Coastal eutrophication and hypoxia remain a persistent environmental crisis despite the great efforts to reduce nutrient loading and mitigate associated environmental damages. Symptoms of this crisis have appeared to spread rapidly, reaching developing countries in Asia with emergences in Southern America and Africa. The pace of changes and the underlying drivers remain not so clear. To address the gap, we review the up-to-date status and mechanisms of eutrophication and hypoxia in global coastal oceans, upon which we examine the trajectories of changes over the 40 years or longer in six model coastal systems with varying socio-economic development statuses and different levels and histories of eutrophication. Although these coastal systems share common features of eutrophication, site-specific characteristics are also substantial, depending on the regional environmental setting and level of social-economic development along with policy implementation and management. Nevertheless, ecosystem recovery generally needs greater reduction in pressures compared to that initiated degradation and becomes less feasible to achieve past norms with a longer time anthropogenic pressures on the ecosystems. While the qualitative causality between drivers and consequences is well established, quantitative attribution of these drivers to eutrophication and hypoxia remains difficult especially when we consider the social economic drivers because the changes in coastal ecosystems are subject to multiple influences and the cause–effect relationship is often non-linear. Such relationships are further complicated by climate changes that have been accelerating over the past few decades. The knowledge gaps that limit our quantitative and mechanistic understanding of the human-coastal ocean nexus are identified, which is essential for science-based policy making. Recognizing lessons from past management practices, we advocate for a better, more efficient indexing system of coastal eutrophication and an advanced regional earth system modeling framework with optimal modules of human dimensions to facilitate the development and evaluation of effective policy and restoration actions.

Finite element methods developed for unfitted meshes have been widely applied to various interface problems. However, many of them resort to non-conforming spaces for approximation, which is a critical obstacle for the extension to $\textbf{H}(\text{curl})$ equations. This essential issue stems from the underlying Sobolev space $\textbf{H}^s(\text{curl};\,\Omega)$, and even the widely used penalty methodology may not yield the optimal convergence rate. One promising approach to circumvent this issue is to use a conforming test function space, which motivates us to develop a Petrov–Galerkin immersed finite element (PG-IFE) method for $\textbf{H}(\text{curl})$-elliptic interface problems. We establish the Nédélec-type IFE spaces and develop some important properties including their edge degrees of freedom, an exact sequence relating to the $H^1$ IFE space and optimal approximation capabilities. We analyse the inf-sup condition under certain assumptions and show the optimal convergence rate, which is also validated by numerical experiments.

Grain refinement has been applied to enhance the materials strength for miniaturization and lightweight design of nuclear equipment. It is critically important to investigate the low-cycle fatigue (LCF) properties of grain refined 316LN austenitic stainless steels for structural design and safety assessment. In the present work, a series of fine-grained (FG) 316LN steels were produced by thermo-mechanical processes. The LCF properties were studied under a fully reversed strain-controlled mode at room temperature. Results show that FG 316LN steels demonstrate good balance of high strength and high ductility. However, a slight loss of ductility in FG 316LN steel induces a significant deterioration of LCF life. The rapid energy dissipation in FG 316LN steels leads to the reduction of their LCF life. Dislocations develop rapidly in the first stage of cycles, which induces the initial cyclic hardening. The dislocations rearrange to form dislocations cell structure resulting in cyclic softening in the subsequent cyclic deformation. Strain-induced martensite transformation appears in FG 316LN stainless steels at high strain amplitude (Δε/2 = 0.8%), which leads to the secondary cyclic hardening. Moreover, a modified LCF life prediction model for grain refined metals predicts the LCF life of FG 316LN steels well.

