Discontinuous Behavior Research Articles

Numerical simulation of a discontinuous gallery lining's behavior, and its interaction with rock

SummaryDeep excavation in some geological media needs lining of the gallery. This could limit the extent of the so‐called excavation damaged zone and the resulting convergence of the material due to tunneling. Boom clay, the reference potential host rock in Belgium for disposal of high‐level radioactive waste, is one of these media for which lining of the gallery walls is essential. A correct simulation of the lining behavior in the course of the excavation process, where the rock comes into contact with the lining, and in the long term, remains a significant challenge in analysis of the whole coupled phenomena of rock in interaction with the lining. This study aims to numerically model the lining behavior. The main objective is to develop a model that could realistically simulate the behavior of a discontinuous lining made of concrete segments. We propose to numerically analyze the response of the blocks in contact with each other and in interaction with rock, with the use of zero‐thickness interface elements. To validate the developed model and a proposed approach, a particular analysis compares the obtained results with the available in situ measurements. This study then discusses the deficiency of the simplistic model that considers a continuous lining. In addition, regarding the contact mechanism on the interface between the rock and the lining, the obtained results demonstrate an interesting relation between the contact phenomena and the shear banding within the rock around the gallery. Copyright © 2017 John Wiley & Sons, Ltd.

Mesoscopic simulation of the electrical conductivity of carbon nanotube reinforced polymers regarding atomistic results

Carbon nanotube reinforced polymers belong to a class of composite materials, which have been largely investigated due to their specific electrical, thermal and mechanical properties. In the case of electrical conductivity of carbon nanotube reinforced polymers, a critical amount of filler material ensures a sharp increase of conductivity. The material forms a percolation pathway and instantly turns the composite into a conductor. Mesoscopic simulations of these materials were carried out to predict electrical conductivity of carbon nanotube reinforced polymers and their critical amounts. This research work deals with percolation thresholds, converging representative volume elements and the effect of the discontinuous behaviour of conductivity considering tunnelling effects found in atomistic approaches on mesoscopic simulation models.

Analytical determination of bifurcations of periodic solution in three-degree-of-freedom vibro-impact systems with clearance

The smooth bifurcation and non-smooth grazing bifurcation of periodic solution of three-degree-of-freedom vibro-impact systems with clearance are studied in this paper. Firstly, six-dimensional Poincaré maps are established through choosing suitable Poincaré section and solving periodic solutions of vibro-impact system. Then, as the analytic expressions of all eigenvalues of Jacobi matrix of six-dimensional map are unavailable, the numerical calculations to search for the critical bifurcation values point by point is a laborious job based on the classical critical criterion described by the properties of eigenvalues. To overcome the difficulty from the classical bifurcation criteria, the explicit critical criterion without using eigenvalues calculation of high-dimensional map is applied to determine bifurcation points of Co-dimension-one bifurcations and Co-dimension-two bifurcations, and then local dynamical behaviors of these bifurcations are further analyzed. Finally, the existence of the grazing periodic solution of the vibro-impact system and grazing bifurcation point are analyzed, the discontinuous grazing bifurcation behavior is studied based on the compound normal form map near the grazing point, the discontinuous jumping phenomenon and the co-existing multiple solutions near the grazing bifurcation point are revealed.

Numerical study on dynamic behavior of slope models including weak layers from deformation to failure using material point method

This paper describes numerical studies on the dynamic behavior of experimental slope models, including various inclined weak layers. These studies were conducted by simulation of shaking table tests using the material point method (MPM), which allows seamless treatment of various considerations, from elastic behavior to discontinuous collapse behavior of slopes, on the basis of an elasto-plastic constitutive law. The simulation results showed that the failure modes, progressive deformation and downward sliding of the numerical slope models, which were similar to that observed in the shaking table tests, can be obtained using the numerical method. In addition, sensitivity analyses of the numerical models used in this study were performed to determine the effects of mesh size, number of particles per cell (PPC) and damping constants on the simulation results. The results of these analyses indicated the use of fine meshes and high damping constants seems to produce sensible results and reduce numerical noises, respectively.

