Symplectic analysis for elastic wave propagation in two-dimensional cellular structures

On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables and the wave propagation problem is then transformed into two-dimensional （2D） symplectic eigenvalue problems, where the extended Wittrick-Williams algorithm is used to ensure that no phase propagation eigenvalues are missed during computation. Three typical cellular structures, square, triangle and hexagon, are introduced to illustrate the unique feature of the symplectic algorithm in higher-frequency calculation, which is due to the conserved properties of the structure-preserving symplectic algorithm. On the basis of the dispersion relations and phase constant surface analysis, the band structure is shown to be insensitive to the material type at lower frequencies, however, much more related at higher frequencies. This paper also demonstrates how the boundary conditions adopted in the finite element modeling process and the structures＇ configurations affect the band structures. The hexagonal cells are demonstrated to be more efficient for sound insulation at higher frequencies, while the triangular cells are preferred at lower frequencies. No complete band gaps are observed for the square cells with fixed-end boundary conditions. The analysis of phase constant surfaces guides the design of 2D cellular structures where waves at certain frequencies do not propagate in specified directions. The findings from the present study will provide invaluable guidelines for the future application of cellular structures in sound insulation.

Two-dimensional SEM image-based analysis of coal porosity and its pore structure

A quantitative analysis of the porosity,pore size distribution,and fractal dimensions of pores is significant for studying the pore structure characteristics of coal.This study utilized 12 anthracite coal samples from the Sihe mining area to explore the pore structure characteristics of the coal therein.Hundred randomly selected points on each sliced coal sample were imaged via scanning electron microscopy,and a total of 1200 images were used for the analysis.The porosity and fractal dimensions of the coal samples were analyzed via digital image processing and box-counting dimension methods.This method is characterized by extensive graphical analysis,and the results are based on statistical methods.These were also used to analyze the structural and development characteristics of the microscopic pores in the coal.The results reveal that the surface porosity obtained via digital image processing was 16.11%lower than that measured experimentally.The fractal dimension and porosity of the pore surface were fitted to a natural logarithmic curve.The rate of change in the pore fractal dimension depends on the porosity such that,to some degree,a greater porosity is associated with more complex pore structures,a higher degree of micropore development,and improved pore connectivity.

Design,Synthesis and Crystal Structure of Two One-dimensional Zigzag Chain-like Compounds

Two one-dimensional chain-like cyanide-bridged compounds, [Fe（Phen）2（CN）2Ni（Cyclam）]（ClO4）2·DMF-2H2O 1 （Cyclam = 1,4,8,11-tetraaza-cyclotetradecane, Phen = 1,10-phenanthroline, and DMF = N,N-dimethylformamide） and [Fe（Phen）2（CN）2Zn（Cyclam）]（PF6）2·CH3CN 2, were prepared by the reaction of [Fe（Phen）2（CN）2]·2H2O with M（Cyclam）^2＋ （M = Ni, Zn）. In complexes 1 and 2, the metal atoms are connected alternatively with CN groups. X-ray structure and IR analyses for 1 and 2 were performed. Structure analysis revealed that both complexes are centrosymmetric and the geometry around each metal atom is an octahedron. The two complexes crystallize in triclinic with space group of P^1-. For 1, a = 10.439（4）, b = 14.976（7）, c = 15.914（8）A,α = 83.168（15）, β = 74.338（15）, γ = 78.023（15）°, V = 2338.3（18）A^3, Z = 2, Mr = 1035.37, Dc = 1.471 g/cm^3, F（000） = 1076,μ = 0.895 mm^-1, the final R = 0.0616 and wR = 0.1414 for 5849 observed reflections （1 〉 2σ（I））. For 2, a = 9.656（6）, b = 15.404（9）, c = 15.822（10）A, α = 78.68（2）, β= 78.917（19）, γ = 77.15（2）°, V = 2223（2）A^3, Z = 2, Mr = 1064.87, Dc = 1.587 g/cm^3, F（000） = 1078,μ = 1.032 mm^-1, the final R = 0.0672 and wR = 0.1595 for 6819 observed reflections （I 〉 2σ（I））.

A Two-dimensional Supramolecular Complex Constructed by 1,10-Phenanthroline Derivative Ligand:Synthesis,Structure and Luminescence

An unusual two-dimensional supramolecular complex, namely, [Cd2（Cl）4（L）2]（1）, has been synthesized by 2-（1 H-imidazo[4,5-f][1,10]phenanthrolin-2-yl）phenol（L） and CdCl2·2.5H2O under hydrothermal conditions. The compound was characterized by elemental analysis, TG and single-crystal X-ray diffraction. It crystallizes in triclinic, space group P1 with a = 10.151（2）, b = 14.119（3）, c = 14.744（3） ？, α = 115.744（4）, β = 108.063（4）, γ = 93.371（4）o, V = 1762.7（7） A°^3, Z = 2, C（38）H（24）Cd2Cl4N8O2, Mr = 991.25, Dc = 1.868 g/cm^3, F（000） = 976, μ（Mo Ka） = 1.560 mm^-1, R = 0.0639 and w R = 0.1307. In 1, two Cd（II） atoms are bridged by two chroline atoms to give a dimer. Neighboring dimers are linked by N–H···Cl hydrogen bonds to afford supramolecular chains, which are further joined together by π-π interactions to result in a supramolecular layer. In addition, luminescent property and thermal behavior of compound 1 have been studied.

