An Elasto-plastic Damage Constitutive Theory Based on Pair Functional Potentials and Slip Mechanism

The deformation work rate can be expressed by the time rate of pair functional potentials which describe the energy of materi- als in terms of atomic bonds and atom embedding interactions. According to Cauchy-Born rule, the relations between the micro- scopic deformations of atomic bonds and electron gas and macroscopic deformation are established. Further, atomic bonds are grouped according to their directions, and atomic bonds in the same direction are simplified as a spring-bundle component. Atom embedding interactions in unit reference volume are simplified as a cubage component. Consequently, a material model com- posed of spring-bundle components and a cubage component is established. Since the essence of damage is the decrease and loss of atomic bonding forces, the damage effect can be reflected by the response functions of these two kinds of components. For- mulating the mechanical responses of two kinds of components, the corresponding elasto-damage constitutive equations are de- rived. Considering that slip is the main plastic deformation mechanism of polycrystalline metals, the slip systems of crystal are extended to polycrystalline, and the slip components are proposed to describe the plastic deformation. Based on the decomposition of deformation gradient and combining the plastic response with the elasto-damage one, the elasto-plastic damage constitutive equations are derived. As a result, a material model iormulated with spring-bundle components, a cubage component and slip components is established. Different from phenomenological constitutive theories, the mechanical property of materials depends on the property of components rather than that directly obtained on the representative volume element. The effect of finite deformation is taken into account in this model. Parameter calibration procedure and the basic characteristics of this model are discussed.

Relational and Euclidean Temporal Space

In mathematics, space encompasses various structured sets such as Euclidean, metric, or vector space. This article introduces temporal space—a novel concept independent of traditional spatial dimensions and frames of reference, accommodating multiple object-oriented durations in a dynamical system. The novelty of building temporal space using finite geometry is rooted in recent advancements in the theory of relationalism which utilizes Euclidean geometry, set theory, dimensional analysis, and a causal signal system. Multiple independent and co-existing cyclic durations are measurable as a network of finite one-dimensional timelines. The work aligns with Leibniz’s comments on relational measures of duration with the addition of using discrete cyclic relational events that define these finite temporal spaces, applicable to quantum and classical physics. Ancient formulas have symmetry along with divisional and subdivisional orders of operations that create discrete and ordered temporal geometric elements. Elements have cyclically conserved symmetry but unique cyclic dimensional quantities applicable for anchoring temporal equivalence relations in linear time. We present both fixed equivalences and expanded periods of temporal space offering a non-Greek calendar methodology consistent with ancient global timekeeping descriptions. Novel applications of Euclid’s division algorithm and Cantor’s pairing function introduce a novel paired function equation. The mathematical description of finite temporal space within relationalism theory offers an alternative discrete geometric methodology for examining ancient timekeeping with new hypotheses for Egyptian calendars.

On Minus Paired-Domination in Graphs

The study of minus paired domination of a graph G=(V,E) is initiated. Let SV be any paired dominating set of G , a minus paired dominating function is a function of the form f∶V→{-1,0,1} such that f(v)= 1 for v∈S, f(v)≤0 for v∈V-S , and f(N)≥1 for all v∈V . The weight of a minus paired dominating function f is w(f)=∑f(v) , over all vertices v∈V . The minus paired domination number of a graph G is γ - p( G )=min{ w(f)|f is a minus paired dominating function of G }. On the basis of the minus paired domination number of a graph G defined, some of its properties are discussed.

Field-Induced Structure and Pair Distribution Function of Fractals

The structure transitions in cluster-cluster aggregation (CCA) and diffusion-limited aggregation (DLA) under external electric fields have been investigated by computer simulations. With the increase of external electric field, there exists a structure transition from disorder to order, i. e., the aggregates change from fractals of diffusion-limited CCA and DLA to the electrorheological chains parallel to electric field. Pair distribution shows, the system changes from local order to long-range order gradually with the external field rising.

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.

