Costate Research Articles

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.

The Mo as electron trapper and donor to modulate the electron of CoP2 in phosphating process

To prepare bifunctional electrocatalyst towards HER and OER is extremely important for promoting the development of electrochemical water splitting technology. Herein, the element doping method is employed to tune the electron environment of cobalt phosphide (CoP). The Mo-doped CoP supported on carbon cloth (CC) is constructed by solvothermal and annealing method. The effect of Mo on the electron modulation of CoP during different phosphating time was studied carefully. It is noted that the Mo play an important role in tuning the electron state of Co and P elements which can trap the electron and was reduced to low valence, then transfer the electron to Co and P. With increasing the phosphating time, the electron transfer phenomenon between Mo and CoP is obvious. Benefiting from the electron engineering of Mo, Co and P as well as thin and wrinkle sheets structure, the optimal electrocatalyst only requires 39 mV and 251 mV to deliver 10 mA cm−2 for HER and OER, respectively. Also, as for the whole water splitting performance, it delivers 10 mA cm−2 at cell voltage of 1.56 V. Importantly, Faraday efficiency of the optimal catalyst achieves 99.9% for HER due to the tuned electron state of Co and P, high ECSA and low Rct.

Localization of two dimensional quantum walks defined by generalized Grover coins

Localization phenomena of quantum walks makes the propagation dynamics of a walker strikingly different from that corresponding to classical random walks. In this paper, we study the localization phenomena of four-state discrete-time quantum walks on two-dimensional lattices with coin operators as one-parameter orthogonal matrices that are also permutative, a combinatorial structure of the Grover matrix. We show that the proposed walks localize at its initial position for canonical initial coin states when the coin belongs to classes which contain the Grover matrix that we consider in this paper, however, the localization phenomena depends on the coin parameter when the class of parametric coins does not contain the Grover matrix.

Electronegativity-Induced Valence State Augmentation of Ni and Co through Electronic Redistribution between Co-Ni3N/CeF3 Interfaces for Oxygen Evolution Reaction

The development of high-performance and inexpensive electrocatalysts for the oxygen evolution reaction is one of the most desired objectives in energy conversion reactions. Due to sluggish reaction kinetics, the commercialization of such processes could not be achieved yet. Choosing an appropriate coupling interface to boost the catalyst performance is essential for the creation of high-efficiency electrocatalysts. Herein, metal-nitride and metal-fluoride heterostructures are reported with an extremely low overpotential of 180 mV at a current density of 10 mA cm–2 for OER application. The Co–Ni3N/CeF3 catalyst shows strong interfacial interaction, causing significant electronic redistribution between Co–Ni3N and CeF3 phases. X-ray photoelectron spectroscopy studies reveal the charge transfer from the Co–Ni3N to the CeF3 phase, resulting in the augmentation in the valence states of Co and Ni and making them highly active sites for the adsorption of intermediates (O*, OH*, and HOO*). This phenomenon is possibly driven by the high polarity of CeF3 due to the presence of highly electronegative F atoms. The stability study of the catalyst was performed for 120 h at large current densities of 100 and 200 mA cm–2. The detailed analysis of the surface reconstruction of Co–Ni3N/CeF3 is also carried out after a long-term stability test. This work offers a fresh look at the possibilities of the design and fabrication of an efficient and low-cost catalyst.

Magnetism and unconventional topology in LaCoO3/SrIrO3 heterostructure

Employing first-principles calculations, we provide microscopic insights on the curious magnetic and topological properties of LaCoO3/SrIrO3 heterostructure, which has been recently synthesized [Kumar Jaiswal et al., Adv. Mater. 34, 2109163 (2022)]. Our computational study unravels transfer of polar charge from SrIrO3 to LaCoO3, thereby reducing the Co valence from 3+ toward 2+, supporting the experimental findings. Our study further reveals the stabilization of the intermediate spin state of Co and strong ferromagnetic Co–Co coupling in the LaCoO3 block of the heterostructure. This, in turn, is found to induce ferromagnetism in the pseudo-tetragonally structured SrIrO3 in the heterostructure geometry, providing an understanding of the origin of magnetism, which is counter-intuitive as both LaCoO3 and SrIrO3 are nonmagnetic in bulk form. Most interestingly, the band structure of ferromagnetic, tetragonal structured SrIrO3 is found to exhibit unconventional topology, manifested as C = 2 double Weyl points, which leads to the observed anomalous Hall effect. Our finding of C = 2 double Weyl points, belonging to the class of charge-2 Dirac points, opens up the possibility of material realization of unconventional topological properties beyond the conventional Dirac and C = 1 Weyl points, which calls for future experiments.

