Transient response of doubly-curved bio-inspired composite shells resting on viscoelastic foundation subject to blast load using improved first-order shear theory and isogeometric approach

Investigating natural-inspired applications is a perennially appealing subject for scientists. The current increase in the speed of natural-origin structure growth may be linked to their superior mechanical properties and environmental resilience. Biological composite structures with helicoidal schemes and designs have remarkable capacities to absorb impact energy and withstand damage. However, there is a dearth of extensive study on the influence of fiber redirection and reorientation inside the matrix of a helicoid structure on its mechanical performance and reactivity. The present study aimed to explore the static and transient responses of a bio-inspired helicoid laminated composite(B-iHLC) shell under the influence of an explosive load using an isomorphic method. The structural integrity of the shell is maintained by a viscoelastic basis known as the Pasternak foundation, which encompasses two coefficients of stiffness and one coefficient of damping. The equilibrium equations governing shell dynamics are obtained by using Hamilton's principle and including the modified first-order shear theory,therefore obviating the need to employ a shear correction factor. The paper's model and approach are validated by doing numerical comparisons with respected publications. The findings of this study may be used in the construction of military and civilian infrastructure in situations when the structure is subjected to severe stresses that might potentially result in catastrophic collapse. The findings of this paper serve as the foundation for several other issues, including geometric optimization and the dynamic response of similar mechanical structures.

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.

Visualizing and witnessing first-order coherence,Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame

A quantum steering ellipsoid(QSE)is a visual characterization for bipartite qubit systems,and it is also a novel avenue for describing and detecting quantum correlations.Herein,by using a QSE,we visualize and witness the first-order coherence(FOC),Bell nonlocality(BN)and purity under non-inertial frames.Also,the collective influences of the depolarizing channel and the non-coherence-generating channel(NCGC)on the FOC,BN and purity are investigated in the QSE formalism.The results reveal that the distance from the center of the QSE to the center of the Bloch sphere visualizes the FOC of a bipartite system,the lengths of the QSE semiaxis visualize the BN,and the QSE's shape and position dominate the purity of the system.One can capture the FOC,BN and purity via the shape and position of the QSE in the non-inertial frame.The depolarizing channel(the NCGC)gives rise to the shrinking and degradation(the periodical oscillation)of the QSE.One can use these traits to visually characterize and detect the FOC,BN and purity under the influence of external noise.Of particular note is that the condition for the QSE to achieve the center of the Bloch sphere cannot be influenced by the depolarizing channel and the NCGC.The characterization shows that the conditions for the disappearance of the FOC are invariant under the additional influences of the depolarizing channel and NCGC.

First-order primal-dual algorithm for sparse-view neutron computed tomography-based three-dimensional image reconstruction

Neutron computed tomography(NCT)is widely used as a noninvasive measurement technique in nuclear engineering,thermal hydraulics,and cultural heritage.The neutron source intensity of NCT is usually low and the scan time is long,resulting in a projection image containing severe noise.To reduce the scanning time and increase the image reconstruction quality,an effective reconstruction algorithm must be selected.In CT image reconstruction,the reconstruction algorithms can be divided into three categories:analytical algorithms,iterative algorithms,and deep learning.Because the analytical algorithm requires complete projection data,it is not suitable for reconstruction in harsh environments,such as strong radia-tion,high temperature,and high pressure.Deep learning requires large amounts of data and complex models,which cannot be easily deployed,as well as has a high computational complexity and poor interpretability.Therefore,this paper proposes the OS-SART-PDTV iterative algorithm,which uses the ordered subset simultaneous algebraic reconstruction technique(OS-SART)algorithm to reconstruct the image and the first-order primal–dual algorithm to solve the total variation(PDTV),for sparse-view NCT three-dimensional reconstruction.The novel algorithm was compared with other algorithms(FBP,OS-SART-TV,OS-SART-AwTV,and OS-SART-FGPTV)by simulating the experimental data and actual neutron projection experiments.The reconstruction results demonstrate that the proposed algorithm outperforms the FBP,OS-SART-TV,OS-SART-AwTV,and OS-SART-FGPTV algorithms in terms of preserving edge structure,denoising,and suppressing artifacts.

