Energy Equilibrium Research Articles

Calculation of the energy of a two-dimensional hydrogen molecule

ABSTRACT The equilibrium distance and energies of singlet and triplet states of a two-dimensional (2D) hydrogen molecule are calculated. Variational calculations were carried out using a multiparameter system of Gaussian functions with correlation multipliers. The results are compared with the calculations performed by other authors. Currently, the most accurate values of the singlet and triplet states energy of the 2D-molecule in two-dimensional systems have been obtained: Es = –5.2843Eh , Et = –2.9277Eh ; the equilibrium state corresponds to the distance Rm = 0.36614ao , where Eh is the Hartree energy, and ao is the Bohr radius. In the mathematical sense, a 2D hydrogen molecule is a direct analog of a pair of shallow hydrogen-like paramagnetic centres in covalent two-dimensional crystals. The energies of the singlet and triplet states of 2DH2 are significantly lower than the corresponding values of the three-dimensional hydrogen molecule (3DH2), while the singlet–triplet splitting is much higher than that of 3DH2. In the equilibrium state, 2DH2 protons are much closer to each other, which leads to a significant increase in correlation effects associated with the direct dependence of the wave function on the interelectron distance compared to 3DH2.

Integrated operation of gas and power system through the P2P market mechanism

AbstractPeer‐to‐peer (P2P) energy trading is a new technology for integrating distributed energy resources (DERs) into the power system. A P2P market allows direct energy trading between end‐users, enables local power and energy equilibrium and supports power grid operations. As a common DER, gas‐fired power plants are employed to deal with the intermittency of the power system due to their flexible characteristics. Therefore, the intermittency in the power system transmits to the gas system through the gas‐fired power plants, which makes the operation of these systems even more interdependent and cost‐effective. This paper proposes a market‐based two‐stage framework for the integrated operation of power and natural gas grids taking into account demand response and both network constraints. In the first stage (scheduling stage), the MINLP‐based optimisation approach is used for the optimal scheduling of two energy carriers considering AC power flow and gas hydraulic calculations for the next 24 h. Then, in the second stage, the continuous double auction (CDA)‐based P2P energy trading approach is used for enabling customers to trade energy with each other. To simulate human trader behaviour and maximises the benefits of customers, the authors considered the optimum bidding strategy through the zero intelligent plus trader model. The simulations executed on a 33‐bus power distribution grid and a 33‐node gas network indicate that the proposed framework can dramatically reduce the total operational cost and improve the performance of both networks. Using only the MINLP optimisation problem, first stage, the total operational cost of both networks is reduced by 15.58%, while the voltage profile at the end of the power grid is improved by about 7%. In the next stage, the total operating cost of both networks is further decreased by 29.31% via implementing the P2P energy trading mechanism.

Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic Programming

Most of the published literature regarding bearing capacity are often focused on linear and associative soils. Concerning the intrinsic strength nonlinearity in dilatancy soils, this study investigates the problem of the seismic bearing capacity in the framework of the kinematic theorem of limit analysis. The conventional linear Mohr–Coulomb criterion is substituted with a nonlinear power law criterion to depict the nonlinearity of the soil strength. The non-associative feature of soil materials is considered by defining a nonlinear dilatancy coefficient. A generalized tangential technique is accordingly introduced to linearize the strength envelope for making the nonlinear criterion tractable in the analysis. A non-symmetrical translational failure mechanism that is comprised of several rigid wedges is used to characterize the failure of the foundation at the limit state. Moreover, the seismic action is considered by the classic pseudo-static method. Based upon the energy equilibrium theory of the upper-bound limit analysis, new analytical solutions are derived from the work-balanced equation with nonlinearity and dilatancy. This rigorous upper-bound solution is formulated as a multivariate optimization problem and is readily addressed by sequential quadratic programming (SQP). To verify the reliability of the new expressions, the present results are compared with already posted solutions and the original pseudo-dynamic solutions. The comparative results show a good agreement with previous works, and the correctness and rationality of the new analytical solutions are validated. The detailed parametric study reveals that, in the non-associative flow soils, the ultimate bearing capacity is significantly decreased with a reduction in the dilatancy coefficient. Particularly in the linear condition, namely m = 1, the larger the internal friction angle is, the more obvious the influence of the non-associative feature on the bearing capacity is.

