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This paper presents a computer-assisted proof of the existence and unimodality of steady-state solutions for the Proudman–Johnson equation which is representative of two-dimensional fluid flow. The proposed approach is based on an infinite-dimensional fixed-point theorem with interval arithmetic, and is another proof by Miyaji and Okamoto (Jpn J Ind Appl Math 36:287–298, 2019). Verification results show the validity of both proofs. [ABSTRACT FROM AUTHOR]

Modal and damage identification based on ambient excitation can greatly improve the efficiency of high-speed railway bridge vibration detection. This paper first describes the basic principles of stochastic subspace identification, peak-picking, and frequency domain decomposition method in modal analysis based on ambient excitation, and the effectiveness of these three methods is verified through finite element calculation and numerical simulation. Then the damage element is added to the finite element model to simulate the crack, and the curvature mode difference and the curvature mode area difference square ratio are calculated by using the stochastic subspace identification results to verify their ability of damage identification and location. Finally, the above modal and damage identification techniques are integrated to develop a bridge modal and damage identification software platform. The final results show that all three modal identification methods can accurately identify the vibration frequency and mode shape, both damage identification methods can accurately identify and locate the damage, and the developed software platform is simple and efficient.

The structural materials in the reactor and the corrosion products in the loop will be activated into radionuclides after being irradiated by strong neutrons. These nuclides and their decay products are the main sources of radiation hazards for workers. Therefore, the efficient and accurate calculation of the inventory of these radionuclides is of great significance for the design of reactor shielding protection, radioactive source items and waste management. In this paper, the neutron activation calculation method based on the mini-max polynomial approximation (MMPA) method was studied. Compared with the traditional neutron activation calculation methods such as the transmutation trajectory analysis method and exponential Euler method, MMPA method has the advantages of good numerical stability, high efficiency and no need to deal with short-lived nuclides alone. Furthermore, two solution strategies based on the MMPA method were studied for activation calculation, including the direct inversion solution strategy and the iterative solution strategy. The first solution strategy was proposed by Yosuke Kawamoto. This solution strategy completed the solution of the nuclide density by directly inverting the coefficient matrix and then calculating the multiplication and addition of multiple matrices. This solution strategy was computationally inefficient because it involved matrix inversion operations and a large number of matrix and vector multiplication operations. Therefore, a second solution strategy was proposed to improve the computational efficiency of the MMPA method. This solution strategy firstly transformed the solution expression of the MMPA method into an iterative expression after appropriate transformation, then obtained the substitution matrix for each iteration based on LU decomposition, and finally completed the solution of the nucleon density by adding multiple matrices. Compared with the first solution strategy, the solution strategy avoids the direct inversion of the matrix, and effectively reduces the number of multiplications of the matrix, so it has higher solution efficiency. Based on the self-developed nuclide inventory calculation code AMAC, the two solution strategies of MMPA method were completed. The correctness of MMPA method applied to neutron activation calculation under multiple conditions was preliminarily verified by typical material activation examples and self-constructed large-scale coefficient matrix examples under irradiation conditions, decay conditions and pulse conditions. The test results show that the calculation results of MMPA method are in good agreement with the calculation results of each reference solution, and the calculation accuracy is equivalent to that of 16 order Chebyshev rational approximation method (CRAM). In terms of computational efficiency, the solution efficiency of the iterative calculation strategy based on MMPA proposed in this paper is significantly higher than that based on direct inversion. The computational efficiency of this calculation strategy is equivalent to that of 16 order CRAM. The MMPA method is feasible in neutron activation calculation, and has good calculation accuracy and high calculation efficiency.

