Reliability analysis of structure with random parameters based on multivariate power polynomial expansion

A new method for calculating the failure probabilityof structures with random parameters is proposed based onmultivariate power polynomial expansion, in which te uncertain quantities include material properties, structuralgeometric characteristics and static loads. The structuralresponse is first expressed as a multivariable power polynomialexpansion, of which the coefficients ae then determined by utilizing the higher-order perturbation technique and Galerkinprojection scheme. Then, the final performance function ofthe structure is determined. Due to the explicitness of theperformance function, a multifold integral of the structuralfailure probability can be calculated directly by the Monte Carlo simulation, which only requires a smal amount ofcomputation time. Two numerical examples ae presented toillustate te accuracy ad efficiency of te proposed metiod. It is shown that compaed with the widely used first-orderreliability method （ FORM） and second-order reliabilitymethod （ SORM）, te results of the proposed method are closer to that of the direct Monte Carlo metiod,and it requires much less computational time.

Static response analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.

Hopping Parameter Expansion Technique in Noise Method for Disconnected Quark Loops

We investigate the effectiveness of the hopping parameter expansion（HPE） combined with the Z（2） noise method in the calculation of the trace of the inverse of Wilson＇s Dirac operator and some other disconnected contributions.A numerical comparison of the standard deviation for the Z（2） noise method and HPE with the Z（2） noise method is carried out. It is found that there are noise reductions in all the quantities we calculated using the HPE with the Z（2） noise method. For the trace of the inverse of Wilson＇s Dirac operator, the HPE can reduce the statistical error by about 60%.

Method to determine parameters in the rainstorm intensity formula

This paper presents a new method to determine parameters in the nonlinear mathematical model of the urban rainfall intensity formula. The method transforms the nonlinear equation into a linear one, and incorperates a damping factor and a step factor to improve the precision of the calculated results. It works out the parameters based on given rainstorm intensity, period of the recurrence of rainstorm and lasting time of the rainfall. The results turns out to have the smallest residual error compared with those obtained by several other methods and satisfy the related standard. The method proves of fast convergence, desirable generality, stability and accuracy, which overcomes the defects of other existing numeral methods.

Rapid determination of source parameters of the M 6.2 Jishishan earthquake in Gansu Province and its application in emergency response

In this study, we swiftly determined the focal parameters(focal mechanism, seismic imaging process, magnitude)of the Jishishan earthquake, leveraging a solved fault model to assess the intensity field and casualties promptly.The investigation began by retrieving the source mechanism through the P-wave initial motion and W-phase method. This enabled us to chart the spatial and temporal distribution of energy release in the source area via the back-projection technique. Following this, we estimated the earthquake's intensity field by merging the source inversion findings with the ground motion prediction equation. This analysis facilitated the evaluation of earthquake casualties, utilizing the theoretical intensity field and a casualty assessment model. Our findings indicate that the fault type is a thrust fault, characterized by a unilateral rupture in the direction of NW, with a rupture length spanning approximately 10–15 km and a duration ranging between 8 and 10 s. The earthquake's magnitude varied from M 5.9 to M 6.2. The demarcated high-intensity areas, as per our intensity assessment, align closely with the actual survey results. Furthermore, the predicted total casualties and identified critical rescue zones closely match the real-world casualty figures. These insights offer crucial technical support for governmental emergency command and rescue operations.

Rediscovering Determinant Expansion on Row or Column Theorem Through Plausible Reasoning

Plausible reasoning is an important approach to reasoning conclusions.In order to cultivate students’habits and abilities to use plausible reasoning,we should give the students a chance to imitate and practice plausible reasoning in our teaching.For our linear algebra course,most of the definitions and theorems in popular linear algebra textbooks are given directly.Thus,we give a concrete process that rediscovers determinant expansion on row or column theorem through plausible reasoning during our teaching to give the students the chance to learn the reasoning.