The Effects on Energy Markets of Achieving a 1.5 °C Scenario.

Net zero emission scenarios are aligned with the criteria for the Paris Agreement to keep global warming below 1.5 °C. By soft-linking an energy model with a macroeconomic model, we create a similar pathway to the net zero emission scenario from the International Energy Agency (IEA) to 2050 both of demand for fossil fuels and total CO2 emissions. Soft-linking entails that we insert endogenous variables from one model into the other model. We implement measures such as CO2 taxes, improved energy efficiency, more renewables in electricity production and other sectors, easier substitution between electricity and fossil fuels for final users, and drastically limiting future production of oil, gas and coal. Our conclusion is that net zero is possible by introducing very strict measures, e.g., a high rate of energy efficiency improvement, far above what has been achieved in the past. While our partial equilibrium energy model, similar to the IEA model, overlooks the potential rebound effects, i.e., more energy used by consumers due to lower prices caused by energy efficiency improvement, our macroeconomic model does capture the rebound effects and has to implement stricter supply-side measures to reduce fossil fuel use to achieve the 1.5 °C scenario.

Energy storage systems with distributed generation in power network reconfiguration using improved artificial bee colony algorithm

Recently, the Distributed Generation (DG) structure has become an important aspect of daily planning and has achieved a variety of functions while maximizing the functionality of utilities. It should balance the energy equilibrium of the system components and the production limit. Uncertainties arise during the operation of the DG, represented by generator power, load requirements and fluctuations in electricity prices. The reactive power problem is the major concern associated with the DG system. This paper analyzes both DG and an energy storage system along with their optimal performance using a specific algorithm. For optimal analysis of DG and ESS, an Improved Artificial Bee Colony Algorithm (IABC) is proposed. The IABC evaluates the performance of distribution network. It takes DG and ESS into account for analyzing optimal design problems, the main goal of which is to minimize their reactive power dispersion functions. In addition, there are barriers to reducing the DG’s operating costs. The proposed method is implemented on the MATLAB platform and tested using the IEEE 33-bus system. To confirm the effectiveness of the proposed method, it will be compared with the existing methods such as artificial bee colony (ABC) and levy-based method, respectively.

Bearing capacity of foundations resting on rock masses subjected to Rayleigh waves

This study investigates the ultimate bearing capacity of shallow foundations resting on rock masses under earthquakes using upper-bound limit analysis. A modified pseudodynamic method (MPD) that considers the influence of Rayleigh waves is initially used to characterize the spatiotemporal variation in earthquake acceleration. The strength of rock masses is governed by the generalized Hoek‒Brown criterion and the plastic flow at failure is assumed to respect the associated flow rule. The generalized tangential technique is introduced to provide a linear approximation of the strength envelope for capturing the equivalent Mohr‒Coulomb strength parameters. The classic nonsymmetrical multi-block translational mechanism, which is capable of assessing a rock-foundation system under asymmetrical load, is reconstructed to portray the velocity discontinuity of the plastic failure region. Based upon the energy equilibrium theorem of the limit analysis, an analytical solution of seismic bearing capacity is derived and then formulated as a multivariate optimization problem. Comparisons show good agreement with the literature and validate the correctness and rationality of this work. Parametric study indicates that the seismic foundation capacity obtained by MPD tends to be conservative compared to the pseudostatic method with the same seismic coefficients, and that the period of a Rayleigh wave has only a slight effect on the bearing capacity. The failure region is more sensitive to the disturbance coefficient than it is to the other rock strength parameters.

Internal Explosion Performance of RDX@Nano-B Composite Explosives.