To solve stability issues of super large cross-sectional tunnel with greater than 20 m across and an overall area greater than 314 m2 during excavation, a new technique named cross rock pillar method (CRPM) is proposed. A physical model test was firstly conducted to investigate the deformation and failure mechanisms of a tunnel using CRPM. In this physical model, a rock-like material simulating the V-class surrounding rock was made and a geomechanical model test bench was developed to simulate and observe the progressive failure process of the tunnel. Furthermore, fiber sensing technology was used to continuously monitor the horizontal strain in different cross sections. Test results show that the cross rock pillars play a significant role in preventing deformation of the surrounding rock during the tunnel excavation. A numerical model was then established to verify the results obtained by the physical model test. The deformation and stability mechanisms of the surrounding rock are determined using CRPM in super large cross-sectional tunnels. Finally, the proposed CRPM was successfully implemented in the Hongqihegou rail station, and the monitoring results show that the surrounding rock was adequately controlled throughout the excavation process. [ABSTRACT FROM AUTHOR]

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Seepage prevention and reinforcement of sandy soft soil layer are the important subjects in geotechnical engineering. A set of constant pressure permeable grouting device has been developed to study the diffusion rule of new permeable polymer in sandy soil layer. Based on the orthogonal experimental design, the effects of grouting pressure, grouting time, sand moisture content and sand porosity on the diffusion of new permeable polymer in sand are studied. Through the establishment of spatial coordinate system, the diffusion range of permeable polymer slurry is studied. The experimental results show that: the main and secondary order affecting the diffusion range of permeable polymer in the X-axis and Y-axis are sand porosity, grouting pressure, grouting time, and sand moisture content. The primary and secondary orders of influencing factors on the Z-axis diffusion range of permeable polymer are sand porosity, grouting time, grouting pressure, and sand moisture content. The effects of grouting pressure, grouting time, sand layer porosity on permeable polymer diffusion and the effect of permeable polymer on soil displacement during diffusion are studied by COMSOL numerical analysis software. The results of numerical analysis show that the grouting pressure, grouting time, and porosity of sand layer promote the diffusion of permeable polymer. The slight deformation of soil mass and small disturbance to soil layer can be caused by slurry during diffusion process. A function model between slurry diffusion range and grouting parameters are established, and verified by numerical simulation for comparison. The results show that the numerical simulation values of permeable polymer grouting results in the three comparison scenarios A1, A2 and A3 are greater than the theoretical calculation values, and the difference between them is not significant. The difference between the calculated value and the theoretical value of the three comparison schemes are 6.3%, 11.7% and 7.39%, respectively. [ABSTRACT FROM AUTHOR]

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper describes some numerical verification procedures to prove the invertibility of a linear operator in Hilbert spaces and to compute a bound on the norm of its inverse. These approaches improve on previous procedures that use an orthogonal projection of the Hilbert space and its a priori error estimations. Several verified examples which confirm the effectiveness of the new procedures are presented. [ABSTRACT FROM AUTHOR]

One-dimensional heat-conduction models in a semi-infinite domain, although forced convection obeys Newton's law of cooling, are challenging to solve using standard integral transformation methods when the boundary condition φ(t) is an exponential decay function. In this study, a general theoretical solution was established using Fourier transform, but φ(t) was not directly present in the transformation processes, and φ(t) was substituted into the general theoretical solution to obtain the corresponding analytical solution. Additionally, the specific solutions and corresponding mathematical meanings were discussed. Moreover, numerical verification and sensitivity analysis were applied to the proposed model. The results showed that T(x,t) was directly proportional to the thermal diffusivity (a) and was inversely proportional to calculation distance (x) and the coefficient of cooling ratio (λ). The analytical solution was more sensitive to the thermal diffusivity than other factors, and the highest relative error between numerical and analytical solutions was roughly 4% under the condition of 2a and λ. Furthermore, T(x,t) grew nonlinearly as the material's thermal diffusivity or cooling ratio coefficient changed. Finally, the analytical solution was applied for parameter calculation and verification in a case study, providing the reference basis for numerical calculation under specific complex boundaries, especially for the study of related problems in the fields of fluid dynamics and peridynamics with the heat-conduction equation. [ABSTRACT FROM AUTHOR]

A numerical verification method is proposed to prove the existence of time-global solutions of complex ordinary differential equations (ODEs), which should be inscribed within a circle with a specified radius r. A conservative quantity is assumed to exist and is calculated to construct the verification conditions. We use a numerical example with a series expansion on the right side of the ODEs to demonstrate how to find such a conservative quantity and how to apply our method. [ABSTRACT FROM AUTHOR]