Investigation of magnetization reversal and domain structures in perpendicular synthetic antiferromagnets by first-order reversal curves and magneto-optical Kerr effect

Perpendicular synthetic-antiferromagnet(p-SAF) has broad applications in spin-transfer-torque magnetic random access memory and magnetic sensors. In this study, the p-SAF films consisting of (Co/Ni)3]/Ir(tIr)/[(Ni/Co)3are fabricated by magnetron sputtering technology. We study the domain structure and switching field distribution in p-SAF by changing the thickness of the infrared space layer. The strongest exchange coupling field(Hex) is observed when the thickness of Ir layer(tIr) is 0.7 nm and becoming weak according to the Ruderman–Kittel–Kasuya–Yosida-type coupling at 1.05 nm,2.1 nm, 4.55 nm, and 4.9 nm in sequence. Furthermore, the domain switching process between the upper Co/Ni stack and the bottom Co/Ni stack is different because of the antiferromagnet coupling. Compared with ferromagnet coupling films, the antiferromagnet samples possess three irreversible reversal regions in the first-order reversal curve distribution.With tIrincreasing, these irreversible reversal regions become denser and smaller. The results from this study will help us understand the details of the magnetization reversal process in the p-SAF.

The Nature of Inertia Explained Using the Field Theory

Analysis of free fall and acceleration of the mass on the Earth shows that using abstract entities such as absolute space or inertial space to explain mass dynamics leads to the violation of the principle of action and reaction. Many scientists including Newton, Mach, and Einstein recognized that inertial force has no reaction that originates on mass. Einstein calls the lack of reaction to the inertial force a serious criticism of the space-time continuum concept. Presented is the hypothesis that the inertial force develops in an interaction of two masses via the force field. The inertial force created by such a field has reaction force. The dynamic gravitational field predicted is strong enough to be detected in the laboratory. This article describes the laboratory experiment which can prove or disprove the hypothesis of the dynamic gravitational field. The inertial force, calculated using the equation for the dynamic gravitational field, agrees with the behavior of inertial force observed in the experiments on the Earth. The movement of the planets in our solar system calculated using that equation is the same as that calculated using Newton’s method. The space properties calculated by the candidate equation explain the aberration of light and the results of light propagation experiments. The dynamic gravitational field can explain the discrepancy between the observed velocity of stars in the galaxy and those predicted by Newton’s theory of gravitation without the need for the dark matter hypothesis.

Active disturbance rejection control on first-order plant

Conventional PI control encounters some problems when dealing with large lag process in the presence of parameter uncertainties.For the typical first-order process,an observerbased linear active disturbance rejection control（LADRC） scheme is presented to cope with the difficulties,and a reduced-order observer scheme is proposed further.Some quantitative dynamic results with regard to non-overshoot characteristics are obtained.Finally,the performance boundaries of LADRC and PI control are explicitly compared with each other,which shows that the former is more superior in most cases.

Consensus problems of first-order dynamic multi-agent systems with multiple time delays

Consensus problems of first-order multi-agent systems with multiple time delays are investigated in this paper. We discuss three cases： 1） continuous, 2） discrete, and 3） a continuous system with a proportional plus derivative controller. In each case, the system contains simultaneous communication and input time delays. Supposing a dynamic multi-agent system with directed topology that contains a globally reachable node, the sufficient convergence condition of the system is discussed with respect to each of the three cases based on the generalized Nyquist criterion and the frequency-domain analysis approach, yielding conclusions that are either less conservative than or agree with previously published results. We know that the convergence condition of the system depends mainly on each agent’s input time delay and the adjacent weights but is independent of the communication delay between agents, whether the system is continuous or discrete. Finally, simulation examples are given to verify the theoretical analysis.

Development of a first-order kinetics-based model for the adsorption of nickel onto peat

The use of peat for the removal of nickel from aqueous solutions has been investigated at various pH values by means of static conditions. The present research shows that the ability of Ni to bind to peat increases as the pH value increases. The solutions reach adsorption equilibrium rapidly. A reasonable kinetic model, first-order in nickel concentration, has been developed and fitted to the adsorption of nickel （Ⅱ） onto peat. The first-order model provides a good correlation to the experimental data. The characteristic parameters of the Langmuir isotherm were determined at various temperatures. The relationship between kinetics and equilibrium isotherms was established through the forward- and backward-rate-constants, k~ and k2, and the equilibrium constant, K.

