Energy Balance Research Articles

Scaling laws and exact results in turbulence *

In this note, we address the validity of certain exact results from turbulence theory in the deterministic setting. The main tools, inspired by the work of Duchon and Robert (2000 Nonlinearity 13 249–55) and Eyink (2003 Nonlinearity 16 137), are a number of energy balance identities for weak solutions of the incompressible Euler and Navier–Stokes equations. As a consequence, we show that certain weak solutions of the Euler and Navier–Stokes equations satisfy deterministic versions of Kolmogorov’s 45 , 43 , 415 laws. We apply these computations to improve a recent result of Hofmanova et al (2023 arXiv:2304.14470), which shows that a construction of solutions of forced Navier–Stokes due to Bruè et al (2023 Commun. Pure Appl. Anal.) and exhibiting a form of anomalous dissipation satisfies asymptotic versions of Kolmogorov’s laws. In addition, we show that the globally dissipative 3D Euler flows recently constructed by Giri et al (2023 arXiv:2305.18509) satisfy the local versions of Kolmogorov’s laws.

GSDME promotes MASLD by regulating pyroptosis, Drp1 citrullination-dependent mitochondrial dynamic, and energy balance in intestine and liver.

Dysregulated metabolism, cell death, and inflammation contribute to the development of metabolic dysfunction-associated steatohepatitis (MASH). Pyroptosis, a recently identified form of programmed cell death, is closely linked to inflammation. However, the precise role of pyroptosis, particularly gasdermin-E (GSDME), in MASH development remains unknown. In this study, we observed GSDME cleavage and GSDME-associated interleukin-1β (IL-1β)/IL-18 induction in liver tissues of MASH patients and MASH mouse models induced by a choline-deficient high-fat diet (CDHFD) or a high-fat/high-cholesterol diet (HFHC). Compared with wild-type mice, global GSDME knockout mice exhibited reduced liver steatosis, steatohepatitis, fibrosis, endoplasmic reticulum stress, lipotoxicity and mitochondrial dysfunction in CDHFD- or HFHC-induced MASH models. Moreover, GSDME knockout resulted in increased energy expenditure, inhibited intestinal nutrient absorption, and reduced body weight. In the mice with GSDME deficiency, reintroduction of GSDME in myeloid cells-rather than hepatocytes-mimicked the MASH pathologies and metabolic dysfunctions, as well as the changes in the formation of neutrophil extracellular traps and hepatic macrophage/monocyte subclusters. These subclusters included shifts in Tim4+ or CD163+ resident Kupffer cells, Ly6Chi pro-inflammatory monocytes, and Ly6CloCCR2loCX3CR1hi patrolling monocytes. Integrated analyses of RNA sequencing and quantitative proteomics revealed a significant GSDME-dependent reduction in citrullination at the arginine-114 (R114) site of dynamin-related protein 1 (Drp1) during MASH. Mutation of Drp1 at R114 reduced its stability, impaired its ability to redistribute to mitochondria and regulate mitophagy, and ultimately promoted its degradation under MASH stress. GSDME deficiency reversed the de-citrullination of Drp1R114, preserved Drp1 stability, and enhanced mitochondrial function. Our study highlights the role of GSDME in promoting MASH through regulating pyroptosis, Drp1 citrullination-dependent mitochondrial function, and energy balance in the intestine and liver, and suggests that GSDME may be a potential therapeutic target for managing MASH.

Optimization of iron electrocoagulation parameters for enhanced turbidity and chemical oxygen demand removal from laundry greywater

This study explores the optimization of iron electrocoagulation for treating laundry greywater, which accounts for up to 38% of domestic greywater. Characterized by high concentrations of surfactants, detergents, and suspended solids, laundry greywater presents complex challenges for treatment processes, posing significant environmental and health risks. Utilizing response surface methodology (RSM), this research developed a second-order polynomial regression model focused on key operational parameters such as the area-to-volume ratio (A/V), current density, electrolysis time, and settling time. Optimal treatment conditions were identified: an A/V ratio of 30 m2/m3, a current density of 10 mA/cm2, an electrolysis duration of 50 min, and a settlement period of 12 h. Under these conditions, exceptional treatment outcomes were achieved, with turbidity removal reaching 94.26% and COD removal at 99.64%. The model exhibited high effectiveness for turbidity removal, with an R2 value of 94.16%, and moderate effectiveness for COD removal, with an R2 value of 75.90%. The interaction between the A/V ratio and electrolysis time particularly underscored their critical role in electrocoagulation system design. Moreover, these results highlight the potential for optimizing electrocoagulation parameters to adapt to daily fluctuations in greywater production and meet specific household reuse needs, such as toilet flushing. This tailored approach aims to maximize contaminant separation and coagulant efficiency, balance energy use and operational costs, and contribute to sustainable water management.

