Insights into Nano-and Micro-Structured Scaffolds for Advanced Electrochemical Energy Storage

Adopting a nano-and micro-structuring approach to fully unleashing the genuine potential of electrode active material benefits in-depth understandings and research progress toward higher energy density electrochemical energy stor-age devices at all technology readiness levels.Due to various challenging issues,especially limited stability,nano-and micro-structured(NMS)electrodes undergo fast electrochemical performance degradation.The emerging NMS scaffold design is a pivotal aspect of many electrodes as it endows them with both robustness and electrochemical performance enhancement,even though it only occupies comple-mentary and facilitating components for the main mechanism.However,extensive efforts are urgently needed toward optimizing the stereoscopic geometrical design of NMS scaffolds to minimize the volume ratio and maximize their functionality to fulfill the ever-increasing dependency and desire for energy power source supplies.This review will aim at highlighting these NMS scaffold design strategies,summariz-ing their corresponding strengths and challenges,and thereby outlining the potential solutions to resolve these challenges,design principles,and key perspectives for future research in this field.Therefore,this review will be one of the earliest reviews from this viewpoint.

Activating Ru in the pyramidal sites of Ru_(2)P-type structures with earth-abundant transition metals for achieving extremely high HER activity while minimizing noble metal content

Rational design of efficient pH-universal hydrogen evolution reaction catalysts to enable large-scale hydrogen production via electrochemical water splitting is of great significance,yet a challenging task.Herein,Ru atoms in the Ru_(2)P structure were replaced with M=Co,Ni,or Mo to produce M_(2-x)Ru_(x)P nanocrystals.The metals show strong site preference,with Co and Ni occupying the tetrahedral sites and Ru the square pyramidal sites of the CoRuP and NiRuP Ru_(2)P-type structures.The presence of Co or Ni in the tetrahedral sites leads to charge redistribution for Ru and,according to density functional theory calculations,a significant increase in the Ru d-band centers.As a result,the intrinsic activity of CoRuP and NiRuP increases considerably compared to Ru_(2)P in both acidic and alkaline media.The effect is not observed for MoRuP,in which Mo prefers to occupy the pyramidal sites.In particular,CoRuP shows state-of-the-art activity,outperforming Ru_(2)P with Pt-like activity in 0.5 M H_(2)SO_(4)(η10=12.3 mV;η100=52 mV;turnover frequency(TOF)=4.7 s^(-1)).It remains extraordinarily active in alkaline conditions(η10=12.9 mV;η100=43.5 mV)with a TOF of 4.5 s^(-1),which is 4x higher than that of Ru_(2)P and 10x that of Pt/C.Further increase in the Co content does not lead to drastic loss of activity,especially in alkaline medium,where,for example,the TOF of Co_(1.9)Ru_(0.1)P remains comparable to that of Ru_(2)P and higher than that of Pt/C,highlighting the viability of the adopted approach to prepare cost-efficient catalysts.

Temperature and structure measurements of heavy-ion-heated diamond using in situ X-ray diagnostics

We present in situ measurements of spectrally resolved X-ray scattering and X-ray diffraction from monocrystalline diamond samples heatedwith an intense pulse of heavy ions.In this way,we determine the samples’heating dynamics and their microscopic and macroscopic structuralintegrity over a timespan of several microseconds.Connecting the ratio of elastic to inelastic scattering with state-of-the-art density functionaltheory molecular dynamics simulations allows the inference of average temperatures around 1300 K,in agreement with predictions fromstopping power calculations.The simultaneous diffraction measurements show no hints of any volumetric graphitization of the material,butdo indicate the onset of fracture in the diamond sample.Our experiments pave the way for future studies at the Facility for Antiproton andIon Research,where a substantially increased intensity of the heavy ion beam will be available.

