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In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative effects and are obtained from the free boundary problems formulated in the works of Dias, Dyachenko, and Zakharov [Phys. Lett. A, 372 (2008), pp. 1297--1302], Jiang et al. [J. Fluid Mech., 329 (1996), pp. 275--307], and Wu, Liu and Yue [J. Fluid Mech., 556 (2006), pp. 45--54]. ; The work of the second author was supported by the Basque Government through the BERC 2018-2021 program and by Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2017-0718 and through project MTM2017-82184-R funded by (AEI/FEDER, UE) and acronym "DESFLU."

Mathematical models are now a popular tool in many applications such as physics, economics and engineering; and provide useful information for decision making and planning. Water pollution in Malaysia has reached a level that needs attention and intervention from environmental department and government. In order to make a strong case, this paper has done a study on measuring the pollution level of Sungai Pinang which is located in Penang Island, Malaysia. Advection-Dispersion equation is one of the mathematical models that often use in evaluating the level of water pollution in the river. This paper applies this model and compares the result of this study with the studies done in the previous research worldwide to evaluate the severity of the pollution. The authors hope that this paper will create awareness to relevant department and also to community in general

In view of the complexity and uncertainty of water resources, this paper chooses an evaluation index system of 13 indicators based on the fuzzy mathematics model in three aspects: water resources, water quality and socioeconomic status. The entropy method was used to determine the weight of the index, and the water resource value of Nanjing in 2011&ndash ; 2015 was dynamically evaluated. The results show that the price of water resources in Nanjing from 2011 to 2015 rose from 3.43 yuan/m3 to 5.94 yuan/m3, showing a clear upward trend, but the corresponding price of water expenditure accounted for a proportion of disposable income from 2.27% to 1.87% during the same time period. This counterfactual trend proves that the current water price in Nanjing is relatively low and is not conducive to the efficient use of water resources. Given the fact that water prices have larger room for growth, the city government could initiate the reform of water pricing system and re-enact the water fee collection standards to achieve optimal allocation of water resources and sustainable development.

Three open source wave models are applied in 2DV to reproduce a large-scale wave flume experiment of bichromatic wave transformations over a steep-sloped dike with a mildly-sloped and very shallow foreshore: (i) the Reynolds-averaged Navier–Stokes equations solver interFoam of OpenFOAM® (OF), (ii) the weakly compressible smoothed particle hydrodynamics model DualSPHysics (DSPH) and (iii) the non-hydrostatic nonlinear shallow water equations model SWASH. An inter-model comparison is performed to determine the (standalone) applicability of the three models for this specific case, which requires the simulation of many processes simultaneously, including wave transformations over the foreshore and wave-structure interactions with the dike, promenade and vertical wall. A qualitative comparison is done based on the time series of the measured quantities along the wave flume, and snapshots of bore interactions on the promenade and impacts on the vertical wall. In addition, model performance and pattern statistics are employed to quantify the model differences. The results show that overall, OF provides the highest model skill, but has the highest computational cost. DSPH is shown to have a reduced model performance, but still comparable to OF and for a lower computational cost. Even though SWASH is a much more simplified model than both OF and DSPH, it is shown to provide very similar results: SWASH exhibits an equal capability to estimate the maximum quasi-static horizontal impact force with the highest computational efficiency, but does have an important model performance decrease compared to OF and DSPH for the force impulse. ; This research was part of the CREST (Climate REsilient CoaST) project (http://www.crestproject.be/en), funded by the Flemish Agency for Innovation by Science and Technology, grant number 150028. The work described in this section was supported by the European Community′s Horizon 2020 Research and Innovation Programme through the grant to HYDRALABPLUS, Contract no. 654110. C.A. acknowledges funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie, grant number 792370. ; Peer Reviewed ; Postprint (published version)

A variational method of mathematical modeling of seismic wave kinematics has been developed at the Department of Seismometry and Geoacoustics of the Faculty of Geology of Lomonosov Moscow State University for studying the kinematics of seismic waves of different types in two-dimensional isotropic media (gradient and layered) is presented. The problem of determining the trajectories of seismic rays was solved by integrating using the Runge-Kutta method a system of differential equations with given initial conditions. The algorithm was studied in order to verify the accuracy and correctness of the solutions obtained, as well as its testing on a number of theoretical models of heterogeneous media. The developed ray tracing method was used to study the effect of the velocity gradient and the geometry of seismic boundaries on the kinematics of reflected waves in multilayer media. Based on the results of mathematical modeling of the kinematics of reflected waves, conclusions were drawn about the limits of applicability of simplified models of horizontally layered media, which often approximate complex inhomogeneous media.