Obesity- and diet-induced plasticity in systems that control eating and energy balance.

In April 2023, the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK), in partnership with the National Institute of Child Health and Human Development, the National Institute on Aging, and the Office of Behavioral and Social Sciences Research, hosted a 2-day online workshop to discuss neural plasticity in energy homeostasis and obesity. The goal was to provide a broad view of current knowledge while identifying research questions and challenges regarding neural systems that control food intake and energy balance. This review includes highlights from the meeting and is intended both to introduce unfamiliar audiences with concepts central to energy homeostasis, feeding, and obesity and to highlight up-and-coming research in these areas that may be of special interest to those with a background in these fields. The overarching theme of this review addresses plasticity within the central and peripheral nervous systems that regulates and influences eating, emphasizing distinctions between healthy and disease states. This is by no means a comprehensive review because this is a broad and rapidly developing area. However, we have pointed out relevant reviews and primary articles throughout, as well as gaps in current understanding and opportunities for developments in the field.

Development and Testing of Small-Scale Flash Dryer for Maize Bran

Sun drying is the most common technique used to dry various food products due to its economic convenience. However, it is not effective owing to its unreliable nature leading to microbial deterioration and aflatoxin contamination of food. In Tanzania, about 1.3 million tonnes of maize bran are at risk of deterioration annually due to improper drying. The aim of this study was to design, fabricate and test an efficient small-scale flash dryer for maize bran. Using principles of material and energy balance, a small-scale flash dryer with a throughput of 500 kg of dry product per hour was designed resulting in a nominal diameter of 387 mm and a drying length of 20 m. Design calculations and drawings were done using MS Excel 2021 and SolidWorks 2018 respectively. Empirical procedures were used to fabricate and test the dryer. The material of construction used in the flash duct was food grade (stainless steel, SS 201). A fuel blend of Waste Engine Oil (WEO) and diesel (85%-15%) was used with a novel heavy oil burner. It was observed that at an inlet air temperature of 150 °C and air velocity of 12 m/s, moist maize bran was dried from 37% to 10% w.b. The fabricated flash dryer's energy efficiency, specific energy consumption, and specific energy utilization are 74%, 3.4 MJ/kg water evaporated, and 1.71 MJ/kg dry maize bran respectively. It was concluded that the fabricated small-scale flash dryer displayed improved energy performance compared to others presented in literature. Better instrumentation was recommended for feedback control on burner operation and process monitoring which further enhances the performance of the fabricated small-scale flash dryer.

Determination of Energy Losses of the Crank Press Mechanism

This paper focuses on determining the friction energy loss in the mechanism of a mechanical crank press. After defining the crank press mechanism and how it works, we describe the energy balance of a technological operation—forming. Four distinct methodologies for calculating friction loss in the mechanism are then presented, namely an empirical method, a spreadsheet calculation utilising force decomposition in a crank mechanism, an analytical calculation of the dynamic behaviour of a press, and a multibody simulation. Each additional approach expands the possibilities for approaching reality, but as the primary aim of the study is to compare the approaches, these possibilities are not exploited. Multibody simulation has proved itself to be accurate and suitable for simulating press mechanisms and investigating their dynamics. Multibody simulation is a much more powerful tool that can lead to a digital twin, which can help us to develop a less energy-demanding press. Confirmation of the multibody simulation results is the main outcome of the comparison and will be used in future work.

