Costate Research Articles

Theoretical analysis of quantum random walks with stress-engineered optics.

Quantum random walks (QRWs) are random processes in which the resulting probability density of the "walker" state, whose movement is governed by a "coin" state, is described in a nonclassical manner. Previously, Q-plates have been used to demonstrate QRWs with polarization and orbital angular momentum playing the roles of coin and walker states, respectively. In this theoretical analysis, we show how stress-engineered optics can be used to develop new platforms for complex QRWs through relatively simple optical elements. Our work opens up new paths to speed up classical-to-quantum transitions in robust photonic networks.

Structural, electronic, transport and magnetic studies of LaCo1 − xNixO3 (x = 0, 0.3) thin films

We present here a study on structural, electronic, transport, and magnetic properties of single-phase (001) oriented compressively strained thin films of LaCoO3 (LCO) and LaCo0.7Ni0.3O3 (LCNO). The films were deposited on the LaAlO3 (001) single crystal substrate using pulsed laser deposition. Electronic structure investigations by x-ray absorption spectroscopy (XAS) measurements at various edges (Co-L3,2, Ni-L3,2, and La-M5,4) confirm +3 charge states for Co, Ni, and La ions in all samples. The XAS study also reveals a transition in the spin state of Co+3 (low spin to intermediate/high spin), which is attributed to induced strain and Ni substitution. Electrical transport measurements suggest the semiconducting behavior for LCO and LCNO thin films in the measured temperature range. We found a drastic change in resistivity (ρ) and magnitude with Ni substitution. An in-depth analysis of the conduction mechanism governing the transport behavior in thin films has been done using various theoretical models. Different conduction mechanisms (Arrhenius law and Effros-Shklovski-type variable range hopping) have been observed to govern conduction in different temperature ranges, suggesting disorder controlled transport in these films. The magnetization measurements show a magnificent increase in saturation magnetization for LCNO and ferromagnetic ordered states, which persists even up to room temperature.

Electronic and magnetic properties of structural defects in SrTiO3(Co)

The synthesis conditions of SrTiO3(Co) samples in which cobalt predominantly enters the A or B sites of the perovskite ABO3 structure are found. EXAFS studies show that the Co impurity at the A site is off-center and is displaced from the site by 1.0 Å. XANES studies reveal two predominant oxidation states of Co: Co2+ at the A site and Co3+ at the B site. First-principles calculations of a number of possible cobalt-containing structural defects reveal defects whose properties are compatible with the experimentally observed Co oxidation state, its local structure, magnetic, electrical, and optical properties.

Magnetic Study of M-type Co-Ti Doped Strontium Hexaferrite Nanocrystalline Particles

The effects of Co-Ti ions substituting Fe3+ ions in strontium hexaferrite nanoparticles synthesized using ball-milling technique were investigated. X-ray diffraction patterns of SrFe12-2xCoxTixO19 (x = 0, 0.2, 0.4, 0.6, 0.8, and 1.0) demonstrated standard SrFe12O19 patterns with space group P63/mmc. The phase purity and the valence state of each ion were examined using X-ray photoelectron spectroscopy. The results indicated a Ti4+ valence state and a coexistence of 2 + and 3 + valence states for Fe and Co. An obvious irreversibility between the zero-field-cooled (ZFC) and field-cooled (FC) magnetization curves was observed below 300 K. The broad peaks in the ZFC curves were attributed to the movement of magnetic domains at temperature (TM). Magnetization hysteresis loops at discrete temperatures between 4 and 300 K showed a ferromagnetic behavior, with high coercive fields and large saturation magnetizations. The change of the saturation magnetization with increasing x revealed spin reorientation behavior at x ≥ 0.4 and remained relatively high for practical applications. The first anisotropy constant decreased with the increase of temperature. With Co-Ti substitution, it remained almost constant up to x = 0.4, and then decreased almost linearly at higher Co-Ti concentrations. Furthermore, the coercive field decreased with increasing x, reaching values suitable for high-density magnetic recording at 300 K in the substitution range 0.4 ≤ x ≤ 0.8.

