Costate Research Articles

Minimum-fuel low-thrust trajectories to the Moon

An approach to solve the problem of optimizing multi-revolution thrust limited trajectories with constant exhaust velocity between the Earth orbit and the orbit around the Moon is considered. An indirect approach is used to solve the lunar trajectory optimization problem, based on the application of the Pontryagin's maximum principle and continuation method. At all segments of the trajectory, the gravities of the Earth, the Moon and the Sun are taken into account. The trajectory to the Moon is divided into geocentric and selenocentric segments, which are connected at the libration point EML1 of the Earth-Moon system. To ensure the choice of the optimal relation between the angular distance and the transfer duration of each segment, the problem of optimizing the trajectory with a fixed angular distance and free time of flight is considered. Solving a sequence of optimization problems for the limited power trajectory, the minimum-thrust trajectory and the minimum-fuel trajectory avoids the need to choose an initial guess for unknown initial costate variables. The numerical examples of optimizing the multi-revolution low-thrust transfers from the highly elliptical orbit around the Earth to the circular orbit around the Moon are given.

Monitored recurrence of a one-parameter family of three-state quantum walks

Monitored recurrence of a one-parameter set of three-state quantum walks on a line is investigated. The calculations are considerably simplified by choosing a suitable basis of the coin space. We show that the Polya number (i.e. the site recurrence probability) depends on the coin parameter and the probability that the walker is initially in a particular coin state for which the walk returns to the origin with certainty. Finally, we present a brief investigation of the exact quantum state recurrence.

Fe-doped Co3O4 anchored on hollow carbon nanocages for efficient electrocatalytic oxygen evolution

In this work, a Fe-doped Co3O4 OER electrocatalyst supported by an N-doped hollow nanocage carbon framework (Fe-Co3O4/NC) was successfully prepared by anion exchange and annealing in an air atmosphere strategy. XRD and HRTEM characterizations confirm that Fe the incorporation of Fe into the lattice of Co3O4. XPS characterization clarifies that the valence state of Co increases after the introduction of Fe, which originates from the electrons transfer from Co2+/Co3+ to Fe3+ and is induced by the valence electron configuration of cations. It simulates Co sites in-situ derived into CoOOH active species during the OER process, which is confirmed by the HRTEM and XPS characterization after the OER stability test. Electrochemical performance tests show that the Fe-Co3O4/NC electrocatalyst only exhibits 275 mV overpotential to achieve a current density of 10 mA/cm2 and stably maintains for 20 h at 100 mA/cm2. Together with 20% Pt/C electrocatalyst, the composed two-electrode system only needs 2.041 V applied potential to achieve 100 mA/cm2 for total water splitting in a self-made membrane electrode device, which has industrial application prospects.

Highly selective production of singlet oxygen by manipulating the spin state of single-atom Co–N moieties and electron localization

Singlet oxygen (1O2) is a reactive species with oxidation selectivity that is preferred in advanced oxidation processes. However, the underlying mechanism of 1O2 selective production remain ambiguous. In this study, we demonstrated that electron localization and high spin state of metal active sites favored peroxymonosulfate (PMS) co-adsorption and dissociation, which promoted selective production of 1O2. Under theoretical guidance, single Co atoms anchored on uneven graphite carbon nitride nanosheet (Co-SA/CMN) was fabricated and exhibited the highest 1O2 production selectivity so far with 87.8% of the PMS consumed was converted to 1O2. The Co-SA/CMN/PMS system exhibited remarkable degradation efficiency to multiple organic pollutants, show strong resistance to environmental interference and robust stability at the device level. Co-SA/CMN/PMS oxidation was assessed as a safe and detoxifying technology, the estrogenic activity and toxicity originating from 17β-estradiol (E2) or its degradation by-products were sufficiently removed. These findings deepen the mechanistic understanding of the origins of high 1O2 production selectivity and provide a rational strategy for precisely controlling 1O2 generation in PMS activation.

