The Class of Atomic Exponential Basis Functions EFup_(n)(x,ω)-Development and Application

The purpose of this paper is to present the class of atomic basis functions(ABFs)which are of exponential type and are denoted by EFupn(x,ω).While ABFs of the algebraic type are already represented in the numerical modeling of various problems inmathematical physics and computationalmechanics,ABFs of the exponential type have not yet been sufficiently researched.These functions,unlike the ABFs of the algebraic type Fupn(x),contain the tension parameterω,which gives them additional approximation properties.Exponential monomials up to the nth degree can be described exactly by the linear combination of the functions EFupn(x,ω).The function EFupn for n=0 is called the“mother”ABF of the exponential type,i.e.,EFup0(x,ω)≡Eup(x,ω).In other words,the functions EFupn(x,ω)are elements of the linear vector space EUPn and retain all the properties of their“mother”function Eup(x,ω).Thus,this paper,in terms of its content and purpose,can be understood as a sequel of the article by Brajcic Kurbasa et al.,which shows the basic properties and application of the basis function Eup(x,ω).This paper presents,in an analogous way,the development and application of the exponential basis functions EFupn(x,ω).Here,for the first time,expressions for calculating the values of the functions EFupn(x,ω)and their derivatives are given in a form suitable for application in numerical analyses,which is shown in the verification examples of the approximations of known functions.

Atomic Spacetime Model Based on Atomic AString Functions

A novel model of spacetime and fields atomization based on Atomic Series over finite Atomic AString Functions is offered. Formulated Atomization Theorems allow representing polynomials, analytic functions, and solutions of field equations including General Relativity via superposition of solitonic atoms which can be associated with flexible spacetime quantum, metriants, or elementary distortions. Spacetime is conceptualized as a lattice of flexible Atomic Solitons adjusting locations to reproduce different metrics and other physical fields. It may offer the variants of unified field theory based on Atomic Solitons where, like in string theory, fields become interconnected having a common mathematical ancestor.

Atomic Exponential Basis Function Eup(x,w) - Development and Application

This paper presents exponential Atomic Basis Functions(ABF),which are called Eup(x;w).These functions are infinitely differentiable finite functions that unlike algebraic up(x)basis functions,have an unspecified parameter-frequency w.Numerical experiments show that this class of atomic functions has good approximation properties,especially in the case of large gradients(Gibbs phenomenon).In this work,for the first time,the properties of exponential ABF are thoroughly investigated and the expression for calculating the value of the basis function at an arbitrary point of the domain is given in a form suitable for implementation in numerical analysis.Application of these basis functions is shown in the function approximation example.The procedure for determining the best frequencies,which gives the smallest approximation error in terms of the least squares method,is presented.

Atomic pair distribution function method development at the Shanghai Synchrotron Radiation Facility

The atomic pair distribution function（PDF） reveals the interatomic distance in a material directly in real-space. It is a very powerful method to characterize the local structure of materials. With the help of the third generation synchrotron facility and spallation neutron source worldwide, the PDF method has developed quickly both experimentally and theoretically in recent years. Recently this method was successfully implemented at the Shanghai Synchrotron Radiation Facility（SSRF）. The data quality is very high and this ensures the applicability of the method to study the subtle structural changes in complex materials. In this article, we introduce in detail this new method and show some experimental data we collected.

Kravchenko atomic transforms in digital signal processing

The modified atomic transformations are constructed and proved.On their basis the new complex analytic wavelets are obtained.The proof of the Fourier transforms existence in L1 and L2 on the basis of the theory of atomic functions(AF)are presented.The numerical experiments of digital time series processing and physical analysis of the results confirm the efficiency of the proposed transforms.

Dynamics of solitons in Bose-Einstein condensate with time-dependent atomic scattering length

The evolution of solitons in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature （Phys. Rev. Lett. 94（2005）050402 and Chin. Phys. Lett. 22（2005） 1855）.

Density Functional Study of the C Atom Adsorption on the α-Fe_2O_3 (001) Surface

The adsorption of C atoms on the α-Fe2O3（001） surface was studied based on density function theory（DFT） ,in which the exchange-correlation potential was chosen as the PBE（Perdew,Burke and Ernzerhof） generalized gradient approximation（GGA） with a plane wave basis set. Upon the optimization on different adsorption sites with coverage of 1/20 and 1/5 ML,it was found that the adsorption of C atoms on the α-Fe2O3（001） surface was chemical adsorption. The coverage can affect the adsorption behavior greatly. Under low coverage,the most stable adsorption geometry lied on the bridged site with the adsorption energy of about 3.22 eV; however,under high coverage,it located at the top site with the energy change of 8.79 eV. Strong chemical reaction has occurred between the C and O atoms at this site. The density of states and population analysis showed that the s,p orbitals of C and p orbital of O give the most contribution to the adsorption bonding. During the adsorption process,O atom shares the electrons with C,and C can only affect the outermost and subsurface layers of α-Fe2O3; the third layer can not be affected obviously.

Atomization Theorems in Mathematical Physics and General Relativity

Formulated Atomization Theorems extend the theory of Atomic AString Functions evolving since the 1970s allowing representation of polynomials, complex analytic functions, and solutions of linear and nonlinear differential equations via Atomic Series over smooth finite Atomic Splines. Noting the preservation of analyticity for Ricci and Einstein tensors, special new theorems are formulated for General Relativity representing spacetime field via superpositions of flexible finite “solitonic atoms” resembling quanta. The novel Atomic Spacetime model correlates with A. Einstein’s 1933 paper predicting a new “atomic theory”. The theorems can be applied to many theories of mathematical physics, elasticity, hydrodynamics, soliton, and field theories for unified representation of fields via series over finite Atomic AString Functions which may offer a unified theory under research where fields are connected with a common mathematical ancestor.

