Conditions for realizing one-point interactions from a multi-layer structure model

A heterostructure composed of N parallel homogeneous layers is studied in the limit as their widths l1, . . . , lN shrink to zero. The problem is investigated in one dimension and the piecewise constant potential in the Schrödinger equation is given by the strengths V1, . . . , VN as functions of l1, . . . , lN, respectively. The key point is the derivation of the conditions on the functions V1(l1), . . . , VN(lN) for realizing a family of one-point interactions as l1, . . . , lN tend to zero along available paths in the N-dimensional space. The existence of equations for a squeezed structure, the solution of which determines the system parameter values, under which the non-zero tunneling of quantum particles through a multi-layer structure occurs, is shown to exist and depend on the paths. This tunneling appears as a result of an appropriate cancellation of divergences.

An evaluation of the capacitive behavior of supercapacitors as a function of the radius of cations using simulations with a constant potential method.

We report on the molecular dynamics atomistic applying the constant potential method to determine the structural and electrostatic interactions at the electrode-electrolyte interface of electrochemical supercapacitors as a function of...

PtAu Nanoparticles Supported by Reduced Graphene Oxide as a Highly Active Catalyst for Hydrogen Evolution

PtAu nanoparticles spontaneously deposited on graphene support, PtAu/rGO, have shown remarkably high catalytic activity for hydrogen evolution reaction (HER) in sulfuric acid solution. SEM images of the PtAu/rGO electrode surface showed that Pt nanoparticles that are non-uniform in size occupy both the edges of previously deposited uniform Au nanoparticles and the edges of graphene support. XPS analysis showed that the atomic percentages of Au and Pt in PtAu/rGO were 0.6% and 0.3%, respectively. The atomic percentage of Au alone on previously prepared Au/rGO was 0.7%. Outstanding HER activity was achieved for the PtAu/rGO electrode, showing the initial potential close to the equilibrium potential for HER and a low Tafel slope of −38 mV/dec. This was confirmed by electrochemical impedance spectroscopy. The chronoamperometric measurement performed for 40 min for hydrogen evolution at a constant potential indicated good stability and durability of the PtAu/rGO electrode.

RATIO OF TOTAL SLOW AND SUPER SLOW CEREBRAL BIOELECTRICAL ACTIVITY IN CHILDREN WITH HYPOXIA

The aim of the study is to identify changes in the total slow and super slow bioelectric activity of the cerebral hemispheres in 8–11-year-old children under reduced oxygen partial pressure in the inhaled air and in norm. Materials and Methods. The authors examined 82 8–11-year-old children. EEG registration was carried out on a complex Russian device "Telepat-103" with computer processing of the results. Slow potentials were recorded using a special computer complex for studying constant potential level (CPL) and cerebral energy consumption "Neuroenergon". Hypoxia was created by a special medical device "Hypoxicator" (Trade Medical). The choice of the oxygen content in the test hypoxic mixture (14 % O2) was based on the results of a three-stage hypoxic test carried out before the complex examination. Results. Hypoxia increases the index and amplitude of delta oscillations and decreases the number of alpha waves in 8–11-year-old children. The results obtained indicate that it is more important to provide the brain with a sufficient amount of oxygen corresponding to its needs than simply to increase the brain blood supply during hypoxia. The study also indicates the contribution of the body's sensitivity to hypoxic response. Under hypoxia, an increase in the constant potential level in the studied brain areas is observed in 8–11-year-old children. An increase in electrical activity during normobaric hypoxia is noted at low baseline values of constant potential level. An increase in the slow electrical brain activity occurs due to the change of brain energy supply according to the biochemical indicators of energy metabolism. Short-term hypoxia is accompanied by a simultaneous increase in slow-wave activity due to delta activity and CPL in 8–11-year-old children. Conclusion. Thus, we can say that a picture of functional brain activity with simultaneous inhibitory phenomena in the cortex is formed. It may reflect the development of a special state of the central nervous system. Key words: constant potential level, electroencephalography, hypoxia, adaptation to hypoxia. Цель работы – выявление изменений суммарной медленной и сверхмедленной биоэлектрической активности полушарий головного мозга у детей в возрасте от 8 до 11 лет в условиях нормального и сниженного парциального давления кислорода во вдыхаемом воздухе. Материалы и методы. Обследовано 82 ребенка 8–11-летнего возраста. Регистрация ЭЭГ осуществлялась на комплексной отечественной установке «Телепат-103» с компьютерной обработкой результатов. Медленные потенциалы фиксировались с помощью специального компьютерного комплекса для исследования уровня постоянных потенциалов (УПП) и энергозатрат головного мозга «Нейроэнергон». Гипоксические условия создавались аппаратом «Гипоксикатор» фирмы Trade Medical. Выбор содержания кислорода в тестирующей гипоксической смеси (14 % О2) основывался на результатах проведенного до комплексного обследования трехступенчатого гипоксического теста. Результаты. У детей от 8 до 11 лет действие гипоксии на головной мозг приводит к возрастанию индекса и амплитуды дельта-колебаний и убыванию числа альфа-волн. Полученные результаты говорят о том, что большое значение имеет не столько усиление кровоснабжения головного мозга при гипоксии, сколько обеспечение мозга достаточным, соответствующим его потребностям, количеством кислорода, а также о роли чувствительности организма к гипоксии. При воздействии гипоксии у детей этого возраста наблюдается возрастание уровня постоянных потенциалов в исследуемых областях головного мозга. При низких фоновых значениях уровня постоянных потенциалов отмечается возрастание электрической активности при нормобарической гипоксии. Возрастание медленной электрической активности головного мозга происходит из-за того, что изменяется энергообеспечение головного мозга по биохимическим показателям энергетического обмена. Действие кратковременной гипоксии сопровождается одновременным возрастанием медленноволновой активности за счет дельта-активности и УПП у детей от 8 до 11 лет. Выводы. Таким образом, можно говорить о том, что формируется своеобразная картина функциональной активности с одновременными тормозными явлениями в коре, что может являться отражением развития особого состояния центральной нервной системы. Ключевые слова: уровень постоянных потенциалов, электроэнцефалография, гипоксия, адаптация к гипоксии.