IDENTIFICATION OF TIME-VARYING MODAL PARAMETERS USING LINEAR TIME-FREQUENCY REPRESENTATION

A new method of parameter identification based on linear time-frequencyrepresentation and Hubert transform is proposed to identity modal parameters of linear time-varyingsystems from measured vibration responses. Using Gabor expansion and synthesis theory, measuredresponses are represented in the time-frequency domain and modal components are reconstructed bytime-frequency filtering. The Hilbert transform is applied to obtain time histories of the amplitudeand phase angle of each modal component, from which time-varying frequencies and damping ratios areidentified. The proposed method has been demonstrated with a numerical example in which a lineartime-varying system of two degrees of freedom is used to validate the identification scheme based ontime-frequency representation. Simulation results have indicated that time-frequency representationpresents an effective tool for modal parameter identification of time-varying systems.

Zero-Thermal Expansion and Heat Capacity of Zirconium Pyrovanadate Doped with Zirconia and Vanadium (V) Oxide

The dominant phase ZrV2O7 material, doped with zirconia and vanadium (V) oxide, was synthesized by solid state reaction and sol-gel methods. X-ray power diffraction patterns show that it is cubic structure. Thermal mechanic analysis measurements exhibit a zero-thermal expansion of this material above 150 degreesC. Meanwhile, the heat capacity dependent on temperature, determined by differential scanning calorimetry, keeps in constant almost in the same temperature range. The relationship between unusual thermal expansion and abnormal heat capacity is discussed with Gruneisen parameter.

Thermal expansion in dysprosium tungstate Dy_(10)W_2O_(21)

The complex oxide Dy_(10)W_2O_(21) was synthesized by a solid-state reactionand isolated in cubic symmetry by an X-ray diffractometry (XRD) method. Differential scanningcalorimetry (DSC) measurements show that the compound is thermodynamically stable. The intrinsicthermal expansion coefficients were determined by extra-power powder X-ray diffractometry from roomtemperature to 1000 deg C: linear coefficient alpha-bar = 1.07 X 10^(-5) deg C^(-1) and bulkcoefficient beta-bar = 3.20 X 10^(-5) deg C^(-1). Dilatometry was used to measure the extrinsicthermal expansion coefficient (9.2 X 10^(-6) deg C^(-1)).

Sub-Harmonic Resonances of Periodic Parameter Excited Oscillators with Discontinuities

It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study the sub-harmonic resonances of highly nonlinear parameter excited oscillating systems with absolute value terms. The non-smoothness of absolute value terms is handled by means of an iteration approach with Fourier expansion. Two typical examples are employed to illustrate the validity and flexibility of this approach. The square residuals of the homotopy-approximations of the two examples decrease to 10-6and 10-5,respectively. Thus,the HAM combining with other methods gives hope to solve complex singular oscillating systems analytically.

Evaluating thermal expansion in fluorides and oxides:Machine learning predictions with connectivity descriptors

Open framework structures(e.g.,ScF_(3),Sc_(2)W_(3O)_(12),etc.)exhibit significant potential for thermal expansion tailoring owing to their high atomic vibrational degrees of freedom and diverse connectivity between polyhedral units,displaying positive/negative thermal expansion(PTE/NTE)coefficients at a certain temperature.Despite the proposal of several physical mechanisms to explain the origin of NTE,an accurate mapping relationship between the structural–compositional properties and thermal expansion behavior is still lacking.This deficiency impedes the rapid evaluation of thermal expansion properties and hinders the design and development of such materials.We developed an algorithm for identifying and characterizing the connection patterns of structural units in open-framework structures and constructed a descriptor set for the thermal expansion properties of this system,which is composed of connectivity and elemental information.Our developed descriptor,aided by machine learning(ML)algorithms,can effectively learn the thermal expansion behavior in small sample datasets collected from literature-reported experimental data(246 samples).The trained model can accurately distinguish the thermal expansion behavior(PTE/NTE),achieving an accuracy of 92%.Additionally,our model predicted six new thermodynamically stable NTE materials,which were validated through first-principles calculations.Our results demonstrate that developing effective descriptors closely related to thermal expansion properties enables ML models to make accurate predictions even on small sample datasets,providing a new perspective for understanding the relationship between connectivity and thermal expansion properties in the open framework structure.The datasets that were used to support these results are available on Science Data Bank,accessible via the link https://doi.org/10.57760/sciencedb.j00113.00100.

