Dispersive shock waves for the Boussinesq Benjamin-Ono equation

In this work the dispersive shock wave solution of a Boussinesq Benjamin-Ono (BBO) equation, the standard Boussinesq equation with dispersion replaced by nonlocal Benjamin-Ono dispersion, isderived. This dispersive shock wave solution is derived using two methods, dispersive shock wavefitting and from a simple wave solution of theWhitham modulation equations for the BBO equation.The first of these yields the two edges of the dispersive shock wave, while the second yields the complete dispersive shock wave solution. As the Whitham modulation equations could not be set in Riemann invariant form, the ordinary differential equations governing the simple wave are solved using a hybrid numerical method coupled to the dispersive shock fitting which provides a suitable boundary condition. The full dispersive shock wave solution is then determined, which is found to be in excellent agreement with numerical solutions of the BBO equation. This hybrid method is a suitable and relatively simple method to fully determine the dispersive shock wave solution of anonlinear dispersive wave equation for which the (hyperbolic) Whitham modulation equations are known, but their Riemann invariant form is not

A surrogate model for computational homogenization of elastostatics at finite strain using high-dimensional model representation-based neural network

We propose a surrogate model for two-scale computational homogenization of elastostatics at finite strains. The macroscopic constitutive law is made numerically available via an explicit formulation of the associated macroenergy density. This energy density is constructed by using a neural network architecture that mimics a high-dimensional model representation. The database for training this network is assembled through solving a set of microscopic boundary value problems with the prescribed macroscopic deformation gradients (input data) and subsequently retrieving the corresponding averaged energies (output data). Therefore, the two-scale computational procedure for nonlinear elasticity can be broken down into two solvers for microscopic and macroscopic equilibrium equations that work separately in two stages, called the offline and online stages. The finite element method is employed to solve the equilibrium equation at the macroscale. As for microscopic problems, an FFT-based collocation method is applied in tandem with the Newton-Raphson iteration and the conjugate-gradient method. Particularly, we solve the microscopic equilibrium equation in the Lippmann-Schwinger form without resorting to the reference medium. In this manner, the fixed-point iteration that might require quite strict numerical stability conditions in the nonlinear regime is avoided. In addition, we derive the projection operator used in the FFT-based method for homogenization of elasticity at finite strain

A Feasibility Study in Application of a Gamma Scattering Technique for Inspecting Density Variation by Monte Carlo Method

Back-scattering gamma-rays have been extensively used for years as a nondestructive tool for inspecting the materials in different fields of the economy. The intensities of Compton scattering gamma-rays from the scattering medium strongly depend on its electron density and therefore in its mass density. This feature is very useful for using it as a viable tool for inspecting material. This work aims to investigate the feasibility of application of gamma scattering technique for inspecting density variation in some construction objects by Monte-Carlo simulation method. The gamma-ray sources of different energies and strengths have been used to  extract  the information of density variation  for  interior of  sample by  recording  the backscattering gamma-rays with a gamma-ray detector. The results of our simulations confirm that the resolution for density variation in the inspected objects is quite good. The results should also prove useful in the optimum design of the nondestructive density gauges.Back-scattering gamma-rays have been extensively used for years as a nondestructive tool for inspecting the materials in different fields of the economy. The intensities of Compton scattering gamma-rays from the scattering medium strongly depend on its electron density and therefore in its mass density. This feature is very useful for using it as a viable tool for inspecting material. This work aims to investigate the feasibility of application of gamma scattering technique for inspecting density variation in some construction objects by Monte-Carlo simulation method. The gamma-ray sources of different energies and strengths have been used to  extract  the information of density variation  for  interior of  sample by  recording  the backscattering gamma-rays with a gamma-ray detector. The results of our simulations confirm that the resolution for density variation in the inspected objects is quite good. The results should also prove useful in the optimum design of the nondestructive density gauges

A surrogate model for computational homogenization of elastostatics at finite strain using high‐dimensional model representation‐based neural network