Functionalization of Screen-Printed Sensors with A High Reactivity Carbonaceous Material for Ascorbic Acid Detection in Fresh-Cut Fruit with Low Vitamin C Content

In this study, carbon screen-printed sensors (C-SPEs) were functionalized with a high reactivity carbonaceous material (HRCM) to measure the ascorbic acid (AA) concentration in fresh-cut fruit (i.e., watermelon and apple) with a low content of vitamin C. HRCM and the functionalized working electrodes (WEs) were characterized by SEM and TEM. The increases in the electroactive area and in the diffusion of AA molecules towards the WE surface were evaluated by cyclic voltammetry (CV) and chronoamperometry. The performance of HRCM-SPEs were evaluated by CV and constant potential amperometry compared with the non-functionalized C-SPEs and MW-SPEs nanostructured with multi-walled carbon nanotubes. The results indicated that SPEs functionalized with 5 mg/mL of HRCM and 10 mg/mL of MWCNTs had the best performances. HRCM and MWCNTs increased the electroactive area by 1.2 and 1.4 times, respectively, whereas, after functionalization, the AA diffusion rate towards the electrode surface increased by an order of 10. The calibration slopes of HRCM and MWCNTs improved from 1.9 to 3.7 times, thus reducing the LOD of C-SPE from 0.55 to 0.15 and 0.28 μM, respectively. Finally, the functionalization of the SPEs proved to be indispensable for determining the AA concentration in the watermelon and apple samples.

On the Mechanistic Origins of the pH-Dependency in Au-Catalyzed Glycerol Electro-Oxidation: Insight from First Principles Calculations

Electrocatalytic oxidation of glycerol (EOG) is an attractive approach to convert surplus glycerol to value-added products. Experiments have shown that EOG activity and selectivity depend on the electrocatalyst, but also on the electrode potential, the pH, and the electrolyte. For broadly employed gold (Au) electrocatalysts, experiments have demonstrated high EOG activity under alkaline conditions with glyceric acid as a primary product, whereas under acidic and neutral conditions Au is almost inactive producing only small amounts of dihydroxyacetone. In the present computational work, we have performed an extensive mechanistic study to understand the pH- and potential- dependency of Au-catalyzed EOG. Our results show that activity and selectivity are controlled by the presence of surface-bound hydroxyl groups. Under alkaline conditions and close to the experimental onset potential, modest OH coverage is preferred accord- ing to our constant potential calculations. This indicates that both Au(OH)ads and Au can be active sites and they cooperatively facilitate the thermodynamically and kinetically feasible formation of glyceric acid thus explaining the experimentally observed high activity and selectivity. Under acidic conditions, hydroxide coverage is negligi- ble and the dihydroxyacetone emerges as the favored product. Calculations predict slow reaction kinetics, however, which explains the low activity and selectivity towards dihydroxyacetone reported in experiments. Overall, our findings highlight that com- putational studies should explicitly account for pH and coverage effects under alkaline conditions for electrocatalytic oxidation reactions to reliably predict electrocatalytic behaviour.

