Isotropic sintering shrinkage of 3D glass-ceramic nanolattices:backbone preforming and mechanical enhancement

There is a perpetual pursuit for free-form glasses and ceramics featuring outstanding mechanical properties as well as chemical and thermal resistance.It is a promising idea to shape inorganic materials in three-dimensional(3D)forms to reduce their weight while maintaining high mechanical properties.A popular strategy for the preparation of 3D inorganic materials is to mold the organic–inorganic hybrid photoresists into 3D micro-and nano-structures and remove the organic components by subsequent sintering.However,due to the discrete arrangement of inorganic components in the organic-inorganic hybrid photoresists,it remains a huge challenge to attain isotropic shrinkage during sintering.Herein,we demonstrate the isotropic sintering shrinkage by forming the consecutive–Si–O–Si–O–Zr–O–inorganic backbone in photoresists and fabricating 3D glass–ceramic nanolattices with enhanced mechanical properties.The femtosecond(fs)laser is used in two-photon polymerization(TPP)to fabricate 3D green body structures.After subsequent sintering at 1000℃,high-quality 3D glass–ceramic microstructures can be obtained with perfectly intact and smooth morphology.In-suit compression experiments and finite-element simulations reveal that octahedral-truss(oct-truss)lattices possess remarkable adeptness in bearing stress concentration and maintain the structural integrity to resist rod bending,indicating that this structure is a candidate for preparing lightweight and high stiffness glass–ceramic nanolattices.3D printing of such glasses and ceramics has significant implications in a number of industrial applications,including metamaterials,microelectromechanical systems,photonic crystals,and damage-tolerant lightweight materials.

Deep learning for determining pure isotropic proton spectra from solidstate spectra

Recently,an article on ^(1)H solid-state NMR spectra was published,in which the authors proposed a deep learning approach to infer the pure isotropic proton NMR spectra obtained at an infinite magic angle spinning(MAS)rate.This approach even allowed to obtain,by far,the best resolved ^(1)H spectra of molecular solids[1](https://doi.org/10.1002/anie.202216607).Deep learning based artificial intelligence is developing rapidly,and its application is deepening.Currently,there are many applications of deep learning in the field of magnetic resonance,such as the reconstruction of the under-sampled multidimensional spectra[2-4],the deconvolution of two-dimensional NMR spectra[5]and noise suppression and weak peak retrial[6],etc.

Comparisons between Isotropic and Anisotropic TV Regularizations in Inverse Acoustic Scattering

This article compares the isotropic and anisotropic TV regularizations used in inverse acoustic scattering. It is observed that compared with the traditional Tikhonov regularization, isotropic and anisotropic TV regularizations perform better in the sense of edge preserving. While anisotropic TV regularization will cause distortions along axes. To minimize the energy function with isotropic and anisotropic regularization terms, we use split Bregman scheme. We do several 2D numerical experiments to validate the above arguments.

Three-dimensional isotropic microfabrication in glass using spatiotemporal focusing of high-repetition-rate femtosecond laser pulses

To improve the processing efficiency and extend the tuning range of 3D isotropic fabrication,we apply the simultaneous spatiotemporal focusing(SSTF)technique to a high-repetition-rate femtosecond(fs)fiber laser system.In the SSTF scheme,we propose a pulse compensation scheme for the fiber laser with a narrow spectral bandwidth by building an extra-cavity pulse stretcher.We further demonstrate truly 3D isotropic microfabrication in photosensitive glass with a tunable resolution ranging from 8μm to 22μm using the SSTF of fs laser pulses.Moreover,we systematically investigate the influences of pulse energy,writing speed,processing depth,and spherical aberration on the fabrication resolution.As a proof-of-concept demonstration,the SSTF scheme was further employed for the fs laser-assisted etching of complicated glass microfluidic structures with 3D uniform sizes.The developed technique can be extended to many applications such as advanced photonics,3D biomimetic printing,micro-electromechanical systems,and lab-on-a-chips.

