Emergence of steady and oscillatory localized structures in a phytoplankton-nutrient model

Co-limitation of marine phytoplankton growth by light and nutrient, both of which are essential for phytoplankton, leads to complex dynamic behavior and a wide array of coherent patterns. The building blocks of this array can be considered to be deep chlorophyll maxima, or DCMs, which are structures localized in a finite depth interior to the water column. From an ecological point of view, DCMs are evocative of a balance between the inflow of light from the water surface and of nutrients from the sediment. From a (linear) bifurcational point of view, they appear through a transcritical bifurcation in which the trivial, no-plankton steady state is destabilized. This article is devoted to the analytic investigation of the weakly nonlinear dynamics of these DCM patterns, and it has two overarching themes. The first of these concerns the fate of the destabilizing stationary DCM mode beyond the center manifold regime. Exploiting the natural singularly perturbed nature of the model, we derive an explicit reduced model of asymptotically high dimension which fully captures these dynamics. Our subsequent and fully detailed study of this model - which involves a subtle asymptotic analysis necessarily transgressing the boundaries of a local center manifold reduction - establishes that a stable DCM pattern indeed appears from a transcritical bifurcation. However, we also deduce that asymptotically close to the original destabilization, the DCM looses its stability in a secondary bifurcation of Hopf type. This is in agreement with indications from numerical simulations available in the literature. Employing the same methods, we also identify a much larger DCM pattern. The development of the method underpinning this work - which, we expect, shall prove useful for a larger class of models - forms the second theme of this article

A nonlocal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates

We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray-Scott system, the hypercycle Eigen and Schuster, angiogenesis, and the generalized Gierer-Meinhardt system. We give some sufficient and explicit conditions for stability by studying the corresponding nonlocal eigenvalue problem in a new range of parameters

Child Maltreatment in Families Receiving Mandatory Versus Voluntary Child Protection Support:A Matched Cohort Study

Child safety is an important outcome of child protection services (CPSs); however, this is often assessed in terms of official registries (e.g., rereports). Little empirical evidence is available about how the frequency of child maltreatment changes during CPS intervention by using self-report measures. The present study evaluates the frequency of child maltreatment experienced by children receiving mandatory child protection support compared to carefully matched children receiving voluntary child protection support. The current study is part of an ongoing Dutch longitudinal study on family violence consisting of several cohorts with similar designs. Both parents and children reported on the frequency of child maltreatment using validated questionnaires at two timepoints, 12 months apart. To facilitate careful comparison, both groups were matched using propensity scores based on background variables, resulting in two groups of N = 178 children. GLMM analyses showed a significant decrease in the mean number of child maltreatment incidents over time in the total group. However, this decrease did not differ for children receiving mandatory and voluntary child protection support. The findings indicate that, despite possible motivational challenges in the mandatory group, mandatory child protection support elicits comparable results as voluntary support. Implications for further research and practice are discussed.</p

Child Maltreatment in Families Receiving Mandatory Versus Voluntary Child Protection Support:A Matched Cohort Study

Child safety is an important outcome of child protection services (CPSs); however, this is often assessed in terms of official registries (e.g., rereports). Little empirical evidence is available about how the frequency of child maltreatment changes during CPS intervention by using self-report measures. The present study evaluates the frequency of child maltreatment experienced by children receiving mandatory child protection support compared to carefully matched children receiving voluntary child protection support. The current study is part of an ongoing Dutch longitudinal study on family violence consisting of several cohorts with similar designs. Both parents and children reported on the frequency of child maltreatment using validated questionnaires at two timepoints, 12 months apart. To facilitate careful comparison, both groups were matched using propensity scores based on background variables, resulting in two groups of N = 178 children. GLMM analyses showed a significant decrease in the mean number of child maltreatment incidents over time in the total group. However, this decrease did not differ for children receiving mandatory and voluntary child protection support. The findings indicate that, despite possible motivational challenges in the mandatory group, mandatory child protection support elicits comparable results as voluntary support. Implications for further research and practice are discussed.</p

