Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.

THE RIEMANN PROBLEM FOR ISENTROPIC COMPRESSIBLE EULER EQUATIONS WITH DISCONTINUOUS FLUX

We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.

HetNets Under Decoupled Uplink and Downlink Access with UE Random Discontinuous Transmission: Local Delay and Energy Efficiency

Due to the limited uplink capability in heterogeneousnetworks (HetNets), the decoupled uplinkand downlink access (DUDA) mode has recently beenproposed to improve the uplink performance. In thispaper, the random discontinuous transmission (DTX)at user equipment (UE) is adopted to reduce the interferencecorrelation across different time slots. By utilizingstochastic geometry, we analytically derive themean local delay and energy efficiency (EE) of an uplinkHetNet with UE random DTX scheme under theDUDA mode. These expressions are further approximatedas closed forms under reasonable assumptions.Our results reveal that under the DUDA mode, there isan optimal EE with respect to mute probability underthe finite local delay constraint. In addition, with thesame finite mean local delay as under the coupled uplinkand downlink access (CUDA) mode, the HetNetsunder the DUDA mode can achieve a higher EE witha lower mute probability.

On the calibration and verification of Voronoi-based discontinuous deformation analysis for modeling rock fracture

Since its introduction,discontinuous deformation analysis(DDA)has been widely used in different areas of rock mechanics.By dividing large blocks into subblocks and introducing artificial joints,DDA can be applied to rock fracture simulation.However,parameter calibration,a fundamental issue in discontinuum methods,has not received enough attention in DDA.In this study,the parameter calibration of DDA for intact rock is carefully studied.To this end,a subblock DDA with Voronoi tessellation is presented first.Then,a modified contact constitutive law is introduced,in which the tensile and shear meso-strengths are modified to be independent of the bond lengths.This improvement can prevent the unjustified preferential failure of short edges.A method for imposing confining pressure is also introduced.Thereafter,sensitivity analysis is performed to investigate the influence of the calculated parameters and meso-parameters on the mechanical properties of modeled rock.Based on the sensitivity analysis,a unified calibration procedure is suggested for both cases with and without confining pressure.Finally,the calibration procedure is applied to two examples,including a biaxial compression test.The results show that the proposed Voronoi-based DDA can simulate rock fracture with and without confining pressure very well after careful parameter calibration.

Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems

Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical experiments.Discontinuous Galerkin(DG)methods are increasingly used for solving PDEs and,as all Galerkin formulations,come with a strong framework for proving the stability and the convergence.Here we propose the use of FC in forming a new basis for the DG framework.

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.

Panel Acoustic Contribution Analysis in Automotive Acoustics Using Discontinuous Isogeometric Boundary Element Method

In automotive industries,panel acoustic contribution analysis(PACA)is used to investigate the contributions of the body panels to the acoustic pressure at a certain point of interest.Currently,PACA is implementedmostly by either experiment-based methods or traditional numerical methods.However,these schemes are effort-consuming and inefficient in solving engineering problems,thereby restraining the further development of PACA in automotive acoustics.In this work,we propose a PACA scheme using discontinuous isogeometric boundary element method(IGABEM)to build an easily implementable and efficient method to identify the relative acoustic contributions of each automotive body panel.Discontinuous IGABEMis more accurate and converges faster than continuous BEM and IGABEM in the interior sound pressure evaluation of automotive compartments.In this work,a contribution ratio is defined to estimate the relative acoustic contribution of the structure panels;it can be calculated by reusing the coefficient matrix that has already been generated in the sound pressure evaluation process.The utilization of the parallel technique enables the proposed method to be more efficient than conventional methods;it is validated in two numerical examples,including a car passenger compartment subjected to realistic boundary conditions.A sound pressure response experiment based on a steel box is conducted to verify the accuracy of the interior sound pressure calculation using discontinuous IGABEM.This work is expected to promote the practical process of IGABEM for application in automotive acoustic problems.

Effect of Free-fall Nozzle Channel Dispersion Angle on TC4 Discontinuous Droplets Pre-breakup in EIGA

The effect of the inlet gas pressure,supplementary gas pressure and nozzle channel dispersion angle on the pre-breakup behavior of Ti-6Al-4V(TC4)discontinuous droplets during EIGA was investigated by combining numerical simulation with experiments.The results show that the axial velocity at the recirculation zone before the stagnation location was first increased and decreased then increased significantly after the peak value,while the pressure of the recirculation zone increased with the increase in inlet pressure.With the supplementary pressure increasing,the velocity magnitude and range of the recirculation zone gradually decreased.As the dispersion angle of the nozzle channel increased,the pre-breakup efficiency of droplets gradually decreased,but the adhesion phenomenon of droplets on the inner wall surface of the nozzle channel(IWSNC)gradually weakened.Under the inlet pressure of 4 MPa,a supplementary pressure of 0.05 MPa,and the dispersion angle of 15°,the uniform and spherical TC4 powders with diameter of 70μm were prepared,which was consistent with the simulation results.The optimized process parameters is a balance between the size of the pre-atomized particles and the back-spraying and bonding phenomenons of droplets.

