Minimum Energy Research Articles

Efficient quantum mechanical minimum free energy path calculation by combining path integral hybrid Monte Carlo and climbing image nudged elastic band methods, and its application to the addition reaction of hydrogen isocyanide to formaldehyde.

We propose an efficient algorithm for a minimum free energy path calculation based on the path integral hybrid Monte Carlo (PIHMC) method by combining the climbing image-nudged elastic band (CI-NEB) and the thermodynamic integration (TI) methods. Here, the CI-NEB and the TI methods are used to find a transition state along the reaction path and evaluate the free energy path, respectively. Our algorithm is applied to the Walden inversion reaction of the hydronium ions (H3O+). The numerical results show that the computational effort by our algorithm is significantly reduced compared to that of the previously proposed algorithm combining PIHMC without losing accuracy. We also demonstrate the importance of temperature and isotope effects on the addition reaction of hydrogen isocyanide to formaldehyde. In this reaction, the nuclear quantum effect causes the structural change at the TS and decreases the energy barrier.

Simulation of light environments inside lunar holes and their associated subsurface caverns

Vertical holes of several tens of meters in diameter and depth have been discovered on the Moon, potentially serving as skylights into subsurface volcanic caverns resembling lava tubes. Because of their scientific importance and potential for use as future lunar bases, these lunar holes and caverns are expected to be targets of intensive exploration in the near future. Using numerical simulations, this study investigates the light environment within a directly and/or indirectly sunlit subsurface cavern accessed through a skylight hole. We specifically analyze the Mare Tranquillitatis Hole (MTH), one of the largest lunar vertical holes, situated near the Moon's nearside meridian. The floor and walls of the hole, and the walls and ceiling of its associated subsurface cavern are lit by reflected sunlight from other parts of the hole and cavern, such as the floors, depending on the solar elevation angle. Furthermore, this paper presents estimation results for camera imaging for a case in which solar elevation angle is 45° in the morning, which is appropriate timing for exploration. Assuming reflectance of 0.1 for the lunar hole and cavern surfaces, we estimate the incident energy onto each pixel of a camera as it descends to the hole's floor. We specifically simulate conditions for a camera with a 12-bit dynamic range, similar to the wide-angle optical navigation camera (ONC-W) onboard the Hayabusa 2 spacecraft. The results suggest that a camera with a fixed gain would struggle to capture both directly and indirectly sunlit areas simultaneously, without saturating bright areas and ensuring minimum incident energy resolution (say, a 10 digital number) for darker areas. To overcome this challenge, adjusting the camera gain based on the hole's and cavern's illumination conditions is necessary.Graphical abstract

A Reformulated-Vortex-Particle-Method-Based Aerodynamic Multi-Objective Design Optimization Strategy for Proprotor in Hover and High-Altitude Cruise

An improved multi-objective design optimization framework is proposed for the efficient design of proprotor blades tailored to specific high-altitude mission requirements. This framework builds upon existing methods by leveraging a reformulated Vortex Particle Method (rVPM) and incorporates three key stages: (1) rapid determination of overall proprotor parameters using a semi-empirical model, (2) optimized blade chord and twist distribution bounds based on minimum energy loss theory, and (3) global optimization with a high-fidelity rVPM-based aerodynamic solver coupled with a multi-objective hybrid optimization algorithm. Applied to a small high-altitude tiltrotor, the framework produced Pareto-optimal proprotor designs with a figure of merit of 0.814 and cruise efficiency of 0.896, exceeding mission targets by over 15%. Key findings indicate that large taper ratios and low twist improve hover performance, while elliptical blade planforms with high twist enhance cruise efficiency, and a tip anhedral further boosts overall performance. This framework streamlines the industrial customization of proprotor blades, significantly reducing the design space for advanced optimization while improving performance in demanding high-altitude environments.