Selective Etching of Sr-Modified and Directionally Solidified Industrial Al–Si Eutectic Alloys for Fabricating Fibrous Eutectic Si

In order to fabricate fibrous eutectic Si, the selective etching of industrial Al–Si eutectic alloys directionally solidified at different growth rates and modified by different amounts of Sr was studied. Flake eutectic and fibrous Si were obtained by selective etching of non-modified, Sr-modified or directionally solidified Al–Si eutectic alloys. The optimal amount of Sr for fabricating branching eutectic Si was 0.04–0.07%. Through directional solidification with a high enough growth rate (more than 200 μm/s), lamellar eutectic Si transforms to fibrous eutectic Si for use in non-modified Al–Si eutectic alloys. The potentiodynamic polarization and cyclic voltammetry methods were used to test the corrosion behavior of non-modified and Sr-modified Al–Si eutectic alloys. With a constant potential of 0.5 V in HCl solution, non-modified Al–Si eutectic alloys displayed initial pitting corrosion and subsequent spalling corrosion, and 0.04% Sr-modified samples displayed uniform pitting corrosion. Compared with non-modified Al–Si eutectic alloys, Sr-modified samples displayed better corrosion resistance with lower current density and shallower pit depth during the same etching conditions.

The Enhanced Effect of Bicarbonate Anion for the Removal of 2,4-Dichlorophenoxyacetic Acid on a Palladium/Nickel-Foam Electrode

Palladium/nickel-foam (Pd/Ni) electrode is used as a typical efficient electrocatalytic electrode for the removal of 2,4-dichlorophenoxyacetic acid (2,4-D) in surface water and industrial wastewater. Many researches had reported how to enhance the dechlorination efficiency of the Pd/Ni electrode by using less Pd loading. However, there are few reports of choosing a suitable electrolyte solution to improve the efficiency of dechlorination. Efforts were made in this work of the different catholyte influenced the dechlorination efficiency. The results showed the fastest removal efficiency of 2,4-D in 34 mmol/L NaHCO3 than in 34 mmol/L NaCl, 34 mmol/L NaClO4, 17 mmol/L Na2SO4 catholyte, respectively on Pd/Ni electrode with pd loading of 0.202 mg/cm2 at constant potential of -0.55 V (vs saturated calomel electrode). The dechlorination current efficiency (CE) was 20.5% in the 34 mmol/L NaHCO3 catholyte more than three times that in 17 mmol/L Na2SO4 catholyte for that HCO3- was the most likely source of protons for adsorbed active hydrogen (H*) in Pd active centers.

Resistance scaling on 4N-carpets

The 4 ⁢ N {4N} -carpets are a class of infinitely ramified self-similar fractals with a large group of symmetries. For a 4 ⁢ N {4N} -carpet F, let { F n } n ≥ 0 {\{F_{n}\}_{n\geq 0}} be the natural decreasing sequence of compact pre-fractal approximations with ⋂ n F n = F {\bigcap_{n}F_{n}=F} . On each F n {F_{n}} , let ℰ ⁢ ( u , v ) = ∫ F N ∇ ⁡ u ⋅ ∇ ⁡ v ⁢ d ⁢ x {\mathcal{E}(u,v)=\int_{F_{N}}\nabla u\cdot\nabla v\,dx} be the classical Dirichlet form and u n {u_{n}} be the unique harmonic function on F n {F_{n}} satisfying a mixed boundary value problem corresponding to assigning a constant potential between two specific subsets of the boundary. Using a method introduced by [M. T. Barlow and R. F. Bass, On the resistance of the Sierpiński carpet, Proc. Roy. Soc. Lond. Ser. A 431 (1990), no. 1882, 345–360], we prove a resistance estimate of the following form: there is ρ = ρ ⁢ ( N ) > 1 {\rho=\rho(N)>1} such that ℰ ⁢ ( u n , u n ) ⁢ ρ n {\mathcal{E}(u_{n},u_{n})\rho^{n}} is bounded above and below by constants independent of n. Such estimates have implications for the existence and scaling properties of Brownian motion on F.