Impact of non-magnetic Zn2+ doping on the structural, magnetic and magnetocaloric properties of Nd0.5Ca0.5Mn1-xZnxO3 (x = 0, 0.05, 0.10) compounds

Nd0.5Ca0.5Mn1-xZnxO3 (x = 0, 0.05, 0.10) polycrystalline perovskite samples were made using the conventional solid-state reaction method to investigate effects of Zn2+ substitution on the structural and magnetic properties, along with exchange bias and magnetocaloric effects. All the bulk compounds belong to Pnma space group with orthorhombic structure. Both charge ordering temperature (TCO) and antiferromagnetic ordering temperature (TN) decreased with increase in Zn concentration. Thermal irreversibility in magnetization in all Zn doped samples indicate a first-order phase transition. At low temperatures soft ferromagnetic nature was observed from the isotherms (M(H)). Field-induced metamagnetic behavior was observed in low-temperature regions. Increasing exchange bias effect with Zinc doping was observed, which reduces with temperature due to thermal fluctuation. Also magnetocaloric effect (MCE) has been calculated for two temperature regimes, 10–65 K and 150–300 K. As observed in temperature-dependent magnetization plot entropy-change parameter switches from negative (above TCO) to positive (below TCO), accompanied by a change in magnetic correlation from ferromagnetic to antiferromagnetic. However, the magnitude of change in entropy decreases with Zn doping, whereas, the same increases at low-temperature region. The destabilization of the CO state and enhanced disorder by the Zn doping plays role behind this variation in MCE behavior.

Bimetal-organic framework-derived porous CoFe2O4 nanoparticles as biocompatible anode electrocatalysts for improving the power generation of microbial fuel cells

HypothesisThe relatively lower power density of Microbial fuel cells (MFCs), primarily resulting from weak biofilm habitation and sluggish extracellular electron transfer (EET) at the anode interface, limits their practical implementation on a large scale. To address this challenge, porous CoFe2O4 nanoparticles could be used as anode electrocatalysts based on the following considerations: (i) the introduction of CoFe2O4 nanoparticles endows the anode with a rough surface that facilitates biofilm formation; (ii) the positively charged Co and Fe ions improve the interfacial affinity of anodes, enabling rapid immobilization and colonization of negatively bacteria; (iii) the multi-valent metal states of Co and Fe can function as electron shuttles, mediating EET process between biofilm and anode. ExperimentsCoFe2O4 nanoparticles prepared with a bimetal-organic framework (B-MOF) as precursor, were modified to the surface of carbon cloth as the anode of MFCs. FindingsMFCs equipped with CoFe2O4 anode achieved a maximum power density of 1026.68 mW m−2, which was approximately 3.4 times higher than that of the pristine carbon cloth. Additionally, the biofilm density and viability on the anode were enhanced after CoFe2O4 modification. Considering the facile fabrication process and superior electrocatalytic performance, the CoFe2O4 nanoparticles are promising electrocatalysts for high performance and cost-effective MFCs.

Insight into Electrochemical Promotion of Cu/Co3O4 Catalysts for the Reverse Water Gas Shift Reaction

AbstractIn this study, Copper‐modified Co3O4 (Cu/Co3O4) catalysts were investigated for the reverse water gas shift (RWGS) reaction at 200–400 °C under different CO2 : H2 ratios. It was found that the electrocatalytic performance of Co3O4 was improved by loading 4 weight percent (wt.%) Cu nanoparticles (average size: 13 nm), which could be then used as an electrode in electrochemical promotion of catalysis (EPOC) studies. Under the applied voltages of +2 V and −1 V, the catalytic rates were suppressed and increased by about 40 % and 14 %, respectively. This was due to the changes in the active oxidation states of Cu and Co caused by O2− migration under polarization, as confirmed by XPS, XRD, and cyclic voltammetry (CV). The study also revealed that the exchange current density (i0) was counter‐correlated with the open‐circuit catalytic rate (r0) and could serve as an informative tool for predicting the catalytic rate, which was demonstrated for the first time in the instance of RWGS reaction.

Structure determination and magnetic studies of triazole chelated Co(II) coordination polymers

AbstractTwo cobalt(II) halide complexes with 1,2,4‐triazole as a ligand were synthesized. Their structures were determined by extended x‐ray absorption fine structure (EXAFS) and powder x‐ray diffraction (XRD). Both complexes [Co(Htrz)Cl2]n (1) and {[Co(Htrz)2(trz)]BF4}n (2) form one‐dimensional polymeric chain and the distances of Co⋯Co are 3.3521(2) Å and 3.8629(2) Å, respectively. The Htrz and Cl− are bridging ligands to connect two Co(II) ions in 1, and the local environment of Co site is in a distorted octahedron with {CoN2Cl4} core. In complex 2, two Htrz and one trz are bridging ligands to connect two Co(II) ions, and the local geometry of Co is in a pseudo octahedron with {CoN6} core. The analysis of Co LII,III‐edge XAS indicates that the Co(II) of both complexes are at high spin state with t2g5eg2 configuration and the crystal field strength (10Dq) is about 1.2 eV. The broken‐symmetry DFT calculations indicate that antiferromagnetic coupling state of Co⋯Co is the most stable state in both complexes; and the coupling constants of 1 and 2 are −0.32 cm−1 and −3.70 cm−1, respectively. Based on the distances of Co⋯Co and coupling constants, such antiferromagnetic interaction is achieved through triazole ligands.