A super wear-resistant coating for Mg alloys achieved by plasma electrolytic oxidation and discontinuous deposition

Magnesium alloys are lightweight materials with great potential,and plasma electrolytic oxidation(PEO)is effective surface treatment for necessary improvement of corrosion resistance of magnesium alloys.However,the∼14µm thick and rough PEO protection layer has inferior wear resistance,which limits magnesium alloys as sliding or reciprocating parts,where magnesium alloys have special advantages by their inherent damping and denoising properties and attractive light-weighting.Here a novel super wear-resistant coating for magnesium alloys was achieved,via the discontinuous sealing(DCS)of a 1.3µm thick polytetrafluoroethylene(PTFE)polymer layer with an initial area fraction(A_(f))of 70%on the necessary PEO protection layer by selective spraying,and the wear resistance was exceptionally enhanced by∼5500 times in comparison with the base PEO coating.The initial surface roughness(Sa)under PEO+DCS(1.54µm)was imperfectly 59%higher than that under PEO and conventional continuous sealing(CS).Interestingly,DCS was surprisingly 20 times superior for enhancing wear resistance in contrast to CS.DCS induced nano-cracks that splitted DCS layer into multilayer nano-blocks,and DCS also provided extra space for the movement of nano-blocks,which resulted in rolling friction and nano lubrication.Further,DCS promoted mixed wear of the PTFE polymer layer and the PEO coating,and the PTFE layer(HV:6 Kg·mm^(−2),A_(f):92.2%)and the PEO coating(HV:310 Kg·mm^(−2),A_(f):7.8%)served as the soft matrix and the hard point,respectively.Moreover,the dynamic decrease of Sa by 29%during wear also contributed to the super wear resistance.The strategy of depositing a low-frictional discontinuous layer on a rough and hard layer or matrix also opens a window for achieving super wear-resistant coatings in other materials.

A LOCAL DISCONTINUOUS GALERKIN METHOD FOR TIME-FRACTIONAL DIFFUSION EQUATIONS

In this paper,a local discontinuous Galerkin(LDG)scheme for the time-fractional diffusion equation is proposed and analyzed.The Caputo time-fractional derivative(of orderα,with 0<α<1)is approximated by a finite difference method with an accuracy of order3-α,and the space discretization is based on the LDG method.For the finite difference method,we summarize and supplement some previous work by others,and apply it to the analysis of the convergence and stability of the proposed scheme.The optimal error estimate is obtained in the L2norm,indicating that the scheme has temporal(3-α)th-order accuracy and spatial(k+1)th-order accuracy,where k denotes the highest degree of a piecewise polynomial in discontinuous finite element space.The numerical results are also provided to verify the accuracy and efficiency of the considered scheme.

FIXED/PREASSIGNED-TIME SYNCHRONIZATION OF QUATERNION-VALUED NEURAL NETWORKS INVOLVING DELAYS AND DISCONTINUOUS ACTIVATIONS: A DIRECT APPROACH

The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous efforts that employed separation analysis and the real-valued control design, based on the quaternion-valued signum function and several related properties, a direct analytical method is proposed here and the quaternion-valued controllers are designed in order to discuss the fixed-time synchronization for the relevant quaternion-valued neural networks. In addition, the preassigned-time synchronization is investigated based on a quaternion-valued control design, where the synchronization time is preassigned and the control gains are finite. Compared with existing results, the direct method without separation developed in this article is beneficial in terms of simplifying theoretical analysis, and the proposed quaternion-valued control schemes are simpler and more effective than the traditional design, which adds four real-valued controllers. Finally, two numerical examples are given in order to support the theoretical results.

