Spherical Shell Model Research Articles

High-Efficiency Forward Modeling of Gravitational Fields in Spherical Harmonic Domain with Application to Lunar Topography Correction

Gravity forward modeling as a basic tool has been widely used for topography correction and 3D density inversion. The source region is usually discretized into tesseroids (i.e., spherical prisms) to consider the influence of the curvature of planets in global or large-scale problems. Traditional gravity forward modeling methods in spherical coordinates, including the Taylor expansion and Gaussian–Legendre quadrature, are all based on spatial domains, which mostly have low computational efficiency. This study proposes a high-efficiency forward modeling method of gravitational fields in the spherical harmonic domain, in which the gravity anomalies and gradient tensors can be expressed as spherical harmonic synthesis forms of spherical harmonic coefficients of 3D density distribution. A homogeneous spherical shell model is used to test its effectiveness compared with traditional spatial domain methods. It demonstrates that the computational efficiency of the proposed spherical harmonic domain method is improved by four orders of magnitude with a similar level of computational accuracy compared with the optimized 3D GLQ method. The test also shows that the computational time of the proposed method is not affected by the observation height. Finally, the proposed forward method is applied to the topography correction of the Moon. The results show that the gravity response of the topography obtained with our method is close to that of the optimized 3D GLQ method and is also consistent with previous results.

Elastic–Plastic Buckling of Scaled Model of Radial Ring-Stiffened Shallow Spherical Shells Based on Energy Method

Stiffened shallow spherical shell has the advantages including high strength and light weight, which allows it to be widely applied in areas including aerospace, submarine and civil engineering. For the design of scaled model for elastic–plastic buckling of a large radially–circumferentially stiffened shallow spherical shell under uniformly distributed pressure and for the purpose of similarity prediction, the similarity relation of the elastic–plastic buckling coefficient of the shell is derived; then by using the dense stiffening theory and considering the dual nonlinearity of geometry and materials, the energy increment formula for the structure under uniformly distributed external pressure is established; next, based on the similarity transformation of the energy increment of the structural system, the generalized similarity condition and similarity relation of elastic–plastic buckling of the structure under uniformly distributed external pressure are identified. Based on the scaling and equivalence of tensile–compressive stiffness and bending stiffness, the distortion scaled model for the prototype is designed. Through numerical simulation, the distortion similarity prediction for elastic–plastic buckling under uniformly distributed pressure of the radially–circumferentially stiffened shallow spherical shell that has square-shaped dimple defects has been conducted; based on the derived similarity relation of elastic–plastic buckling of stiffened plate, the similarity prediction for the elastic–plastic buckling of orthogonally stiffened plate in the plane under unidirectional uniformly distributed pressure has been conducted. The results indicate that the load–displacement curve, buckling load, and buckling mode of the distortion similarity scaled model, combined with the established radial displacement scaling factor expression, the scaling relation of tension–compression stiffness, and the similarity relation of buckling mode, can effectively predict the elastic–plastic buckling characteristics of its prototype structure. The research results can provide theoretical reference for the design and test of the scaled model with distortion of elastic–plastic buckling of similar stiffened large shell structures.

Efficient magnetic forward modeling for strongly magnetized bodies: An iterative integral equation approach

Magnetic surveying encounters challenges in high-precision detection and inversion on strongly magnetized bodies. Nonuniform magnetization caused by self-demagnetization and mutual magnetization makes magnetic field calculation using analytical formulas impractical. The previous discrete numerical methods have suffered from computational inefficiency or low accuracy. To resolve this issue, we develop an algorithm to solve the magnetic field integral equation for calculating the magnetization state of high-susceptibility bodies, combining the improved spatial convolution forward approach with the adaptive relaxation iteration method. To address the excessive computational burden in the magnetization field between 3D voxel arrays of the discrete model, we construct the circular convolution kernel matrix directly when the subsurface space is divided with an equidistant grid, significantly reducing redundant computations. Then, the fast Fourier transform is used to accelerate the forward discrete circular convolution operation. In addition, we derive an iterative computation scheme that adaptively adjusts the relaxation factor based on magnetic field changes to correct the effective magnetization for algorithm convergence. From a pragmatic perspective, equating the cuboid to equal-volume sphere subdivisions is developed to enhance computational efficiency further by approximately 50% despite sacrificing slight accuracy. The sphere and spherical shell models validate the algorithm accuracy, efficiency, and convergence. Furthermore, we analyze the characteristics of the mutual magnetization effect among magnetic bodies under different magnetization conditions. Finally, the applicability of the algorithm is demonstrated with a realistic example. Our algorithm shows promise for precisely exploring highly magnetized minerals, underground pipelines, and unexploded ordnance.