Fundamental Perspectives on the Electrochemical Water Applications of Metal-Organic Frameworks

Metal-organic frameworks(MOFs),a family of highly porous materials possessing huge surface areas and feasible chemical tunability,are emerging as critical functional materials to solve the growing challenges associated with energy-water systems,such as water scarcity issues.In this contribution,the roles of MOFs are highlighted in electrochemical-based water applications(i.e.,reactions,sensing,and separations),where MOF-based functional materials exhibit outstanding performances in detecting/removing pollutants,recovering resources,and harvesting energies from different water sources.Compared with the pristine MOFs,the efficiency and/or selectivity can be further enhanced via rational structural modulation of MOFs(e.g.,partial metal substitution)or integration of MOFs with other functional materials(e.g.,metal clusters and reduced graphene oxide).Several key factors/properties that affect the performances of MOF-based materials are also reviewed,including electronic structures,nanoconfined effects,stability,conductivity,and atomic structures.The advancement in the fundamental understanding of these key factors is expected to shed light on the functioning mechanisms of MOFs(e.g.,charge transfer pathways and guest-host interactions),which will subsequently accelerate the integration of precisely designed MOFs into electrochemical architectures to achieve highly effective water remediation with optimized selectivity and long-term stability.

The application of synchrotron X-ray techniques to the study ofrechargeable batteries

The increased use of rechargeable batteries in portable electronic devices and the continuous develop-ment of novel applications （e.g. transportation and large scale energy storage）, have raised a strong de-mand for high performance batteries with increased energy density, cycle and calendar life, safety andlower costs. This triggers significant efforts to reveal the fundamental mechanism determining batteryperformance with the use of advanced analytical techniques. However, the inherently complex character-istics of battery systems make the mechanism analysis sophisticated and difficult. Synchrotron radiationis an advanced collimated light source with high intensity and tunable energies. It has particular ad-vantages in electronic structure and geometric structure （both the short-range and long-range structure）analysis of materials on different length and time scales. In the past decades, synchrotron X-ray tech-niques have been widely used to understand the fundamental mechanism and guide the technologicaloptimization of batteries. In particular, in situ and operando techniques with high spatial and temporalresolution, enable the nondestructive, real time dynamic investigation of the electrochemical reaction,and lead to significant deep insights into the battery operation mechanism. This review gives a brief introduction of the application of synchrotron X-ray techniques to the inves-tigation of battery systems. The five widely implicated techniques, including X-ray diffraction （XRD）, PairDistribution Function （PDF）, Hard and Soft X-ray absorption spectroscopy （XAS） and X-ray photoelectronspectroscopy （XPS） will be reviewed, with the emphasis on their in situ studies of battery systems during cycling.

Unraveling transition-metal-mediated stability of spinel oxide via in situ neutron scattering

The energy materials performance is intrinsically determined by structures from the average lattice structure to the atom arrangement, valence, and distribution of the containing transition metal(TM) elements. Understanding the mechanism of the structure transition and atom rearrangement via synthesis or processing is key to expediting the exploration of excellent energy materials. In this work, in situ neutron scattering is employed to reveal the real-time structure evolution, including the TM-O bonds, lattice,TM valence and the migration of the high-voltage spinel cathode LiNi_(0.5)Mn_(1.5)O_(4). The transition-metalmediated spinel destabilization under the annealing at the oxygen-deficient atmosphere is pinpointed.The formation of Mn^(3+) is correlated to the TM migration activation, TM disordered rearrangement in the spinel, and the transition to a layered-rocksalt phase. The further TM interdiffusion and Mn^(3+) reduction are also revealed with multi-stage thermodynamics and kinetics. The mechanisms of phase transition and atom migrations as functions of temperature, time and atmosphere present important guidance on the synthesis in various-valence element containing oxides.