Bridging One Health: Computational design of a multi-epitope messenger RNA vaccine for cross-species immunization against Nipah virus

Background and Aim: Nipah virus (NiV) poses a threat to human and animal health, particularly swine, which serve as primary vectors for human transmission. Despite its severe risks, no NiV vaccine currently exists for humans or animal hosts; thus, innovative vaccine development approaches that address cross-species transmission are required. This study was computationally designed to evaluate a multi-epitope messenger RNA (mRNA) vaccine targeting NiV for human and swine immunization. Materials and Methods: B and T lymphocyte epitopes were identified from NiV structural proteins using multiple epitope prediction tools. All epitopes were linked to form a multi-epitope construct, and various adjuvant combinations were analyzed for physicochemical properties and immune simulation. Molecular docking and dynamics were employed to visualize the construct’s interaction with a host immune receptor. Signal peptides were added to the construct, and mRNA sequences were generated using LinearDesign. The minimum free energies (MFEs) and codon adaptation indices (CAI) were used to select the final mRNA sequence of the vaccine construct. Results: Computational tools predicted 10 epitopes within NiV structural proteins that can be recognized by human and swine immune receptors. The construct with β-defensin 2 adjuvant was selected as the final immunogenic region after showing favorable immunogenicity profiles and physicochemical properties. The final vaccine sequence had higher MFE and CAI compared to the BioNTech/Pfizer BNT162b2 and Moderna mRNA-1273 vaccines. Conclusion: The multi-epitope mRNA vaccine designed in this study shows promising results as a potential NiV vaccine candidate. Further in vivo and in vitro studies are required to confirm the efficacy. Keywords: computational design, cross-species immunization, messenger RNA vaccine, multi-epitope, Nipah virus.

Synthesis, spectroscopic, computational, topology, and molecular docking studies on N,N'-(4-methyl-1,3-phenylene)bis(1-(2,4-dichlorophenyl)methanimine)

The study extensively examined N,N'-(4-methyl-1,3-phenylene)bis(1-(2,4-dichlorophenyl)methanimine) (6D). Advanced spectroscopic techniques, including IR, Raman, NMR, and UV-VIS spectroscopies, were employed to analyse the molecule. The Schiff base was ultimately confirmed using NMR spectrum analysis. The UV-VIS study revealed a notable bathochromic change in the compound, indicating their electronic transitions. By using the HOMO–LUMO bond gap the titled compound reactivity sites were identified. The compound 6D HOMO–LUMO band gap is 3.70 eV. Various wave function investigations like MESP, HOMO–LUMO, RDG, ELF, LOL, and ALIE were conducted to elucidate the distribution of electronic charge, providing valuable insights into the behaviour of molecules. The biological probability of the synthesised compound was extensively assessed using a docking study. Using MEP and HOMO–LUMO investigations, we confirm nucleophilic and electrophilic attacking sites. In the docking study, the protein Bovine cytochrome bc1 complex stigma Tellin bound (PDB ID–1PP9) was downloaded. The docking study identified the most stable minimum binding energy is –6.26 kcal/mol.

(Ph3P)4C4P4: Effect of substitution on the Oligomerization of carbon phosphide radicals

AbstractDehalogenation of (PBr)2C2(PPh3)2 with potassium graphite, KC8, leads to Cs‐P4C4(PPh3)4, which can be viewed as a PPh3 adduct of a Cs‐symmetric P4C4 cage. An isolable intermediate was found and in combination with DFT calculations, the structure of a S4‐symmetric P4C4(PPh3)4 cage is proposed for this species. That a 1,3‐diphosphete type Ph3P→P2C2←PPh3 heterocycle is a short‐lived intermediate in the dehalogenation reaction is indicated by trapping experiments which allowed to isolate and fully characterize the [Fe(CO)4] complexes [Fe(CO)4(κ‐P−P2C2{PPh3}2] and [(Fe(CO)4)2(μ2‐κ‐P−P2C2{PPh3}2]. The conversion of S4‐P4C4(PPh3)4 to Cs‐P4C4(PPh3)4 prompted a (re)investigation of the isomerization of various P4X4 species (X=S, NH, NMe; CH2), which shows that these proceed on Minimum Energy Reaction Pathways (MERPs) with two transition states embracing one intermediate. In contrast, the isomerization S4‐P4C4(PR3)4 to Cs‐P4C4(PR3)4 is a one‐step process.