Precision modelling of leaf area index for enhanced surface temperature partitioning and improved evapotranspiration estimation

Remote Sensing-based two-source model is widely used to estimate crop evapotranspiration (ET), involving one key step of partitioning land surface temperature (LST) into canopy and soil temperatures (Tc and Ts). Leaf area index (LAI) plays a significant part in available energy allocation during this process. However, the asymptotic saturation problem makes the mismatch between vegetation index and LAI. In this study, two-stage LAI models were developed through the red-edge chlorophyll index (CIred-edge) considering the hysteresis between them. Considering the distinct characteristics, modeling LAI by one-degree linear equations for sunflower (C3), linear and exponential functions for maize (C4) were presented in the distinguished grow-up and senescence periods. The two-source energy balance (TSEB) and hybrid dual-source scheme and trapezoid framework-based evapotranspiration (HTEM) models were selected to estimate Tc, Ts, ET, and its components contrastively. The established LAI models and other modified parameters were then integrated into the two models to improve the estimation of Tc, Ts, and ET (named the R-TSEB and R-HTEM models, respectively). Results demonstrated that the partitioned Tc & Ts became closer to the measurements after utilizing the presented LAI models. For daily ET, the R-TSEB and R-HTEM models alleviated the overestimation and underestimation existing in the original two models, respectively. At monthly and seasonal scales compared to the water balance results (ETwb), the ET of R-TSEB model had significant promotion, including the determination coefficient (R2), mean relative error (RE), root mean square error (RMSE), and model agreement index (d) with values of 0.87, 6.54%, 11.65 mm, and 0.95, from the according values of 0.80, 12.85%, 17.60 mm, and 0.90 for the TSEB model, respectively. The estimated ET by the R-HTEM model was more consistent with ETwb than the HTEM model. These results indicate that the established LAI models can enhance ET estimation and further advance water cycle understanding.

The Multifaceted Interactions of Dictyostelium Atg1 with Mitochondrial Function, Endocytosis, Growth, and Development

Autophagy is a degradative recycling process central to the maintenance of homeostasis in all eukaryotes. By ensuring the degradation of damaged mitochondria, it plays a key role in maintaining mitochondrial health and function. Of the highly conserved autophagy proteins, autophagy-related protein 1 (Atg1) is essential to the process. The involvement of these proteins in intracellular signalling pathways, including those involving mitochondrial function, are still being elucidated. Here the role of Atg1 was investigated in the simple model organism Dictyostelium discoideum using an atg1 null mutant and mutants overexpressing or antisense-inhibiting atg1. When evaluated against the well-characterised outcomes of mitochondrial dysfunction in this model, altered atg1 expression resulted in an unconventional set of phenotypic outcomes in growth, endocytosis, multicellular development, and mitochondrial homeostasis. The findings here show that Atg1 is involved in a tightly regulated signal transduction pathway coordinating energy-consuming processes such as cell growth and multicellular development, along with nutrient status and energy production. Furthermore, Atg1’s effects on energy homeostasis indicate a peripheral ancillary role in the mitochondrial signalling network, with effects on energy balance rather than direct effects on electron transport chain function. Further research is required to tease out these complex networks. Nevertheless, this study adds further evidence to the theory that autophagy and mitochondrial signalling are not opposing but rather linked, yet strictly controlled, homeostatic mechanisms.

Techno economic and life cycle assessment of olefin production through CO2 hydrogenation within the power-to-X concept

The paper deals with exhaustive process modelling, techno-economic and life cycle assessment (TEA/LCA) of olefin (ethylene and propylene) production through captured CO2 and electrolytic hydrogen. Olefins are important building block chemicals with several applications and carbon capture and utilisation (CCU) can provide a sustainable production route. The proposed system involves direct air capture (DAC) of CO2; proton exchange membrane (PEM) water electrolysis for hydrogen production, methanol synthesis, methanol to olefins (MTO) upgrade, and power generation from off-shore wind turbines. This study proposes a new integrated process as the first attempt to holistically assess a whole CCU assembly aiming at olefins production. Processing modelling has been implemented using the Aspen plus V12.1 and MATLAB R2022a software to solve the mass and energy balances of each unit operation. The modelling results showed a carbon efficiency of 72.3% to ethylene and propylene. In addition, the process is designed and integrated in such a way that no external heat supply is required. A specific energy consumption (SEC) of 150 MJ/kg olefins (41 kWh/kg) has been estimated. A minimum selling price of £3.67 per kg of olefins is required for the proposed process to break-even. The sensitivity analysis has revealed that the major cost driver is the cost of electricity. In addition, the life cycle assessment (LCA) has exposed that the proposed synthesis route of olefins has the potential to reduce the global warming potential (GWP) by 47% compared to fossil - based production. The outcomes of this study can be beneficial to engineering conceptual studies, policy makers and contribute new information to the CCU academic community.