Nonparametric Probability Density Estimation via Interpolation Filtering

In this paper, we discuss nonparametric estimation of the probability density function (PDF) of a univariate random variable. This problem has been the subject of a vast amount of scientific literature in many domains, while statisticians are mainly interested in the analysis of the properties of proposed estimators, and engineers treat the histogram as a ready-to-use tool for a data set analysis. By considering histogram data as a numerical sequence, a simple approach for PDF estimation is presented in this paper. It is based on basic notions related to the reconstruction of a continuous-time signal from a sequence of samples. When estimating continuous PDFs, it is shown that the proposed approach is as accurate as kernel-based estimators, widely adopted in the statistical literature. Conversely, it can provide better accuracy when the PDF to be estimated exhibits a discontinuous behavior. The main statistical properties of the proposed estimators are derived and then verified by simulations related to the common cases of normal and uniform density functions. The obtained results are also used to derive optimal, i.e., minimum integral of the mean square error, estimators.

Motion of double pendulum colliding with an obstacle of rough surface

The externally excited and damped vibration of the double pendulum in the vertical plane are considered. The pendulum can collide many times during the motion with a motionless obstacle having the rough surface. The double pendulum colliding with this object has been modeled as a piecewise smooth system constrained by the unilateral constraint. In the relatively long time between the collisions, the differential equations govern the motion of the pendulum. When the contact with the obstacle appears, the pendulum exhibits a discontinuous behavior. An important element of the solving algorithm is aimed on the continuous tracking of the position of the pendulum in order to detect the collision with the unilateral constraints and to determine the state vector of the pendulum at the impact time instant. A single collision is described by the Euler’s laws of motion in the integral form. The equations are supplemented by the Poisson’s hypothesis and Coulomb’s law of friction. The friction law is formulated for the instantaneous values of the reaction forces. The values of their impulses depend on the existence of a slip between the contacting bodies. Therefore, the Coulomb law cannot be generalized for the linear impulses of the forces in a simple way. We have applied the Routh method in order to solve the problem. The method has a simple geometrical interpretation in the impulse space. The angular velocities of both pendulum parts as well as the reaction forces at the joints of the system, which change in stepwise manner, have been presented in the paper.

A non-conventional discontinuous Lagrangian for viscous flow

Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.

A Comparative Study on the Hot Working Behavior of Inconel 718 and ALLVAC 718 Plus

Hot compression tests were performed on Inconel 718 and ALLVAC 718 PLUS (718+) at temperatures and strain rates in ranges of 1223 K to 1373 K (950 °C to 1100 °C) and 0.001–1 s−1, respectively. Discontinuous yield behavior was observed in the flow curves of both alloys. For both alloys, the drop in stress at the yield point (yield drop) was maximized at 0.01 to 1 s−1. The alloy 718+ showed larger yield drop than 718 over the studied deformation conditions. The different yield behaviors were attributed to the various chemical compositions. The peak strain for both alloys increased in temperature range of 1223 K to 1273 K (950 to 1000 °C) and strain rates of 0.01 to 1 s−1. This uncommon behavior was ascribed to the change in the mechanism of microstructural evolution from continuous to discontinuous dynamic recrystallization (DRX). The kinetics of DRX was described by the Avrami equation and the exponent was determined at different deformation conditions. The Avrami exponent increased in the middle values of Zener–Hollomon (Z) parameters, i.e., 29.3 < lnZ < 32.9 for 718 and 31.4 < lnZ < 34.5 for 718+. The unusual variation of the Avrami exponent was attributed to the change in the mechanism of DRX.

要素サイズ敏感性のない連続体損傷力学モデルの検討

A discontinuous material behavior such as ductile fracture and fatigue failure is predicted actively in various fields by FEM. There is continuum damage mechanics as a method to evaluate the discontinuous material behavior in a framework of continuum mechanics. However, the predicted behavior based on the method depends strongly on finite element size. Then, improvement of damage evolution equation and damage limit equation in continuum damage mechanics is discussed to reduce the mesh-dependence. These equations are extended based on finite element size and evaluated strain gradient. The predicted material property such as fracture strain in tensile test based on new equations corresponds to experimental result. Additionally, the prediction accuracy is higher than conventional mesh-independence model. Especially, the higher the tensile strength of material is, the higher the prediction accuracy is.