An Extensive Computational Investigation of Mycobacterium tuberculosis Pantothenate Synthetase Inhibitors from Diverse‐Lib Compounds Library

AbstractAntibiotics have played a crucial role in significantly reducing the incidence of tuberculosis (TB) infection worldwide. Even before the mid‐20th century, the mortality rate of TB onset within five years was around 50 %. So, the introduction of antibiotics has changed the scenario of TB from a serious threat to a manageable one. However, the emergence of resistance to anti‐TB drugs poses a significant challenge. So, to overcome this situation the therapeutic approaches and drug targets need to be reformed. This study focused on finding potential inhibitors by targeting Pantothenate Synthetase, a crucial enzyme for Mycobacterium tuberculosis (Mtb) survival, through computational drug discovery methods. Molecular docking and virtual screening were employed to identify potential inhibitors from Diverse‐lib. Four compounds, namely CID2813602, 24357538, CID753354, and CID4798023, exhibited strong binding energies and stable interaction with the target protein. Further assessment of these compounds through MD simulation and Post MD simulation showed significant dynamic stability. The minimum energy transition calculated using the free energy landscape analysis of these compounds when docked with Pantothenate Synthetase confirmed the stability of each complex due to its minimum energy production. The free binding energy calculation of each complex also showed the intramolecular interaction contributes to the strong binding affinity of the compounds within the enzyme's active site clarifying their mechanisms of action. This research showcases the effectiveness of computational methods in promptly identifying potential anti‐TB drugs, paving the way for future experimental validation and optimization. It holds promise for the development of new treatments targeting drug‐resistant TB strains.

Gain-based Green Ant Colony Optimization for 3D Path Planning on Remote Sensing Images

Metaheuristic algorithms are powerful methods for handling complexities in 3D environments because of their adaptability property. This paper proposes a gain-based, green-ant colony optimization (GGACO) method for 3D path planning on remote sensing images. Shortest paths do not always imply minimum energy consumption. Moreover, computational complexity tends to increase in the case of higher-dimensional data. A novel method is proposed to alleviate this issue, one that provides an efficient path with minimum energy consumption by adding a gain quantity during its search. The results are validated using performance measures, viz., path length, time, and energy cost. Real-time images, along with their corresponding ground truth and “digital surface models (DSM)”, have been sourced from the “International Society for Photogrammetry and Remote Sensing (ISPRS)”. Comparisons have been made against state-of-the-art algorithms and analyzed. Finally, the convergence and stability of the proposed method have been verified; it has been found that the proposed method outperforms the existing method by 6%, 11% and 5% regarding length, computation time, and energy, respectively.

Rethinking max-min planning on energy-efficient software-defined networking for 5G networks.

Energy efficiency plays an important role in intelligent networking for 5G networks, which concerns environmental, financial, and performance aspects of intelligent networking for 5G networks. To this end, network designers propose energy-efficient approaches to reduce energy consumption of networks and to raise network performance by switching off the links/nodes with low loads or at idle status. The existing energy-efficient approaches can be formulated as a max-min optimal problem, namely maximizing network/node/port throughput via minimum energy consumption. The max-min planning investigates energy efficiency only from the links/nodes perspective. The max-min planning for energy-efficient networking, if not carefully designed from the network-wide standpoint, can lead to lower energy efficiency for the whole network due to lack of global planning, which in turn results in the degraded performance due to network un-connectivity after closing the nodes/links. In this paper we rethink the max-min planning framework on energy-efficient software-defined networking for intelligent networking of 5G networks, which takes in account combining network connectivity and maximum network flow with minimum energy consumption. Our framework aims at how to deliver dynamic end-to-end traffic demands with the appropriate network topology by building data forwarding plane with maximum network flow and control plane with network connectivity. We discuss the associated challenges and implementation issues. A dynamic max-min planning framework depending on dynamic end-to-end traffic demands is presented to achieve network-wide energy efficiency. Numerical results show the improved energy efficiency performance for the whole network.