Synthesis and One-dimensional Structure of Cobalt(Ⅱ) Complex [(NaOC_2H_5)CoL_2]_n

The treatment of bis(2-hydroxybenzyl)-amine(HL) with NaOH and Co(Ⅱ)(NO) 2 gives isostructural one-dimensional coordination polymers [(NaOC2H5)CoL2]n(1). The cobalt ions have an octahedral geometry and are coordinated by two crystallographically independent ligands which are further linked by μ -O\-\{phenol\} bridged Co and Na atoms to give a one-dimentional structure.

Two-dimensional Supramolecular Structure of a Mercury(Ⅱ) Iodide Complex with Organosulfide

A mercury（Ⅱ） iodide complex with organosulfide [Hg（pymt）（pymtH）I] 1 （pymt = the anion of pyrimidine-2-thiolate） has been synthesized by slow evaporation of the solution at room temperature and structurally characterized by single-crystal X-ray diffraction. Basic ideas and data collected are given. X-ray diffraction analysis reveals that complex 1 is mononuclear. Crystallographic data： C8H7HgIN4S2, Mr = 550.79, monoclinic system, space group P21/c, a = 11.218（4）, b = 9.551（3）, c = 15.877（4） A^°, β = 129.697（15）°, V = 1308.9（7） A^°^3, Z = 4, Mr = 550.79, Dc = 2.795 g/cm^3, F（000） = 995, μ（MoKa） = 14.415 mm^-1, 2（MoKa） = 0.71073 A^°, T= 293（2） K, 2θmax = 54.9°, GOOF= 1.053, the final R = 0.0310 and wR = 0.0742 for 2547 observed reflections with I 〉 2σ（I） （refinement on F^2）. Complex 1 is connected through hydrogen bonds to give a one-dimensional supramolecular chain structure. Furthermore, π-π interactions are also found between the pyrimidine rings with the center-to-center distances of 3.439（4） and 3.603（4） A^°, so complex 1 expands the chains into a two-dimensional network.

Synthesis, Characterization and Crystal Structure Determination of a Thiocyanato Bridged One-dimensional Polymeric Complex of Cadmium(Ⅱ)

A new one-dimensional polymeric complex [Cd（SCN）2（H2O）]L （L = N,N′-bis（furan- 2-ylmethylene）hydrazine） has been synthesized and characterized by IR, UV spectra, TG-DTA technique and single-crystal X-ray diffraction analysis. It crystallizes in triclinic, pace group P1^- with a = 5.9268（8）, b = 10.8678（15）, c = 13.3671（19） A, α = 109.295（2）, β = 95.092（2）, γ = 97.8580（10）°, V = 796.70（19）A^3, Z = 2, C12H10CdN4O3S2, Mr = 434.76, μ = 1.648 mm^-1, Dc = 1.812 g/cm^3, F（000） = 428, R = 0.0308 and wR = 0.0769. The crystal structure reveals that the structure of [Cd（SCN）2（H2O）]n features di-μ-1,3-thiocyante bridges and 1D chains. The octahedrally coordinated Cd atom is surrounded by one oxygen atom from water molecule, three S atoms and two N atoms from five di-μ-1,3 thiocyanato bridges. The Cd atoms are connected by two di-μ-1,3 thiocyanato bridges with the Cd（1）…Cd（1A） separation of 4.239（1） A and Cd（1）...Cd（1B） of 5.852（1）/~. In addition, the one-dimensional straight chain structure is further connected by multiform intermolecular N-H…O hydrogen bonds and π-π interactions to form a three-dimensional supramolecular structure.

Creative Teaching + Creative Class = Creative Products + Additional Value—A Case Study of Course Reform of Three-dimension Structure

The teaching model of "creative Teaching + creative class = creative products + additional value" was proposed, so as to cultivate students' design creativity and practical ability by changing teaching concepts and curriculum of Three-dimension Structure, and using new materials for spatial creativity training. This paper acclaims that only if the traditional teaching concepts of Three-dimension Structrue are abandoned, students' specialty fully used, the teaching effect will be improved effectively.