Existence and stability of hole solutions to complex Ginzburg-Landau equations

We consider the existence and stability of the hole, or dark soliton, solution to a Ginzburg-Landau perturbation of the defocusing nonlinear Schroedinger equation (NLS), and to the nearly real complex Ginzburg-Landau equation (CGL). By using dynamical systems techniques, it is shown that the dark soliton can persist as either a regular perturbation or a singular perturbation of that which exists for the NLS. When considering the stability of the soliton, a major difficulty which must be overcome is that eigenvalues may bifurcate out of the continuous spectrum, i.e., an edge bifurcation may occur. Since the continuous spectrum for the NLS covers the imaginary axis, and since for the CGL it touches the origin, such a bifurcation may lead to an unstable wave. An additional important consideration is that an edge bifurcation can happen even if there are no eigenvalues embedded in the continuous spectrum. Building on and refining ideas first presented in Kapitula and Sandstede (Physica D, 1998) and Kapitula (SIAM J. Math. Anal., 1999), we show that when the wave persists as a regular perturbation, at most three eigenvalues will bifurcate out of the continuous spectrum. Furthermore, we precisely track these bifurcating eigenvalues, and thus are able to give conditions for which the perturbed wave will be stable. For the NLS the results are an improvement and refinement of previous work, while the results for the CGL are new. The techniques presented are very general and are therefore applicable to a much larger class of problems than those considered here.Comment: 41 pages, 4 figures, submitte

From future diets to dishes: communicating dietary shift associated with a 1.5°C scenario for Brazil, China, Sweden and the United Kingdom

Introduction: With the pressing need to mitigate greenhouse gas emissions, this study aims to simplify complex data from Integrated Assessment Models (IAMs). It focuses on identifying dietary shifts that align with the 1.5°C global warming limit as stipulated by the Paris Agreement. Methods: The research utilises the IMAGE Integrated Assessment Model and applies the Diets, Dishes, Dish Ingredients (DDDI) communication framework. This methodology enables the visualisation of potential dietary and dish composition changes, thereby making the data more comprehensible to a broader audience. Results: The study effectively translates traditional IAM outputs into accessible visualisations. These visual tools provide a nuanced understanding of a low greenhouse gas diet, extending its relevance beyond academia to include professionals in diet and nutrition. Discussion: This research stands as a significant advancement in the field, lowering the barrier to understanding sustainable diets for the future. It enriches the existing dialogue on dietary change and climate goals and serves as a catalyst for further research and practical applications in diverse contexts

Phase Slips and the Eckhaus Instability

We consider the Ginzburg-Landau equation, $\partial_t u= \partial_x^2 u + u - u|u|^2$, with complex amplitude $u(x,t)$. We first analyze the phenomenon of phase slips as a consequence of the {\it local} shape of $u$. We next prove a {\it global} theorem about evolution from an Eckhaus unstable state, all the way to the limiting stable finite state, for periodic perturbations of Eckhaus unstable periodic initial data. Equipped with these results, we proceed to prove the corresponding phenomena for the fourth order Swift-Hohenberg equation, of which the Ginzburg-Landau equation is the amplitude approximation. This sheds light on how one should deal with local and global aspects of phase slips for this and many other similar systems.Comment: 22 pages, Postscript, A

The role of peatland degradation, protection and restoration for climate change mitigation in the SSP scenarios

Peatlands only cover a small fraction of the global land surface (∼3%) but store large amounts of carbon (∼600 GtC). Drainage of peatlands for agriculture results in the decomposition of organic matter, leading to greenhouse gas (GHG) emissions. As a result, degraded peatlands are currently responsible for 2%–3% of global anthropogenic emissions. Preventing further degradation of peatlands and restoration (i.e. rewetting) are therefore important for climate change mitigation. In this study, we show that land-use change in three SSP scenarios with optimistic, recent trends, and pessimistic assumptions leads to peatland degradation between 2020 and 2100 ranging from −7 to +10 Mha (−23% to +32%), and a continuation or even an increase in annual GHG emissions (−0.1 to +0.4 GtCO2-eq yr−1). In default mitigation scenarios without a specific focus on peatlands, peatland degradation is reduced due to synergies with forest protection and afforestation policies. However, this still leaves large amounts of GHG emissions from degraded peatlands unabated, causing cumulative CO2 emissions from 2020 to 2100 in an SSP2-1.5 °C scenario of 73 GtCO2. In a mitigation scenario with dedicated peatland restoration policy, GHG emissions from degraded peatlands can be reduced to nearly zero without major effects on projected land-use dynamics. This underlines the opportunity of peatland protection and restoration for climate change mitigation and the need to synergistically combine different land-based mitigation measures. Peatland location and extent estimates vary widely in the literature; a sensitivity analysis implementing various spatial estimates shows that especially in tropical regions degraded peatland area and peatland emissions are highly uncertain. The required protection and mitigation efforts are geographically unequally distributed, with large concentrations of peatlands in Russia, Europe, North America and Indonesia (33% of emission reductions are located in Indonesia). This indicates an important role for only a few countries that have the opportunity to protect and restore peatlands with global benefits for climate change mitigation