Floating-point numbers represent only a subset of real numbers. As such, floating-point arithmetic introduces approximations that can compound and have a significant impact on numerical simulations. We introduce encapsulated error, a new way to estimate the numerical error of an application and provide a reference implementation, the Shaman library. Our method uses dedicated arithmetic over a type that encapsulates both the result the user would have had with the original computation and an approximation of its numerical error. We thus can measure the number of significant digits of any result or intermediate result in a simulation. We show that this approach, although simple, gives results competitive with state-of-the-art methods. It has a smaller overhead, and it is compatible with parallelism, making it suitable for the study of large-scale applications. [ABSTRACT FROM AUTHOR]

In the present paper, we develop a novel method for structural health monitoring of multi-storey frame structures with the capability to detect and localise local damage. The method uses so-called spatial incompatibility filters, which are continuously distributed strain-type sensors only sensitive to incompatibilities. In the first part of the paper the concept of incompatibility filters is introduced for multi-storey frame structures and it is shown how these filters can be used to detect and localise local cracks in frame structures. In the second part of the paper we study the use of incompatibility filters put into practice by piezoelectric sensor networks for structural health monitoring of a three-storey frame structure. The design of the piezoelectric sensor network is based on an analytical analysis of the frame structure within the framework of the method developed in the first part of the paper and a numerical verification using three-dimensional Finite Elements completes the paper

We propose a verification method for specification of homoclinic orbits as application of our previous work for constructing local Lyapunov functions by verified numerics. Our goal is to specify parameters appeared in the given systems of ordinary differential equations (ODEs) which admit homoclinic orbits to equilibria. Here we restrict ourselves to cases that each equilibrium is independent of parameters. The feature of our methods consists of Lyapunov functions, integration of ODEs by verified numerics, and Brouwer's coincidence theorem on continuous mappings. Several techniques for constructing continuous mappings from a domain of parameter vectors to a region of the phase space are shown. We present numerical examples for problems in 3 and 4-dimensional cases. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to obtain rigorous numerical enclosures for solutions of Lane–Emden's equation − Δ u = | u | p − 1 u with homogeneous Dirichlet boundary conditions. We prove the existence of a nondegenerate solution u nearby a numerically computed approximation u ̂ together with an explicit error bound, i.e., a bound for the difference between u and u ̂. In particular, we focus on the sub-square case in which 1 < p < 2 so that the derivative p | u | p − 1 of the nonlinearity | u | p − 1 u is not Lipschitz continuous. In this case, it is problematic to apply the classical Newton-Kantorovich theorem for obtaining the existence proof, and moreover several difficulties arise in the procedures to obtain numerical integrations rigorously. We design a method for enclosing the required integrations explicitly, proving the existence of a desired solution based on a generalized Newton-Kantorovich theorem. A numerical example is presented where an explicit solution-enclosure is obtained for p = 3 / 2 on the unit square domain Ω = (0 , 1) 2. [ABSTRACT FROM AUTHOR]

This paper presents some improved infinity norm estimations related to computer-assisted proofs of the Kolmogorov problem, which comprises the Navier-Stokes equations for the flow in a two-dimensional flat torus under a special driving force. These estimations and the basic idea behind them play important roles in accurate enclosing of solutions for such type of nonlinear differential equations. Several comparisons of concrete values confirm the effectiveness of the presented approach. [ABSTRACT FROM AUTHOR]

In Terasaka et al. JSIAM Lett. (2020), we have proposed numerical verification methods to construct local Lyapunov functions around non-hyperbolic equilibria using non-linear transformations by up to third degree polynomials. In the present study, we extend these methods by proving that polynomials of an arbitrary degree can be applied to define the transformations and show an example problem where we have to use a fifth-degree polynomial to construct local Lyapunov functions. [ABSTRACT FROM AUTHOR]