Investigation of the Minimum Ignition Energy Required for Combustion of Coal Dust Blended with Fugitive Methane

Ventilation Air Methane (VAM) significantly contributes to global warming. Capturing and mitigating these emissions can help combat climate change. One effective method is the thermal decomposition of methane, but it requires careful control to prevent explosions from the high temperatures involved. This research investigates the influence of methane concentration and coal dust particle properties on the minimum ignition energy (MIE) required for fugitive methane thermal decomposition and flame propagation properties. This knowledge is crucial for the mining industry to effectively prevent and mitigate accidental fires and explosions in VAM abatement plants. Coal dust samples from three different sources were selected for this study. Experiments were conducted using a modified Hartmann glass tube and a Thermal Gravimetric Analyser (TGA). The chemical properties of coal dust were determined through ultimate and proximate analysis. The particle size distribution was determined using a Mastersizer 3000 apparatus (manufactured by Malvern Panalytical, Malvern, UK). The results showed that the MIE is significantly affected by coal dust particle size, with smaller particles (<74 µm) requiring less energy to ignite compared to coarser particles. Additionally, blending methane with coal dust further reduces the MIE. Introducing methane concentrations of 1% and 2.5% into the combustion space reduced the MIE by 25% and 74%, respectively, for the <74 µm coal dust size fraction. It was observed that coal dust concentration can either raise or lower the MIE. Larger coal dust concentrations, acting as a heat sink, reduce the likelihood of ignition and increase the MIE. This effect was noted at a methane concentration of 2.5% and coal dust levels above 3000 g/m3. In contrast, small amounts of coal dust had little impact on MIE variation. Moreover, the presence of methane during combustion increased the upward flame travel distance and propagation velocity. The flame’s vertical travel distance increased from 124 mm to 300 mm for a coal dust concentration of 300 g·m−3 blended with 1% and 2.5% methane, respectively.

Data-driven computation of adjoint sensitivities without adjoint solvers: An application to thermoacoustics

Adjoint methods have been the pillar of gradient-based optimization for decades. They enable the accurate computation of a gradient (sensitivity) of a quantity of interest with respect to all system parameters in one calculation. When the gradient is embedded in an optimization routine, the quantity of interest can be optimized for the system to have the desired behavior. Adjoint methods, however, require the system's governing equations and their Jacobian. In this paper, we propose a computational strategy to infer the adjoint sensitivities from data when the governing equations might be unknown (or partly unknown), and noise might be present. The key component of this strategy is an echo state network, which learns the dynamics of nonlinear regimes with varying parameters, and it evolves dynamically via a hidden state. Although the framework does not make assumptions on the dynamical system, we focus on thermoacoustics, which are governed by nonlinear and time-delayed systems. First, we show that a parameter-aware echo state network (ESN) infers the parametrized dynamics. Second, we derive the adjoint of the ESN to compute two types of sensitivity: (i) parameter sensitivity, which is the gradient of a time-averaged cost functional with respect to physical or design parameters of the system, and (ii) initial condition sensitivity, which is the gradient of a cost functional of the final state with respect to the initial condition. Third, we propose the thermoacoustic echo state network (T-ESN), which embeds the physical knowledge in the network architecture for improved generalization. Fourth, we apply the framework to a variety of nonlinear thermoacoustic regimes of a prototypical system. We show that the T-ESN accurately infers the correct adjoint sensitivities of the acoustic energy with respect to the flame parameters and initial conditions. The results are robust to noisy data, from periodic, through quasiperiodic, to chaotic regimes. The inferred adjoint sensitivities are employed to suppress an instability via steepest descent. We show that a single network predicts the nonlinear bifurcations on unseen scenarios, which allows it to converge to the minimum of the acoustic energy. This work opens new possibilities for gradient-based data-driven design optimization. Published by the American Physical Society 2024