High-throughput physiological phenotyping of crop evapotranspiration at the plot scale

ContextPlatforms and instrumentation for Field High-Throughput Plant Phenotyping (FHTPP) are well developed to measure important traits for crop breeding and agronomic studies. However, the research has focused on morphological and spectral traits; and approaches to estimate major physiological processes such as evapotranspiration (ET) for small experimental plots are lacking. ObjectiveIn this study, we put forward a new analytical framework to estimate plot-scale ET by integrating frequent phenotyping data (multispectral and thermal infrared images, canopy reflectance, and LiDAR point clouds) from a FHTPP system (known as NU-Spidercam), the weather data, a simplified two-source energy balance model, and reference ET and crop coefficient calculation. MethodsThe new plot-scale ET method was tested on five field experiments involving maize and soybean crops over two growing seasons, with the different treatment levels of irrigation water. Estimated plot-scale ET was accumulated across the growing reason for each plot, and its association with grain yield was investigated with regression analysis. ResultsThe result showed that plot-scale accumulated ET captured the seasonal trend of plot water use and clearly differentiated the irrigation treatments. Strong linear correlations were observed between plot-scale ET and grain yield, with R2 values ranging from 0.35 to 0.93 (average R2 = 0.71). Plot-scale ET appeared to be a more steady and stronger predictor of grain yield across the seasons than several other morphological and spectral traits including crop height, green pixel fraction, canopy temperature depression, and red-edge normalized difference vegetation index. ConclusionHigh spatial and temporal resolution of the field phenotyping data, along with the new analytical framework reported, successfully estimated ET at small plot scale, which is difficult to achieve with other systems or methods. SignificancesOur work of estimating ET at the plot-scale can be adopt to other ground-based platforms and drones, thus empowers physiologists, breeders, and agronomists for high-throughput phenotyping of water-use related traits and drought response evaluation.

Numerical and Experimental Determination of Selected Performance Indicators of the Liquid Flat-Plate Solar Collector under Outdoor Conditions

The paper proposes applying an in-house mathematical model of a liquid flat-plate solar collector to calculate the collector time constant. The described model, proposed for the first time in an earlier study, is a one-dimensional distributed parameter model enabling simulations of the collector operation under arbitrarily variable boundary conditions. The model is based on the solution of energy balance equations for all collector components. The formulated differential equations are solved iteratively using an implicit difference scheme. To obtain a stable numerical solution, it is necessary to use appropriate steps of time and spatial division. These were found by comparing the results obtained from the model with the results of the analytical solution available in the literature for the transient state, which constitutes the novelty of the present study. The accuracy of the results obtained from the model was verified experimentally by comparing the measured and calculated history of the fluid temperature at the outlet of the collector. The calculation of the collector time constant is proposed in the paper as an example of the model’s practical application. The results of the time constant calculation were compared with the values obtained experimentally on the test stand. This is another novelty of the presented research. The analysed collector instantaneous efficiency was then calculated for selected outdoor conditions. The presented mathematical model can also be used to verify the correctness of the collector operation. By comparing, on an ongoing basis, the measured and calculated values of the fluid temperature at the collector outlet, conclusions can be drawn about the process of solar glass fouling or glycol gelling. The simplicity of the model and the low computational demands enable such comparisons in an online mode.

