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The arcticle gives a spatial gas-dynamic formulation of the backpressure problem, which describes the change in pressure in front of an accelerating projectile when it moves along the bore. This takes into account the geometry of the front of the projectile and its influence on the formation of the shock wave. An unsteady spatial flow of the displaced medium ahead of the projectile body without and taking into account the forces of viscosity is considered. The paper considers the solution to the problem of throwing a body using the energy of gunpowder combustion. The internal ballistics problem, which determines the dynamics of the projectile movement, is solved in terms of averaged parameters. A two-step Runge-Kutta scheme with a second order of accuracy is used to numerically integrate a system of ordinary differential equations in time. The control volume method is used for the numerical solution of the system of gas-dynamic equations. The gas parameters at the boundaries of the control volumes are determined using a self-similar solution to the problem of the decay of an arbitrary discontinuity. A comparison is presented of taking into account the backpressure as the pressure behind the detached shock wave, obtained from the analytical solution of the problem of the supersonic motion of a flat piston in a pipe at a constant velocity, and the pressure acting on the projectile, determined from the solution of nonstationary one-dimensional and spatial (axisymmetric) equations of gas dynamics. It was found that taking into account the viscosity practically does not affect the results of calculating the backpressure, while taking into account the shape of the front part of the projectile leads to a significant difference in the pressure fields behind the front of the shock wave compared to the solution in the framework of the one-dimensional formulation of the problem, where the shape of the front part of the projectile cannot be taken into account. It is concluded that this can significantly affect the results of modeling the ballistics of a shot at high throwing speeds.

The discontinuity in a fractured land in landslide application could be represented by the metal defects in the physical modeling that will usually reduce the mass of the metal. The scale factor n is important for interpreting the field data using the physical model data. In this physical modeling (n = 100), the anomaly targets are aluminum plates and aluminum plates with the discontinuities. It is assumed the nonconductive environment. In the free-air condition which has zero conductivity is become representative of this environment. In the zero conductivity, the secondary field from the medium is not presence. In this condition, there are no phase differences between transmitted electromagnetic fields and that was received by the receiver. The discontinuity in this term is any treatment or defect that causes disruption or leads to a reduction in response triggered by the eddy currents. The discontinuities used on the thin plates and flaws will interrupt or reduce the eddy current flow on the plate, thereby reducing the induced voltage on the receiving coil and increasing its effective impedance. This is the basis of eddy current measurement. The electromagnetic field response to a metal that has discontinuities will change the eddy current portion. The eddy current that changes, therefore, will change the second field so that the percent response (% Response) of the receiver in the Geometry Normalized Electromagnetic System (GNES) instrument will also change.

The object of this paper is the study of a periodic structure formed by identical mufflers or expansion chambers by a new method called ”Interface Response Function” or ”Green’s Function”. This method is very well known in solid physics but remains unrecognized in acoustics. The objective is to investigate the acoustic attenuation performance of expansion chamber by developing analytical expressions. The present work focuses on the acoustic characteristics of wave transmission and the band structure across a cell and then to the entire network. The effect of the discontinuity between two waveguide is not taken account. The theoretical analysis is for a one-dimensional rigid waveguide. It is reported that the viscothermic effect is ignored.

A set of mixture equations is used for the simulation of a two phase flow system using Lax-Friedrichs method. The governing equations are used to obtain numerical solutions of the gas volume fraction and the liquid phase velocity for the water faucet problem. It is observed that the liquid phase velocity is in excellent agreement with the analytical trends. The only deviations that are found are near the regions of discontinuity. The gas volume fraction at different time instants shows significant deviations from the analytical values. The peak values as well as the location of the peak values of gas volume fraction are far from the analytical values. This may be attributed to the highly dissipative and dispersive nature of the Lax-Friedrichs method. Another possible reason for this behavior is the oscillations in gas phase velocity. The present set of equations is able to describe a two phase system with reasonable accuracy and much simpler mathematics.A set of mixture equations is used for the simulation of a two phase flow system using Lax-Friedrichs method. The governing equations are used to obtain numerical solutions of the gas volume fraction and the liquid phase velocity for the water faucet problem. It is observed that the liquid phase velocity is in excellent agreement with the analytical trends. The only deviations that are found are near the regions of discontinuity. The gas volume fraction at different time instants shows significant deviations from the analytical values. The peak values as well as the location of the peak values of gas volume fraction are far from the analytical values. This may be attributed to the highly dissipative and dispersive nature of the Lax-Friedrichs method. Another possible reason for this behavior is the oscillations in gas phase velocity. The present set of equations is able to describe a two phase system with reasonable accuracy and much simpler mathematics.