Dynamics Simulation on the Associative Properties of Amphiphilic Functional Monomer Modified Polyacrylamide Copolymers

A kind of amphiphilic functional monomer was selected to modify polyacrylamide （PAM） or partially hydrolyzed polyacrylamide （HPAM）. The relative properties of the modified polyacrylamide （HM-PAM） and modified partially hydrolyzed polyacrylamide （HM-HPAM） such as radius of gyration （Rg）, hydrodynamic radius （RH）, and radial distribution functions （RDFs） have been studied to find the intrinsic relation between the microstructure of the polymer chain and the intrinsic viscosities with changing the amotmt of modified monomers from 1% to 4%. The simulation results show that, compared to HPAM, HM-HPAM has a better performance in increasing viscosity when the percentage of modified monomers is 2% and has a stronger salt tolerance when the modified monomers is 4%. Furthermore, a complex hydrogen bonding network was revealed with the analysis of radial distribution functions （RDFs） and the pair correlation function was used to investigate the diffusivity of Na^＋ and carbon atoms in the COO^- group.

Molecular Dynamics Simulation of Diffusion of Vitamin C in Water Solution

Under different temperatures and concentrations, the diffusion of Vitamin C （VC） in water solution was exam- ined by molecular dynamics simulation. The diffusion coefficients were calculated based on the Einstein equation. The influences of temperature, concentration, and simulation time on the diffusion coefficient were discussed. The results showed that at higher temperature and lower concentration the normal diffusions appear relatively late, but the linear range of mean square displacement curves continues longer than that at lower temperature and higher concentration. At the same temperature, the normal diffusion time increases and the diffusion coefficient decreases as the simulation concentration increases. These simulation results are in good agreement with experiments. Analyses of the pair correlation functions of the simulation systems showed that hydrogen bonds are mainly formed be- tween the hydrogen atoms of VC molecules and oxygen atoms of H20 molecules, rather than between the O atoms of VC molecules and H atoms of H20 molecules. The diffusion coefficient is higher as the interaction between water molecules and VC molecules is stronger when VC concentration is lower. The water in the model systems affects the diffusion of VC molecules by the short-range repulsion of O（H20）-O（H20） pairs and the non-bond interaction of H（H20）-H（H20） pairs. The short-range repulsion of O（H20）-O（H20） pairs is greater when VC concentration is higher, the diffusion of VC is weaker. The greater the non-bond interaction of H（H20）-H（H20） pairs is, the higher the VC diffusion is. It is expected that this study can provide a theoretical direction for the experiments on the mass transfer of VC in water solution.

COMPACT DIFFERENCE SCHEMES FOR THE DIFFUSION AND SCHRODINGER EQUATIONS. APPROXIMATION, STABILITY, CONVERGENCE, EFFECTIVENESS, MONOTONY

Various compact difference schemes （both old and new, explicit and implicit, one-level and two-level）, which approximate the diffusion equation and SchrSdinger equation with periodical boundary conditions are constructed by means of the general approach. The results of numerical experiments for various initial data and right hand side are presented. We evaluate the real order of their convergence, as well as their stability, effectiveness, and various kinds of monotony. The optimal Courant number depends on the number of grid knots and on the smoothness of solutions. The competition of various schemes should be organized for the fixed number of arithmetic operations, which are necessary for numerical integration of a given Cauchy problem. This approach to the construction of compact schemes can be developed for numerical solution of various problems of mathematical physics.

Unusually high electron density in an intermolecular non-bonding region:Role of metal substrate

It has been demonstrated that intermolecular interaction,crucial in a plenty of chemical and physical processes,may vary in the presence of metal surface.However,such modification is yet to be quantitatively revealed.Here,we present a systematical density functional theory study on adsorbed bis（para-pyridyl）acetylene（BPPA） tetramer on Au（111） surface.We observed unusually high electron density between two head-to-head N atoms,an intermolecular ＂non-bonded＂ region,in adsorbed BPPA tetramer.This exceptional electron density originates from the wavefunction hybridization of the two compressed N lone-electron-pair states of two BPPA,as squeezed by a newly revealed N-Au-N threecenter bonding.This bond,together with the minor contribution from N...H-C intermolecular hydrogen bonding,shortens the N-N distance from over 4 A to 3.30 A and offers an attractive lateral interacting energy of 0.60 eV,effectively to a surface-confined in-plane pressure.The overlapped non-bonding vvavefunction hybridization arising from the effective pressure induced by the N-Au-N three-center bonding,as not been fully recognized in earlier studies,was manifested in non-contact Atomic Force Microscopy.