Boron powder is an additive for metalized explosives with great application potential. To improve the energy release ability of boron powder, the composites of RDX and nano-boron (RDX@Nano-B) were prepared by the spray-drying process, and the metalized explosives based on it were designed (named PBX-B1). The detonation heat and explosion pressure of boron-containing explosives PBX-B1 under vacuum and air conditions were measured and analyzed by an internal explosion test. On the other hand, the equilibrium pressure and energy release of the PBX-B1 explosive system after detonation were analyzed and compared with that of an explosive formulation of the same composition (named PBX-B2). Results showed that the detonation heat of PBX-B1 was 7456 J/g in a vacuum environment, which was 34.8% higher than that of RDX (5530 J/g). However, in the air environment, the detonation heat of PBX-B1 increased by 19.2% compared with that in the vacuum environment, and the explosive gas products mainly included N2, NOx, CO, H2O, CH4, HCN, and CO2. The peak pressure and equilibrium pressures of PBX-B1 were 11.2 and 0.42 MPa, which were increased by 155% and 75% compared with the vacuum environment, respectively. It is worth noting that, compared with that of PBX-B2, the released energy in the aerobic combustion stage and equilibrium pressure of PBX-B1 were increased by 49.8% and 10.5%. This study demonstrated the strategy of improving the energy release of boron-containing metalized explosives through the design of an explosive microstructure, which provides important clues for the design of higher-energy metalized explosives.

Equilibrium Energy and Entropy of Vortex Filaments in the Context of Tornadogenesis and Tornadic Flows

Equilibrium Energy and Entropy of Vortex Filaments in the Context of Tornadogenesis and Tornadic Flows

Ab initio methods for the computation of physical properties and performance parameters of electrochemical energy storage devices.

With the rapid development of electric vehicles and mobile technologies, there is a high demand for electrochemical energy storage devices and electrochemical energy conversion devices. Devices meeting these needs include metal-ion batteries (MIBs), supercapacitors (SCs), electrochromic devices (ECDs), and multifunctional devices such as electrochromic batteries and supercapatteries. Currently, the goal has been the enhancement of operational parameters and physical properties that results in a higher performance of these devices. In the case of batteries, SCs, and supercapatteries, scientists seek to improve the equilibrium voltage, energy density, power, capacitance, and charge rate. In the case of ECDs, the focus is on improvement of the optical modulation and coloration efficiency. However, synthesis and characterization of new materials, or of materials with optimized properties, is time consuming and highly expensive. Computational simulation of materials can expedite the experimental endeavor by modelling novel atomic structures and predicting device performance. This is possible using ab initio theories and applying physical principles that allow us to understand the underlying mechanisms governing the behavior of materials in these devices. Taking as a point of departure density functional theory (DFT), in this review, we discuss the first principles methods used for the computation of physical properties and performance parameters of electrochemical energy storage devices. A wide coverage of DFT is given, dealing with the strengths and weaknesses of the most popular functionals used in the field of electrochemical energy storage. With these tools, ab initio methods for the computation of basic properties such as effective mass, mobility, optical band gap, transmissivity, conductivity (ionic and electronic), and criteria for structure stability (cohesive energy, formation energy, adsorption energy, and phonon frequency) are addressed. We also highlight the first principles techniques for the calculation of performance parameters in MIBs, SCs, and ECDs.

Equilibrium Energies of Layered Composite and Two-Phase Media Under Periodic and Zero Boundary Conditions on Displacement Fields

Based on estimates for equilibrium energies for composite media with zero and periodic boundary conditions, we study the existence of an equilibrium state under the same boundary conditions as in the case of a two-phase medium.