Metal-atom-doped W18O49 nanowires for electrocatalytic oxygen evolution reaction in alkaline medium

• The Co-W 18 O 49 nanowires were designed as OER electrocatalysts for oxygen evolution reaction in alkaline medium. • The incorporation of Co atoms can effectively modulate localized charge distribution of Co-W 18 O 49 nanowires. • The high-spin state of Co 3+ cations is benefited for the optimization of bonding strength between Co sites and the adsorbed oxygen species. Non-noble transition metal oxides (TMOs) are promising catalysts with improved catalytic activity and stability in oxygen evolution reaction (OER). However, the structural complexity of TMO-based electrocatalysts renders the determination of the active sites and OER mechanisms challenging. Here, we demonstrate that the OER activity of Co-doped one-dimensional W 18 O 49 (Co-W 18 O 49 ) is intrinsically dominated by the surface structure and electronic properties of the octahedral sites and Co–O–W bonds. Compared with RuO 2 and W 18 O 49 heterogeneous electrocatalysts, Co-W 18 O 49 exhibits higher turnover frequency, attaining 1.97 s −1 at 500 mV overpotential. The results indicate that Co substitution contributes to the localized charge distribution of the active octahedral sites constructed by the Co–O–W bonds under OER conditions. Here, we determine the mechanism of TMOs for the OER, which may be applied to various other TMOs for OER electrocatalyst design.

Reducible Co3+–O Sites of Co–Ni–P–Ox on CeO2 Nanorods Boost Acidic Water Oxidation via Interfacial Charge Transfer-Promoted Surface Reconstruction

Developing efficient and durable earth-abundant electrocatalysts for the acidic oxygen evolution reaction (OER) is the bottleneck for water splitting using proton-exchange membrane electrolyzers. Herein, a heterostructured CeO2 nanorod-supported Co–Ni–P oxide (CeO2/Co-Ni–P–Ox) catalyst is prepared for acidic OER electrocatalysis and the valence states of Co is precisely tuned from 2 to 2.51 by introducing heterojunction interfaces and trace P atoms. The increased Co states favor the in situ transformation of surface Co2+–O sites into highly active reducible Co3+–O sites, which promotes the deprotonation of water molecules and accelerates the OER kinetics. Therefore, this catalyst exhibits extraordinarily low OER overpotentials of 166 and 262 mV at 5 and 10 mA cm–2, respectively, in 0.5 M H2SO4, which are among the best reported for precious-metal-free electrocatalysts so far. The stability of the catalyst is also greatly improved due to the increased vacancy formation energy of the Co site that restricts its dissolution in an acid.

Fast Degradation of Rhodamine B by In Situ H2O2 Fenton System with Co and N Co-Doped Carbon Nanotubes.

In this study, an E-fenton oxidation system based on Co-N co-doped carbon nanotubes (Co-N-CNTs) was designed. The Co-N-CNTs system showed fast degradation efficiency and reusability for the degradation of rhodamine B (RhB). The XRD and SEM results showed that the Co-N co-doped carbon nanotubes with diameters ranging from 40 to 400 nm were successfully prepared. The E-Fenton degradation performance of Co-N-CNTs was investigated via CV, LSV and AC impedance spectroscopy. The yield of H2O2 could reach 80 mg/L/h within 60 min, and the optimal voltage and preparation temperature for H2O2 yield in this system was -0.7 V (vs. SCE) and 800 °C. For the target pollutant of RhB, the fast removal of RhB was obtained via the Co-N-CNTS/E-Fenton system (about 91% RhB degradation occurred during 60 min), and the •OH played a major role in the RhB degradation. When the Fe2+ concentrations increased from 0.3 to 0.4 mM, the RhB degradation efficiency decreased from 91% to about 87%. The valence state of Co in the Co-N-C catalyst drove a Co2+/Co3+ cycle, which ensured the catalyst had good E-Fenton degradation efficiency. This work provides new insight into the mechanism of an E-Fenton system with carbon-based catalysts for the efficient degradation of RhB.

Doping of Cr to Regulate the Valence State of Cu and Co Contributes to Efficient Water Splitting.