Novel polymer acceptors achieving 10.18% efficiency for all-polymer solar cells

Polymer acceptors based on extended fused ring p skeleton has been proven to be promising candidates for all-polymer solar cells(all-PSCs), due to their remarkable improved light absorption than the traditional imide-based polymer acceptors. To expand structural diversity of the polymer acceptors, herein,two polymer acceptors PSF-IDIC and PSi-IDIC with extended fused ring p skeleton are developed by copolymerization of 2,20-((2 Z,20 Z)-((4,4,9,9-tetrahexadecyl-4,9-dihydro-s-indaceno [1,2-b:5,6-b']dithio phene-2,7-diyl)bis(methanylylidene))bis(3-oxo-2,3-dihydro-1 H-indene-2,1-diylidene))dimalononitrile(IDIC-C16) block with sulfur(S) and fluorine(F) functionalized benzodithiophene(BDT) unit and silicon(Si) atom functionalized BDT unit, respectively. Both polymer acceptors exhibit strong light absorption.The PSF-IDIC exhibits similar energy levels and slightly higher absorption coefficient relative to the PSi-IDIC. After blended with the donor polymer PM6, the functional atoms on the polymer acceptors show quite different effect on the device performance. Both of the acceptors deliver a notably high open circuit voltage(V_(OC)) of the devices, but PSi-IDIC achieves higher V OCthan PSF-IDIC. All-PSC based on PM6:PSi-IDIC attains a power conversion efficiency(PCE) of 8.29%, while PM6:PSF-IDIC-based device achieves a much higher PCE of 10.18%, which is one of the highest values for the all-PSCs reported so far. The superior device performance of PM6:PSF-IDIC is attributed to its higher exciton dissociation and charge transport, decreased charge recombination, and optimized morphology than PM6:PSi-IDIC counterpart. These results suggest that optimizing the functional atoms of the side chain provide an effective strategy to develop high performance polymer acceptors for all-PSCs.

Curvature and Size Effects on Reactivities of Mono-to Octa-vacancies in a(5,5) Single-walled Carbon Nanotube

Defect curvature was developed based on our previously proposed direction curvature theory. Defect curvature, as a universal criterion, was used to identify vacancy formation energies E_f of mono-vacancies to octa-vacancies in a（5,5） tube. An ab initio calculation results showed that E_f decreased with increasing the defect curvature K_（V_s）（s = 1~8）. The structures with removed carbon atoms along zigzag chain or the tubular axis were the most stable in each kind of Vs, because their corresponding K_（V_s） was the largest. In addition, local product structures disturbed the variation rule of E_f as K_（V_s）. There was an odd-even oscillation rule in the smallest E_f among each kind of Vs as the s value and vacancies V2, V4 and V6 were more stable. The stabilities of the related vacancy structures were confirmed by two dissociation processes.

Ultra-low lattice thermal conductivity and promising thermoelectric figure of merit in borophene via chlorination

Monolayer boron-based materials are of current interests due to its polymorphism.Herein,motivated by the recent experimental synthesis of semiconducting hydrogenatedαʹ-borophene and the regulation of the physical properties in layered materials by surface functionalization,we study the thermal and electronic properties ofαʹ-borophene with three different types of gas functional groups(H,F,and Cl)based on first-principles and Boltzmann transport theory.It is found thatαʹ-borophene can be well stabilized by fluorination and chlorination and maintain the semiconductor nature.More interestingly,when hydrogen is replaced with fluorine or chlorine,the lattice thermal conductivity changes from 24.3 to 5.2 or 0.73 W/(m·K)along armchair direction at 300 K,exhibiting a huge reduction by two orders of magnitude.The main reason is the decrease of both phonon group velocities and acoustic phonon relaxation time resulting from the strong phonon mode softening due to the weaken B-B bond strength and heavier atomic mass of fluorine and chlorine.Consequently,the chlorinatedαʹ-borophene exhibits a high thermoelectric figure of merit~2 at 300 K along armchair direction.Our study illustrates the importance of the modulation of transport properties by gas functional groups,which may promote the thermoelectric application of boron-based materials.

Big-data-accelerated aperiodic Si/Ge superlattice prediction for quenching thermal conduction via pattern analysis

Thermal conductivity of material is one of the basic physical properties and plays an important role in manipu-lating thermal energy.In order to accelerate the prediction of material structure with desired thermal property,machine learning algorithm has been widely adopted.However,in the optimization of multivariable material structure such as different lengths or proportions,the machine learning algorithm may be required to be recon-ducted again and again for each variable,which will consume a lot of computing resources.Recently,it has been found that the thermal conductivity of aperiodic superlattices is closely related to the degree of the structural ran-domness,which can also be reflected in their local pattern structures.Inspired by these,we propose a new pattern analysis method,in which machine learning only needs to be carried out for one time,and through which the optimal structure of different variables with low thermal conductivity can be obtained.To verify the method,we compare the thermal conductivities of the structure obtained by pattern analysis,conventional machine learning,and previous literature,respectively.The pattern analysis method is validated to greatly reduce the prediction time of multivariable structure with high enough accuracy and may promote further development of material informatics.