Quantum Chemical Model Calculations of Adhesion and Dissociation between Epoxy Resin and Si-Containing Molecules

There is no doubt that when solid surfaces are modified, the functional groups and atoms directly bonded to solid atoms play a major role in adsorption interactions with molecules or resins. In this study, the adhesion and dissociation between epoxy resin and molecules containing Si atoms were analyzed. The analysis, conducted in contact with the solid surface of silicon, utilized quantum chemical calculations based on a molecular model. We compared some Si-containing molecular models to test quantum chemical calculations that contribute to the study of adhesion and dissociation between epoxy resins and solid surfaces somehow other than simple potential energy curve calculations. The AFIR (artificial force induced reaction) method, implemented in the GRRM (global reaction route mapping) program, was employed to separate an epoxy resin model molecule and three types of silicon compounds (Si(CH3)2(OH)2, Si(CH3)4, and (CH3)2SiF2) in three directions, determining their minimum dissociation energy when changing the applied energy by 2.5 kJ/mol. In systems with weak hydrogen bonds, such as Si(CH3)4 or (CH3)2SiF2, the energy required for dissociation was not large; however, in systems with strong hydrogen bonds, such as Si(CH3)2(OH)2, dissociation was more difficult in the vertical direction. Although anisotropy due to hydroxyl groups was calculated in the horizontal direction, dissociation remained relatively easy.

6-Methoxyflavone improves anxiety, depression, and memory by increasing monoamines in mice brain: HPLC analysis and in silico studies

Abstract 6-Methoxyflavone (6-MOF) is a flavonoid that has been reported to be a GABA-A receptor agonist and reverses cisplatin-induced hyperalgesia and allodynia. Considering the varied neuropharmacological profile of 6-MOF, this study was intended to determine the pharmacological effects of 6-MOF on locomotion, anxiety, novel object recognition (NOR), depression, spatial memory, socialization behavior, nest-building behavior, and depression in various groups of mice. Selected groups of mice were injected with 25, 50, and 75 mg/kg 6-MOF. Using HPLC-UV, the frontal cortex, striatum, and hippocampus of the sacrificed mice were analyzed for the levels of vitamin C, dopamine, serotonin, noradrenaline, adenosine, and its metabolites. Statistical analysis showed significant results in socialization behavior and elevated plus maze with 75 mg/kg. In Y-maze, NOR 6-MOF showed significant results at all three doses, while in tail suspension test (TST), 50 and 75 mg/kg showed significant results; however, no statistical significance was observed in nest-building behavior; 50 and 75 mg/kg 6-MOF showed significant results in the Morris water maze. 6-MOF raised vitamin C levels in the frontal cortex and hippocampus. Serotonin, dopamine, and nor-adrenaline levels were raised in the hippocampus and striatum. It has also imparted region-specific neuroprotection by improving adenosine and its metabolite levels. In silico studies performed using PyRx have shown that the minimum binding energy of 6-MOF with antioxidant enzyme is −7.1 k/cal/mol. The binding energy showed that 6-MOF was successfully docked with an anti-oxidant enzyme. In conclusion, in silico and behavioral studies showed that 6-MOF can be a potential candidate for the treatment of cognitive decline, anxiety, and depression.