Finite element approximations of parabolic optimal control problem with measure data in time

ABSTRACT The purpose of this paper is to study the a priori error analysis of finite element method for parabolic optimal control problem with measure data in a bounded convex domain. The solution of the state equation of this kind of problem exhibits low regularity which introduces some difficulties for both theory and numerics of finite element method. We first prove the existence, uniqueness and regularity results for the solutions of control problem under low regularity assumption on the state variable. For numerical approximations, we use continuous piecewise linear functions for the state and co-state variables, and piecewise constant functions for the control variable. Both spatially discrete and fully discrete finite element approximations of the control problem are analyzed. We derive a priori error estimates of order for the state, co-state and control variables for the spatially discrete problem. A time discretization scheme based on implicit backward-Euler method is applied to obtain error estimates of order for the state, co-state and control variables. Numerical results are presented to illustrate our theoretical findings.

Co-Ni based hybrid transition metal oxide nanostructures for cost-effective bi-functional electrocatalytic oxygen and hydrogen evolution reactions

Water splitting is widely regarded as one of the promising technologies for hydrogen fuel production and foreshadowed to assist in meeting the global energy demand as a sustainable and reliable energy technology. In this regard, we report on the facile chemical synthesis of hybrid Cobalt (Co) and Nickel (Ni) oxide nanostructure for low-cost bi-functional electrocatalytic water splitting applications. Their crystalline characteristics and chemical structure were studied using X-ray diffraction and Fourier-Transform infrared (FT-IR) spectrum. The nanostructure morphology was investigated by scanning and high-resolution transmission electron microscopy (SEM/HRTEM). The 2+ and 3+ valence state of Co and Ni metal ions was identified using X-ray photoelectron spectroscopy (XPS). The hybrid oxide electrocatalyst was found to display an excellent oxygen/hydrogen evolution reaction (OER/HER activity) in alkaline condition. The realization of random heterojunction configuration across the hybrid nanostructures was found to offer an improved conductivity and enhanced charge transfer capability to promote the gas evolution kinetics. Overpotential value of 203 and 378 mV was registered from the respective OER and HER polarization curves (for current density of ±10 mA cm−2). Tafel slope of 87 mV/dec for OER and 90 mV/dec for HER along with the long-term stability results authenticated the anodic/cathodic characteristics of hybrid oxides for overall water splitting applications.

The mechanism of magnetostructural transition in Heusler alloy Co2V1.5Ga0.5

Recently, magnetic field induced low magnetization tetragonal martensite to high magnetization cubic austenite transformation has been realized in Heusler alloy Co50V34Ga16 (Applied Physics Letters112, 211903 (2018)). In this paper, first-principles calculations have been performed on Heusler alloy Co2V1.5Ga0.5 to reveal the mechanism for magnetostructural transition. It has been found that the alloy prefers to crystallize into ferromagnetic L21 type structure at austenite, with Co atoms tending to occupy the Wyckoff sites A (0, 0, 0) and C (0.5, 0.5, 0.5), V atoms occupying at site B (0.25, 0.25, 0.25), Ga and the extra V atoms entering D (0.75, 0.75, 0.75) site. Moments of Co and V atoms parallel to each other and a total formula moment of 2.95 μB is achieved. A potential of tetragonal distortion from ferromagnetic cubic structure to non-magnetic tetragonal structure has been predicted from the view of energetically favorable state. The stability of tetragonal Co2V1.5Ga0.5 is further confirmed by the phonon spectrum. The peaks of dx2-y2 and dz2 states for Co and V(D) 3d states near the Fermi level for the cubic structure split at the tetragonal structure, implying the structural transition is mainly attributed to the band Jahn-Teller effect. The hybridization between the Co 3d states and the 3d states of V at D site plays an important role in the martensitic transformation. A volume contraction of 1.3% is obtained accompanying with the magnetostructural transition.

Electrolyzer with hierarchical transition metal sulfide and phosphide towards overall water splitting

Transition metal sulfide (TMS) and phosphide (TMP) have been considered as efficient catalysts for electrochemical water splitting. Here, we have reported an effective strategy to synthesize TMS- and TMP-assembled hierarchical anode (CuS@CoS2) and cathode (Cu3P@Co2P) for oxygen evolution reaction (OER) and hydrogen evolution reaction (HER), respectively. It is found that the three-dimensional (3D) hierarchical electrodes not only provide a large number of active sites to promote the apparent catalytic activity, but also present tuned valence state of Co, which enhances the intrinsic activity of the active sites. Therefore, the CuS@CoS2 anode possesses excellent OER activity with an overpotential of 230 mV at a current density of 10 mA/cm2, and the Cu3P@Co2P cathode exhibits good HER performance with a low overpotential of 95 mV at a current density of 10 mA/cm2. Impressively, the CuS@CoS2//Cu3P@Co2P electrolyzer deliver a current density of 10 mA/cm2 at a cell voltage of 1.55 V for overall water splitting, which is better than most reported TMS and TMP based catalysts.