Effects of sequential decay on collective flows and nuclear stopping power in heavy-ion collisions at intermediate energies

In this study, the rapidity distribution, collective flows, and nuclear stopping power in ^(197)Au+^(197)Au collisions at intermediate energies were investigated using the ultrarelativistic quantum molecular dynamics(UrQMD) model with GEMINI++ code. The UrQMD model was adopted to simulate the dynamic evolution of heavy-ion collisions, whereas the GEMINI++ code was used to simulate the decay of primary fragments produced by UrQMD. The calculated results were compared with the INDRA and FOPI experimental data. It was found that the rapidity distribution, collective flows, and nuclear stopping power were affected to a certain extent by the decay of primary fragments, especially at lower beam energies. Furthermore, the experimental data of the collective flows and nuclear stopping power at the investigated beam energies were better reproduced when the sequential decay effect was included.

Nonlinear branched flow of intense laser light in randomly uneven media

Branched flow is an interesting phenomenon that can occur in diverse systems.It is usually linear in the sense that the flow does not alter the properties of the medium.Branched flow of light on thin films has recently been discovered.It is therefore of interest to know whether nonlinear light branching can also occur.Here,using particle-in-cell simulations,we find that in the case of an intense laser propagating through a randomly uneven medium,cascading local photoionization by the incident laser,together with the response of freed electrons in the strong laser fields,triggers space–time-dependent optical unevenness.The resulting branching pattern depends dramatically on the laser intensity.That is,the branching here is distinct from the existing linear ones.The observed branching properties agree well with theoretical analyses based on the Helmholtz equation.Nonlinear branched propagation of intense lasers potentially opens up a new area for laser–matter interaction and may be relevant to other branching phenomena of a nonlinear nature.

Laser peeler regime of high-harmonic generation for diagnostics of high-power focused laser pulses

A method for measuring the intensity of focused high-power laser pulses based on numerical simulation of high-harmonic generation in the laser peeler regime is proposed.The dependence of the efficiency of high-harmonic generation on the laser pulse intensity and the spatial parameters during interaction with solid targets is studied numerically.The simulation clearly shows that the amplitude of the generated harmonics depends on the laser pulse parameters.The proposed method is simpler than similar intensity measurement techniques and does not require complex preparation.

Mathematical Aspects of SU (2) and SO(3,R) Derived from Two-Mode Realization in Coordinate-Invariant Form

Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.

Fabrication and characterization of rugate structures composed of SiO_(2) and Nb_(2)O_(5)

Gradient index layers and rugate structures were fabricated on a Leybold Syrus pro deposition system by plasma-assisted coevaporation of the low index material silica and the high index material niobium pentoxide.To obtain information about the compositional profiles of the produced layers,cross sectional transmission electron microscopy was used in assistance to deposition rate data recorded by two independent crystal monitors during the film preparation.The depth dependent concentration profiles were transformed to refractive index gradients by means of effective medium approximation.Based on the refractive index gradients the corresponding samples`transmission and reflection spectra could be calculated by utilizing matrix formalism.The relevance of the established refractive index profiles could be verified by comparison of the calculated spectra with the measured ones.

Approach to a Proof of the Riemann Hypothesis by the Second Mean-Value Theorem of Calculus

By the second mean-value theorem of calculus (Gauss-Bonnet theorem) we prove that the class of functionswith an integral representation of the form with a real-valued function which is non-increasing and decreases in infinity more rapidly than any exponential functions , possesses zeros only on the imaginary axis. The Riemann zeta function as it is known can be related to an entire functionwith the same non-trivial zeros as . Then after a trivial argument displacement we relate it to a function with a representation of the form where is rapidly decreasing in infinity and satisfies all requirements necessary for the given proof of the position of its zeros on the imaginary axis z=iy by the second mean-value theorem. Besides this theorem we apply the Cauchy-Riemann differential equation in an integrated operator form derived in the Appendix B. All this means that we prove a theorem for zeros of on the imaginary axis z=iy for a whole class of function which includes in this way the proof of the Riemann hypothesis. This whole class includes, in particular, also the modified Bessel functions for which it is known that their zeros lie on the imaginary axis and which affirms our conclusions that we intend to publish at another place. In the same way a class of almost-periodic functions to piece-wise constant non-increasing functions belong also to this case. At the end we give shortly an equivalent way of a more formal description of the obtained results using the Mellin transform of functions with its variable substituted by an operator.