Water electrolysis in alkaline media is the most promising technology for hydrogen production, but efficient electrocatalysts are required to reduce the overpotential in HER and OER processes. In this work, the multicomponent transition metal catalyst Cr-Cu/CoOx was loaded on copper foam by electrodeposition and annealing, and the catalyst exhibited excellent electrochemical activity. The HER overpotential is 21 mV and the OER overpotential is 252 mV at a current density of 10 mA cm-2. The overall water splitting voltage is 1.51 V, even better than the Pt/C//RuO2 two-electrode system (1.61 V). The excellent performance of this catalyst is mainly derived from the close synergistic interaction among Cu, Co, and Cr. The doping of Cr modulates the valence states of Cu and Co at the active sites and improves the adsorption of various reaction intermediates. Density functional theory (DFT) calculations show that the doping of Cr can optimize the adsorption of the reaction intermediate H*. Meanwhile, the high-valent Cr and Co promote hydrolysis through strong adsorption with OH-. The present work provides a reasonable strategy for designing low-cost transition metals as efficient catalysts for water electrolysis.

A two-layer Crank–Nicolson linear finite element methods for second-order hyperbolic optimal control problems

In this paper, we consider a two-layer Crank–Nicolson scheme combined with linear finite element approximation for second-order hyperbolic optimal control problems with control constraints. For state and co-state variables, their time derivatives are first reduced to a first-order system then discretized by the two-layer Crank–Nicolson scheme and their space derivatives are discretized by linear finite elements. The control variable is dealt with variational discretization technique. Optimal priori error estimates for state, co-state and control variables are derived. Some numerical examples are presented to illustrate the theoretical convergence rate.

Adaptive global energy optimal management strategy based on the Pontryagin’s minimum principle: An isolated microgrid example

Optimal control is a common control strategy to solve complex non-linear systems. Pontryagin’s minimum principle, as a typical optimal control theory, is widely used in energy management systems. Due to the randomness of new energy generation and the diversity of load power consumption, microgrid energy management system is a complex non-linear stochastic system. The efficient operation of microgrid energy management strategy largely depends on the real-time performance of the control algorithm. Pontryagin’s minimum principle is an offline control strategy, whose co-state variable λ depends on expert experience and needs to be manually adjusted according to different working conditions, so it is difficult to achieve real-time optimal control. First, the energy management system model of island-type microgrid is established in this paper. In order to improve the economy of power generation and prevent battery over-charge or over-discharge, the state of charge (SOC) change of battery pack is comprehensively considered, and the fuel cost and pollutant treatment cost are taken as the objective function. Second, an adaptive Pontryagin’s minimum principle energy management strategy is proposed. By introducing the penalty mechanism and adjusting the parameters adaptively, the problem that the open-loop control of Pontryagin’s minimum principle needs to adjust the co-state variables in real time is solved. Comparative experiments show that compared with Pontryagin’s minimum principle and particle swarm optimization, adaptive Pontryagin’s minimum principle can not only limit battery SOC within the ideal range but also effectively reduce the daily operation cost of microgrid. Experimental results verify the effectiveness of the proposed algorithm.

End-to-End Optimization of Power-Limited Earth–Moon Trajectories

The aim of this study is to analyze lunar trajectories with the optimal junction point of geocentric and selenocentric segments. The major motivation of this research is to answer two questions: (1) how much of the junction of the trajectory segments at the libration point between the Earth and the Moon is non-optimal? and (2) how much can the trajectory be improved by optimizing the junction point of the two segments? The formulation of the end-to-end optimization problem of power-limited trajectories to the Moon and a description of the method of its solution are given. The proposed method is based on the application of the maximum principle and continuation method. Canonical transformation is used to transform the costate variables between geocentric and selenocentric coordinate systems. For the initial guess, a collinear libration point between the Earth and the Moon is used as a junction point, and the transformation to the optimal junction of these segments is carried out using the continuation method. The developed approach does not require any user-supplied initial guesses. It provides the computation of the optimal transfer duration for trajectories with a given angular distance and facilitates the incorporation of the perturbing accelerations in the mathematical model. Numerical examples of low-thrust trajectories from an elliptical Earth orbit to a circular lunar orbit considering a four-body ephemeris model are given, and a comparison is made between the trajectories with an optimal junction point and the trajectories with a junction of geocentric and selenocentric segments at the libration point.

CO Inversion on a NaCl(100) Surface: A Multireference Quantum Embedding Study.