Effects of Nonstoichiometry and Plastic Deformation on Charge and Spin States of Cobalt Ions in LnBaCo2BaO5.5 – δ (Ln = Tb, Eu): Soft X-ray Absorption Spectroscopy Studies

We present results of soft X-ray absorption spectroscopy studies of nonstoichiometric Tb1 ‒ yBa1 +yCo2 –xO5.5 – δ cobaltites and EuBaCo2O5.5 cobaltite powders subjected to mechanical impact (milling in a ball mill). It was established that in octahedra of Tb1 – yBa1 + yCo2 – xO5.5 – δ cobaltates Co3+ ions are in the high spin state. In EuBaCo2O5.5 powder after milling in a ball mill, a surface area (5–10 nm) of particles was found to be decomposed into Co3O4, BaCO3, and EuCoO3 phase components. A knowledge of the low-spin state of Co3+ ions in EuCoO3 and Co3O4 and possibilities of surface-sensitive soft X-ray absorption spectroscopy have allowed to determine the composition of the EuBaCo2O5.5 sample (subjected to ball milling) near its surface, which is inaccessible to standard X-ray phase analysis.

Effect of nonmagnetic substitution on the magnetic correlation of the frustrated Ca3CoMn1-xGaxO6 (0≤x≤0.2)

For the spin-chain compound Ca3CoMnO6, the perfect Co/Mn ionic order causes the lost of ↑↑↓↓ long-range antiferromagnetic order. The lost long-range magnetic order results in the emergence of short range magnetic correlation interaction, forming the so called “order by disorder” phenomenon. In present paper, nonmagnetic Ga3+-doped Ca3CoMn1-xGaxO6 compounds were prepared. The influence of Ga3+ substitution on the structure and magnetic order of Ca3CoMn1-xGaxO6 were investigated. It is found that the solid solubility of Ga3+ cation in Ca3CoMn1-xGaxO6 is 0.2 < x < 0.3. With introducing of Ga3+ cation, the oxidation state of some Co cations changes from Co2+ to Co3+. Magnetization measurements reveal that doped with nonmagnetic Ga3+ weakens the formation of short range magnetic order and enhances the antiferromagnetic transition temperature. As a result, more robust long rang antiferromagnetic order is established and the transition field that causes the ↑↑↓↓ spin state of Co–Mn–Co–Mn chain to ↑↑↓↑ state increases obviously. Meanwhile, the shortened short range magnetic correlation in Ga3+ doped Ca3CoMn1-xGaxO6 can be driven more easily by the thermal activation energy and a quicker dynamic behavior was observed in time windows.

Strain-controlled carbon nitride: A continuously tunable membrane for gas separation

Introducing strain during membrane separation is an excellent strategy for achieving controllable separation performance. Herein, a continuously tunable carbon nitride (CN) membrane was investigated under the tensile strain of 0.00–10.00% for gas separation by using density functional theory (DFT) and molecular dynamic (MD) simulations. The DFT calculations showed that CN membrane exhibited a decreasing gas diffusion energy barrier and increasing diffusion rate and permeance with the increase in applied tensile strain. The “open” and “closed” states for gas molecules penetrating CN membrane can thus be regulated by the controlled strain. The transition points of “open” and “closed” states for H2, CO2, CO, N2, and CH4, based on their permeances, occurred under 0.00%, 0.41%, 2.17%, 2.78%, and 8.62% strains, respectively. The results of MD simulations match well with the DFT results. Thus, CN membrane can be performed for the continuous gas separation of CH4, N2, CO, CO2, and H2 from mixtures under controlled strain. This work highlighted strain-controlled carbon nitride as a potential continuously tunable membrane for light gas separation, and opened a promising avenue for the screening of industrial gas separation membranes.