Negative thermal expansion in NbF_(3)and NbOF_(2):A comparative theoretical study

Thermal expansion control is always an obstructive factor and challenging in high precision engineering field.Here,the negative thermal expansion of NbF_(3)and NbOF_(2)was predicted by first-principles calculation with density functional theory and the quasi-harmonic approximation(QHA).We studied the total charge density,thermal vibration,and lattice dynamic to investigate the thermal expansion mechanism.We found that the presence of O induced the relatively strong covalent bond in NbOF_(2),thus weakening the transverse vibration of F and O in NbOF_(2),compared with the case of NbF_(3).In this study,we proposed a way to tailor negative thermal expansion of metal fluorides by introducing the oxygen atoms.The present work not only predicts two NTE compounds,but also provides an insight on thermal expansion control by designing chemical bond type.

NUMERICAL SIMULATION FOR DYNAMIC INITIAL SHOCK PARAMETERS OF COUPLING CHARGE ON BOREHOLE WALL UNDER THE ACTION OF HIGH EXPLOSIVES

According to detonation theory and hydrodynamic principle, a physical model has been set up in this paper. Based on the model a methodology for calculating dynamic initial shock parameters such as shock pressure pm shock wave velosity Dm etc. of coupling charge on borehole wall has ben developed. The shock parameters have been calculated when high explosives works on granite, limestone and marble respectively. The magnitude of every parameter on borehole wall has been obtained from ignited dot to the end of borehole along axial direction. Some important conclusions are also gained.

From the Hubble Constant to the Black Hole Model. Universe Expansion with Matter Creation and a New Perspective on Dark Energy Observations

Comparison of the Hubble parameter with cosmological quantities strongly supports the black hole model for the description of the Universe evolution. Such evolution requires matter creation and has implications for what is currently referred to as “dark energy” and the “cosmological constant”.

Prediction method of physical parameters based on linearized rock physics inversion

A linearized rock physics inversion method is proposed to deal with two important issues, rock physical model and inversion algorithm, which restrict the accuracy of rock physics inversion. In this method, first, the complex rock physics model is expanded into Taylor series to get the first-order approximate expression of the inverse problem of rock physics;then the damped least square method is used to solve the linearized rock physics inverse problem directly to get the analytical solution of the rock physics inverse problem. This method does not need global optimization or random sampling, but directly calculates the inverse operation, with high computational efficiency. The theoretical model analysis shows that the linearized rock physical model can be used to approximate the complex rock physics model. The application of actual logging data and seismic data shows that the linearized rock physics inversion method can obtain accurate physical parameters. This method is suitable for linear or slightly non-linear rock physics model, but may not be suitable for highly non-linear rock physics model.

Improvement of LCM model and determination of model parameters at watershed scale for flood events in Hongde Basin of China

Considering the fact that the original two-parameter LCM model can only be used to investigate rainfall losses during the runoff period because the initial abstraction is not included, the LCM model was redefined as a three-parameter model, including the initial abstraction coefficient l, the initial abstraction Ia, and the rainfall loss coefficient R. The improved LCM model is superior to the original two-parameter model, which only includes r and R, where r is the initial rainfall loss index and can be calculated with l using the Soil Conservation Service curve number （SCS-CN） method, with r = 1/（1 ＋ λ）. The trial method was used to determine the parameter values of the improved LCM model at the watershed scale for 15 flood events in the Hongde Basin in China. The results show that larger r values are associated with smaller R values, and the parameter R ranges widely from 0.5 to 2.0. In order to improve the practicability of the LCM model, r = 0.833 with λ = 0.2 is reasonable for simplifying calculation. When the LCM model is applied to arid and semi-arid regions, rainfall without yielding runoff should be deducted from the total rainfall for more accurate estimation of rainfall-runoff.