Theoretical aspects of structure, electronic, optical and elastic properties of Ca(1-x)CxSe mixed alloys in binary and ternary phases

The structural, optoelectronic, and elastic properties of Carbon doped Calcium Selenide binary and ternary semiconductor alloys with the general form of Ca(1-x)CxSe, 0 ≤ x ≤ 1 in B1 and B3 phases have been scrutinized adopting augmented plane wave plus local orbital methods within density functional theory applying different approximations like the Local density approximation (LDA), Wu-Cohen-Generalized Gradients Approximation (WC-GGA) and modified Becke-Johnson (mBJ). Structural properties summarize the crystal structure, relevant atomic positions, lattice constant, Bulk modulus B0, minimum energy E0, and minimum volume V0. Elastic constants confirm the structure stability of the B1 and B3 phases. The band gap was modified from a wider for appropriate optoelectronic devices application to narrow that enhanced the range of applicability of these binary and ternary semiconductor compounds for optoelectronic device applications. Whereas optical properties which include the study of zero frequency limit of static dielectric constant ε0(ω) with its real and imaginary parts, static refractive index n(0), optical reflectivity R(ω), optical absorption coefficient α(ω), optical conductivity σ(ω), and loss function L(ω) studied comprehensively to get real electrical and optical properties of these materials and give semiconductor market best alternative candidate which shows its effectiveness in the visible, ultraviolet and infrared region of the electromagnetic spectrum. Obtained results compared together and with the available experimental along with theoretical work on these binary and ternary Carbon-doped Alkaline earth Selenide.

Reentrant Condensation of Polyelectrolytes Induced by Diluted Multivalent Salts: The Role of Electrostatic Gluonic Effects.

We explore the reentrant condensation of polyelectrolytes triggered by multivalent salts, whose phase-transition mechanism remains under debate. We propose a theory to study the reentrant condensation, which separates the electrostatic effect into two parts: a short-range electrostatic gluonic effect because of sharing of multivalent ions by ionic monomers and a long-range electrostatic correlation effect from all ions. The theory suggests that the electrostatic gluonic effect governs reentrant condensation, requiring a minimum coupling energy to initiate the phase transition. This explains why diluted salts with selective multivalency trigger a polyelectrolyte phase transition. The theory also uncovers that strong adsorption of multivalent ions onto ionic monomers causes low-salt concentrations to induce both collapse and reentry transitions. Additionally, we highlight how the incompatibility of uncharged polyelectrolyte moieties with water affects the polyelectrolyte phase behaviors. The obtained results will contribute to the understanding of biological phase separations if multivalent ions bound to biopolyelectrolytes play an essential role.

Estimating reaction barriers with deep reinforcement learning1

Stable states in complex systems correspond to local minima on the associated potential energy surface. Transitions between these local minima govern the dynamics of such systems. Precisely determining the transition pathways in complex and high-dimensional systems is challenging because these transitions are rare events, and isolating the relevant species in experiments is difficult. Most of the time, the system remains near a local minimum, with rare, large fluctuations leading to transitions between minima. The probability of such transitions decreases exponentially with the height of the energy barrier, making the system’s dynamics highly sensitive to the calculated energy barriers. This work aims to formulate the problem of finding the minimum energy barrier between two stable states in the system’s state space as a cost-minimization problem. It is proposed to solve this problem using reinforcement learning algorithms. The exploratory nature of reinforcement learning agents enables efficient sampling and determination of the minimum energy barrier for transitions.

Self-aggregation and microhydration mechanisms of monoethanolamine: Far-infrared identification of large-amplitude hydrogen bond libration.