Novel nano-architectured water splitting photoanodes based on TiO2-nanorod mats surface sensitized by ZIF-67 coatings

We report on the synthesis, characterization and application to water photo-dissociation of micrometer-long self-ordered TiO2 nanorod (TDNR) mats, surface sensitized by deposition of cobalt dodecahedral Zeolitic Imidazolate Framework (ZIF-67) coatings. TDNR mats have been grown over glass/FTO substrates from titanium (IV) butoxide, by using a solvothermal procedure at 150 °C. Homogeneous micrometer-thick mats of ~120 nm wide TDNRs (surface density ~15–20 nanorods per μm2) have been obtained. The TDNR mats have been impregnated by crystalline coatings of ZIF-67 MOF. Four different photoelectrodes, containing different amounts of ZIF-67, have been prepared and characterized. X-ray photoelectron spectroscopy analysis revealed that the oxidation state of Co is CoII. The presence of MOF at the surface of TDNRs has been found to greatly impact the optical properties of TiO2: light absorption is shifted to the Vis region. The apparent band-gaps of the composites were determined from Tauc's plots. The photoelectrodes have been used as photoanodes for water photooxidation in Na2SO4 aqueous solutions. I–V curves have been measured under chopped illumination conditions by linear sweep voltammetry (LSV), under Vis and UV–Vis irradiation. The dynamics of charge transfer at the interface has been investigated by photoelectrochemical impedance spectroscopy (PEIS). In the dark, all photoelectrodes present a capacitive behavior with a high impedance. Under Vis irradiation, only one time constant is observed, and all photoelectrodes impedances are found in the 105–106 Ω cm2 range. Such values are consistent with the observed photocurrents. Under UV–Vis light, PEIS spectra appeared flattened and therefore the data have been fitted with two time constants, with a model considering the presence of surface states at the interface. The photoanode presenting the highest photocurrent (16 h of MOF growth) also displays the lowest value for the charge transfer resistance from trap states, clearly evidencing the role of the MOF as a surface co-catalyst with a beneficial effect for water splitting. The presence of MOF at the surface has been also found to increase the rate of charge recombination. The observed photocurrent has been found to be a result of the dynamic interplay between charge transfer and recombination microscopic processes.

Preparation, characterization and photocatalytic activity of nickel-substituted CoFe2O4: exploration of changes in the micro structural parameters and distribution of cations in the lattice

NixCo1−x Fe2O4 (x = 0.0, 0.3, 0.6 and 0.9) samples were prepared by sol-gel combustion method and were characterized by various analytical techniques. The tetrahedral (A) and octahedral (B) radius permits one to calculate the edge length and bond length of M–O at A and B sites. Cation distribution is used to calculate the ionic radius of tetrahedral and octahedral sites and oxygen positional parameter. We investigated the effects of Ni+2 substitutions on structural and electrochemical properties of CoFe2O4. Due to difference in the ionic radius of Ni2+ and Fe3+ for tetrahedral site and Co2+ and Fe3+ for octahedral site the changes are observed in the structural parameter like hopping length at tetrahedral (LA) site and octahedral (LB) and x-ray density. Ni0.6Co0.4 Fe2O4 shows lower charge transfer resistivity compared to other composition. UV-visible spectra of CoFe2O4, Ni0.3Co0.7Fe2O4, Ni0.6Co 0.4Fe2O4 and Ni 0.9Co 0.1Fe2O4 shows wide absorption and the calculated band gap values were found to be 2.59, 2.24, 2.17 and 2.41 eV respectively. The continue absorption implies active d-d transitions involving transition metals present in the composite. The PL spectra show lesser recombination of photogenerated charge carriers for Ni0.6Co 0.4Fe2O4 catalyst compared to other catalysts. Lower intensity peak represents the lower recombination rate. The chemical environment and elemental binding states of Co, Ni, Fe and O were confirmed by XPS analysis. Photocatalytic activity follows in the decreasing order Ni0.6Co0.4Fe2O4 > Ni0.9Co0.1 Fe2O4 > Ni0.3Co0.7 Fe2O4 > CoFe2O4. Superoxide, perhydroxy radical and hydroxyl free radicals are involved in the degradation of Alizarin Red S (ARS).

Enhanced Activity of C2N-Supported Single Co Atom Catalyst by Single Atom Promoter.

The remarkable chemical activity of metal single-atom catalysts (SACs) lies in their unique electronic states associated with the low-coordination nature of single-atom sites. Yet, electronic state manipulation normally requires direct contact with other atoms, which inevitably changes the low-coordination environment. Herein, we found by first-principle calculations that the activity of a Co SAC for HCOOH dehydrogenation is appreciably enhanced via electronic state manipulation by a noncontact single atom promoter. A Co atom and a Sn/Ge/Pb atom are anchored in the same cavity of a graphitic C2N monolayer. Surprisingly, the nonbonded promoter makes two far splitting spin states of Co almost degenerate via charge redistribution of C2N support. Further, the high-spin Co gives a remarkably low reaction barrier comparable to Pt or Pd catalysts. Our results demonstrate that the activity of a SAC can be tuned via a noncontact promoter, casting new insights into electronic state modulation of SACs on graphene-like support.