A posteriori error estimates of semidiscrete mixed finite element methods for quadratic optimal control problems involving linear parabolic equations are developed. The state and co-state are discretised by Raviart-Thomas mixed finite element spaces of order k, and the control is approximated by piecewise polynomials of order k (k ≥ 0). We derive our a posteriori error estimates for the state and the control approximations via a mixed elliptic reconstruction method. These estimates seem to be unavailable elsewhere in the literature, although they represent an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

This article is to discuss the bilinear and linear immersed finite element (IFE) solutions generated from the algebraic multigrid solver for both stationary and moving interface problems. For the numerical methods based on finite difference formulation and a structured mesh independent of the interface, the stiffness matrix of the linear system is usually not symmetric positive-definite, which demands extra efforts to design efficient multigrid methods. On the other hand, the stiffness matrix arising from the IFE methods are naturally symmetric positive-definite. Hence the IFE-AMG algorithm is proposed to solve the linear systems of the bilinear and linear IFE methods for both stationary and moving interface problems. The numerical examples demonstrate the features of the proposed algorithms, including the optimal convergence in both L2 and semi-H1 norms of the IFE-AMG solutions, the high efficiency with proper choice of the components and parameters of AMG, the influence of the tolerance and the smoother type of AMG on the convergence of the IFE solutions for the interface problems, and the relationship between the cost and the moving interface location.

In this paper, the time-dependent Maxwell’s equations used to modeling wave propagation in dispersive lossy bi-isotropic media are investigated. Existence and uniqueness of the modeling equations are proved. Two fully discrete finite element schemes are proposed, and their practical implementation and stability are discussed.

This article extends the finite element method of lines to a parabolic initial boundary value problem whose diffusion coefficient is discontinuous across an interface that changes with respect to time. The method presented here uses immersed finite element (IFE) functions for the discretization in spatial variables that can be carried out over a fixed mesh (such as a Cartesian mesh if desired), and this feature makes it possible to reduce the parabolic equation to a system of ordinary differential equations (ODE) through the usual semi-discretization procedure. Therefore, with a suitable choice of the ODE solver, this method can reliably and efficiently solve a parabolic moving interface problem over a fixed structured (Cartesian) mesh. Numerical examples are presented to demonstrate features of this new method.

Two experiments were conducted to test the hypothesis that the parallel processing of the target language (TL) during source language (SL) comprehension in interpreting may be influenced by two factors: (i) link strength from SL to TL, and (ii) the interpreter's cognitive resources supplement to TL processing during SL comprehension. The influence of the first factor was supported by the contrasting performance on bidirectional SL and TL interpreting tasks by unbalanced bilingual student interpreters, and the second factor was supported by the contrasting performance between participants’ two developmental stages in interpreting. Implications are discussed.

The authors consider in this paper the inverse problem of finding a pair of functions (u, p) such that

where F, f, E, s, αi, βi, γi, gi, i = 1, 2, are given functions.

The existence and uniqueness of a smooth global solution pair (u, p) which depends continuously upon the data are demonstrated under certain assumptions on the data.

In this paper we study a nonlocal parabolic/elliptic system which models thermistor behaviour in cases where heat losses to the surrounding gas play a significant role. The existence of time periodic solutions for the system is established through Faedo-Galerkin approximations and the Leray–Schauder degree theory. We show that for the small gas pressure case, the temperature of the time periodic solutions is positive. Moreover we consider the long time behaviour of the system and prove the existence of a uniform attractor. Finally, the finite dimensionality of the attractor is discussed.

Quantitative analyses of cross-sectional areas of the thalami, caudate nuclei, and lentiform nuclei were performed in 29 preterm infants (16 males, 13 females; mean age 29.6 weeks, age range 27 to 24 weeks,) with periventricular leukomalacia (PVL). MRI was carried out in the infants between 9 and 18 months of corrected age and in 16 control infants. Bilateral thalami, caudate nuclei, lentiform nuclei, cerebral hemispheres, and cerebellum were measured by computer. Ratios of the areas of the thalami (Th), caudate nuclei (Ca), lentiform nuclei (Le), and cerebral hemispheres (CH) to that of the cerebellum (Ce) were calculated in each infant. The ratio of Th:Ce was significantly smaller in infants with moderate and severe PVL than in the control group bilaterally. Abnormal intensity areas were not observed in the thalami in any infants with PVL. CH:Ce was also smaller in infants with severe PVL than in the control group. No significant difference was observed between the groups in ratios Le:Ce or Ca:Ce. Results of our study suggest that the volume of the thalami is reduced and that thalamic involvement is present in infants with white matter lesions who have moderate to severe PVL.