Poroelastodynamic responses and elastic moduli of a transversely isotropic porous cylinder under forced deformation test

Existing transversely isotropic poroelastodynamics solutions are limited to infinite domains and without experimental validation. Furthermore, there is a lack of analytical simulations for the elastic moduli dispersion of fluid-saturated porous cylinders. To address these three limitations and investigate the mechanisms of moduli dispersion, we present the analytical solutions of the poromechanical responses and the elastic moduli dispersion of a transversely isotropic, fluid-saturated, finite porous cylinder subjected to a forced deformation test. Through an example, we demonstrate the effects of loading frequency, boundary conditions, and material's anisotropy, dimension, and permeability on the responses of pore pressure,force, displacement, and dynamic elastic moduli of the cylinder. The specimen's responses are significantly influenced by the frequency of the applied load, resulting in a drained state at low frequencies and an undrained state at high frequencies. At high frequencies, the sample behaves identically for an open or a closed lateral boundary, and permeability has insignificant effects. The dynamic elastic moduli are mainly controlled by the loading frequency and the ratio of the sample's radius to its height. Lastly,we show excellent matches between the newly derived analytical solution and laboratory measurements on one clay and two shale samples from Mont Terri.

Solving elastic wave equations in 2D transversely isotropic media by a weighted Runge-Kutta discontinuous Galerkin method

Accurate wave propagation simulation in anisotropic media is important for forward modeling, migration and inversion. In this study, the weighted Runge-Kutta discontinuous Galerkin (RKDG) method is extended to solve the elastic wave equations in 2D transversely isotropic media. The spatial discretization is based on the numerical flux discontinuous Galerkin scheme. An explicit weighted two-step iterative Runge-Kutta method is used as time-stepping algorithm. The weighted RKDG method has good flexibility and applicability of dealing with undulating geometries and boundary conditions. To verify the correctness and effectiveness of this method, several numerical examples are presented for elastic wave propagations in vertical transversely isotropic and tilted transversely isotropic media. The results show that the weighted RKDG method is promising for solving wave propagation problems in complex anisotropic medium.

Guide and control of thermal conduction with isotropic thermodynamic parameters based on a rotary-concentrating device

A rotary-concentrating device for thermal conduction is constructed to control and guide thermal energy transmitting in elastic plates.The designed device has the ability of concentrating for thermal conduction and controlling the processes of thermal diffusion in a plate.The multilayered isotropic material properties of the rotary-concentrating device are derived based on the transformation and rotary medium method and a rotation parameter to control the thermal diffusion process is introduced.The efficiency of the rotary-concentrating device for thermal conduction is verified.Stability of temperature fields in a plate with the rotary-concentrating device is analyzed to study the performance of rotary-concentrating.Numerical examples show that the constructed rotary-concentrating device for thermal conduction can effectively rotate and focus on the thermal energy into the device for a wide range of diffusion temperatures,which can enhance the thermal conduction.Therefore,this study can provide a theoretical support for potential applications in fields of energy harvesting and thermal conduction control.

Physical Transformations of Agri-Food Products during Their Convective Drying: Characterization of the Contraction and Isotropicity of Okra

The physical transformations in terms of contraction of okra dimensions during convective drying were examined. During drying, the lateral and longitudinal dimensions of okra decrease over time. The lateral dimensions go from their initial value to around 53%, 65% and 66% of this value after 530 min. The length of the two samples used goes from 8.65 and 9.02 cm to 6.79 and 7.52 cm after 14,300 min, i.e. a variation of 78.50% and 83.37%. All the two directions give variations almost linear depending on the water content. These linear contractions result in a volume contraction of the okra. It considerably decreases in volume during the drying process. The volume goes from 831.32 cm3 to 367.57 cm3 in min, a variation of 44.22%. The isotropic index reveals that okra does not behave the same in the lateral and longitudinal directions. It contracts its diameter more than its length.

Quantum Codes Do Not Increase Fidelity against Isotropic Errors

In this article, we study the ability of error-correcting quantum codes to increase the fidelity of quantum states throughout a quantum computation. We analyze arbitrary quantum codes that encode all qubits involved in the computation, and we study the evolution of n-qubit fidelity from the end of one application of the correcting circuit to the end of the next application. We assume that the correcting circuit does not introduce new errors, that it does not increase the execution time (i.e. its application takes zero seconds) and that quantum errors are isotropic. We show that the quantum code increases the fidelity of the states perturbed by quantum errors but that this improvement is not enough to justify the use of quantum codes. Namely, we prove that, taking into account that the time interval between the application of the two corrections is multiplied (at least) by the number of qubits n (due to the coding), the best option is not to use quantum codes, since the fidelity of the uncoded state over a time interval n times smaller is greater than that of the state resulting from the quantum code correction.