LOCALIZED COHERENT STRUCTURES OF THE (2+1)-DIMENSIONAL HIGHER ORDER BROER-KAUP EQUATIONS

By using the extended homogeneous balance method, the localized coherent structures are studied. A nonlinear transformation was first established, and then the linearization form was obtained based on the extended homogeneous balance method for the higher order (2 + 1)-dimensional Broer-Kaup equations. Starting from this linearization form equation, a variable separation solution with the entrance of some arbitrary functions and some arbitrary parameters was constructed. The quite rich localized coherent structures were revealed. This method, which can be generalized to other (2 + I) -dimensional nonlinear evolution equation, is simple and powerful.

A novel box-counting method for quantitative fractal analysis of threedimensional pore characteristics in sandstone

Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.

Fractal Dimension of Pore Structure of Combustible Cartridge Cases

A fractal pore structure model of combustible cartridge cases was established by virtue of the fractal geometry. Pore structure information, such as backbone fractal dimension and pore fractal dimension, of four kinds of combustible cartridge case were obtained by mercury intrusion porosimetry (MIP) . The formation mechanism of fractal pore structure of combustible cartridge was studied. The results show that the backbone fractal dimension consists of the component and influenced by the component number and size of components; the pore percolation fractal dimension reflects the pore structures of components; and the fractal dimension of pore structure is positively relative to the tensile strength of combustible cartridge case.

Fermionic Covariant Prolongation Structure for a Super Nonlinear Evolution Equation in 2+1 Dimensions

The integrability of a （2＋1）-dimensional super nonlinear evolution equation is analyzed in the framework of the fermionie covariant prolongation structure theory. We construct the prolongation structure of the multidimen- sional super integrable equation and investigate its Lax representation. Furthermore, the Backlund transformation is presented and we derive a solution to the super integrable equation.

NMR research on deterioration characteristics of microscopic structure of sandstones in freeze-thaw cycles

In order to study the deterioration characteristics of the microscopic structure of sandstones in freeze-thaw cycles, tests of180 freeze-thaw cycles were performed on sandstone specimens. The nuclear magnetic resonance （NMR） technique was applied tothe measurement of sandstone specimens and analysis of the magnetic resonance imaging. Then, the fractal theory was employed tocompute the fractal dimension values of pore development of rocks after different freeze-thaw cycles. The results show that the massand porosity of rocks grow with the increase of freeze-thaw cycles. According to the NMR T2 distribution of sandstones, the poresizes of rock specimens increase after 180 freeze-thaw cycles, especially that of the medium-sized and small-sized pores. The spatialdistribution of sandstone pores after freeze-thaw cycles has fractal features within certain range, and the fractal dimension ofsandstones tends to increase gradually.

Prediction of Protein OmpH in Structure of C47-8 Pasteurella multocida

[Objective] This study aimed to predict the structure of protein OmpH from Pasteurella multocida C47-8 （PmC47-8） strain of yak. [Method] Online BLAST, signal peptide prediction, secondary structure prediction and protein characteristics of sequencing result of gene OmpH from PmC47-8 strain were analyzed. [Result] The similarities of gene OmpH from PmC47-8 with the published 81 OmpH genes were between 84% and 99%; a signal peptide was found with the cleavage sites between 20 and 21 in the polypeptide; secondary structure prediction showed that folding structure accounted for 49.8% and loop structure for 50.2%; it predicted that there were 7 O-glycosylation sites in OmpH protein with the amino acid residual sites of 2, 45, 48, 330, 716, 721, 723, respectively, and 2 N-glycosylation sites with the amino acid residual sites of 15 and 35. [Conclusion] This study lays the foundation for the study on the immunity of OmpH gene from yak.

Full-Sized Pore Structure and Fractal Characteristics of Marine-Continental Transitional Shale: A Case Study in Qinshui Basin, North China

Based on 10 shale samples collected from 4 wells in Qinshui Basin,we investigate the full-sized pore structure and fractal characteristics of Marine-Continental transitional shale by performing organic geochemistry,mineralogical composition,Nitrogen gas adsorption(N2 adsorption)and Nuclear Magnetic Resonance(NMR)measurements and fractal analysis.Results show that the TOC content of the shale samples is relatively high,with an average value of 2.44wt%,and the thermal evolution is during the mature-over mature stage.The NMR T2 spectrum can be used to characterize the fullsized pore structure characteristics of shale.By combining N2 adsorption pore structure parameters and NMR T2 spectrums,the surface relaxivity of samples are calculated to be between 1.7877 um/s and 5.2272 um/s.On this basis,the T2 spectrums are converted to full-sized pore volume and surface area distribution curves.The statistics show that the pore volume is mainly provided by mesopore,followed by micropore,and the average percentages are 65.04%and 30.83%respectively;the surface area is mainly provided by micropore,followed by mesopore,and the average percentages are 60.8004%and 39.137%respectively;macropore contributes little to pore volume and surface area.The pore structure characteristics of shale have no relationship with TOC,but strong relationships with clay minerals content.NMR fractal dimensions Dmicro and Dmeso have strong positive relationships with the N2 adsorption fractal dimensions D1 and D2 respectively,indicating that Dmicro can be used to characterize the fractal characteristics of pore surface,and Dmeso can be used to characterize the fractal characteristics of pore structure.The shale surface relaxivity is controlled by multiple factors.The increasing of clay mineral content,pore surface area,pore surface fractal dimension and the decreasing of average pore size,will all lead to the decreasing of shale surface relaxivity.