The strong tendency for self-aggregation together with an intriguing mechanism for the microhydration of monoethanolamine (MEA) have been explored by low-temperature far-infrared cluster spectroscopy in doped neon "quantum" matrices at 4K complemented by high-level quantum chemical modeling. In addition to the assignment of new mid-infrared perturbed intramolecular transitions, a distinct far-infrared transition is unambiguously assigned to the concerted large-amplitude hydrogen bond librational motion of the MEA homodimer. This observation confirms a global "head-to-head" intermolecular potential energy minimum associated with the formation of a compact doubly intermolecular OH⋯N hydrogen-bonded cyclic structure, where both monomeric intramolecular OH⋯N hydrogen bonds are broken upon complexation. By means of relative mixing ratio dependencies, dedicated annealing procedures, and selective complexation between MEA and isotopic H216O and H218O samples, distinct far-infrared transitions associated with large-amplitude intra-molecular hindered OH torsional motion and inter-molecular H2O librational (hindered c-type overall rotational) motion of the MEA monohydrate are furthermore assigned unambiguously for the first time. These spectroscopic observations reveal an intriguing metastable conformation, where H2O acts as a OH⋯O hydrogen bond donor to the hydroxy group instead of the amino group of MEA upon microhydration in the cryogenic neon environment, where the microhydration strengthens the intramolecular OH⋯N hydrogen bond of MEA due to hydrogen bond cooperativity.

Effects of internal intervention in tubes on shock wave attenuation, formation and propagation of flame during high-pressure hydrogen release

Experiments on the impacts of the combination of fin structure and expansion chamber on shock wave attenuation, hydrogen ignition, and flame characteristics during high-pressure hydrogen release were carried out. The fin is a four-edged platform hollowed out on all sides. The inflated upper and lower tube walls are located 85, 95, and 105 mm away from the nickel burst disk. With the incident shock wave traveling through the fin, the reflected shock and the superposition of multiple reflected shock waves appear, and the reflected shock wave intensity can equal that of the release pressure. The decrease of the incident shock wave intensity behind the fin leads to the decrease of the non-uniformity of the mixed layer temperature, further causing the decrease of the flame propagation velocity. The presence of fins increases the probability of ignition in the fin region and the critical release pressure for ignition is significantly lower than that in the barrier free tube, mainly because the fin inside intensifies the hydrogen/air mixture, resulting in a lower minimum ignition energy required for self-ignition. Furthermore, the decrease of flame propagation velocity leads to the increase of hydrogen consumption inside the tube and the decrease of shock overpressure outside.

Understanding public acceptability of climate policies in Europe

ABSTRACT Urgent and decisive government action to mitigate greenhouse gas emissions is more likely when the proposed measures are popular among the public. This paper compares the drivers of European public support for three alternative policies to combat climate change: carbon taxation, renewable energy subsidies, and minimum energy efficiency standards that apply to household appliances. We combine survey data with regional socio-economic and environmental indicators to provide a comprehensive, comparative analysis of policy acceptance that accounts for the geographic context in which these policies would be implemented. By comparing the drivers among three climate policies, we identify a rural-urban gap in predicting public perception of carbon taxation, which does not exist in the other policies. We also found a positive relationship between regional exposure to fine particular matter (PM2.5) and public support for climate policy, providing novel insights into the influence of environmental factors on public perceptions. This research highlights the importance of environmental and socio-economic context in predicting climate policy acceptance and offers valuable implications for policymakers seeking to garner public support for effective climate change mitigation strategies.

New Insight into Quantity-Dependent Self-Assembly Pattern of Light Levitating Droplet Clusters.

It has been reported that the self-assembly pattern of light levitating droplet clusters above the hot gas-liquid interface is dependent on the quantity of droplets. However, the already-reported theoretical explanation of the quantity-dependent self-assembly pattern cannot work well when the quantity of the light levitating droplet exceeds 15. Herein, we propose a new theoretical perspective to understand the self-assembly of a light levitating droplet cluster by referring to the classical densest packing problem of identical rigid circles in a larger circle with the introduction of the minimum total potential energy principle. Amazingly, the theoretical results obtained by this new approach agree well with experimental results, even though the quantity of the light levitating droplet is up to 142. This study deepens our understanding of the quantity-dependent self-assembly pattern of the light levitating droplet clusters and provides significant inspiration for other analogous self-assembly phenomena.