The subject of this paper is to study a periodic structure composed of a number of identical structural components that are joined together to form a whole complex. Each elementary cell is formed by a simple muffler or expansion chamber. We know that the expansion chamber is often used to reduce noise in automotive. The present work focuses on the acoustic characteristics of the transmission and dispersion of a cell and the entire network. The objective is to investigate the acoustic attenuation performance of expansion chamber by developing analytical expressions. The problem is examined essentially by the method of the transfer matrixand then a comparison with the results obtained by the Sylvester theorem method is made in the case of a finite periodic network. The effect of the discontinuity between two waveguide is not taken account. The theoretical analysis is for a 1-D rigid waveguide. It is reported that the effect of the higher modes and the viscothermic effects are ignored.

In the present paper, we have evaluated the phase transformation and elastic properties of MnO at high pressure by formulating effective interionic interaction potential. The elastic constants, including the long-range Coulomb and van der Waals (vdW) interactions and the short-range repulsive interaction of up to second-neighbor ions within the Hafemeister and Flygare approach, are derived. Assuming that both the ions are polarizable, we employed the Slater-Kirkwood variational method to estimate the vdW coefficients. From the present study, we predict a structural phase transition from NaCl structure (B1) to CsCl structure (B2). The estimated value of the phase transition pressure (Pt) and the magnitude of the discontinuity in volume at the transition pressure are consistent as compared to the other theoretical data. The variations of elastic constants with pressure follow a systematic trend identical to that observed in others compounds of NaCl type structure family.

The paper deals with the use of a global radial basis function collocation method (Kansa method) to problems described by differential equations with non-continuous coefficients. The derivative of the solution in such problems can possess a jump, which is difficult to capture by global methods. Therefore, to take advantage of the power of this technique, reflecting in very high order of convergence, in the paper, some modifications that allow to apply the method to such problems are introduced. One of these modifications divides the solution domain into subdomains, in which the coefficients are continuous and uses appropriate continuity conditions on the interface, the other one introduces additional degrees of freedom into the interpolant and uses additional interface conditions to increase accuracy of the solution. The approaches are examined by one-dimensional benchmark problems.

The results of comparative study of the WENO-type monotonization methods for numerical solution of the Euler equations computed by the discontinuous Galerkin method are presented. The variants of the technique based on Lagrangian and Hermitian interpolation are analyzed. Test simulations for the Sod problem, which solution contains a shock wave, a rarefaction wave, and a contact discontinuity, are performed. The merits and demerits of the considered variants of the limiters including the questions of the numerical solution monotonicity, numerical dissipation magnitude, computational costs and extensibility of software implementation are investigated.

In this paper, the basic principle and application of extended finite element method (XFEM) are expounded based on the model of plate structure crack. Simulating crack location by level set method; the discontinuity of crack can be supplemented through introducing Heaviside functions and crack tip reinforcement function. On this basis, the damage model of edge crack and center crack under the same boundary condition are established. The displacements of each node in the two Situations are given and explained the application of damage model in two aspects.In this paper, the basic principle and application of extended finite element method (XFEM) are expounded based on the model of plate structure crack. Simulating crack location by level set method; the discontinuity of crack can be supplemented through introducing Heaviside functions and crack tip reinforcement function. On this basis, the damage model of edge crack and center crack under the same boundary condition are established. The displacements of each node in the two Situations are given and explained the application of damage model in two aspects.

This paper deals with the numerical investigation of ellipticity of the boundary value problem for isothermal finite strain elasto-plasticity. Ellipticity can be lost when softening occurs. A discontinuity surface then appears in the considered material body and this is associated with the ill-posedness of the boundary value problem. In the paper the condition for ellipticity loss is derived using the deformation gradient and the first Piola-Kirchhoff stress tensor. Next, the obtained condition is implemented and numerically tested within symbolic-numerical tools AceGen and AceFEM using the benchmark of an elongated rectangular plate with imperfection in plane stress and plane strain conditions.

The goal of this paper is to establish a staggered scheme for the shallow water model. The model is taken from [1], which include energy dissipation term. The study examines the temporal stability of the uniform flow using monochromatic waves. The result shows that the roll-waves occur and stable if and only if the Froude number is less than four. We simulate roll-waves by using finite difference in staggered grid. For the linear case this method is capable validating this condition. Moreover, momentum conservative scheme is used to handle advection term thus the evolution of roll-waves can be investigated. We found that this method is able to capture shock discontinuity. From the result, we investigate the effect of Froude number, Reynold and the value of σ. We also found that for supercritical Froude number (F > 1) with low Reynold number the shocks appear faster than the higher number.

This study aims to establish a numerical strategy allowing to take into account the capillary and wetting issues, considered on the macroscopic scale as a discontinuity of pressure at the fluid-gas interface, and surface tension force balance at the local scale. This modelling is based on the Brinkman/Darcy and Stokes equations solved by a finite element stabilized method. Specific numerical methods are implemented to deal with the discontinuity of pressure field across the flow front. One of the challenges lies in modelling across scales capillary force effects in infusion-based processes to scale-up rules for flows at the process scale, because the computation cost of numerical simulations at local scales is too not tractable industrially.