Isospin Symmetry Breaking in Atomic Nuclei

In this paper, the importance of isospin symmetry and its breaking in elucidating the properties of atomic nuclei is reviewed. The quark mass splitting and the electromagnetic origin of the isospin symmetry breaking (ISB) for the nuclear many-body problem is discussed. The experimental data on isobaric analogue states cannot be described only with the Coulomb interaction, and ISB terms in the nucleon–nucleon interaction are needed to discern the observed properties. In the present work, the ISB terms are explicitly considered in nuclear energy density functional and spherical shell model approaches, and a detailed investigation of the analogue states and other properties of nuclei is performed. It is observed that isospin mixing is largest for the N = Z system in the density functional approach

Dark matter reconstruction from stellar orbits in the Galactic centre

Context. Current constraints on distributed matter in the innermost Galactic centre (such as a cluster of faint stars and stellar remnants, dark matter, or a combination thereof) based on the orbital dynamics of the visible stars closest to the central black hole typically assume simple functional forms for the distributions. Aims. We aim to take a general model-agnostic approach in which the form of the distribution is not constrained by prior assumptions on the physical composition of the matter. This approach yields unbiased, entirely observation-driven fits for the matter distribution and places constraints on our ability to discriminate between different density profiles (and consequently between physical compositions) of the distributed matter. Methods. We constructed a spherical shell model with the flexibility to fit a wide variety of physically reasonable density profiles by modelling the distribution as a series of concentric mass shells. We tested this approach in an analysis of mock observations of the star S2. Results. For a sufficiently large and precise data set, we find that it is possible to discriminate among several physically motivated density profiles. However, for data coming from current and expected next generation observational instruments, the potential for profile distinction will remain limited by the precision of the instruments. Future observations will still be able to constrain the overall enclosed distributed mass within the apocentre of the probing orbit in an unbiased manner. We interpret this in the theoretical context of constraining the secular versus non-secular orbital dynamics. Conclusions. Our results show that while stellar data over multiple orbits of currently known stars will eventually yield model-agnostic constraints for the overall amount of distributed matter within the probe’s apocentre in the innermost Galactic centre, an unbiased model distinction made by determining the radial density profile of the distribution is, in principle, out of the measurement accuracy of the current and next-generation instruments. Constraints on dark matter models will therefore remain subject to model assumptions and will not be able to significantly downsize the zoo of candidate models.

3D large-scale forward modeling of gravitational fields using triangular spherical prisms with polynomial densities in depth