In a companion paper, we present the theoretical development of a new robust, relaxation-free iteration scheme for multiphysics k -eigenvalue problems. These types of problems are essential to the study of computational reactor physics and in particular whole-core, high-fidelity simulation codes. The deterministic whole-core simulation tools invariably rely on the coarse mesh finite difference (CMFD) acceleration for fast convergence. However, the use of CMFD-accelerated transport in multiphysics problems coupled via Picard iteration is not robust and is frequently treated with relaxation. In this paper, we build on our previous theoretical work that uses Fourier analysis to prove how stability and efficient convergence can be achieved in the multiphysics problem by appropriately loosening the convergence criteria of the low-order diffusion acceleration equations. Specifically, we develop a methodology for estimating a key problem-dependent parameter, the feedback intensity, required by the nearly optimally partially converged coarse mesh finite difference (NOPC-CMFD) method. We then describe the implementation of NOPC-CMFD in the Michigan Parallel Characteristics Transport (MPACT) code and perform several numerical calculations. Problems ranging from a single pressurized water reactor (PWR) fuel rod to a full-core PWR cycle depletion are analyzed to assess the performance and robustness of NOPC-CMFD over a wide range of conditions that consider multiple forms of multiphysics feedback. The results verify the theoretical predictions of our companion paper, illustrating that the NOPC-CMFD is superior to current CMFD or nonlinear diffusion acceleration schemes that use relaxation. Overall, the method is able to recover the performance of traditional CMFD in problems without feedback for a wide range of conditions. This was observed to result in a substantial reduction, up to 40%, of the run time in whole-core cycle depletion problems. [ABSTRACT FROM AUTHOR]

This article introduces a new quantitative model for the geological strength index (GSI) based on attribute mathematics theory. This new attribute evaluation index system of GSI consists of the rock mass block index, the joint spacing, the number of joint sets, the absolute weathering index, the large-scale undulation, and the small-scale undulation. Recently, based on attribute mathematics theory, the attribute mathematics evaluation model of GSI was established for identifying and classifying the geological strength index. Finally, based on the confidence criterion and the method of linear interpolation, a quantitative model for the geological strength index is established. To verify the model, an improved numerical method is introduced. Meanwhile, the equivalent transformation method of the Hoek–Brown strength criterion and Mohr–Coulomb strength criterion is cited. The problems in the determination of the reinforcement time to support surrounding rock are solved by the analysis of the construction process mechanics. A new concept called section displacement deviation is proposed for effective comparison of the monitoring data and the simulation predictions. Project applications prove that this quantitative method has strong pertinence and high accuracy and can organically combine geological surveys, experimental data, statistics, and expert opinions, so this evaluation method can decrease the subjectivity of research decisions. The method of the attribute mathematics evaluation of GSI provides a new approach to quantifying the GSI system. [ABSTRACT FROM AUTHOR]

This paper proposes a method for rigorously analyzing the sign-change structure of solutions of elliptic partial differential equations subject to one of the three types of homogeneous boundary conditions: Dirichlet, Neumann, and mixed. Given explicitly estimated error bounds between an exact solution u and a numerically computed approximate solution u ^ , we evaluate the number of sign-changes of u (the number of nodal domains) and determine the location of zero level-sets of u (the location of the nodal line). We apply this method to the Dirichlet problem of the Allen–Cahn equation. The nodal line of solutions of this equation represents the interface between two coexisting phases. [ABSTRACT FROM AUTHOR]

In this study, a popular co-flow thrust vectoring system, which is superior to typical Coanda nozzles with one main jet, is examined experimentally and compared with 2D and 3D computational fluid dynamics results. High Speed Orienting Momentum with Enhanced Reversibility nozzle concept is the base design to proposed configuration which uses a control jet additional to the main jet for better and active enhancement on the flow vectoring and streamlined side-walls resulted in less flow blockage. This comparatively novel concept is utilized in an experimental setup to direct the thrust of aerial vehicles. The system includes two inlets (inlet1, inlet2) with different jet velocities and one pintle to separate and smoothly direct these jets and a converging-diverging nozzle to enclose these components. Experimental study is accomplished with four different configurations of inlet1 and inlet2 as 15 m/s and 10 m/s; 20 m/s and 10 m/s; 30 m/s and 10 m/s, and 45 m/s and 10 m/s, respectively. The tangential velocities on the curved surfaces are successfully measured utilizing a micro-manometer (Pitot tube) so that attachments/detachments of jets on the exit walls and deflection angles are calculated for each inlet velocities. The current experimental study also revealed that 3D assumption of computational fluid dynamics of Coanda effect is highly accurate and deflection angle results are not far from experimental results with the average deficit of only 5.44 %. As the result, 3D verification study resembles to experimental study in terms of deflection angles for all configurations. [ABSTRACT FROM AUTHOR]