Third order nonlinear optical properties and electrochemical performance of La2CoMnO6 double perovskite

La2CoMnO6 double perovskite was synthesized via modified combustion route. XRD with Rietveld refinement confirms monoclinic structure with space group of P21/n. Irregular shaped porous morphology was determined from FE-SEM and elemental analysis was done using EDAX spectra. Existence of mixed valence state of Co and Mn were verified by XPS spectra and its bandgap was determined using Tauc plot. Vibrational analysis validates the formation of perovskite phase and degeneracy in Raman modes/thermal broadening provides signature vibrational bands corresponding to stretching and bending motions of MnO6 and CoO6. Supercapacitor performance using La2CoMnO6 as electrode material exhibits 84% of cyclic stability after 500 cycles. The material exhibits a combined saturable and reverse saturable absorption behaviour under open aperture and self-defocusing nature due to thermal effect under closed aperture measurements with Z-scan method, using continuous wave irradiation. These findings confirmed that La2CoMnO6 manganite can be used for energy storage and photonic applications.

Perturbed‐analytic direct transcription for optimal control (PADOC)

AbstractThe herein coined PADOC (perturbed‐analytic direct transcription for optimal control) stands for a new transcription method for direct trajectory optimization. We construct PADOC on a novel segmented decomposition method that provides series solutions for nonlinear problems. To transcribe the infinite dimensional problem into a finite one, PADOC comes along with a new solution approach, namely, the herein coined average nonlinear programming (aNLP). The aNLP theorem suggests generating a staircase optimal solution (low resolution) and turning it into a distributed optimal solution (high resolution) by exploiting the Hamiltonian of the problem. The analytic architecture provides PADOC with an analytic connection of a truncated order between the discrete nodes of the solution. This renders stability, accuracy within an analytic resolution, robustness, and a cut‐down in the number of the decision variables in the frame of NLP. We also prove that the multipliers associated with the Karush–Kuhn–Tucker optimality conditions in the frame of NLP (as transcribed by PADOC) correspond to a backward analytic solution for the costate equations. We finally show distinct features of PADOC through some examples.

Structural, magnetic and optical properties of disordered double perovskite Gd2CoCrO6 nanoparticles.

We have synthesized disordered double perovskite Gd2CoCrO6 (GCCO) nanoparticles with an average particle size of 71 ± 3 nm by adopting a citrate sol-gel method to investigate their structural, magnetic, and optical properties. Rietveld refinement of the X-ray diffraction pattern showed that GCCO is crystallized in a monoclinic structure with space group P21/n, which is further confirmed by Raman spectroscopic analysis. The absence of perfect long-range ordering between Co and Cr ions is confirmed by the mixed valence states of Co and Cr. A Néel transition was observed at a higher temperature of TN = 105 K compared to that of an analogous double perovskite Gd2FeCrO6 due to a greater degree of magnetocrystalline anisotropy of Co than Fe. Magnetization reversal (MR) behavior with a compensation temperature of Tcomp = 30 K was also observed. The hysteresis loop obtained at 5 K exhibited the presence of both ferromagnetic (FM) and antiferromagnetic (AFM) domains. Super-exchange and Dzyaloshinskii-Moriya (DM) interactions between various cations via oxygen ligands are responsible for the observed FM or AFM ordering in the system. Furthermore, UV-visible and photoluminescence spectroscopy demonstrated the semiconducting nature of GCCO with a direct optical bandgap of 2.25 eV. The Mulliken electronegativity approach revealed the potential applicability of GCCO nanoparticles in photocatalytic H2 and O2 evolution from water. Due to a favorable bandgap and potentiality as a photocatalyst, GCCO can be a promising new member of double perovskite materials for photocatalytic and related solar energy applications.

Identification of high ionic conducting members (M(III) = Co, Ni) in the new lithium rich Li4.50M0.50TeO6 (M(III) = Co, Ni, In) series.

Many new lithium-excess compounds with rock-salt related structures have been extensively studied in recent years to discover high-capacity electrode materials for lithium-ion batteries. In the present work, lithium rich layered tellurates, Li4.50M0.50TeO6 (M(III) = Co, Ni, In), are added to the existing series of Li4.50M0.50TeO6 (M(III) = Cr, Mn, Fe, Al, and Ga) oxides. Structural investigations revealed their stabilization in the space group C2/m with a new cationic ordering. The structure consists of (Li1.50M0.50TeO6)3- honeycomb arrays along the ab plane by the edge sharing of TeO6 with (Li/M)O6 octahedra. The honeycomb arrays are separated by the intermediate layer of Li alone in Li4.50Co0.50TeO6. On the other hand, in the Ni and In analogues, the interlayer region consists of Li with Te, and Li with In ions, respectively. XPS studies confirmed the +3 oxidation state of Co and Ni ions. The appearance of a strong band at 680 nm resulting from LMCT (O → Co) in the UV-vis DRS data of the Li4.50Co0.50TeO6 sample further indicated the presence of Co3+ (d6, low spin) ions. The absence of characteristic Ni2+ bands at around ∼650 and 740 nm supported Ni3+ ions. Li4.50Co0.50TeO6 showed diamagnetic behaviour, while Li4.50Ni0.50TeO6 displayed paramagnetic nature. A negative θ (-14(2)) K has been obtained in the temperature region of 300-100 K for Li4.50Ni0.50TeO6 representing dominant antiferromagnetic interactions. At 2 K, Li4.50Ni0.50TeO6 unveiled a non-linear trend with no significant hysteresis and nearly saturation at 5 T field indicating the existence of additional interactions. Li4.50Co0.50TeO6 and Li4.50Ni0.50TeO6 exhibited significant conductivity values of 0.016 and 0.003 S cm-1, respectively, at 300 °C, thereby opening up further studies in this direction.