Correction and Supplement to Approach for a Proof of Riemann Hypothesis by Second Mean-Value Theorem

From the theorem 1 formulated in [1], a set of functions of measure zero within the set of all corresponding functions has to be excluded. These are the cases where the Omega functions Ω(u)?are piece-wise constant on intervals of equal length and non-increasing due to application of second mean-value theorem or, correspondingly, where for the Xi functions Ξ(z)?the functions Ξ(y)y are periodic functions on the imaginary axis y with?z=x+iy. This does not touch the results for the Omega function to the Riemann hypothesis by application of the second mean-value theorem of calculus and the majority of other Omega functions in the suppositions, but makes their derivation correct. The corresponding calculations together with a short recapitulation of the main steps to the basic equations for the restrictions of the mean-value functions and the application to piece-wise constant Omega functions (staircase functions) are represented.

Boundary Conditions for Sturm-Liouville Equation with Transition Regions and Barriers or Wells

By means of expansions of rapidly in infinity decreasing functions in delta functions and their derivatives, we derive generalized boundary conditions of the Sturm-Liouville equation for transitions and barriers or wells between two asymptotic potentials for which the solutions are supposed as known. We call such expansions “moment series” because the coefficients are determined by moments of the function. An infinite system of boundary conditions is obtained and it is shown how by truncation it can be reduced to approximations of a different order (explicitly made up to third order). Reflection and refraction problems are considered with such approximations and also discrete bound states possible in nonsymmetric and symmetric potential wells are dealt with. This is applicable for large wavelengths compared with characteristic lengths of potential changes. In Appendices we represent the corresponding foundations of Generalized functions and apply them to barriers and wells and to transition functions. The Sturm-Liouville equation is not only interesting because some important second-order differential equations can be reduced to it but also because it is easier to demonstrates some details of the derivations for this one-dimensional equation than for the full three-dimensional vectorial equations of electrodynamics of media. The article continues a paper that was made long ago.

Factorization of Cyclotomic Polynomials with Quadratic Radicals in the Coefficients

In this article we continue the consideration of geometrical constructions of regular n-gons for odd n by rhombic bicompasses and ruler used in [1] for the construction of the regular heptagon (n=7). We discuss the possible factorization of the cyclotomic polynomial in polynomial factors which contain not higher than quadratic radicals in the coefficients whereas usually the factorization of the cyclotomic polynomials is considered in products of irreducible factors with integer coefficients. In considering the regular heptagon we find a modified variant of its construction by rhombic bicompasses and ruler. In detail, supported by figures, we investigate the case of the regular tridecagon (n=13) which in addition to n=7 is the only candidate with low n (the next to this is n=769 ) for which such a construction by rhombic bicompasses and ruler seems to be possible. Besides the coordinate origin we find here two points to fix for the possible application of two bicompasses (or even four with the addition of the complex conjugate points to be fixed). With only one bicompass one has in addition the problem of the trisection of an angle which can be solved by a neusis construction that, however, is not in the spirit of constructions by compass and ruler and is difficult to realize during the action of bicompasses. As discussed it seems that to finish the construction by bicompasses the correlated action of two rhombic bicompasses must be applied in this case which avoids the disadvantages of the neusis construction. Single rhombic bicompasses allow to draw at once two circles around two fixed points in such correlated way that the position of one of the rotating points on one circle determines the positions of all the other points on the second circle in unique way. The known case n=17 embedded in our method is discussed in detail.

Common Properties of Riemann Zeta Function, Bessel Functions and Gauss Function Concerning Their Zeros

The behavior of the zeros in finite Taylor series approximations of the Riemann Xi function (to the zeta function), of modified Bessel functions and of the Gaussian (bell) function is investigated and illustrated in the complex domain by pictures. It can be seen how the zeros in finite approximations approach to the genuine zeros in the transition to higher-order approximation and in case of the Gaussian (bell) function that they go with great uniformity to infinity in the complex plane. A limiting transition from the modified Bessel functions to a Gaussian function is discussed and represented in pictures. In an Appendix a new building stone to a full proof of the Riemann hypothesis using the Second mean-value theorem is presented.