As typical karst products, caves are highly concealed, thus resulting in the increase of rock permeability and the deterioration of rock mechanics. When the shield tunnel passes through karst area, the confined water cave near the excavation face can easily result in hazards such as water inrush, shield head drooping. Therefore, it is important to determine the critical safety distance between the karst cave and the shield tunnel. In this paper, a three-dimensional failure model was built when the karst cave was located in front of the tunnel. And then the corresponding analytical solution to the critical safety distance between regular karst cave and tunnel was deduced based on upper bound theorem of limit analysis. Additionally, the sensitivity curve of different parameters to critical safety distance was drawn by using the Matlab program, aiming to analyze the effects of rock mass parameters, karst cave parameters and geometric parameters on critical safety distance. Based on the optimizing dichotomy and rock mass instability criterion, the reliability of the above critical safety distance formula was further verified by using COMSOL Multiphysics. The results confirmed that this method can provide reference for the design and construction of karst tunnel in the future. [ABSTRACT FROM AUTHOR]

This paper presents some computer-assisted procedures to prove the invertibility of a second-order linear elliptic operator and to compute a bound for the norm of its inverse. These approaches are based on constructive L 2 -norm estimates of the Laplacian and improve on previous procedures that use projection and a priori error estimations. Several examples which confirm the actual effectiveness of the procedures are reported. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamical response of a nonlinear piezoelectric energy harvester under a hard harmonic excitation and assesses its output power. The system is composed of a unimorph cantilever beam with a tip mass and exposed to an harmonic tip excitation with a hard forcing amplitude. First, the governing dimensionless nonlinear electromechanical ordinary differential equations (ODEs) are obtained. Next, the multiple scales method (MSM) is exploited to provide an approximate-analytical solution for the ODEs in hard and soft forcing scenarios. It is observed that, the hard force results in sub- and super-harmonic resonances. The MSM-based solutions are then validated by a numerical integration method and a good agreement is observed between the approximate-analytical and numerical results. Furthermore, utilizing the MSM-based solutions for the subharmonic, superharmonic, and soft primary resonances cases, the associated frequency and force response curves are constructed. It is revealed that the hard excitation leads to a remarkable voltage generation in the secondary resonances; this leads to a broadband energy harvesting. In addition, the time-domain electrical responses of the secondary resonances are also obtained and compared with each other. Finally, the three-dimensional graphs of the electrical power versus detuning parameter and time constant ratio in the cases of the secondary resonances are plotted. The results show that the optimum output power of the superharmonic resonance is considerably larger than the maximum power of the subharmonic resonance case. [ABSTRACT FROM AUTHOR]

Verification of a groundwater flow model by radiocarbon (14C) data are presented taking into consideration the paleo-hydrogeological changes. Northeastern area of the Great Hungarian Plain was a deep-lying flat area, and its central part (Nyírség) has been uplifted in the last 15,000 years. These geological events have drastically changed the hydrogeological conditions of Nyírség. The groundwater flow system is composed of the Quaternary-Pliocene-Upper Pannonian clastic sediments. Groundwater flow modeling has been performed to define the main lateral and vertical flow directions and velocities controlling the propagation of the environmental radioactive tracer 14C. Solute-transport modeling was used to calculate the 14C activity. The recent steady-state groundwater flow velocity was reduced to a reasonable value characterizing the average flow velocity over the 15 ka simulation period using "trial and error" method. The best fit between the simulated and measured 14C data was achieved by assuming 0.4 flow velocity reduction factor. Results indicate that the present steady-state flow model with this flow velocity reduction factor is capable of reproducing the observed 14C data taking into account the effect of the significant uplift of the part of the land surface in the last 15 ka in NE Hungary. [ABSTRACT FROM AUTHOR]