Gestational bisphenol A exposure alters energy homeostasis and adult hypothalamic neurogenesis in female mice

Regulation of physiological homeostasis, including energy balance, is thought to be modified by low levels of adult neurogenesis in the hypothalamus. Hormones such as oestradiol can influence both embryonic and adult hypothalamic neurogenic programs, demonstrating a sensitivity of hypothalamic neural progenitor cells to endogenous hormones. Previously we showed that gestational exposure to environmental levels of the xenoestrogen bisphenol A (BPA) changed neural progenitor cell behaviors in the embryo; however, we did not examine if these changes were permanent to affect adult neurogenesis. Here we investigated whether adult neuro- and/or gliogenesis were altered in mice prenatally exposed to BPA and placed on a high-fat diet challenge. Gestationally exposed adult female mice on a standard diet gained less weight than non-BPA controls, whereas gestationally exposed BPA females on a high-fat diet gained more weight than controls. Males exposed to gestational BPA showed no differences in weight gain relative to control males. Concomitantly, adult neurogenesis was increased in the VMH, DMH, and PVN of adult female mice exposed to BPA on standard diet, suggesting that disrupted adult neurogenesis might perturb normal energy balance regulation in females. These results add to growing evidence that low-dose BPA exposure in utero causes changes to adult hypothalamic function.

Spatio-Temporal Behavior of Land Surface Temperatures (LSTs) in Central Chile, Using Terra MODIS Images

Land surface temperature (LST) is one of the most important variables in the physical processes of surface energy and water balance. The temporal behavior of LST was analyzed between the latitudes 32°00′ S and 34°24′ S (Valparaíso and Metropolitana regions of Chile) for three summer months (December, January, and February) in the 2000–2017 period, using the Terra MODIS image information and applying the Mann–Kendall test. The results show an increase in LST in the study area, particularly in the Andes mountain range in January (5240 km2), which mainly comprises areas devoid of vegetation and eternal snow and glaciers, and are zones that act as water reserves for the capital city of Santiago. Similarly, vegetated areas such as forests, grasslands, and shrublands also show increasing trends in LST but over smaller surfaces. Because this study is regional, it is recommended to improve the spatial and temporal resolutions of the images to obtain conclusions on more local scales.

A multi-stage techno-economic model for harnessing flexibility from IoT-enabled appliances and smart charging systems: Developing a competitive local flexibility market using Stackelberg game theory

The increasing integration of renewable energy sources with power systems has led to greater uncertainties, heightening the need for more flexible services. Demand-side resources can provide significant flexibility cost-effectively, making it crucial to design new business models to harness their flexible capacities. Hence, this paper introduces a three-stage techno-economic framework designed to enhance the exploitation of flexible capacities from demand-side resources such as Internet-of-Things (IoT)-Enabled Appliances (IEAs), Battery-Integrated Rooftop Solar Panels (BIRSPs), and Electric Vehicle (EV) smart charging systems in the local flexibility market. The proposed framework operates in three stages. First, smart homes with IEAs, BIRSPs, and smart charging systems assess their flexibility and report it to their Microgrid (MG) operators. Next, MG operators optimize strategies to maximize market returns and report capacities to the Distribution System Operator (DSO). Finally, the DSO manages flexibility transactions based on MG inputs. A Stackelberg game theory model using a gradient-based method updates the coupling variables between market parties, ensuring convergence in the second and third stages within a decentralized space with limited information sharing. Implemented on a modified IEEE 69-node distribution system, the model fully utilizes the potential of smart homes, including IEAs, BIRSPs, and smart charging systems in the local flexibility market. It reduces the Upstream Network (UN) share in the local flexibility market by 56.86% and decreases DSO costs for energy balancing by 22.36%.

27-Hydroxycholesterol acts on estrogen receptor α expressed by POMC neurons in the arcuate nucleus to modulate feeding behavior.

Oxysterols are metabolites of cholesterol that regulate cholesterol homeostasis. Among these, the most abundant oxysterol is 27-hydroxycholesterol (27HC), which can cross the blood-brain barrier. Because 27HC functions as an endogenous selective estrogen receptor modulator, we hypothesize that 27HC binds to the estrogen receptor α (ERα) in the brain to regulate energy balance. Supporting this view, we found that delivering 27HC to the brain reduced food intake and activated proopiomelanocortin (POMC) neurons in the arcuate nucleus of the hypothalamus (POMCARH) in an ERα-dependent manner. In addition, we observed that inhibiting brain ERα, deleting ERα in POMC neurons, or chemogenetic inhibition of POMCARH neurons blocked the anorexigenic effects of 27HC. Mechanistically, we further revealed that 27HC stimulates POMCARH neurons by inhibiting the small conductance of the calcium-activated potassium (SK) channel. Together, our findings suggest that 27HC, through its interaction with ERα and modulation of the SK channel, inhibits food intake as a negative feedback mechanism against a surge in circulating cholesterol.