To take the sphericity of the Earth into account, tesseroids are often utilized as grid elements in large-scale gravitational forward modeling. However, such elements in a latitude–longitude mesh suffer from degenerating into poorly shaped triangles near poles. Moreover, tesseroids have limited flexibility in describing laterally variable density distributions with irregular boundaries and also face difficulties in achieving completely equivalent division over a spherical surface that may be desired in a gravity inversion. We develop a new method based on triangular spherical prisms (TSPs) for 3D gravitational modeling in spherical coordinates. A TSP is defined by two spherical surfaces of triangular shape, with one of which being the radial projection of the other. Due to the spherical triangular shapes of the upper and lower surfaces, TSPs enjoy more advantages over tesseroids in describing mass density with different lateral resolutions. In addition, such an element also allows subdivisions with nearly equal weights in spherical coordinates. To calculate the gravitational effects of a TSP, we assume the density in each element to be polynomial along radial direction so as to accommodate a complex density environment. Then, we solve the Newton’s volume integral using a mixed Gaussian quadrature method, in which the surface integral over the spherical triangle is calculated using a triangle-based Gaussian quadrature rule via a radial projection that transforms the spherical triangles into linear ones. A 2D adaptive discretization strategy and an extension technique are also combined to improve the accuracy at observation points near the mass sources. The numerical experiments based on spherical shell models show that the proposed method achieves good accuracy from near surface to a satellite height in the case of TSPs with various dimensions and density variations. In comparison with the classical tesseroid-based method, the proposed algorithm enjoys better accuracy and much higher flexibility for density models with laterally irregular shapes. It shows that to achieve the same accuracy, the number of elements required by the proposed method is much less than that of the tesseroid-based method, which substantially speeds up the calculation by more than 2 orders. The application to the tessellated LITHO1.0 model further demonstrates its capability and practicability in realistic situations. The new method offers an attractive tool for gravity forward and inverse problems where the irregular grids are involved.

Reconciling Mars InSight Results, Geoid, and Melt Evolution With 3D Spherical Models of Convection

AbstractWe investigate the geodynamic and melting history of Mars using 3D spherical shell models of mantle convection, constrained by the recent InSight mission results. The Martian mantle must have produced sufficient melt to emplace the Tharsis rise by the end of the Noachian–requiring on the order of 1–3 × 109 km3 of melt after accounting for limited (∼10%) melt extraction. Thereafter, melting declined; however, abundant evidence for limited geologically recent volcanism necessitates some present‐day melt even in the cool mantle inferred from InSight data. We test models with two mantle activation energies and a range of crustal Heat Producing Element (HPE) enrichment factors and initial core‐mantle boundary temperatures. We also test the effect of including a hemispheric (spherical harmonic degree‐1) step in lithospheric thickness to model the Martian dichotomy. We find that a higher activation energy (350 kJ mol−1) rheology produces present‐day geotherms consistent with InSight results, and crustal HPE enrichment factors of 5–10‐times produce localized melting near or up to present‐day. The 10‐times crustal HPE enrichment is consistent with both InSight and geochemical results and also produces present‐day geoid power spectra consistent with Mars. However, calculations that match the present‐day geoid power spectra require more than 60% melt extraction to produce the Tharsis swell. The addition of a degree‐1 hemispheric dichotomy, as an equatorial step in lithospheric thickness, does not significantly improve upon melt production or the geoid.

Toward a new approach for the pygmy dipole resonance in even–even nuclei. Application to isotopes 144,148,150,152,154Sm

A many-body Hamiltonian consisting of a spherical shell model mean-field term, a pairing interaction for alike nucleons and a dipole–dipole interaction, with the dipole operator involving a cubic term in the radial coordinate, was studied within a quasiparticle random-phase approximation and applied numerically to five even–even isotopes of Sm. The resulting wavefunctions were further used to calculate the B(E1) values, which at their turn were employed to calculate the photoabsorption cross section, integrated moments of the cross section and energy weighted sum rule (EWSR). The calculated cross section and its integrated moments were compared with the available data, and a good agreement was observed. Two regions were distinguished: one corresponding to the pygmy dipole resonance (PDR) (1–10 MeV) and the other to the giant dipole resonance (GDR) (10–20 MeV), which were studied separately. The peaks belonging to each of the two ranges were analyzed in detail. The PDR states were located around the neutron separation energy and were mainly formed by the collective isoscalar and neutron collective states. The PDR states describe oscillations of the neutron excess against protons from the isospin-saturated core. The character of the states from the GDR region, isoscalar or isovector, is also pointed out. The PDR states carry only 0.8%–2.7% of the total EWSR and 0.4%–5.9% of the total E1 strength. The dependence of the dipole strength on nuclear deformation is evidenced. A comment on the cross section splitting into two branches for deformed isotopes is included. The r-cubic term and nuclear deformation have opposite effects on the dipole strength. In addition, it diminishes the effect of nonconservation of the center of mass momentum. The famous Thomas–Reiche–Kuhn sum rule formula is generalized to the case of the Schiff dipole momentum. The new sum rule is well satisfied. The projected spherical single-particle basis used in our formalism allows for a unified description of spherical transitional and deformed isotopes.