Effect of Steel Slag and Granulated Blast-furnace Slag on the Mechanical Strength and Pore Structure of Cement Composites

Reuse of solid industrial wastes is an effective approach to develop low-carbon construction materials. This paper examines how two materials, steel slag（ST） and granulated blast-furnace slag（SL） impact the mechanical performance and pore structure of cement-based systems. Analysis was done on the variations of the porosity, pore size, and pore volume distribution with the curing age and replacement content, and the fractal dimensions of pore surfaces. The results suggested that systems with both supplementary materials had lower early strengths than pure cement, but could generally surpass pure cement paste after 90 d; higher SL content was particularly helpful for boosting the late strengths. The addition of ST increased the porosities and mean pore sizes at each age, and both increased with ST content; SL was helpful for decreasing the system＇s late porosity（especially harmless pores below 20 nm）; The lowest porosity and mean pore size were obtained with 20% SL. Both systems had notably fractal characteristics on pore surfaces, with ST systems showing the highest dimensions at 10% ST, and SL systems at 20% SL. Compressive strength displayed a significant linear increase with fractal dimension.

Periodic oscillation and fine structure of wedge-induced oblique detonation waves

An oblique detonation wave for a Mach 7 inlet flow over a long enough wedge of 30 turning angle is simulated numerically using Euler equation and one-step rection model.The fifth-order WENO scheme is adopted to capture the shock wave.The numerical results show that with the compression of the wedge wall the detonation wave front structure is divided into three sections：the ZND model-like strcuture,single-sided triple point structure and dual-headed triple point strucuture.The first structure is the smooth straight,and the second has the characteristic of the triple points propagating dowanstream only with the same velocity,while the dual-headed triple point structure is very complicated.The detonation waves facing upstream and downstream propagate with different velocities,in which the periodic collisions of the triple points cause the oscillation of the detonation wave front.This oscillation process has temporal and spatial periodicity.In addition,the triple point trace are recorded to obtain different cell structures in three sections.

Continental- Margin Structure of Northeast China and Its Adjacent Areas

The continental margin of Northeast China and its adjacent areas is composed of two tectonic belts. The inner belt is a collage made up of fragments resulting from breakup of an old land with the north part related to the evolution of the Palaeo-Asian Ocean and the south part to the evolution of the Palaeo - Pacific Ocean. The outer belt is a Mesozoic terrane, which is a melange made up of fragments of the Late Palaeozoic to Early Mesozoic oceanic crust and the Late M esozoic trench accumulations.There existed another ocean-the Palaeo - Pacific Ocean during the period from the closing of the Palaeo-Asian Ocean to the opening of the modern Pacific Ocean or from the Devonian to Jurassic, and the ocean-floor spreading of the Palaeo - Pacific Ocean led to the formation of the above-mentioned tectonic belts. The development of the strike-slip fault system after the Late Jurassic and the formation of an epicontinental volcano -plutonic rock belt in the Late Cretaceous to Early Tertiary are attributed to the interaction between the modern Pacific plate and the Eurasian plate.

Synthesis and Structure of 2-Isobutyl-6-(2',4'-dichlorophenyl)imidazo[2,1-b]-1,3,4-thiadiazole

The crystal structure of the title compound, 2-isobutyl-6-(2?4?dichlorophenyl)- imidazo[2,1-b]-1,3,4-thiadiazole (C14H13Cl2N3S, Mr = 326.23), has been synthesized by the treatment of 2-amino-5-isobutyl-1,3,4-thiadiazole with a-chloroaceto-2,4-dichlorophenone and determined by single-crystal X-ray diffraction. The crystal belongs to monoclinic, space group P21/n with a = 12.483(7), b = 8.420(4), c = 14.998(8) ? b = 105.770(10)? V = 1517.0(14) 3, Z = 4, Dc = 1.428 g/cm3, S = 0.902, m(MoKa) = 0.558 mm-1, F (000) = 672, R = 0.0579 and wR = 0.1186. The X-ray analytic results showed that all ring atoms in the imidazothiadiazole moiety are almost coplanar. The dihedral angel between the phenyl group and hetero-cycle is 16.8(0.2)?