Activation of AMPD2 drives metabolic dysregulation and liver disease in mice with hereditary fructose intolerance

Hereditary fructose intolerance (HFI) is a painful and potentially lethal genetic disease caused by a mutation in aldolase B resulting in accumulation of fructose-1-phosphate (F1P). No cure exists for HFI and treatment is limited to avoid exposure to fructose and sugar. Using aldolase B deficient mice, here we identify a yet unrecognized metabolic event activated in HFI and associated with the progression of the disease. Besides the accumulation of F1P, here we show that the activation of the purine degradation pathway is a common feature in aldolase B deficient mice exposed to fructose. The purine degradation pathway is a metabolic route initiated by adenosine monophosphate deaminase 2 (AMPD2) that regulates overall energy balance. We demonstrate that very low amounts of fructose are sufficient to activate AMPD2 in these mice via a phosphate trap. While blocking AMPD2 do not impact F1P accumulation and the risk of hypoglycemia, its deletion in hepatocytes markedly improves the metabolic dysregulation induced by fructose and corrects fat and glycogen storage while significantly increasing the voluntary tolerance of these mice to fructose. In summary, we provide evidence for a critical pathway activated in HFI that could be targeted to improve the metabolic consequences associated with fructose consumption.

Unveiling the energetic complexity of noncovalent interactions in halogenated dimers

AbstractThe understanding of noncovalent interactions is crucial in explaining critical phenomena such as self‐assembly, chemical reactivity, and crystallization. This work examines the energetic diversity of conformations and local minima for several halogenated dimers, represented as R‐X (R = H, F, CH3, CF3; X = Cl, Br, I). Thousands of configurations are randomly generated and refined through geometric optimizations to yield a diverse set of molecular conformers. Frequency calculations were performed for all optimized conformers to confirm that they are local minima. The noncovalent interactions in optimized dimers of halogen‐containing molecules were analyzed with atom in molecules (AIM) method and symmetry‐adapted perturbation theory (SAPT). Additionally, a protocol for generating machine learning models to recover accurate predictions of the physically meaningful SAPT energy components with minor computational cost is presented. These results deepen our understanding of the intricate energy balance and dedicated equilibrium of different noncovalent interactions in halogenated dimers.

Investments in Fixed Capital of the Oil and Gas Region as an Indicator of Its Readiness for the Financial Embargo and Transformation of the Global Energy Balance

Investments in Fixed Capital of the Oil and Gas Region as an Indicator of Its Readiness for the Financial Embargo and Transformation of the Global Energy Balance

Decomposing the effective radiative forcing of anthropogenic aerosols based on CMIP6 Earth system models