This paper presents an improved method for determining the invertibility of second-order linear elliptic operators with a bound on the norm of their inverses by computers in a mathematically rigorous sense. This approach is an improvement on a previous method (Nakao et al. in Jpn J Ind Appl Math 32:19–32, 2015) which used a projection and constructive a priori error estimates. Several examples confirming the effectiveness of the proposed procedure are reported. [ABSTRACT FROM AUTHOR]

This paper presents the investigation of the root causes of the fast degradation of a railway crossing. The dynamic performance of the crossing was assessed using the sensor-based crossing instrumentation, and the measurement results were verified using the multi-body system (MBS) vehicle-crossing model. Together with the field inspections, the measurement and simulation results indicate that the fast crossing degradation was caused by the high wheel-rail impact forces related to the hunting motion of the passing trains. Additionally, it was shown that the train hunting was activated by the track geometry misalignment in front of the crossing. The obtained results have not only explained the extreme values in the measured responses, but also shown that crossing degradation is not always caused by the problems in the crossing itself, but can also be caused by problems in the adjacent track structures. The findings of this study were implemented in the condition monitoring system for railway crossings, using which timely and correctly aimed maintenance actions can be performed.

The paper shows a technique of two-dimensional modelling of railway truss bridge girders. The model accounts for joint action of girders and steel-concrete composite deck. Namely, influence of the deck on span flexural rigidity and internal force distribution in truss members are taken into account. The technique is capable of reflecting various arrangements of cross beam to truss flange connection as well as various concrete slab longitudinal rigidity (uncracked/cracked). Application example of test loaded bridge span is given. The accuracy of assessment of span flexural stiffness and internal forces distribution of presented procedure is similar to 3D beam/shell element model results accuracy. The presented technique is suitable for preliminary design of truss bridges and verification of other computational methods.

This paper presents a correlation analysis of the structural dynamic responses and weather conditions of a railway crossing. Prior to that, the condition monitoring of the crossing as well as the indicators for crossing condition assessment are briefly introduced. In the correlation analysis, strong correlations are found between acceleration responses with irregular contact ratios and the fatigue area. The correlation results between the dynamic responses and weather variables indicate the influence of weather on the performance of the crossing, which is verified using a numerical vehicle-crossing model developed using the multi-body system (MBS) method. The combined correlation and simulation results also indicate degraded track conditions of the monitored crossing. In the condition monitoring of railway crossings, the findings of this study can be applied to data measurement simplification and regression, as well as to assessing the conditions of railway crossings.

Partial expansion was observed in stratified subsidence during foundation pit dewatering. However, the phenomenon was suspected to be an error because the compression of layers is known to occur when subsidence occurs. A slice of the subsidence cone induced by drawdown was selected as the prototype. Model tests were performed to investigate the phenomenon. The underlying confined aquifer was generated as a movable rigid plate with a hinge at one end. The overlying layers were simulated with remolded materials collected from a construction site. Model tests performed under the conceptual model indicated that partial expansion occurred in stratified settlements under coordination deformation and consolidation conditions. During foundation pit dewatering, rapid drawdown resulted in rapid subsidence in the dewatered confined aquifer. The rapidly subsiding confined aquifer top was the bottom deformation boundary of the overlying layers. Non-coordination deformation was observed at the top and bottom of the subsiding overlying layers. The subsidence of overlying layers was larger at the bottom than at the top. The layers expanded and became thicker. The phenomenon was verified using numerical simulation method based on finite difference method. Compared with numerical simulation results, the boundary effect of the physical tests was obvious in the observation point close to the movable endpoint. The tensile stress of the overlying soil layers induced by the underlying settlement of dewatered confined aquifer contributed to the expansion phenomenon. The partial expansion of overlying soil layers was defined as inversed rebound. The inversed rebound was induced by inversed coordination deformation. Compression was induced by the consolidation in the overlying soil layers because of drainage. Partial expansion occurred when the expansion exceeded the compression. Considering the inversed rebound, traditional layer-wise summation method for calculating subsidence should be revised and improved. [ABSTRACT FROM AUTHOR]