Investigation of Zebrafish Embryo Membranes at Epiboly Stage through Electrorotation Technique.

A preliminary exploration of the physiology and morphology of the zebrafish embryo (ZFE) during the late-blastula and early-gastrula stages through its electrical properties was performed, applying the electrorotation (ROT) technique. This method, based on induced polarizability at the interfaces, was combined with an analytical spherical shell model to obtain the best fit of empirical data and the desired information, providing a means of understanding the role of different membranes. Suspended in two solutions of low conductivity, the major compartments of the ZFE were electrically characterized, considering morphological data from both observed records and data from the literature. Membrane integrity was also analyzed for dead embryos. The low permeability and relatively high permittivity obtained for the chorion probably reflected both its structural characteristics and external conditions. Reasonable values were derived for perivitelline fluid according to the influx of water that occurs after the fertilization of the oocyte. The so-called yolk membrane, which comprises three different and contiguous layers at the epiboly stage, showed atypical electrical values of the membrane, as did the yolk core with a relatively low permittivity. The internal morphological complexity of the embryo itself could be addressed in future studies by developing an accurate geometric model.

Sensitivity and uncertainty propagation in buckling of spherical shells under external pressure

The simple analytical model of spherical shell buckling suggested in the previous publication in the TWS journal is applied to studying the response of the structure to different perturbations given as random variables. Among them probing radial force, energy barrier and geometrical imperfections are considered as factors decreasing uniform buckling pressure. The model is expanded to the case of imperfect shells. The propagation of uncertainty of perturbations is studied by estimation the standard deviation of the buckling load. Monte Carlo method and the propagation of error formula based on Tailor expansion are used. The application of the methods to design buckling pressure estimation is discussed.

Acoustic radiation performance of an egg-shaped multilayer shell of revolution under deep-sea environment

As one of the bionic designs, the egg-shaped pressure shell has potential use for future deep-sea underwater vehicles. This paper numerically investigates the acoustic radiation performance of an egg-shaped multilayer shell of revolution, by comparing with the spherical one. Firstly, the numerical model of a three-layer spherical shell is constructed for simplified calculation by using ABAQUS finite element software; and the three-dimensional sono-elastic calculation platform (THAFTS-Acoustic) is used to calculate the acoustic radiation response. On this basis, effects of the mesh size and the closed virtual impedance surface (CVIS) on the calculation accuracy of acoustic radiation response are studied, so that the accuracy of present numerical method is verified by comparing with the exact solution. Secondly, the numerical model of a three-layer egg-shaped shell of revolution is developed, of which the total mass is the same with the spherical one. The acoustic radiation responses of the egg-shaped shell excited by both dynamic pressure and force loadings are calculated and evaluated in detail. The advantages and drawbacks of the multilayer egg-shaped shell in acoustic radiation performance are discussed. Finally, the static pressure resistance of the egg-shaped shell is also studied.

Microsecond Isomer at the N=20 Island of Shape Inversion Observed at FRIB.

Excited-state spectroscopy from the first experiment at the Facility for Rare Isotope Beams (FRIB) is reported. A 24(2)-μs isomer was observed with the FRIB Decay Station initiator (FDSi) through a cascade of 224- and 401-keV γ rays in coincidence with ^{32}Na nuclei. This is the only known microsecond isomer (1 μs≤T_{1/2}<1 ms) in the region. This nucleus is at the heart of the N=20 island of shape inversion and is at the crossroads of the spherical shell-model, deformed shell-model, and abinitio theories. It can be represented as the coupling of a proton hole and neutron particle to ^{32}Mg, ^{32}Mg+π^{-1}+ν^{+1}. This odd-odd coupling and isomer formation provides a sensitive measure of the underlying shape degrees of freedom of ^{32}Mg, where the onset of spherical-to-deformed shape inversion begins with a low-lying deformed 2^{+} state at 885keV and a low-lying shape-coexisting 0_{2}^{+} state at 1058keV. We suggest two possible explanations for the 625-keV isomer in ^{32}Na: a 6^{-} spherical shape isomer that decays by E2 or a 0^{+} deformed spin isomer that decays by M2. The present results and calculations are most consistent with the latter, indicating that the low-lying states are dominated by deformation.