Numerical modeling of seismic wavefields in transversely isotropic media with a compact staggered-grid finite difference scheme

To deal with the numerical dispersion problem, by combining the staggeredgrid technology with the compact finite difference scheme, we derive a compact staggered- grid finite difference scheme from the first-order velocity-stress wave equations for the transversely isotropic media. Comparing the principal truncation error terms of the compact staggered-grid finite difference scheme, the staggered-grid finite difference scheme, and the compact finite difference scheme, we analyze the approximation accuracy of these three schemes using Fourier analysis. Finally, seismic wave numerical simulation in transversely isotropic （VTI） media is performed using the three schemes. The results indicate that the compact staggered-grid finite difference scheme has the smallest truncation error, the highest accuracy, and the weakest numerical dispersion among the three schemes. In summary, the numerical modeling shows the validity of the compact staggered-grid finite difference scheme.

Elasto-plastic analysis of masonry with anisotropic plastic material model

This paper establishes an anisotropic plastic material model to analyze the elasto-plastic behavior of masonry in plane stress state.Being an anisotropic material,masonry has different constitutive relation and fracture energies along each orthotropic axes.Considering the unique material properties of masonry,a new yield criterion for masonry is proposed combining the Hill's yield criterion and the Rankine's yield criterion.The new yield criterion not only introduces compression friction coefficient of shear but also considers yield functions for independent stress state along two material axes of tension.To solve the involved nonlinear equations in numerical analysis,several nonlinear methods are implemented,including Newton-Raphson method for nonlinear equations and Implicit Euler backward mapping algorithm to update stresses.To verify the proposed material model of masonry,a series of tests are operated.The simulation results show that the new developed material model implements successfully.Compared with isotropic material model,the proposed model performs better in elasto-plastic analysis of masonry in plane stress state.The proposed anisotropic model is capable of simulating elasto-plastic behavior of masonry and can be used in related applications.

Assimilation of temperature and salinity using isotropic and anisotropic recursive filters in Tropic Pacific

A data assimilation scheme used in the updated Ocean three-dimensional Variational Assimila- tion System （OVALS）, OVALS2, is described. Based on a recursive filter （RF） to estimate the background error covariance （BEC） over a predetermined scale, this new analysis system can be implemented with anisotropic and isotropic BECs. Similarities and differences of these two BEC schemes are briefly discussed and their impacts on the model simulation are also investigated. An idealized experiment demonstrates the ability of the updated analysis system to construct different BECs. Furthermore, a set of three years experiments is implemented by assimilating expendable bathythermograph （XBT） and ARGO data into a Tropical Pacific circulation model. The TAO and WOA01 data are used to validate the assimilation results. The results show that the model simu- lations are substantially improved by OVALS2. The inter-comparison of isotropic and anisotropic BEC shows that the corresponding temperature and salinity produced by the anisotropic BEC are almost as good as those obtained by the isotropic one. Moreover, the result of anisotropic RF is slightly closer to WOA01 and TAO than that of isotropic RF in some special area （e.g. the cold tongue area in the Tropic Pacific）.

ISOTROPICALIZED SPLINE INTEGRAL EQUATION METHOD FOR THE ANALYSIS OF ANISOTROPIC PLATES

In the view of Reissner's and Kirchhoff's theories, respectively, we formulate the isotropicalized governing equations for the anisotropic plates, and give the proof of the equivalence relation between these two plate-models for the simply-supported rectangular orthotropic plates. The well-known fundamental solutions of the isotrqpic plates are utlized for the spline integral equation analysis of anisotropic plates.Even with sparse meshes the satisfactory results can be obtained. The analysis of plates on two-parameter elastic foundation is so simple as the common case that only a few terms should be added to the formulas of fictitious loads.

The Effects of Chemical (isotropic) and Anisotropic Etching Processes on the Roughening of Nanocomposite Substrates

Simulation results of roughening of nanocomposite materials during both isotropic and anisotropic etching processes based on the level set method are presented. It is clearly shown that the presence of two phases with different etching rates affects the development of surface roughness and that some roughness characteristics obey simple scaling laws. In addition, certain scaling laws that describe the time dependence of the root mean square （rms） roughness w for various etching processes and different characteristics of the nanocomposite materials are determined.