First-order Derivative Spectrophotometry for the Determination of Vitamin C in Medicament

A novel method for the determination of vitamin C（Vc） is proposed in this article. After the reaction with Folin-Ciocalteau reagent at ambient temperature, Vc solution was scanned at 750--1100 nm, and its first-order derivative spectrum were obtained from the original spectrum. The values of derivative selected at 995 nm were used for determination. It was proved that Vc could quickly react with Folin-Ciocalteau reagent within 5 min and the product was quite stable for a long time. The conditions required for this method is not very complicated, its precision and accuracy are similar to those of the iodometric titration described in Chinese Pharmacopoeia, and the limit of detection is 0.312 μg/mL. The determination of the results of vitamin C tablet, pill, and injection demonstrates that this method has wide pharmaceutical applications.

First-Order Symmetry Energy Induced by Neutron-Proton Mass Difference

The 1st-order symmetry energy coefficient of nuclear matter induced merely by the neutron-proton （n p） mass difference is derived analytically, which turns out to be completely model-independent. Based on this result, （npDM） the 1st-order symmetry energy Esym,1 （A） of heavy nuclei such as 2~spb induced by the np mass difference is investigated with the help of a local density approximation combined with the Skyrme energy density functionals. Although /U（npDM） Esym,1 （A） is small compared with the second-order symmetry energy, it cannot be dropped simply for an accurate estimation of nuclear masses as it is still larger than the rms deviation given by some accurate mass formulas. It is therefore suggested that one perhaps needs to distinguish the neutron mass from the proton one in the construction of nuclear density funetionals.

Characteristic-knowledge-aided spectral detection of high frequency first-order sea echo

To detect high frequency （HF） first-order sea echo spectra contaminated with ships, ionosphere interference, and other, a new characteristic-knowledge-aided detection method is proposed. With 2-D image features in range-Doppler spectrum, the trend of first-order sea echoes is extracted as indicative information by a multi-scale filter. Detection rules for both single and splitting first-order sea echoes are given based on the characteristic knowledge combining the indicative information with the global characteristics such as amplitude, symmetry, continuity, etc. Compared with the classical algorithms, the proposed method can detect and locate the first-order sea echo in the HF band more accurately especially in the environment with targets/clutters smearing. Experiments with real data verify the validity of the algorithm.

Extraction of P-and S-wave angle-domain common-image gathers based on first-order velocity-dilatation-rotation equations

Accuracy of angle-domain common-image gathers(ADCIGs)is the key to multiwave AVA inversion and migration velocity analysis,and of which Poynting vectors of pure P-and S-wave are the decisive factors in obtaining multi-component seismic data ADCIGs.A Poynting vector can be obtained from conventional velocity-stress elastic wave equations,but it focused on the propagation direction of mixed P-and S-wave fields,and neither on the propagation direction of the P-wave nor the direction of the S-wave.The Poynting vectors of pure P-or pure S-wave can be calculated from first-order velocity-dilatation-rotation equations.This study presents a method of extracting ADCIGs based on first order velocitydilatation-rotation elastic wave equations reverse-time migration algorithm.The method is as follows:calculating the pure P-wave Poynting vector of source and receiver wavefields by multiplication of P-wave particle-velocity vector and dilatation scalar,calculating the pure S-wave Poynting vector by vector multiplying S-wave particle-velocity vector and rotation vector,selecting the Poynting vector at the time of maximum P-wave energy of source wavefield as the propagation direction of incident P-wave,and obtaining the reflected P-wave(or converted S-wave)propagation direction of the receiver wavefield by the Poynting vector at the time of maximum P-(S-)wave energy in each grid point.Then,the P-wave incident angle is computed by the two propagation directions.Thus,the P-and S-wave ADGICs can obtained Numerical tests show that the proposed method can accurately compute the propagation direction and incident angle of the source and receiver wavefields,thereby achieving high-precision extraction of P-and S-wave ADGICs.