A new counterweight design method for shaking table test models of single-layer spherical latticed shells

Shaking table test is one of the effective methods to study the dynamic behaviors of single-layer latticed shells, and the dynamic behavior of a shaking table test model is significantly affected by the size and installation way of the counterweight. Considering the characteristics of the single-layer latticed shells and the requirement of the test model similarity design, the size of the counterweight needed is normally large. To accommodate the counterweight in the test model, one way is to install the counterweight on the nodes directly and the other way is to enlarge the node size directly to account for the counterweight. Both the methods change the size and configuration of the nodes significantly, which brings additional bending moment and torque forces to the bars or causes a non-negligible reduction of the effective length of the bars. Those problems caused by the counterweight will have considerable influence on the evaluation of the seismic behavior of the single-layer latticed shells. A new counterweight design method is proposed by using multiple layers of upper and lower paired spherical steel shells assembled around a node, which improves the shortcomings of the traditional counterweight in the shaking table test model of single-layer spherical latticed shell (SLSLS). Thin rubber cushions are adopted between two layers of steel counterweight layers to help accommodate the local defects of the counterweight layers when they are not manufactured perfectly so that the counterweight layers can be tightly fixed to the node. With the new method, the improved counterweigh is installed around the node to avoid producing additional forces and keep the satisfaction with the design of the effective length of the bars. The effectiveness of the proposed counterweight design method is verified through theoretical analysis and numerical simulation of the test models. To carry out the finite element (FE) analysis of the test models, the seismic waves input way and the FE model updating method are improved. The static stability capacity of the bars and SLSLSs, and dynamic characteristics and dynamic stability capacity of SLSLSs are discussed to compare the improved counterweight with the traditional counterweight. The applicability of the new counterweight design method to the similarity ratios of the dynamic behaviors of the test models and the prototypes of SLSLSs is also studied under different rise-span ratios and grid-making.

The Proxy-SU(3) Symmetry in Atomic Nuclei

The microscopic origins and the current predictions of the proxy-SU(3) symmetry model of atomic nuclei were reviewed. Beginning with experimental evidence for the special roles played by nucleon pairs with maximal spatial overlap, the proxy-SU(3) approximation scheme is introduced; its validity is demonstrated through Nilsson model calculations and its connection to the spherical shell model. The major role played by the highest weight-irreducible representations of SU(3) in shaping up the nuclear properties is pointed out, resulting in parameter-free predictions of the collective variables β and γ for even–even nuclei in the explanation of the dominance of prolate over oblate shapes in the ground states of even–even nuclei, in the prediction of a shape/phase transition from prolate to oblate shapes below closed shells, and in the prediction of specific islands on the nuclear chart in which shape coexistence is confined. Further developments within the proxy-SU(3) scheme are outlined.

EmulART: Emulating radiative transfer—a pilot study on autoencoder-based dimensionality reduction for radiative transfer models

Dust is a major component of the interstellar medium. Through scattering, absorption and thermal re-emission, it can profoundly alter astrophysical observations. Models for dust composition and distribution are necessary to better understand and curb their impact on observations. A new approach for serial and computationally inexpensive production of such models is here presented. Traditionally these models are studied with the help of radiative transfer modelling, a critical tool to understand the impact of dust attenuation and reddening on the observed properties of galaxies and active galactic nuclei. Such simulations present, however, an approximately linear computational cost increase with the desired information resolution. Our new efficient model generator proposes a denoising variational autoencoder (or alternatively PCA), for spectral compression, combined with an approximate Bayesian method for spatial inference, to emulate high information radiative transfer models from low information models. For a simple spherical dust shell model with anisotropic illumination, our proposed approach successfully emulates the reference simulation starting from less than 1% of the information. Our emulations of the model at different viewing angles present median residuals below 15% across the spectral dimension and below 48% across spatial and spectral dimensions. EmulART infers estimates for sim 85% of information missing from the input, all within a total running time of around 20 minutes, estimated to be 6times faster than the present target high information resolution simulations, and up to 50times faster when applied to more complicated simulations.