Dynamical Analysis of Sputtering at Threshold Energy Range： Modelling of Ar＋Ni（100） Collision System

The sputtering process of Ar＋Ni（100） collision systems is investigated by means of constant energy molecular dynamics simulations. The Ni（100） slab is mimicked by an embedded-atom potential, and the interaction between the projectile and the surface is modelled by using the reparametrized ZBL potential. Ni atom emission from the lattice is analysed over the range of 20-50 eV collision energy. Sputtering yield, angular and energy distributions of the scattered Ar and of the sputtered Ni atoms are calculated, and compared to the available theoretical and experimental data.

Photoluminescent Properties of ZnO Films Deposited on Si Substrates

The photoluminescence of ZnO films deposited on Si substrates by reactive dc sputtering has been studied by using a synchrotron radiation(SR)light source.The excitation spectra show a strong excitation band around 195 nm related to 390 nm emission band.Under SR vacuum ultraviolet excitation,a new emission band peaked at 290 nm was found for the first time,besides the ultraviolet emission band(390 nm)and green band(520 nm).

Exciton Condensates and Superconductors-Technical Differences and Physical Similarities

We review several recent theoretical and experimental results in the study of exciton condensates. This includes the present experimental advances in the study of exciton condensates both using layers and coupled bilayers. We will shortly illustrate the different phases of exciton condensates. We focus especially on the Bardeen-Cooper-Schrieffer-like phase and illustrate the similarities to superconductors. Afterwards, we want to illustrate several recent advances and proposals for measuring the different phases of superconductors. In the remainder of this short review, we will provide an outlook for the possibilities and complications for future technical applications of exciton condensates.

Dissipative Quantum Computing with Majorana Fermions

We describe a scheme for universal quantum computation with Majorana fermions. We investigate two possible dissipative couplings of Majorana fermions to external systems, including metallic leads and local phonons. While the dissipation when coupling to metallic leads to uninteresting states for the Majorana fermions, we show that coupling the Majorana fermions to local phonons allows to generate arbitrary dissipations and therefore universal quantum operations on a single QuBit that can be enhanced by additional two-QuBit operations.

Construction of Regular Heptagon by Rhombic Bicompasses and Ruler

We discuss a new possible construction of the regular heptagon by rhombic bicompasses explained in the text as a new geometric mean of constructions in the spirit of classical constructions in connection with an unmarked ruler (straightedge). It avoids the disadvantages of the neusis construction which requires the trisection of an angle and which is not possible in classical way by compasses and ruler. The rhombic bicompasses allow to draw at once two circles around two fixed points in such correlated way that the position of one of the rotating points (arms) on one circle determines the position of the points on the other circle. This means that the positions of all points (arms) on both circles are determined in unique way.

Generating Functions for Products of Special Laguerre 2D and Hermite 2D Polynomials

The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials. Furthermore, the generating function for mixed products of Laguerre 2D and Hermite 2D polynomials and for products of two Hermite 2D polynomials is calculated. A set of infinite sums over products of two Laguerre 2D polynomials as intermediate step to the generating function for products of Laguerre 2D polynomials is evaluated but these sums possess also proper importance for calculations with Laguerre polynomials. With the technique of operator disentanglement some operator identities are derived in an appendix. They allow calculating convolutions of Gaussian functions combined with polynomials in one- and two-dimensional case and are applied to evaluate the discussed generating functions.

Spin excitation spectra of spin–orbit coupled bosons in an optical lattice

Spin-wave excitation plays important roles in the investigation of the magnetic phases. In this paper, we study the spin-wave excitation spectra of two-component Bose gases with spin-orbit coupling in a deep square optical lattice using the spin-wave theory. We find that, while the excitation spectrum of the vortex crystal phase is gapless with a linear dispersion in the vicinity of the minimum point, the spectra of the commensurate spiral spin phase and the skyrmion crystal phase are gapped. Significantly, the spin fluctuations strongly destabilize the classical ground state of the skyrmion phase with the appearance of an imaginary part in the eigenfrequencies of spin excitations. Such features of the spin excitation spectra provide further insights into the exotic spin phases.