Bifurcations of periodic motion in a three-degree-of-freedom vibro-impact system with clearance

The smooth bifurcation and grazing non-smooth bifurcation of periodic motion of a three-degree-of-freedom vibro-impact system with clearance are studied in this paper. Firstly, a periodic solution of vibro-impact system is solved and a six-dimensional Poincaré map is established. Then, for the six-dimensional Poincaré map, the analytic expressions of all eigenvalues of Jacobi matrix with respect to parameters are unavailable. This implies that with application of the classical critical criterion described by the properties of eigenvalues, we have to numerically compute eigenvalues point by point and check their properties to search for the bifurcation points. Such the numerical calculation is a laborious job in the process of determining bifurcation points. To overcome the difficulty that originates from the classical bifurcation criteria, the explicit critical criteria without using eigenvalues calculation of high-dimensional map are applied to determine bifurcation points of Co-dimension-one period doubling bifurcation and Co-dimension-one Neimark–Sacker bifurcation and Co-dimension-two Flip–Neimark–Sacker bifurcation, and then local dynamical behaviors of these bifurcations are analyzed. Moreover, the directions of period doubling bifurcation and Neimark–Sacker bifurcation are analyzed by center manifold reduction theory and normal form approach. Finally, the existence of the grazing periodic motion of the vibro-impact system is analyzed and the grazing bifurcation point is obtained, the discontinuous grazing bifurcation behavior is studied based on the compound normal form map near the grazing point, the discontinuous jumping phenomenon and co-existing multiple solutions near the grazing bifurcation point are revealed.

Heterogeneous nucleation and heat flux avalanches in La(Fe, Si)13 magnetocaloric compounds near the critical point

The phase transformation kinetics of LaFe11.41Mn0.30Si1.29-H1.65 magnetocaloric compound is addressed by low rate calorimetry experiments. Scans at 1 mK/s show that its first order phase transitions are made by multiple heat flux avalanches. Getting very close to the critical point, when the transition becomes of the second order type, the step-like discontinuous behaviour associated with avalanches is smoothed out and the thermal hysteresis disappears. This result is confirmed by magneto-resistivity measurements and allows to obtain accurate values of the temperature hysteresis (ΔThyst = 0.37 K) at zero external magnetic field and of the critical field (Hc = 1.19 T). The number and magnitude of heat flux avalanches change as the magnetic field strength is increased, showing the interplay between the intrinsic energy barrier between phases and the microstructural disorder of the sample.

Hubbard pair cluster in the external fields. Studies of the chemical potential

The chemical potential of the two-site Hubbard cluster (pair) embedded in the external electric and magnetic fields is studied by exact diagonalization of the Hamiltonian. The formalism of the grand canonical ensemble is adopted. The influence of temperature, Hubbard on-site Coulombic energy $U$ and electron concentration on the chemical potential is investigated and illustrated in figures. In particular, a discontinuous behaviour of the chemical potential (or electron concentration) in the ground state is discussed.

Analysis of the Magnetic Susceptibility as a Function of Temperature for the α, β and γ Phases of Oxygen

We analyse the magnetic susceptibility χ as a function of temperature (zero pressure) for the transitions of α- β, β- γ and γ-liquid below and above the transition temperatures for oxygen according to a power-law formula. The observed data are used from the literature, and the values of the critical exponents for the magnetic susceptibility are deduced close to the phase transitions in oxygen. Our exponent values give a logarithmic singularity for the magnetic susceptibility χ in the vicinity of Tc as in the specific heat at constant magnetic field, CM. Our exponent values (γ≃ 0) are not in agreement with the predictions for the magnetic susceptibility (γ≃ 1) of some theoretical models, which undergo essentially a second order transition. Our analysis gives an indication that the α- β transition is a weak first order (less discontinuity in χ), whereas the β- γ and γ-liquid transitions are closer to a first order (more discontinuous behaviour than the α- β transition in oxygen). The effect of the magnetic interactions on the α- β, β- γ and γ-liquid transitions in oxygen is explained.

