EXPONENTIAL CONVERGENCE FOR NONLINEAR SPDES WITH DOUBLE REFLECTING WALLS

The present article is devoted to nonlinear stochastic partial differential equations with double reflecting walls driven by possibly degenerate,multiplicative noise.We prove that the corresponding Markov semigroup possesses an exponentially attracting invariant measure through asymptotic coupling,in which Foias-Prodi estimation and the truncation technique are crucial for the realization of the Girsanov transform.

Mathematical Modeling of Moored Ship Motion in Arbitrary Harbor utilizing the Porous Breakwater

The motion of the moored ship in the harbor is a classical hydrodynamics problem that still faces many challenges in naval operations,such as cargo transfer and ship pairings between a big transport ship and some small ships.A mathematical model is presented based on the Laplace equation utilizing the porous breakwater to investigate the moored ship motion in a partially absorbing/reflecting harbor.The motion of the moored ship is described with the hydrodynamic forces along the rotational motion(roll,pitch,and yaw)and translational motion(surge,sway,and heave).The efficiency of the numerical method is verified by comparing it with the analytical study of Yu and Chwang(1994)for the porous breakwater,and the moored ship motion is compared with the theoretical and experimental data obtained by Yoo(1998)and Takagi et al.(1993).Further,the current numerical scheme is implemented on the realistic Visakhapatnam Fishing port,India,in order to analyze the hydrodynamic forces on moored ship motion under resonance conditions.The model incorporates some essential strategies such as adding a porous breakwater and utilizing the wave absorber to reduce the port’s resonance.It has been observed that these tactics have a significant impact on the resonance inside the port for safe maritime navigation.Therefore,the current numerical model provides an efficient tool to reduce the resonance within the arbitrarily shaped ports for secure anchoring.

Simulation of thermal and humid environment of rural residence envelope inner surface during the plum rains season in Changsha China

The Plum Rains Season(PRS)has the typical characteristics of outdoor air temperature dramatic changes and high air humidity in the hot summer and cold winter region in China.Even if the indoor heat source and moisture production is constant,when the outdoor air temperature rises rapidly during high air humidity PRS,the build-ing envelope temperature heats up much more slower than the indoor air temperature and therefore the wall surface temperature is lower than the indoor air dewpoint which leads to condensation phenomenon,resulting in deterioration of insulation performance,mouldy walls,deterioration of indoor air quality.At present,there is a lack of research on the factors affecting condensation in rural residence during PRS.This paper evaluates the impact of occupants’habit of window opening modes and building construction parameters on the building envelope surface condensation in Changsha during PRS.Using Designer’Simulation Toolkit(DeST)simulated and analysed the impact of key parameters such as window-to-wall ratio,exterior wall reflectivity,window opening mode(open/close),and external wall insulation on the building indoor thermal and humid environment.The condensation risk X is proposed to evaluate the condensation possibility on the building envelope’s inner sur-face.The results show that from the perspective of anti-condensation:The rural residential building in Changsha should balance the window-wall ratio against better natural lighting;Keeping windows closed during PRS can effectively alleviate the condensation problem while the insulation in the external wall layer could aggravate the condensation.