Non-Cooperative Games for Privacy-Preserving and Cost-Efficient Smart Grid Energy Management

In this paper, we design privacy-preserving and cost-efficient energy management strategies for smart grid users that are equipped with renewable energy sources. The adversary is assumed to employ a factorial hidden Markov model based inference for load disaggregation, and the corresponding joint log-likelihood of the model is utilized as the privacy measure. The studied dynamic pricing model is applicable to a commodity-limited market, where the price of unit amount of energy is determined by the users’ aggregated power request. The users’ energy management strategies are designed under a non-cooperative game framework, where each user aims to optimize a weighted sum objective of both privacy measure and energy cost saving. The users’ non-cooperative game is shown to admit a unique pure strategy Nash equilibrium. As an extension, a computational-efficient distributed Nash equilibrium energy management strategy seeking method is proposed, which also avoids the privacy leakage due to the sharing of payoff functions between users. The performance of practical designs of the energy management strategies in the equilibrium is finally illustrated by numerical experiments.

Concurrent production and purification of glycolic acid from mixed esters via selective hydrolysis reactions catalyzed and thermodynamically promoted by MgO

Methyl glycolate (MG) in the presence of methyl levulinate (MLE) was selectively converted into magnesium glycolate via MgO-mediated hydrolysis reactions under mild conditions. The conversion of MG reached 95.2% while that of MLE was 15.1%, with reaction selectivity of 100%. After facile isolation procedures, the magnesium glycolate was readily transformed into glycolic acid, monomer of biodegradable plastic, with recovery rate of 90.2%. The basic sites with medium strength on MgO dominated the catalytic activity. The precipitation of magnesium glycolate led to the shift of chemical equilibrium for MG hydrolysis. DFT calculation results showed that the energy barriers for MG hydrolysis were smaller than those for MLE hydrolysis by 46–47 kJ/mol. Both the shift of chemical equilibrium and lower energy barriers contributed to the much higher reactivity of MG compared to MLE. This paper sheds light on the selective hydrolysis of esters and complete hydrolysis of an ester.

Nearby galaxies in the LOFAR Two-metre Sky Survey

Context. Magnetic fields, which regulate stellar feedback and star formation in galaxies, are key to understanding galaxy evolution. Aims. We probe the origin of magnetic fields in late-type galaxies, measuring magnetic field strengths and exploring whether magnetic fields are only passive constituents of the interstellar medium or whether, being part of the local energy equilibrium, they are active constituents. Methods. We measure equipartition magnetic field strengths in 39 galaxies from the second data release of the LOFAR Two-metre Sky Survey (LoTSS-DR2) at 144 MHz with 6 arcsec angular resolution (0.1–0.7 kpc). For a subset of nine galaxies, we obtain atomic and molecular mass surface densities using H I and CO(2-1) data from the THINGS and HERACLES surveys, respectively. These data are at 13 arcsec angular resolution, which corresponds to 0.3–1.2 kpc at the distances of our galaxies. We measure kinetic energy densities using H I and CO velocity dispersions. Results. We find a mean magnetic field strength of 3.6–12.5 μG with a mean of 7.9 ± 2.0 μG across the full sample. The magnetic field strength has the tightest and steepest relation with the total gas surface density, with B ∝ ΣH I+H20.309 ± 0.006. The relations with the star-formation rate surface density and molecular gas surface density have significantly flatter slopes. After accounting for the influence of cosmic-ray transport, we find an even steeper relation of B ∝ ΣH I+H20.393 ± 0.009. Conclusions. These results suggest that the magnetic field is regulated by a B–ρ relation, which has its origin in the saturation of the small-scale dynamo. This is borne out by an agreement of kinetic and magnetic energy densities, although local deviations do exist, in particular in areas of high kinetic energy densities where the magnetic field is sub-dominant.

Semiclassical Theory of Multistage Nonequilibrium Electron Transfer in Macromolecular Compounds in Polar Media with Several Relaxation Timescales