We propose a surrogate model for two-scale computational homogenization of elastostatics at finite strains. The macroscopic constitutive law is made numerically available via an explicit formulation of the associated macroenergy density. This energy density is constructed by using a neural network architecture that mimics a high-dimensional model representation. The database for training this network is assembled through solving a set of microscopic boundary value problems with the prescribed macroscopic deformation gradients (input data) and subsequently retrieving the corresponding averaged energies (output data). Therefore, the two-scale computational procedure for nonlinear elasticity can be broken down into two solvers for microscopic and macroscopic equilibrium equations that work separately in two stages, called the offline and online stages. The finite element method is employed to solve the equilibrium equation at the macroscale. As for microscopic problems, an FFT-based collocation method is applied in tandem with the Newton-Raphson iteration and the conjugate-gradient method. Particularly, we solve the microscopic equilibrium equation in the Lippmann-Schwinger form without resorting to the reference medium. In this manner, the fixed-point iteration that might require quite strict numerical stability conditions in the nonlinear regime is avoided. In addition, we derive the projection operator used in the FFT-based method for homogenization of elasticity at finite strain

Accelerating the distance-minimizing method for data-driven elasticity with adaptive hyperparameters

Data-driven constitutive modeling in continuum mechanics assumes that abundant material data are available and can effectively replace the constitutive law. To this end, Kirchdoerfer and Ortiz proposed an approach, which is often referred to as the distance-minimizing method. This method contains hyperparameters whose role remains poorly understood to date. Herein, we demonstrate that choosing these hyperparameters equal to the tangent of the constitutive manifold underlying the available material data can substantially reduce the computational cost and improve the accuracy of the distance-minimizing method. As the tangent of the constitutive manifold is typically not known in a data-driven setting, and as it can also change during an iterative solution process, we propose an adaptive strategy that continuously updates the hyperparameters on the basis of an approximate tangent of the hidden constitutive manifold. By several numerical examples we demonstrate that this strategy can substantially reduce the computational cost and at the same time also improve the accuracy of the distance-minimizing method

FIRST - Flexible interactive retrieval SysTem for visual lifelog exploration at LSC 2020

Lifelog can provide useful insights of our daily activities. It is essential to provide a flexible way for users to retrieve certain events or moments of interest, corresponding to a wide variation of query types. This motivates us to develop FIRST, a Flexible Interactive Retrieval SysTem, to help users to combine or integrate various query components in a flexible manner to handle different query scenarios, such as visual clustering data based on color histogram, visual similarity, GPS location, or scene attributes. We also employ personalized concept detection and image captioning to enhance image understanding from visual lifelog data, and develop an autoencoderlike approach for query text and image feature mapping. Furthermore, we refine the user interface of the retrieval system to better assist users in query expansion and verifying sequential events in a flexible temporal resolution to control the navigation speed through sequences of images

TextANIMAR: Text-based 3D Animal Fine-Grained Retrieval

3D object retrieval is an important yet challenging task, which has drawn more and more attention in recent years. While existing approaches have made strides in addressing this issue, they are often limited to restricted settings such as image and sketch queries, which are often unfriendly interactions for common users. In order to overcome these limitations, this paper presents a novel SHREC challenge track focusing on text-based fine-grained retrieval of 3D animal models. Unlike previous SHREC challenge tracks, the proposed task is considerably more challenging, requiring participants to develop innovative approaches to tackle the problem of text-based retrieval. Despite the increased difficulty, we believe that this task has the potential to drive useful applications in practice and facilitate more intuitive interactions with 3D objects. Five groups participated in our competition, submitting a total of 114 runs. While the results obtained in our competition are satisfactory, we note that the challenges presented by this task are far from being fully solved. As such, we provide insights into potential areas for future research and improvements. We believe that we can help push the boundaries of 3D object retrieval and facilitate more user-friendly interactions via vision-language technologies.Comment: arXiv admin note: text overlap with arXiv:2304.0573

A numerical scheme and some theoretical aspects for the cylindrically and spherically symmetric sine-Gordon equations

A finite difference formula based on the predictor–corrector technique is presented to integrate the cylindrically and spherically symmetric sine-Gordon equations numerically. Based on various numerical observations, one property of the waves of kink type is conjectured and used to explain their returning effect. Several numerical experiments are carried out and they are in excellent agreement with the existing results. In addition, the corresponding modulation solution for the two-dimensional ring-shaped kink is extended to that in three-dimension. Both numerical and theoretical aspects are utilized to verify the reliability of the proposed numerical scheme and thus the analytical modulation solutions

Wronskian formulation and Ansatz method for bad Boussinesq equation

In this work, two variants of the bad Boussinesq equation are studied. A Wronskian formulation is constructed for the solutions of the first equation. Various samples of real and complex solutions are given in accordance with zero and non-zero eigenvalues of the associated linear system of differential equations. Although the Wronskian formulation can also be derived for the second equation, a direct Ansatz method is proposed and successfully applied to obtain real solutions. The method is presented in this paper with concrete examples