Do you get tired of socializing? An empirical explanation of discontinuous usage behaviour in social network services

Based upon the stressor-strain-outcome framework, this study proposes that perceived system feature overload, information overload, and social overload are stressors which induce strain, in terms of social network fatigue and dissatisfaction. Both of social network fatigue and dissatisfaction further influence discontinuous use intention. The empirical results indicate that three types of perceived overload exert greater effects on social network fatigue than dissatisfaction, both of which further increase users’ intention of discontinuance. The study also finds that demographic characteristics, such as gender and age, also have moderating effects on these relationships.

A tessellated continuum approach to thermal analysis: discontinuity networks

Tessellated continuum mechanics is an approach for the representation of thermo-mechanical behaviour of porous media on tessellated continua. It involves the application of iteration function schemes using affine contraction and expansion maps, respectively, for the creation of porous fractal materials and associated tessellated continua. Highly complex geometries can be produced using a modest number of contraction mappings. The associated tessellations form the mesh in a numerical procedure. This paper tests the hypothesis that thermal analysis of porous structures can be achieved using a discontinuous Galerkin finite element method on a tessellation. Discontinuous behaviour is identified at a discontinuity network in a tessellation; its use is shown to provide a good representation of the physics relating to cellular heat exchanger designs. Results for different cellular designs (with corresponding tessellations) are contrasted against those obtained from direct analysis and very high accuracy is observed.

Inverse scattering transform for the defocusing nonlinear Schrödinger equation with fully asymmetric non-zero boundary conditions

We formulate the inverse scattering transform (IST) for the defocusing nonlinear Schrödinger (NLS) equation with fully asymmetric non-zero boundary conditions (i.e., when the limiting values of the solution at space infinities have different non-zero moduli). The theory is formulated without making use of Riemann surfaces, and instead by dealing explicitly with the branched nature of the eigenvalues of the associated scattering problem. For the direct problem, we give explicit single-valued definitions of the Jost eigenfunctions and scattering coefficients over the whole complex plane, and we characterize their discontinuous behavior across the branch cut arising from the square root behavior of the corresponding eigenvalues. We pose the inverse problem as a Riemann–Hilbert Problem on an open contour, and we reduce the problem to a standard set of linear integral equations. Finally, for comparison purposes, we present the single-sheet, branch cut formulation of the inverse scattering transform for the initial value problem with symmetric (equimodular) non-zero boundary conditions, as well as for the initial value problem with one-sided non-zero boundary conditions, and we also briefly describe the formulation of the inverse scattering transform when a different choice is made for the location of the branch cuts.

Calorimetry of a Bose-Einstein-condensed photon gas.

Phase transitions, as the condensation of a gas to a liquid, are often revealed by a discontinuous behaviour of thermodynamic quantities. For liquid helium, for example, a divergence of the specific heat signals the transition from the normal fluid to the superfluid state. Apart from liquid helium, determining the specific heat of a Bose gas has proven to be a challenging task, for example, for ultracold atomic Bose gases. Here we examine the thermodynamic behaviour of a trapped two-dimensional photon gas, a system that allows us to spectroscopically determine the specific heat and the entropy of a nearly ideal Bose gas from the classical high temperature to the Bose-condensed quantum regime. The critical behaviour at the phase transition is clearly revealed by a cusp singularity of the specific heat. Regarded as a test of quantum statistical mechanics, our results demonstrate a quantitative agreement with its predictions at the microscopic level.