Abstract. Anthropogenic aerosols play a major role in the Earth–atmosphere system by influencing the Earth's radiative budget and precipitation and consequently the climate. The perturbation induced by changes in anthropogenic aerosols on the Earth's energy balance is quantified in terms of the effective radiative forcing (ERF). In this work, the present-day shortwave (SW), longwave (LW), and total (i.e., SW plus LW) ERF of anthropogenic aerosols is quantified using two different sets of experiments with prescribed sea surface temperatures (SSTs) from Earth system models (ESMs) participating in the Coupled Model Intercomparison Project Phase 6 (CMIP6): (a) time-slice pre-industrial perturbation simulations with fixed SSTs (piClim) and (b) transient historical simulations with time-evolving SSTs (histSST) over the historical period (1850–2014). ERF is decomposed into three components for both piClim and histSST experiments: (a) ERFARI, representing aerosol–radiation interactions; (b) ERFACI, accounting for aerosol–cloud interactions (including the semi-direct effect); and (c) ERFALB, which is due to temperature, humidity, and surface albedo changes caused by anthropogenic aerosols. We present spatial patterns at the top-of-atmosphere (TOA) and global weighted field means along with inter-model variability (1 standard deviation) for all SW, LW, and total ERF components (ERFARI, ERFACI, and ERFALB) and for every experiment used in this study. Moreover, the inter-model agreement and the robustness of our results are assessed using a comprehensive method as utilized in the IPCC Sixth Assessment Report. Based on piClim experiments, the total present-day (2014) ERF from anthropogenic aerosol and precursor emissions is estimated to be −1.11 ± 0.26 W m−2, mostly due to the large contribution of ERFACI to the global mean and to the inter-model variability. Based on the histSST experiments for the present-day period (1995–2014), similar results are derived, with a global mean total aerosol ERF of −1.28 ± 0.37 W m−2 and dominating contributions from ERFACI. The spatial patterns for total ERF and its components are similar in both the piClim and histSST experiments. Furthermore, implementing a novel approach to determine geographically the driving factor of ERF, we show that ERFACI dominates over the largest part of the Earth and that ERFALB dominates mainly over the poles, while ERFARI dominates over certain reflective surfaces. Analysis of the inter-model variability in total aerosol ERF shows that SW ERFACI is the main source of uncertainty predominantly over land regions with significant changes in aerosol optical depth (AOD), with eastern Asia contributing mostly to the inter-model spread of both ERFARI and ERFACI. The global spatial patterns of total ERF and its components from individual aerosol species, such as sulfates, organic carbon (OC), and black carbon (BC), are also calculated based on piClim experiments. The total ERF caused by sulfates (piClim-SO2) is estimated at −1.11 ± 0.31 W m−2, and the OC ERF (piClim-OC) is −0.35 ± 0.21 W m−2, while the ERF due to BC (piClim-BC) is 0.19 ± 0.18 W m−2. For sulfates and OC perturbation experiments, ERFACI dominates over the globe, whereas for BC perturbation experiments ERFARI dominates over land in the Northern Hemisphere and especially in the Arctic. Generally, sulfates dominate ERF spatial patterns, exerting a strongly negative ERF especially over industrialized regions of the Northern Hemisphere (NH), such as North America, Europe, and eastern and southern Asia. Our analysis of the temporal evolution of ERF over the historical period (1850–2014) reveals that ERFACI clearly dominates over ERFARI and ERFALB for driving the total ERF temporal evolution. Moreover, since the mid-1980s, total ERF has become less negative over eastern North America and western and central Europe, while over eastern and southern Asia there is a steady increase in ERF magnitude towards more negative values until 2014.

How to design optimal brain stimulation to modulate phase-amplitude coupling?

Objective. Phase-amplitude coupling (PAC), the coupling of the amplitude of a faster brain rhythm to the phase of a slower brain rhythm, plays a significant role in brain activity and has been implicated in various neurological disorders. For example, in Parkinson’s disease, PAC between the beta (13–30 Hz) and gamma (30–100 Hz) rhythms in the motor cortex is exaggerated, while in Alzheimer’s disease, PAC between the theta (4–8 Hz) and gamma rhythms is diminished. Modulating PAC (i.e. reducing or enhancing PAC) using brain stimulation could therefore open new therapeutic avenues. However, while it has been previously reported that phase-locked stimulation can increase PAC, it is unclear what the optimal stimulation strategy to modulate PAC might be. Here, we provide a theoretical framework to narrow down the experimental optimisation of stimulation aimed at modulating PAC, which would otherwise rely on trial and error. Approach. We make analytical predictions using a Stuart–Landau model, and confirm these predictions in a more realistic model of coupled neural populations. Main results. Our framework specifies the critical Fourier coefficients of the stimulation waveform which should be tuned to optimally modulate PAC. Depending on the characteristics of the amplitude response curve of the fast population, these components may include the slow frequency, the fast frequency, combinations of these, as well as their harmonics. We also show that the optimal balance of energy between these Fourier components depends on the relative strength of the endogenous slow and fast rhythms, and that the alignment of fast components with the fast rhythm should change throughout the slow cycle. Furthermore, we identify the conditions requiring to phase-lock stimulation to the fast and/or slow rhythms. Significance. Together, our theoretical framework lays the foundation for guiding the development of innovative and more effective brain stimulation aimed at modulating PAC for therapeutic benefit.