N-Doped Graphene Oxide Decorated with PtCo Nanoparticles for Immobilization of Double-Stranded Deoxyribonucleic Acid and Investigation of Clenbuterol-Induced DNA Damage.

We demonstrate here a facile hydrothermal-assisted formation of PtCo alloy nanoparticles (NPs) and their simultaneous anchoring on the graphitic surface of N-doped graphene oxide (NGO). Doping induced nanopores in the carbon surface to facilitate the uniform and homogeneous anchoring of alloy nanoparticles. It was revealed that the formation of PtCo NPs on an NGO interface plodded excellent tendency toward double-stranded deoxyribonucleic acid (dsDNA). The dsDNA immobilization was enabled by the presence of several oxidation states of Pt and Co. The same property was further used to monitor the direct detection of dsDNA damage induced by clenbuterol via screen-printed carbon electrodes. Cyclic voltammetric and electrochemical impedance spectroscopic characterization traced well the dsDNA attachment on the modified electrode surface. Differential pulsed voltammetry was further used as a tool to monitor the characteristic guanine peak before and after incubating with clenbuterol used as a damage probe for the dsDNA. The findings can further be appurtenant in exploring dsDNA immobilization protocols and developing analytical methods for determination of various dsDNA damaging agents.

Bézier curve parametrisation and echo state network methods for solving optimal control problems of SIR model

In this work, we introduce an optimal control problem with two control variables of the SIR (susceptible-infected-recovered) epidemic model to minimise the infective and susceptible individuals. To solve the control problem, we use direct Bernstein–Bézier parametrisation of the control variables and metaheuristic optimisation methods of an objective function, and indirect methods, adaptive critic design (ACD) with echo state networks (ESNs) and Pontryagin's maximum principle. We propose Bernstein–Bézier parametrisation and ESNs based algorithms to solve optimal control problems for systems governed by differential equations. We use ACD with ESNs to approximate co-state equations. Our simulations have shown that the proposed two methods are able to solve optimal control problems.

Convergence and superconvergence of variational discretization for parabolic bilinear optimization problems

In this paper, we investigate a variational discretization approximation of parabolic bilinear optimal control problems with control constraints. For the state and co-state variables, triangular linear finite element and difference methods are used for space and time discretization, respectively, superconvergence in H^{1}-norm between the numerical solutions and elliptic projections are derived. Although the control variable is not discrete directly, convergence of second order in L^{2}-norm is obtained. These theoretical results are confirmed by two numerical examples.

Effect of Underlying Cobalt Content on Oxygen Reduction Reaction Activity at Pt-Skin/Pt100-XCox (111) Single Crystal Electrodes