Stability of Geothermal Convection in Anisotropic River Beds

The onset of thermal convection, due to heating from below in a system consisting of a fluid layer overlying a porous layer with anisotropic permeability and thermal diffusivity, is investigated analytically. The porous medium is both anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity vector and in thermal conductivity with principal directions coincident with the coordinate axes. The Beavers-Joseph condition is applied at the interface between the two layers. Based on parallel flow approximation theory, a linear stability analysis is conducted to study the geothermal river beds system and documented the effects of the physical parameters describing the problem. The critical Rayleigh numbers for both the fluid and porous layers corresponding, to the onset of convection arising from sudden heating and cooling at the boundaries are also predicted. The results obtained are in agreement with those found in the past for particular isotropic and anisotropic cases and for limiting cases concerning pure porous media and for pure fluid layer. It has demonstrated that the effects of anisotropic parameters are highly significant.

The Behavior of Recycled Concrete through the Application of an Isotropic Damage Model

The main goal of this paper is to describe the mechanical behavior of the CDW recycled concrete in compression, using an isotropic damage model adapted to the variation of the replacement rate of natural aggregates by recycled ones. The isotropic model by Mazars was used as a constitutive equation for the CDW concrete and its adjustment parameters, A and B, were written as quadratic polynomials according to the aggregates replacement rate. The model was evaluated for conventional and recycled concretes. For the latter ones, the aggregates replacement ratios evaluated were 50% and 100%. The results show good approximation between the analytical and numerical values obtained with the adapted isotropic damage model and experimental concrete results for both compressive and flexural strength.

Applying resolved-scale linearly forced isotropic turbulence in rational subgrid-scale modeling

In previous attempts of rational subgrid-scale (SGS) modeling by employing the Kolmogorov equation of filtered (KEF) quantities, it was necessary to assume that the resolved-scale second-order structure function is stationary. Forced isotropic turbulence is often used as a framework for establishing and validating such SGS models based on stationary restrictions, for it generates statistical stationary samples. However, traditional forcing method at low wavenumbers cannot provide an analytic form of forcing term for a complete KEF in physical space, which has been illustrated to be essential in the modeling of such SGS models. Thus, an alternative forcing method giving an analytic forcing term in physical space is needed for rational SGS modeling. Giving an analytic linear driving term in physical space, linearly forced isotropic turbulence should be considered an ideal theoretical framework for rational SGS modeling. In this paper, we demonstrate the feasibility of establishing a rational SGS model with stationary restriction based on linearly forced isotropic turbulence. The performance of this rational SGS model is validated. We, therefore, propose the use of linearly forced isotropic turbulence as a complement to free-decaying isotropic turbulence and low-wavenumber forced isotropic turbulence for SGS model validations.

Torsional vibration of a pipe pile in transversely isotropic saturated soil

This study considers the torsional vibration of a pipe pile in a transversely isotropic saturated soil layer. Based on Biot＇s poroelastic theory and the constitutive relations of the transversely isotropic medium, the dynamic governing equations of the outer and inner transversely isotropic saturated soil layers are derived. The Laplace transform is used to solve the governing equations of the outer and inner soil layers. The dynamic torsional response of the pipe pile in the frequency domain is derived utilizing 1D elastic theory and the continuous conditions at the interfaces between the pipe pile and the soils. The time domain solution is obtained by Fourier inverse transform. A parametric study is conducted to demonstrate the influence of the anisotropies of the outer and inner soil on the torsional dynamic response of the pipe pile.

Pure bending of simply supported circular plate of transversely isotropic functionally graded material

This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).

THE NON-AXISYMMETRICAL DYNAMIC RESPONSE OF TRANSVERSELY ISOTROPIC SATURATED POROELASTIC MEDIA

The Blot's wave equations of transversely isotropic saturated poroelastic media excited hy non-axisymmetrical harmonic source were solved by means of Fourier expansion and Hankel transform. Then the components of total stress in porous media are expressed with the solutions of Biot's wave equations. The method of research on non-axisymmetrical dynamic response of saturated porous media is discussed, and a numerical result is presented.