Determination of the parameters of a linear-viscoelastic thin layer using the normally-incident ultrasonic waves

This paper proposes a method of simultaneous determination of the four layer parameters （mass density, longitudinal velocity, the thickness and attenuation） of an immersed linear-viscoelastic thin layer by using the normally-incident reflected and transmitted ultrasonic waves. The analytical formula of the layer thickness related to the measured trans- mitted transfer functions is derived. The two determination steps of the four layer parameters are developed, in which acoustic impedance, time-of-flight and attenuation are first determined by the reflected transfer functions. Using the derived formula, it successively calculates and determines the layer thickness, longitudinal velocity and mass density by the measured transmitted transfer functions. According to the two determination steps, a more feasible and simplified measurement setups is described. It is found that only three signals （the reference waves, the reflected and transmitted waves） need to be recorded in the whole measurement for the determination of the four layer parameters. A study of the stability of the determination method against the experimental noises and the error analysis of the four layer parameters are made. This study lays the theoretical foundation of the practical measurement of a linear-viscoelastic thin layer.

DETERMINATION OF CREEP PARAMETERS FROM INDENTATION CREEP EXPERIMENTS

The possibilities of determining creep parameters for a simple Norton law material are explored from indentation creep testing. Using creep finite element analysis the creep indentation test technique is analyzed in terms of indentation rates at constant loads. Emphasis is placed on the relationships between the steady creep behavior of indentation systems and the creep property of the indented materials. The role of indenter geometry, size effects and macroscopic constraints is explicitly considered on indentation creep experiments. The influence of macroscopic constraints from the material systems becomes important when the size of the indenter is of the same order of magnitude as the size of the testing material. Two methods have been presented to assess the creep property of the indented material from the indentation experimental results on the single-phase-material and two-phase-material systems. The results contribute to a better mechanical understanding and extending the application of indentation creep testing.

S Phase Cell Percentage Normalized BrdU Incorporation Rate, a New Parameter for Determining S Arrest

In this study, a new parameter, S phase cell percentage （S fraction） normalized BrdU （SFN-BrdU） incorporation rate, was introduced to detect $ arrest. The results showed a positive linear correlation between the BrdU incorporation rate and the S fraction in unperturbed 16HBE cells. Theoretical analysis indicated that only S arrest could result in a decrease in the SFN-BrdU incorporation rate. Additionally, the decrease in SFN-BrdU incorporation rate and the activation of DNA damage checkpoints further demonstrated that S arrest was induced by diethyl sulfate treatment of 16HBE cells. In conclusion, $FN-BrdU incorporation rate can be used to detecting S arrest.

Rheological Behaviour for Polymer Melts and Concentrated SolutionsPart Ⅱ: Material Function with Nagai Chain Constraints and Determination of Their Parameters from Flow Curves

An integral constitutive equation and a set of material functions for describing the strain history of polymer melts were formulated in terms of the Cauchy-Green and Finger tensors. A simple memory function and the dependence of ηo and τt on M3.4 were derived from the theory of non-linear viscoelasticity with constraints of entanglements for polymer melts and substituted into the Oldroye-Walters-Fredickson constitutive equation. An integral constitutive equation for polymer melts was consequently obtained. Some material functions of the constitutive equation related to certain 'test flow' are examined as follows : (1) simple steady shear flow; (2) steady elongation flow; (3) small-amplitude oscillatory shear flow; (4) stress growth upon the inception of steady shear elongation flow; (5) stress relaxation (modulus and compllance). These theoretical relations for simple steady shear flow were compared with experimental data from our laboratory and references for various polymer melts and concentrated solutions. A good agreement between the theory and experiment was achieved.