A multithreaded parallel upwind sweep algorithm for the S_(N) transport equations discretized with discontinuous finite elements

The complex structure and strong heterogeneity of advanced nuclear reactor systems pose challenges for high-fidelity neutron-shielding calculations. Unstructured meshes exhibit strong geometric adaptability and can overcome the deficiencies of conventionally structured meshes in complex geometry modeling. A multithreaded parallel upwind sweep algorithm for S_(N) transport was proposed to achieve a more accurate geometric description and improve the computational efficiency. The spatial variables were discretized using the standard discontinuous Galerkin finite-element method. The angular flux transmission between neighboring meshes was handled using an upwind scheme. In addition, a combination of a mesh transport sweep and angular iterations was realized using a multithreaded parallel technique. The algorithm was implemented in the 2D/3D S_(N) transport code ThorSNIPE, and numerical evaluations were conducted using three typical benchmark problems:IAEA, Kobayashi-3i, and VENUS-3. These numerical results indicate that the multithreaded parallel upwind sweep algorithm can achieve high computational efficiency. ThorSNIPE, with a multithreaded parallel upwind sweep algorithm, has good reliability, stability, and high efficiency, making it suitable for complex shielding calculations.

Adaptive Fixed-Time Synchronization of Delayed Memristor-Based Neural Networks with Discontinuous Activations

Fixed-time synchronization(FTS)of delayed memristor-based neural networks(MNNs)with discontinuous activations is studied in this paper.Both continuous and discontinuous activations are considered forMNNs.And the mixed delays which are closer to reality are taken into the system.Besides,two kinds of control schemes are proposed,including feedback and adaptive control strategies.Based on some lemmas,mathematical inequalities and the designed controllers,a few synchronization criteria are acquired.Moreover,the upper bound of settling time(ST)which is independent of the initial values is given.Finally,the feasibility of our theory is attested by simulation examples.

A Sub-element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods

In this paper,a new strategy for a sub-element-based shock capturing for discontinuous Galerkin(DG)approximations is presented.The idea is to interpret a DG element as a col-lection of data and construct a hierarchy of low-to-high-order discretizations on this set of data,including a first-order finite volume scheme up to the full-order DG scheme.The dif-ferent DG discretizations are then blended according to sub-element troubled cell indicators,resulting in a final discretization that adaptively blends from low to high order within a single DG element.The goal is to retain as much high-order accuracy as possible,even in simula-tions with very strong shocks,as,e.g.,presented in the Sedov test.The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing.The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.

A continuous/discontinuous deformation analysis(CDDA)method based on deformable blocks for fracture modeling

In the framework of finite element meshes,a novel continuous/discontinuous deformation analysis(CDDA)method is proposed in this paper for modeling of crack problems.In the present CDDA,simple polynomial interpolations are defined at the deformable block elements,and a link element is employed to connect the adjacent block elements.The CDDA is particularly suitable for modeling the fracture propagation because the switch from continuous deformation analysis to discontinuous deformation analysis is natural and convenient without additional procedures.The SIFs(stress intensity factors)for various types of cracks,such as kinked cracks or curved cracks,can be easily computed in the CDDA by using the virtual crack extension technique(VCET).Both the formulation and implementation of the VCET in CDDA are simple and straightforward.Numerical examples indicate that the present CDDA can obtain high accuracy in SIF results with simple polynomial interpolations and insensitive to mesh sizes,and can automatically simulate the crack propagation without degrading accuracy.

Comparative Analysis of Continuous versus Intermittent Proton Pump Inhibitor Therapy in Patients with Upper Gastrointestinal Bleeding Due to Ulcers

Upper gastrointestinal bleeding (UGIB) presents as a prevalent clinical challenge, with annual incidence rates ranging from 80 to 150 cases per 100,000 individuals. Guidelines for managing patients with UGIB due to bleeding ulcers recommend a continuous infusion of proton pump inhibitors (PPI). However, studies comparing intermittent dosing of PPI therapy show that this regimen achieves similar clinical benefits. If the clinical efficacy remains equivalent, intermittent dosing will be more cost-effective for patients and the health care system. Our research study aims to analyze the comparative effectiveness of intermittent versus continuous PPI therapy after endoscopic treatment in patients with UGIB, focusing on such endpoints as rebleeding risk at 3-and 7-day mortality rates. Methods: Resources searched included MEDLINE, EMBASE, PUBMED, and the Cochrane Central Register of Controlled Trials databases from January 2010 through December 2023 with the inclusion of meta-analysis, systematic review, review, or ACG guideline recommendations. Results of the analysis show how recommendations regarding high vs. low PPI regimen changed over time: from no difference in regimen in 2010 to recommending continuous regimen in 2012 to declaring insufficient evidence between choosing one regimen over another in 2013 to determine that both regimens were comparable to each other in 2014-2018 and finally to recommending both regimens in 2021. To conclude, our review shows that in patients with bleeding ulcers and high-risk endoscopic findings, intermittent PPI therapy is non-inferior to continuous PPI infusion for three days, seven days bleeding risk or mortality rates;however, it remains challenging to determine the most optimal intermittent regimen due to heterogeneity of RCTs included in meta-analyses, and further trials will need to be performed.