Spatially resolved mid-infrared observations of the circumstellar environment of the born-again object FG Sge

Context. FG Sge has evolved from the hot central star of the young planetary nebula Hen 1–5 to a G–K supergiant in the last 100 yr. It is one of the three born-again objects that have been identified as of yet, and they are considered to have undergone a thermal pulse in the post-asymptotic giant branch evolution. Aims. We present mid-infrared spectro-interferometric observations of FG Sge and probe its dusty environment. Methods. FG Sge was observed with MIDI at the Very Large Telescope Interferometer at baselines of 43 and 46 m between 8 and 13 µm. Results. The circumstellar dust environment of FG Sge was spatially resolved, and the Gaussian fit to the observed visibilities results in a full width at half maximum of ~10.5 mas. The observed mid-infrared visibilities and the spectral energy distribution can be fairly reproduced by optically thick (τV ≈ 8) spherical dust shell models consisting of amorphous carbon with an inner radius rin of ~30 R★ (corresponding to a dust temperature of 1100 ± 100 K). The dust shell is characterized with a steep density profile proportional to r−3.5±0.5 from the inner radius rin to (5–10) × rin, beyond which it changes to r−2. The dust mass is estimated to be ~ 7 × 10−7 M⊙, which translates into an average total mass-loss rate of ~ 9 × 10−6 M⊙ yr−1 as of 2008 with a gas-to-dust ratio of 200 being adopted. In addition, the 8–13 µm spectrum obtained with MIDI with a field of view of 200 mas does not show a signature of the polycyclic aromatic hydrocarbon (PAH) emission, which is in marked contrast to the spectra taken with the Spitzer Space Telescope six and 20 months before the MIDI observations with wide slit widths of 3″.6–10″. This implies that the PAH emission originates from an extended region of the optically thick dust envelope. Conclusions. The dust envelope of FG Sge is much more compact than that of the other born-again stars’ Sakurai’s object and V605 Aql, which might reflect the difference in the evolutionary status. The PAH emission from the extended region of the optically thick dust envelope likely originates from the material ejected before the central star became H-deficient, and it may be excited by the UV radiation from the central star escaping through gaps among dust clumps and/or the bipolar cavity of a disk-like structure.

Fast calculation of gravitational effects using tesseroids with a polynomial density of arbitrary degree in depth

Fast and accurate calculation of gravitational effects on a regional or global scale with complex density environment is a critical issue in gravitational forward modelling. Most existing significant developments with tessroid-based modelling are limited to homogeneous density models or polynomial ones of a limited order. Moreover, the total gravitational effects of tesseroids are often calculated by pure summation in these methods, which makes the calculation extremely time-consuming. A new efficient and accurate method based on tesseroids with a polynomial density up to an arbitrary order in depth is developed for 3D large-scale gravitational forward modelling. The method divides the source region into a number of tesseroids, and the density in each tesseroid is assumed to be a polynomial function of arbitrary degree. To guarantee the computational accuracy and efficiency, two key points are involved: (1) the volume Newton’s integral is decomposed into a one-dimensional integral with a polynomial density in the radial direction, for which a simple analytical recursive formula is derived for efficient calculation, and a surface integral over the horizontal directions evaluated by the Gauss–Legendre quadrature (GLQ) combined with a 2D adaptive discretization strategy; (2) a fast and flexible discrete convolution algorithm based on 1D fast Fourier transform (FFT) and a general Toepritz form of weight coefficient matrices is adopted in the longitudinal dimension to speed up the computation of the cumulative contributions from all tesseroids. Numerical examples show that the gravitational fields predicted by the new method have a good agreement with the corresponding analytical solutions for spherical shell models with both polynomial and non-polynomial density variations in depth. Compared with the 3D GLQ methods, the new algorithm is computationally more accurate and efficient. The calculation time is significantly reduced by 3 orders of magnitude as compared with the traditional 3D GLQ methods. Application of the new algorithm in the global crustal CRUST1.0 model further verifies its reliability and practicability in real cases. The proposed method will provide a powerful numerical tool for large-scale gravity modelling and also an efficient forward engine for inversion and continuation problems.