Many specific features of ultrafast electron transfer (ET) reactions in macromolecular compounds can be attributed to nonequilibrium configurations of intramolecular vibrational degrees of freedom and the environment. In photoinduced ET, nonequilibrium nuclear configurations are often produced at the stage of optical excitation, but they can also be the result of electron tunneling itself, i.e., fast redistribution of charges within the macromolecule. A consistent theoretical description of ultrafast ET requires an explicit consideration of the nuclear subsystem, including its evolution between electron jumps. In this paper, the effect of the multi-timescale nuclear reorganization on ET transitions in macromolecular compounds is studied, and a general theory of ultrafast ET in non-Debye polar environments with a multi-component relaxation function is developed. Particular attention is paid to designing the multidimensional space of nonequilibrium nuclear configurations, as well as constructing the diabatic free energy surfaces for the ET states. The reorganization energies of individual ET transitions, the equilibrium energies of ET states, and the relaxation properties of the environment are used as input data for the theory. The effect of the system-environment interaction on the ET kinetics is discussed, and mechanisms for enhancing the efficiency of charge separation in macromolecular compounds are analyzed.

Studies on Parameters Affecting Temperature of Liquid Steel and Prediction Using Modified AdaBoost.RT Algorithm Ensemble Extreme Learning Machine

The present work aimed to develop a predictive model for the end temperature of liquid steel in advance to support the smooth functioning of a vacuum tank degasser (VTD). An ensemble model that combines extreme learning machine (ELM) with a self-adaptive AdaBoost.RT algorithm was established for the regression problem. Based on analyzing the energy equilibrium of the VTD system, the factors were determined for predicting the end temperature of liquid steel. To establish a hybrid ensemble prediction model, an ELM algorithm was selected as the ensemble predictor due to its strong performance and robustness, and a modification of the AdaBoost.RT algorithm is proposed to overcome the drawback of the original AdaBoost.RT by embedding statistical theory to dynamically self-adjust the threshold value. For efficient VTD operations, an ensemble model that combines ELM with the self-adaptive AdaBoost.RT algorithm was established to model the end temperature of liquid steel. The proposed approach was analyzed and validated on actual production data derived from a steelmaking workshop in Baosteel. The experimental results reveal that the proposed model can improve the generalization performance, and the accuracy of the model is feasible for the secondary steel refining process. In addition, a polynomial equation is obtained from the ensemble predictive model for calculating the value of the end temperature. The predicted results are in good agreement with the actual data with <1.7% error.

A New Molecular Insight in Effects of Alcohol Co-Solvents on Miscibility of Anhydrous Ethanol/Diesel Blends

Abstract Sustainable policy leads to partially replace fossil diesel by bio-fuels and ethanol/diesel blends. The major challenge is how to enhance miscibility of ethanol with diesel. Molecular dynamics simulation was applied to study the effects of alcohol co-solvents on miscibility of ethanol with diesel. The 1-heptanol, 1-decanol, n-butanol, and butanol isomers were selected as co-solvents. The diesel model was constructed to quantitatively characterize miscibility and obtain interaction of ethanol and diesel. The solubility parameters, structural feature, and energy properties were analyzed. The results showed that long-chain alcohol co-solvents contributed to miscibility of blends. The aromatics had more effects on miscibility than linear alkanes and cycloalkanes. Radial distribution function results showed that straight-chain alcohols or high linearity co-solvents promoted miscibility of ethanol than branched alcohols. The energy analysis revealed that the hydrogen bonding and van der Waals interaction were the main driving forces to improve miscibility, while polarization interaction had no major contribution. The hydrogen bonding dominated for short-chain alcohols, while van der Waals interaction was vital for long-chain alcohols. The coordination of hydrogen bonding and van der Waals energy in dynamic equilibrium led to the optimal miscibility.

Modification of the model of charging dielectrics under electron beam irradiation