Scale-space effect and scale hybridization in image intelligent recognition of geological discontinuities on rock slopes

Geological discontinuity(GD)plays a pivotal role in determining the catastrophic mechanical failure of jointed rock masses.Accurate and efficient acquisition of GD networks is essential for characterizing and understanding the progressive damage mechanisms of slopes based on monitoring image data.Inspired by recent advances in computer vision,deep learning(DL)models have been widely utilized for image-based fracture identification.The multi-scale characteristics,image resolution and annotation quality of images will cause a scale-space effect(SSE)that makes features indistinguishable from noise,directly affecting the accuracy.However,this effect has not received adequate attention.Herein,we try to address this gap by collecting slope images at various proportional scales and constructing multi-scale datasets using image processing techniques.Next,we quantify the intensity of feature signals using metrics such as peak signal-to-noise ratio(PSNR)and structural similarity(SSIM).Combining these metrics with the scale-space theory,we investigate the influence of the SSE on the differentiation of multi-scale features and the accuracy of recognition.It is found that augmenting the image's detail capacity does not always yield benefits for vision-based recognition models.In light of these observations,we propose a scale hybridization approach based on the diffusion mechanism of scale-space representation.The results show that scale hybridization strengthens the tolerance of multi-scale feature recognition under complex environmental noise interference and significantly enhances the recognition accuracy of GD.It also facilitates the objective understanding,description and analysis of the rock behavior and stability of slopes from the perspective of image data.

Enhanced measurement precision with continuous interrogation during dynamical decoupling

Dynamical decoupling(DD)is normally ineffective when applied to DC measurement.In its straightforward implementation,DD nulls out DC signal as well while suppressing noise.This work proposes a phase relay method that is capable of continuously interrogating the DC signal over many DD cycles.We illustrate its efficacy when applied to the measurement of a weak DC magnetic field with an atomic spinor Bose-Einstein condensate.Sensitivities approaching standard quantum limit or Heisenberg limit are potentially realizable for a coherent spin state or a squeezed spin state of 10000 atoms,respectively,while ambient laboratory level noise is suppressed by DD.Our work offers a practical approach to mitigate the limitations of DD to DC measurement and would find other applications for resorting coherence in quantum sensing and quantum information processing research.

THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

This paper is mainly about the spectral properties of a class of Jacobi operators(H_(c,b)u)(n)=c_(n)u(n+1)+c_(n-1)u(n-1)+b_(n)u(n),.where∣c_(n)−1∣=O(n^(−α))and b_(n)=O(n^(−1)).We will show that,forα≥1,the singular continuous spectrum of the operator is empty.

Discontinuation of therapy in inflammatory bowel disease: Current views

The timely introduction and adjustment of the appropriate drug in accordance with previously well-defined treatment goals is the foundation of the approach in the treatment of inflammatory bowel disease(IBD).The therapeutic approach is still evolving in terms of the mechanism of action but also in terms of the possibility of maintaining remission.In patients with achieved long-term remission,the question of de-escalation or discontinuation of therapy arises,considering the possible side effects and economic burden of long-term therapy.For each of the drugs used in IBD(5-aminosalycaltes,immunomodulators,biological drugs,small molecules)there is a risk of relapse.Furthermore,studies show that more than 50%of patients who discontinue therapy will relapse.Based on the findings of large studies and meta-analysis,relapse of disease can be expected in about half of the patients after therapy withdrawal,in case of monotherapy with aminosalicylates,immunomodulators or biological therapy.However,longer relapse-free periods are recorded with withdrawal of medication in patients who had previously been on combination therapies immunomodulators and anti-tumor necrosis factor.It needs to be stressed that randomised clinical trials regarding withdrawal from medications are still lacking.Before making a decision on discontinuation of therapy,it is important to distinguish potential candidates and predictive factors for the possibility of disease relapse.Fecal calprotectin level has currently been identified as the strongest predictive factor for relapse.Several other predictive factors have also been identified,such as:High Crohn's disease activity index or Harvey Bradshaw index,younger age(<40 years),longer disease duration(>40 years),smoking,young age of disease onset,steroid use 6-12 months before cessation.An important factor in the decision to withdraw medication is the success of re-treatment with the same or other drugs.The decision to discontinue therapy must be based on individual approach,taking into account the severity,extension,and duration of the disease,the possibility of side adverse effects,the risk of relapse,and patient’s preferences.