimensional stochastic Navier-Stokes equation (SNSE) on a smooth bounded domain, driven by affine-linear multiplicative white noise and with random initial conditions and Dirichlet boundary conditions. The random initial condition is allowed to anticipate the forcing noise. Our main objective is to prove the existence of a solution to the SNSE under sufficient Malliavin regularity of the initial condition. To this end we employ anticipating calculus techniques

A passive-active dynamic insulation system for all climates

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An Option Pricing Model with Memory

We obtain option pricing formulas for stock price models in which the drift and volatility terms are functionals of a continuous history of the stock prices. That is, the stock dynamics follows a nonlinear stochastic functional differential equation. A model with full memory is obtained via approximation through a stock price model in which the continuous path dependence does not go up to the present: there is a memory gap. A strong solution is obtained by closing the gap. Fair option prices are obtained through an equivalent (local) martingale measure via Girsanov's Theorem and therefore are given in terms of a conditional expectation. The models maintain the completeness of the market and have no arbitrage opportunities

ANALYSIS OF ENGINE CHARACTERISTICS AND EMISSIONS FUELED BY IN-SITU MIXING OF SMALL AMOUNT OF HYDROGEN IN COMPRESSED NATURAL GAS

The use of gaseous fuels in internal combustion engines has long been observed as a possible method of reducing emissions while maintaining engine performance and efficiency. Most of the research interests is focused on the use of compressed natural gas as alternative fuel, mainly due to its wide availability, high thermal efficiency and lower exhaust emissions compared to other hydrocarbon fuels. But compressed natural gas has the penalty of slow burning velocity and poor lean burn ability. One effective way to solve this problem is to mix the compressed natural gas with a fuel that possesses the high burning velocity. Hydrogen is the best additive candidate to natural gas due to its unique characteristics in promoting flame propagation speed, which stabilizes the combustion process. This research investigated the engine characteristics and emissions of a CNG-DI engine fueled by low levels of hydrogen enrichment (lower than 10%) in CNG utilizing an in-situ mixing system. Prior to the main experiment, two pre-experiments were conducted to determine the best and most suitable parameters for optimization of engine performance, combustion as well as emissions. The first experiment was to determine the suitable injector type to be used, and it was found that the wide cone angle injector of 70o was better for the applications. The second experiment was to determine the suitable injection timing, and it was discovered that the earlier injection timing was the best for this work. In this research, the engine used was a 4-stroke single cylinder, with a swept volume of 399.25 cc and a compression ratio of 14:1. The injection timing was set to 300o crank angle before top dead center as determined in the pre-experiment; the engine speed from 2000 to 4000 rpm and the spark timing for all the operating conditions were set to maximum brake torque. All the experiments were conducted at full load and relative air-fuel ratio λ =1.0. The injection pressure was fixed at 14 bar for all the cases. The findings revealed that the brake torque, brake power and brake mean effective pressure increased with the increase of hydrogen fraction at low and medium engine speeds. The brake specific energy consumption decreased and brake thermal efficiency increased with the increase of hydrogen percentage. In general, significant changes have been observed with the engine characteristics at low engine speed but the rate of increase/decrease of the parameters decreased was less significant with the addition of higher percentages of hydrogen as well as with the increase in engine speeds. For all the cases, the cylinder pressure and the heat release rate increased while the flame developement and rapid combustion duration decreased with the increase in the amount of hydrogen in the blends. The phenomenon was more obvious at the low engine speed, suggesting that the effect of hydrogen addition in the enhancement of burning velocity plays more important role at relatively low cylinder air motion. Exhaust THC, CO and CO2 concentrations decreased with the increase of hydrogen fraction due to the increase in hydrogen to carbon ratio (H/C). However, the variation in the NOx emissions was found to be negligible with the addition of hydrogen

Improving Building Fabric Energy Efficiency in Hot-Humid Climates using Dynamic Insulation

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