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Sediment plumes generated by seafloor mining vehicles represent a major environmental concern in polymetallic nodule harvesting operations. This study investigates plume dispersion induced by sediment disturbances during mining using numerical simulations based on the similarity principle. A representative mining region is modeled, and the motion of mining vehicles is simulated to define the sediment disturbance source. The simulations employ the experimentally validated P-T Euler model (Particle–Turbulence Interaction Euler model) to examine the effects of sediment release velocity and ambient current velocity on plume dispersion characteristics. The results show that increasing the sediment release velocity primarily enhances the initial turbidity flux and significantly expands the plume core diffusion range, indicating that mining disturbances dominate near-field plume behavior. In contrast, the ambient current velocity strongly controls plume morphology and transport, promoting upward transport, long-range advection, and enhanced turbulent dissipation that governs far-field dispersion. Overall, plume diffusion is initially controlled by mining-induced sediment release but becomes increasingly dominated by ambient flow during large-scale transport. These findings provide a theoretical basis for predicting sediment plume behavior and assessing potential environmental impacts in deep-sea mining areas.

Using the implicit Euler and Milstein approximation schemes, the conditions for the pathwise convergence rate of these approximations to the solution of the fractional SDEs with stochastic forcing are found.

In this paper, we focus on fractional stochastic differential equations (FSDEs) with a stochastic forcing term, i.e., to FSDE, we add a stochastic forcing term. Using the implicit scheme of Euler’s approximation, the conditions for the existence and uniqueness of the solution of FSDEs with a stochastic forcing term are established. Such equations can be applied to considering FSDEs with a permeable wall.

We characterize the time-series properties of group-level consumption, income, and interest rates using microdata. We relate the coefficients of moving average representations to structural parameters of theoretical models of consumption behavior. Using long time series of cross sections to construct synthetic panel data for the United Kingdom, we find that for high-educated individuals the Euler equation restrictions are not rejected, the elasticity of intertemporal substitution is higher than one, and there is evidence of \"excess smoothness\" of consumption. Low-educated individuals, conversely, exhibit excess sensitivity of consumption to past income, and the elasticity of intertemporal substitution is not statistically different from zero.

In this paper, we improve the Navier–Stokes flow solver developed by Sun et al. based on the spectral volume method (SV) in the following two aspects: the development of a more efficient implicit/p-multigrid solution approach, and the use of a new viscous flux formula. An implicit preconditioned LU-SGS p-multigrid method developed for the spectral difference (SD) Euler solver by Liang is adopted here. In the original SV solver, the viscous flux was computed with a local discontinuous Galerkin (LDG) type approach. In this study, an interior penalty approach is developed and tested for both the Laplace and Navier–Stokes equations. In addition, the second method of Bassi and Rebay (also known as BR2 approach) is also implemented in the SV context, and also tested. Their convergence properties are studied with the implicit BLU-SGS approach. Fourier analysis revealed some interesting advantages for the penalty method over the LDG method. A convergence speedup of up to 2-3 orders is obtained with the implicit method. The convergence was further enhanced by employing a p-multigrid algorithm. Numerical simulations were performed using all the three viscous flux formulations and were compared with existing high order simulations (or in some cases, analytical solutions). The penalty and the BR2 approaches displayed higher accuracy than the LDG approach. In general, the numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.

Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where some of the coefficients are nonzero using classical multivariate statistics evaluated at each point. The problem is to find the P-value of the maximum of such a random field of test statistics. We approximate this by the expected Euler characteristic of the excursion set. Our main result is a very simple method for calculating this, which not only gives us the previous result of Cao and Worsley [Ann. Statist. 27 (1999) 925-942] for Hotelling's T², but also random fields of Roy's maximum root, maximum canonical correlations [Ann. Appl. Probab. 9 (1999) 1021-1057], multilinear forms [Ann. Statist. 29 (2001) 328-371], $\\overline{\\chi}^{2}$ [Statist. Probab. Lett 32 (1997) 367-376, Ann. Statist. 25 (1997) 2368-2387] and χ² scale space [Adv. in Appl. Probab. 33 (2001) 773-793]. The trick involves approaching the problem from the point of view of Roy's union-intersection principle. The results are applied to a problem in shape analysis where we look for brain damage due to nonmissile trauma.

The purpose of this paper is to test for the presence of habit formation in consumption decisions using household panel data. We apply the test proposed by Meghir and Weber (1996) to a Spanish panel data set in which households are observed for up to eight consecutive quarters. This temporal dimension is crucial, because it allows us to take into account time invariant unobserved heterogeneity across households ('fixed effects') and, therefore, to investigate whether the relationship between current and past consumption reflects habits or heterogeneity. Our results confirm the importance of accounting for fixed effects when analysing intertemporal consumption decisions allowing for time non-separabilities.

We study vesicles formed by lipid bilayers that are governed by an elastic bending energy and on which the lipids laterally separate forming two different phases. The energy laden phase interfaces may be modeled as curves on the hypersurface representing the membrane (sharp interface model). The phase field methodology is another powerful tool to model such phase separation phenomena where thin layers describe the interfaces (diffuse interface model). For both approaches we characterize equilibrium shapes in terms of the Euler-Lagrange equations of the total membrane energy subject to constraints on the area of the two phases and the volume. We further show by matching appropriate formal asymptotic expansions that the sharp interface model is obtained from the diffuse interface model as the thickness of the phase interface tends to zero. The essential challenge lies in the fact that also the geometry of the membrane is unknown and depends on a small parameter representing the interface thickness.

Our problem is to find a good approximation to the P-value of the maximum of a random field of test statistics for a cone alternative at each point in a sample of Gaussian random fields. These test statistics have been proposed in the neuroscience literature for the analysis of fMRI data allowing for unknown delay in the hemodynamic response. However the null distribution of the maximum of this 3D random field of test statistics, and hence the threshold used to detect brain activation, was unsolved. To find a solution, we approximate the P-value by the expected Euler characteristic (EC) of the excursion set of the test statistic random field. Our main result is the required EC density, derived using the Gaussian Kinematic Formula.

We briefly describe an advanced 3D gas dynamical model developed for the simulation of theenvironment of active cometary nuclei. The model canhandle realistic nucleus shapes and alternative physical models for the gas and dust production mechanism.The inner gas coma structure is computed by solving self-consistently(a) near to the surface the Boltzman Equation(b) outside of it, Euler or Navier-Stokes equations.The dust distribution is computed from multifluid ``zero-temperature'' Euler equations,extrapolated with the help of a Keplerian fountain model.The evolution of the coma during the nucleus orbital and spin motion,is computed as a succession of quasi-steady solutions. Earlier versions of the model using simple,``paedagogic'' nuclei have demonstrated that the surface orographyand the surface inhomogeneity contribute similarly to structuring the near-nucleusgas and dust coma,casting a shadow on the automatic attribution of such structures to ``active areas''.The model was recently applied to comet P/Halley, for whichthe nucleus shape is available. In the companion paper of this volume,we show that most near-nucleus dust structuresobserved during the 1986 Halley flybys are reproduced, assuming that the nucleus is strictly homogeneous. Here, we investigate the effect of shape perturbations and homogeneityperturbations. We show that the near nucleus gas coma structure is robust vis-a-vissuch effects. In particular, a random distribution of active and inactive areaswould not affect considerably this structure, suggesting that such areas,even if present, could not be easily identified on images of the coma.