The R&D of highly active and durable cathode catalysts for the oxygen reduction reaction (ORR) is very important for polymer electrolyte fuel cells (PEFCs). Bimetallic alloys of Pt such as Pt-Co exhibit higher ORR activities than that of pure Pt.1 For polycrystalline Pt alloy electrodes, the kinetically-controlled area-specific current densities (jk ) for the ORR strongly depend on the bulk Co composition.2 It is essential to analyze the mechanism of the increased ORR activity at well-defined Pt-alloys by multilateral techniques. Recently, we have demonstrated the composition dependence of jk at a series of (111), (110), and (100) faces of Pt100−xCox single crystal electrodes, on which well-defined Pt-skin layers were formed by annealing in H2.3 The Pt-skin/Pt73Co27(111) electrode exhibited the highest jk value, which was about 27 times higher than that on pure Pt(111). In the present research, we have examined the effect of layer-by-layer composition, measured under electrochemical conditions, of three different Pt100−xCox(111) electrodes with varying Co bulk content (x = 17, 25, 30 at.%) on the ORR activity. The Pt100−xCox(111) single crystal electrodes (ca. 3.5 mm in diameter and 1.5 mm in thickness) were prepared in the same manner as described in our previous work.3 The Co composition in bulk was evaluated by use of X-ray photoelectron spectroscopy (XPS). Prior to the all measurements, the Pt100−xCox(111) electrodes were heat-treated at 1170 K in 100% H2 to prepare the well-defined surface. In-situ surface X-ray scattering (SXS) measurements were carried out at synchrotron radiation facilities (SPring-8 and the Photon Factory) in the same manner as described previously.4 After filling the electrochemical cell with N2-purged 0.1 M HClO4, the working electrode was polarized at 0.4 V vs. RHE. Structure parameters from the topmost to fourth layers were determined from the least-squares fitting to X-ray reflectivity data [(00) crystal truncation rod (CTR)] with a kinematical calculation based on a specific interfacial model. Figure 1 shows the dependence of jk at 0.9 V vs. RHE on x, together with layer-by-layer composition of Pt and Co analyzed by in situ SXS. The composition of the topmost layer was found to be Pt 98 at.% for all three alloys, regardless of Co content, i.e., a Pt-skin layer was formed on the surface of the Pt-Co(111) single crystal electrodes. In contrast, the Co content in the second layer changed significantly with the Co content in bulk. It is striking that the second layer of Pt75Co25(111) (Pt3Co(111)) was nearly pure Co, 98 at.%, where the jk value was close to the maximum value, ca. 25 times higher than that of pure Pt(111). At Co 30 at.% in bulk, jk decreased, and the Co content in the second layer (32 at.%) was very similar to that in bulk. The Co content in the third layer ranged from ca. 20 at.% to ca. 30 at.% in the three kind electrodes. Thus, the ORR activities of Pt-skin/Pt100−xCox(111) electrodes were strongly correlated with the enrichment of Co in the second layer. It was found by ex-situ angle-resolved, grazing-incidence XPS (ARGI-XPS) for Pt-skin/ Pt73Co27(111) that Co in the subsurface layers was positively charged, which was completely different from the electronic state of Co(II)O.4 Such an electronically positive state of Co is reasonably explained by an electron transfer from Co into the Pt-skin layer, which has been linked to a d-band center downshift. This work was supported by funds for the SPer-FC project from NEDO and a Grant-in-Aid (No. 25410007) for Scientific Research MEXT of Japan. We wish to thank Dr. K. Tamura of the Japan Atomic Energy Agency and Drs. I. Hirosawa and T. Watanabe of SPring-8 for their help with the CTR fitting program and SXS measurements, respectively. The synchrotron radiation experiments were performed as projects approved by the PAC (No. 2016G059) and by JASRI (2016A1184 and 2016B1551). References V. R. Stamenkovic, B. S. Mun, K. J. J. Mayrhofer, P. N. Ross, N. M. Markovic, J. Rossmeisl, J. Greeley, J. K. Nørskov, Angew. Chem. Int. Ed., 45, 2897 (2006).T. Toda, H. Igarashi, H. Uchida, M. Watanabe, J. Electrochem. Soc. 146, 3750 (1999).S. Kobayashi, M. Wakisaka, D. A. Tryk, A. Iiyama, H. Uchida, J. Phys. Chem. C, 121,11234 (2017).S. Kobayashi, M. Aoki, M. Wakisaka, T. Kawamoto, R. Shirasaka, K. Suda, D. A. Tryk, J. Inukai, T. Kondo, H. Uchida, ACS Omega, 3, 154 (2018). Figure 1

Pitaya pulp structural cobalt–carbon composite for efficient hydrogen generation from borohydride hydrolysis

The design and synthesis of high efficiency catalysts for hydrogen generation and storage are the key factors for large-scale hydrogen use. Herein, a Pitaya pulp structural cobalt-based carbon nanocatalyst is synthesized. The 5–10 nm Co/CoOx particles are uniformly distributed in the 500-nm spherical carbon matrix and enable efficient catalytic performance during hydrogen generation from the alkaline NaBH4 and NH3BH3 solutions at 3998 mL min−1·gCo−1 for NaBH4 and 4677 mL min−1·gCo−1 for NH3BH3. The catalyst nanoparticles were prepared by a facile one-pot solution reaction, pyrolysis at high temperature, and oxidation in air. The coexistence of various valence states of Co in the composite material is observed by utilizing various characterization methods. Co nanoparticles fixed in the carbon matrix effectively prevent particles from aggregation and loss. This unique structure's similarity with Pitaya pulp, its synergistic effects, and its self-stirring mode enable its effective catalytic performance and good stability. The results provide a reference direction for the design and synthesis of unique structure catalysts for efficient hydrogen production.

Extended finite element methods for optimal control problems governed by Poisson equation in non-convex domains

This paper analyzes two eXtended finite element methods (XFEMs) for linear quadratic optimal control problems governed by Poisson equation in non-convex domains. We follow the variational discretization concept to discretize the continuous problems, and apply an XFEM with a cut-off function and a classic XFEM with a fixed enrichment area to discretize the state and co-state equations. Optimal error estimates are derived for the state, co-state and control. Numerical results confirm our theoretical results.