Ultrasonic P-Wave Reflection Monitoring of Soil Erosion for Erosion Function Apparatus

Abstract Erosion of soils in river, lake, and seabeds is an important component for scour estimation and design of underwater structures. This is because the scour can cause severe structural damage to underwater foundations or embankments. The erosion function apparatus (EFA) method is widely used to estimate the erosion rate of soils in the laboratory, where a soil protrusion of 1 mm thick is exposed to water flow and the time taken to erode this protrusion is measured. However, determining this erosion time is a difficult task because it is only visually inspected, and this can cause considerable measurement errors. Therefore, this study explored the feasibility of using an ultrasonic P-wave reflection monitoring method to more quantitatively assess the erosion rate that otherwise has been measured by visual inspection. The erosion rates were monitored using ultrasonic transducers mounted above a soil surface during the EFA testing on the prepared soil samples containing different clay fractions. Via the P-wave monitoring results, several important semi-quantitative observations were made: an increase in erosion resistance with an increase in the clay fraction, a discontinuous erosion behavior of fine-grained soils with sudden removal of soil lumps by water flows, a continuous erosive action of coarse-grained soils, and inherent heterogeneous erosion even at a specimen scale (i.e., the scale of milli-to-centimeter). While both the P-wave monitoring method and the visual inspection showed similar estimation on the erosion rate, the former was found to provide overall better quantitative assessment, particularly in conditions of very slow or rapid erosion and in the conditions with high turbidity water, unevenly eroded sample surfaces, or limited control on the soil protruding thickness.

Evolution of the Piezomagnetic Field of Ferromagnetic Steels Subjected to Cyclic Tensile Stress with Variable Amplitudes

In this research, the evolutions of the piezomagnetic fields of ferromagnetic steels under cyclic tensile stress with variable amplitudes were investigated. The piezomagnetic signals of initially undemagnetized Q345 and U75V steel samples were measured by an APS 428D fluxgate magnetometer. It was found that the magnetic field reversal points vary perceptibly in the initial cycles, and then relax to a more gradual rate of change. The drastic variations of the magnetic field reversals may be utilized to characterize the early stages of plastic deformation. The discontinuous piezomagnetic behaviors occurred during the loading process reveal that the piezomagnetic field is highly sensitive to stress and microstructural changes. The total magnetic fields and the irreversible magnetic fields show apparently different variation characteristics in the elastic and plastic stages. Based on the theory of the interaction between dislocation and domain wall, as well as the related models of the magneto-mechanical effect, the experimental results are discussed.

Characterizing Biophysical Features Driving the Self-Assembly of Microtubule Nano-Arrays

Microtubules (MTs) are biopolymeric filaments important in several cellular functions, including maintaining cell structure and providing platforms for intracellular transport. Biopolymers, including MTs, are being explored as nanostructure templates (i.e., for nanowire synthesis) due to their dimensions, self-assembly dynamics and versatile chemical functionalization. MTs have unique self-assembly processes scaling from polymerization of tubulin at the nanometer, to the head-to-tail micron-scale assembly of mature MTs, forming segmented nano-arrays. Controlling nano-array assembly requires characterization of the physicochemical properties driving self-assembly. Modelling studies have mapped the electrostatic potential of MTs and found that they are overall negatively charged with oppositely charged ends, suggesting electrostatically attractive interactions may drive assembly. Structural studies, however, suggest that end-to-end interactions of tubulin are driven by hydrophobic interactions. We demonstrate that biophysical features including electrostatics, hydrophobicity and temperature regulate the assembly of MT nano-arrays. Electrostatically shielding MTs, thus shielding the electrostatically polar ends, using salts resulted in increased rate of nano-array assembly. These results suggest that (1) decreasing the overall negative charge of MTs decreases electrostatic repulsion, increasing the probability of end-to-end interactions and (2) shielding electrostatically attractive ends of the MTs does not inhibit end-to-end interactions, suggesting that self-assembly is driven predominately by hydrophobic interactions. Finally, data exploring the role of temperature suggests that increasing temperature causes MT filaments to undergo a phase transition resulting in a discontinuous Arrhenius behavior. Together, these results provide insights into tunable parameters driving self-assembly of MT nano-arrays. Adjusting these parameters to optimize assembly will greatly aid in the application of biopolymeric templates for use in nanomaterials applications. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.