First-principles study of Co and Ni excess effects on crystal structure and phase stability of Co&lt;sub&gt;2&lt;/sub&gt;NiGa alloy

Using the first-principles exact muffin-tin orbital method combined with the coherent potential approximation, the crystal structure and site occupation, martensitic transformation, magnetic moment and elastic constant for each of Co&lt;sub&gt;2+&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Ni&lt;sub&gt;1–&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Ga, Co&lt;sub&gt;2+&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;NiGa&lt;sub&gt;1–&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;, Co&lt;sub&gt;2–&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Ni&lt;sub&gt;1+&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Ga and Co&lt;sub&gt;2&lt;/sub&gt;Ni&lt;sub&gt;1+&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Ga&lt;sub&gt;1–&lt;i&gt;x&lt;/i&gt; &lt;/sub&gt;(0 ≤ &lt;i&gt;x&lt;/i&gt; ≤ 0.4) alloys with Co and Ni excess at 0 K are systematically investigated. It is shown that most of the austenitic phases of the alloys have &lt;i&gt;X&lt;/i&gt;A stable structure, and the excess Co and Ni atoms occupy the insufficient atomic positions, and it is inversely occupied only when Ni replaces Ga. With the increase of &lt;i&gt;x&lt;/i&gt;, the total electron energy of &lt;i&gt;L&lt;/i&gt;1&lt;sub&gt;0&lt;/sub&gt; relative to &lt;i&gt;X&lt;/i&gt;A of only two Ga-insufficient alloys gradually decreases, for the former, the tetragonal shear elastic constant gradually increases, but for the latter, it gradually decreases. It is indicated that the martensitic transformation is promoted by the substitution of both Co and Ni for Ga in the energy and mechanics, and the martensitic transformation temperature is expected to increase. The values of total magnetic moment (&lt;i&gt;μ&lt;/i&gt;&lt;sub&gt;tot&lt;/sub&gt;) of the &lt;i&gt;X&lt;/i&gt;A phase and &lt;i&gt;L&lt;/i&gt;1&lt;sub&gt;0&lt;/sub&gt; phase of each alloy are mainly contributed by Co atoms, but onlya relatively small portion by Ni atoms. And the values of &lt;i&gt;μ&lt;/i&gt;&lt;sub&gt;tot&lt;/sub&gt; of two phases in the four alloys have the same relationship with &lt;i&gt;x&lt;/i&gt;, and the difference between them with the same compositions is not more than about 0.32 &lt;i&gt;μ&lt;/i&gt;&lt;sub&gt;B&lt;/sub&gt; . The analyses of electronic structure calculations show that the distributions of spin-down electronic density of states of Co and Ni atoms near the Fermi energy level have contributed significantly to the stability of &lt;i&gt;L&lt;/i&gt;1&lt;sub&gt;0&lt;/sub&gt; relative to the &lt;i&gt;X&lt;/i&gt;A phase, which is attributed to the Jahn-Teller effect. The above results are expected to provide a theoretical reference for the optimal design of the structure and properties of Co&lt;sub&gt;2&lt;/sub&gt;NiGa-based ternary alloys.

Time-Fuel-Optimal Navigation of a Commercial Aircraft in Cruise With Heading and Throttle Controls Using Pontryagin’s Maximum Principle

In this research, we consider the commercial aircraft trajectory optimization problem for a general cruise model with arbitrary spatial wind fields to be solved using the Pontryagin’s maximum principle. The model features two fundamental controls, namely “throttle setting” (appearing as a singular control) and “heading angle” (appearing as a regular control). For a problem with state-inequality constraints and minimum time-fuel objective, we show that the optimal “heading angle” can be described through the classic Zermelo’s navigation identity. We also demonstrate, by analyzing the switching function, that the singular “throttle setting” can be characterized through a feedback function that relies on both the optimal states and “heading angle”. The switching-point algorithm is employed to solve a case study where we inspect the optimality conditions and graph the optimal controls together with the optimal state and co-state variables.