Shell model foundations of the proxy-SU(3) symmetry: Nucleon pairs creating nuclear deformation

Abstract Proxy-SU(3) symmetry is an approximation scheme extending the Elliott SU(3) algebra of the sd shell to heavier shells, in order to make possible the application of the symmetry properties in cutting down the size of the required calculations. When introduced in 2017, the approximation had been justified by calculations carried out within the Nilsson model, an elementary shell model based on a 3-dimensional harmonic oscillator with cylindrical symmetry, applicable to deformed nuclei. Recently our group managed to map the cartesian basis of the Elliott SU(3) model onto the spherical shell model basis, fully clarifying the approximations used within the proxy-SU(3) scheme and paving the way for using the proxy-SU(3) approximation in shell model calculations for heavy nuclei. As a by-product, the relation of the 0[110] Nilsson pairs used in proxy-SU(3) to the earlier used de Shalit-Goldhaber pairs and Federman-Pittel pairs has been clarified. The connection between the proxy-SU(3) scheme and the spherical shell model has also been worked out in the original framework of the Nilsson model, with identical results.

Precise mix-design of Ultra-High Performance Concrete (UHPC) based on physicochemical packing method: From the perspective of cement hydration

• A physicochemical packing method to optimize the design of UHPC is proposed. • A new equivalent particle size distribution of hydrated cement is calculated. • The macro characteristics of the newly developed UHPC is evaluated. • The hydration kinetics of the newly developed UHPC is evaluated. • The microstructure development of the newly developed UHPC is evaluated. It is widely accepted that Ultra-High Performance Concrete (UHPC) could be designed by the employment of Modified Andreasen and Andersen (MAA) particle packing model. However, the traditional MAA model only takes into account that dry particles reach the dense packing status under physical conditions, without considering the chemical hydration of wet cement particles. To solve this problem, this study adopts a physicochemical packing method to optimize the mix-design of UHPC through establishing a new equivalent particle size distribution of hydrated cement by applying a multilayer spherical shell model. Based on this, the mix proportion of UHPC is redesigned and the properties of the optimized UHPC are evaluated afterwards. The results show that the optimized mix-design leads to higher particle packing density of UHPC, thereby improving the durability on the premise of guaranteeing the workability and mechanical properties. Meanwhile, the optimized mix-design can also achieve denser micro structures of UHPC matrix, which provides a valuable reference to design UHPC more scientifically and reasonably.

Construction and Verification of Spherical Thin Shell Model for Revealing Walnut Shell Crack Initiation and Expansion Mechanism

Walnut shell breaking is the first step of deep walnut processing. This study aims to investigate the mechanical properties and fracture state of the Qingxiang walnut shell under unidirectional load and guide the complete separation of the walnut shell and kernel. The spherical thin shell model of the walnut (the fitting error is less than 5%) was established and verified. The process from the initiation to the expansion of walnut cracks was analyzed. The crack expansion rate was estimated in terms of the crack fracture regularity on the shell’s surface. Based on the momentless theory and finite element simulation analysis, we found that the stress on the shell surface in the concentrated force action region was gradient distributed from inside to outside and that the internal forces were equal in all directions in the peripheral force action region. The unidirectional impact shell-breaking experiments confirmed the reliability of our spherical thin shell model and verified our hypothesis of walnut shell fracture along the longitudinal grain. Our results can provide a theoretical basis for the development and structural optimization of shell-breaking machinery.