In this paper, a number of drawbacks and contradictions of the existing models of charging dielectric targets under irradiation with defocused electron beams of moderate energies (0.2–20 keV) are briefly noted. In order to streamline and coordinate all experimental results and theoretical information concerning the phenomenon of charging under electron irradiation, it was necessary to reconsider some postulates of the standard model based on a simple dependence of the electron emission coefficient σ on irradiating electron energy E0. It is shown that the decisive role in establishing the equilibrium state of charging dielectrics is played by not only establishing the equilibrium value σ = 1, but also by reaching a certain critical value of the field Fin in the near-surface area of the target. This field is due to the generation of the two-layer bipolar distribution of charges. It enhances the electron emission owing to increasing the depth at which secondary electrons emerge and also owing to the previously neglected contribution of primary thermalized electrons. As a result, there occurs a fundamental transformation of the dependence of the total electron emission coefficient σc for a charged dielectric on the energy of primary electrons as compared to the case of an uncharged dielectric. Consequently, the value of the equilibrium energy E2C, at which σ = 1, is changed. It is established that times of reaching equilibrium states for electron emission δ(t) and for surface potentials Vs(t) may differ by orders of magnitude. Also, the charging kinetics is significantly affected by the process of radiation-induced formation of defects in the irradiated dielectric, which results in two charging time constants—fast and long-term ones.

Lean Thinking into the modular construction of industrial buildings. Identifying the role of daylight

The necessity of energy equilibrium in industrial building stock must be addressed at design level in order to optimise use of materials without jeopardising the functional outcome. To do so effectively, the designer should incorporate a light use vs availability balance that will harness as much natural light resources as possible without creating unfavourable conditions due to over-exposure and thermal gains/losses. This work is an exploration between the relationship of sustainability with Lean thinking in the backdrop of sustainable and Lean construction. Exploring the benefits of lean and sustainable construction is about exploring how one can bring about great environmental, economic and social gains with the minimization of energy use, natural waste, environmental impacts as along with the creation of a healthy and productive work environment are the focus of sustainability in the construction industry. In effect answering how Daylight and Lean Thinking Principles can lead to optimizing Industrial buildings in terms of design and execution.

Effective Stiffness of Thin-Walled Beams with Local Imperfections.

Thin-walled beams are increasingly used in light engineering structures. They are economical, easy to manufacture and to install, and their load capacity-to-weight ratio is very favorable. However, their walls are prone to local buckling, which leads to a reduction of compressive, as well as flexural and torsional, stiffness. Such imperfections can be included in such components in various ways, e.g., by reducing the cross-sectional area. This article presents a method based on the numerical homogenization of a thin-walled beam model that includes geometric imperfections. The homogenization procedure uses a numerical 3D model of a selected piece of a thin-walled beam section, the so-called representative volume element (RVE). Although the model is based on the finite element method (FEM), no formal analysis is performed. The FE model is only used to build the full stiffness matrix of the model with geometric imperfections. The stiffness matrix is then condensed to the outer nodes of the RVE, and the effective stiffness of the cross-section is calculated by using the principle of the elastic equilibrium of the strain energy. It is clear from the conducted analyses that the introduced imperfections cause the decreases in the calculated stiffnesses in comparison to the model without imperfections.

A fully coupled thermo-hydro-mechanical model for fractured rock masses in cold regions

Freezing-thawing disasters are caused by the coupling effect of thermo-hydro-mechanical (THM) activity in rock masses at low temperatures, which seriously threatens the safety of rock mass engineering in cold regions. The accuracy of the coupled THM model is controlled by coupling parameters, such as the migration velocity of unfrozen water, equivalent thermal conductivity, and freezing point. The main difference in the THM coupling process between the frozen rock mass and frozen soil is the anisotropy caused by fractures, and the main difference between the frozen rock mass and normal rock mass is the existence of the ice-water phase transitions. In this paper, the governing equations for THM coupling of fractured rock masses at low temperatures are established, including the mechanical equilibrium equation, continuity equation and energy conservation equation. These equations include the effect of fractures, ice-water phase transitions, water migration and thermal expansion and contraction, which can also be degenerated to equations for rock masses without fractures. Then, the main parameters for the THM analysis are studied. The migration velocity of unfrozen water is closely related to the fractures, temperature, pressure, and phase transitions. Based on the energy conservation law, the expression of the equivalent thermal conductivity is proposed, which is a function of the geometric parameters of fractures, the thermal conductivity of each component, and the content of unfrozen water. Finally, the correctness of the proposed model are validated by Neaupane's experiment and an actual open-pit slope.