We develop a multireference quantum embedding model to investigate a recent experimental observation of the isomerization of vibrationally excited CO molecules on a NaCl(100) surface [Science 2020, 367, 175-178]. To explore this mechanism, we built a reduced potential energy surface of CO interacting with NaCl(100) using a second-order multireference perturbation theory, modeling the adsorbate-surface interaction with our previously developed active space embedding theory (ASET). We considered an isolated CO molecule on NaCl(100) and a high-coverage CO monolayer (1/1), and for both we generated potential energy surfaces parametrized by the CO stretching, adsorption, and inversion coordinates. These surfaces are used to determine stationary points and adsorption energies and to perform a vibrational analysis of the states relevant to the inversion mechanism. We found that for near-equilibrium bond lengths, CO adsorbed in the C-down configuration is lower in energy than in the O-down configuration. Stretching of the C-O bond reverses the energetic order of these configurations, supporting the accepted isomerization mechanism. The vibrational constants obtained from these potential energy surfaces show a small (< 10 cm-1) blue- and red-shift for the C-down and O-down configurations, respectively, in agreement with experimental assignments and previous theoretical studies. Our vibrational analysis of the monolayer case suggests that the O-down configuration is energetically more stable than the C-down one beyond the 16th vibrational excited state of CO, a value slightly smaller than the one from quasi-classical trajectory simulations (22nd) and consistent with the experiment. Our analysis suggests that CO-CO interactions in the monolayer play an important role in stabilizing highly vibrationally excited states in the O-down configuration and reducing the barrier between the C-down and O-down geometries, therefore playing a crucial role in the inversion mechanism.

Comparison of lithium sulphate borate glass cathode materials with single Mn and Co doping and dual Mn–Co doping

Single Mn and Co doping to dual Co and Mn ions in lithium sulphate (Li2S) borate-based glasses system is carefully studied as new glass cathode for future Li-ion battery. The B–O bonding in glass network and the oxidation states of Co, Mn and S ions in glass structure are investigated using synchrotron-based IR spectroscopy and XANES. The pseudo-capacitance behavior of the CV curves indicates and confirms that Co2+/Co3+ and Mn2+/Mn3+ are in mixed oxidation states. Surprisingly, in this work, the 3Mn5Co glass composition exhibits the highest specific capacitance value of 121.12 F g−1. This shows a better enhancement of electrochemical properties using dual Mn–Co doping in glass structure rather than a single doping.

Electro‐optical Properties of ZnSe Doped with Gd and (Ag,Gd) Phosphors

AbstractTo understand the position of donor‐ acceptor level and nature of electronic state of activators and co‐ activators, the photo luminescence (PL) and electroluminescence (EL) emission spectra of Znse: Gd and Zn Se: (Ag, Gd) phosphors, have been recorded at room temperature. The method of preparation of phosphors is described. Voltage and frequency dependence of electroluminescent has also b been described. The light output varies as been studied for a wide range of frequencies. It is observed that the EL emission spectra of these phosphors are shifted towards lower wavelength sides on increasing the field frequency.

Interpolated coefficient characteristic finite element method for semilinear convection–diffusion optimal control problems

In this paper, a fully discrete interpolated coefficient characteristic finite element approximation is proposed for optimal control problems governed by time-dependent semilinear convection–diffusion equations, where the hyperbolic part of the state equation is first treated by directional derivatives and then discretized by backward difference, the semilinear term is dealt with interpolation coefficient finite elements technique. A priori error estimates for the control, state and co-state variables are derived. Theoretic results are confirmed by a numerical example.

Modeling and Control of the Extreme Ideology Transmission Dynamics in a Society

In this work, we propose a mathematical model to analyze the spread of extreme ideology in society. The so-called SERTA model divides the entire population into five compartments, namely susceptible, extremist, recruiter, treatment, and aware, to describe the state of the willingness of community members toward extreme ideology. We first present a model with constant control, i.e., a model without a dynamical control instrument, and provide the stability analysis of its equilibrium points based on the basic reproduction number. We then reformulate the model into an optimal control framework by introducing three control variables, namely prevention, disengagement, and deradicalization, to enable intervention of the dynamical process. The optimality conditions are obtained by employing Pontryagin's maximum principle, showing the optimal interdependence of state, co-state, and control variables. Numerical simulations based on the well-known Runge-Kutta algorithm and forward-backward sweep method are carried out to evaluate the effectiveness of control strategies under different scenarios. From the simulation results, it is found that by applying the three controls, the optimum solution is obtained. Besides that, in this study, disengagement contributes the most effect in suppressing extremist and recruiter populations, both by using single control and multiple controls.