A study on equivalence of nonlinear energy dissipation between first-order computational homogenization(FOCH)and re duce d-order homogenization(ROH)methods

Nowadays,studies on the mechanism of macro-scopic nonlinear behavior of materials by accumulation of micro-scopic degradation are attracting more attention from researchers.Among numerous approaches,multiscale methods have been proved as powerful and practical approaches in predicting macro-scopic material status by averaging and homogenizing physical information from associated micro-scopic mate-rial behavior.Usually in mechanical problem,the stress,consistent material modulus,and possible mate-rial state variables are quantities in interest through the upscaling process.However,the energy-related quantities are not studied much.Some initiative work has been done in the early year including but not limited to the Hill-Mandel condition in multiscale framework,which gives that the macro-scopic elastic strain energy density can be computed by volumetric averaging of that in the micro-scale.However,in the nonlinear analysis,the energy dissipation is an important quantity to measure the degradation status.In this manuscript,two typical multiscale methods,the first-order computational homogenization(FOCH)and reduced-order homogenization(ROH),are adopted to numerically analyze a fiber-reinforced compos-ite material with capability in material nonlinearity.With numerical experiments,it can be shown that energy dissipation is the same for both approaches.

Fuzzy stochastic generalized reliability studies on embankment systems based on first-order approximation theorem

In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.

Determining the moment of inertia of triaxial Mars with updated global gravity models

The principal moments of inertia(PMIs)with the principal axes are usually taken as the dynamic figure parameters of Mars;they can be deduced from satellite-observed degree-two gravitational potentials in recent global gravity models and from the dynamic ellipticities resulting from precession observations.These PMIs are natural and significant for the geodetic,geophysical,and geodynamic problems of Mars,which are functions of internal density distributions.In this study,a closed and concise formula for determining the PMIs of the entire planet and its core was developed based on the second invariants of gravity and a multipole expansion.We deduced the polar oblateness J^(2)and the equatorial ellipticity J_(22)of Mars to be 1.9566×10^(−3)and 6.3106×10^(−5),respectively.The preferred principal moments of inertia of Mars are A=2.66589×1036 kg·m^(2),B=2.66775×10^(36)kg·m^(2),and C=2.68125×10^(36)kg·m^(2).These values indicate that Mar is slightly triaxial.The equatorial principal moment of inertia of the Martian core is 1.46008×10^(35)kg·m^(2),accounting for~5.47%of the planet’s PMI;this result is critical for investigating the density and size of the core of Mars,and the planet’s free core nutation.

A POSTERIORI ERROR ESTIMATE OF THE DSD METHOD FOR FIRST-ORDER HYPERBOLIC EQUATIONS

A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illustrate the accuracy and feasibility of this method.

Mapping wind by the first-order Bragg scattering of broad-beam high-frequency radar

Mapping wind with high-frequency(HF)radar is still a challenge.The existing second-order spectrum based wind speed extraction method has the problems of short detection distances and low angular resolution for broadbeam HF radar.To solve these problems,we turn to the first-order Bragg spectrum power and propose a space recursion method to map surface wind.One month of radar and buoy data are processed to build a wind spreading function model and a first-order spectrum power model describing the relationship between the maximum of first-order spectrum power and wind speed in different sea states.Based on the theoretical propagation attenuation model,the propagation attenuation is calculated approximately by the wind speed in the previous range cell to compensate for the first-order spectrum in the current range-azimuth cell.By using the compensated first-order spectrum,the final wind speed is extracted in each cell.The first-order spectrum and wind spreading function models are tested using one month of buoy data,which illustrates the applicability of the two models.The final wind vector map demonstrates the potential of the method.

Meshfree First-order System Least Squares

We prove convergence for a meshfree first-order system least squares(FOSLS) partition of unity finite element method(PUFEM).Essentially,by virtue of the partition of unity,local approximation gives rise to global approximation in H(div)∩H(curl). The FOSLS formulation yields local a posteriori error estimates to guide the judicious allotment of new degrees of freedom to enrich the initial point set in a meshfree dis- cretization.Preliminary numerical results are provided and remaining challenges are discussed.

Conformal Invariance and Noether Conserved Quantities of First-Order Lagrange Systems

In this paper the conformal invariance by infinitesimal transformations of first-order Lagrange systems is discussed in detail. The necessary and sumeient conditions of conformal invariance by the action of infinitesimal transformations being Lie symmetry simultaneously are given. Then we get the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.