Compendia of shock data have been assembled across national laboratories across the world. Previous work has shown a threshold in behaviour for materials; the weak shock limit. This corresponds to the stress state at which the shock is overdriven in a single front. Here the shock velocity-particle velocity data for elements and compounds has been systematically analysed to note discontinuities in the data. A range of materials show such features and the form of the discontinuity in each case is analysed. Some of these are found to correspond to martensitic phase transformations as expected whilst others are more difficult to classify. Particular groups within the elements show characteristic forms according to their groupings within the periodic table. Typical datasets are presented and trends in behaviour are noted for a range of elements.

Continuous monitoring for damage detection on large fluid filled pipe-like structures is needed. To address this, we propose the use of the first order torsional mode and the detection of extra modes generated from an artificial discontinuity. The generation and detection of the propagated signals is carried out by a microfiber composite (MFC) sensor. Signals are post-processed with short time Fourier transform analysis. Numerical results were obtained and experimentally tested on a stainless steel pipe A-36 (43.6 and 48.2 mm in inner and outer diameter, respectively). It was found that it is possible to identify an artificial discontinuity by detecting the generated extra modes after its interaction with the propagated guided wave modes.

This talk discusses the concept of solutions of piecewise smooth, discontinuous differential equations. Recent results of [1] are presented, which give new insight into the solution close to the intersection of two discontinuity hyper-surfaces. The study is connected to space regularizations where, close to the discontinuities, the vector field is smoothed out by linear (bi-linear) interpolation.

In non-destructive evaluation of composites, an efficient method for mapping damage is critical for assessing the severity of damage in a specimen. Phase congruency (PC) is a technique for detecting edges in images. This paper adapts this technique to map damage in composite plates. The method utilizes two-dimensional wavefield measurements of a guided wave propagating through the specimen. Each time step of the two-dimensional wavefield is analyzed with the modified PC measure. The results of each time step are aggregated yielding a full field map of the specimen identifying the damage. The approach was validated on numerical and experimental data sets for simulated damage in a plate. In concept, the PC measure exploits the fact that the phase of the spatial Fourier components of a signal have an equal value at a discontinuity. To do this, the measure compares the magnitude of the sum of the components to the sum of the magnitude of the components. The upper bound of this ratio is unity. PC values approaching unity indicate the phases of each the components are aligned and identify a discontinuity. This measure was adapted for the present case; a strong interrogating wave dominates the wavenumber spectrum obscuring low amplitude wavenumber information related to discontinuities. The resulting technique provides a map of damage in a two-dimensional space without necessitating the use of a model or baseline measurement.

In this study, a Dirac system that contains discontinuity conditions is considered. Then, by modifying some known techniques for the investigated problem the existence and uniqueness results of solutions are obtained.

In this work we consider the problem of the propagation of non stationary stress waves in an elastic body with a rectangular hole in the linear formulation. The wave process is caused by applying an external dynamic load on the front boundary of the rectangular region and the lateral boundaries are free of the stress. The lower boundary of the rectangular region is rigidly fixed, and the contour of the rectangular hole is free from the stress. The problem is solved by using the difference method of the spatial characteristics. On the basis of the developed numerical methods it is obtained the computational finite - difference relations of the dynamic problems at the corner points of the rectangular hole, where the first and second derivatives of the unknown functions have a discontinuity of the first kind. We analyze the dynamic stress fields in an elastic body with a rectangular hole and we studied the concentration of dynamic stresses in the vicinity of the corner points of the rectangular opening.

We examine the asymptotics of a piecewise-quartic Lagrange interpolation used to fit reduced data in arbitrary Euclidean space which are sampled more-or-less uniformly. The unknown interpolation knots are guessed here according to the so-called exponential parameterization which depends on a single parameter λ ∈ [0, 1]. In this work we demonstrate numerically an abrupt discontinuity in the quality of the discussed interpolation scheme yielding a slow linear convergence order for all λ ∈ [0, 1). On the other hand, as well-known the quality of the curve approximation for λ = 1 sharply increases to the fast sharp quartic order which can be further accelerated for special subfamilies of more-or-less uniform samplings.

A rarefied gas flow induced around a flat plate with a uniformly heated single side in a closed vessel, which is also known as the radiometric flow, is considered. Its steady behavior is investigated on the basis of the Bhatnagar‐Gross‐Krook (BGK) model of the Boltzmann equation and the diffuse reflection boundary condition for a wide range of the Knudsen number, by means of an accurate finite‐difference method which gives a correct description of the discontinuity contained in the velocity distribution function. It is found that a thermal edge flow is induced along the plate on both heated and unheated sides near the edge, that drives the overall circulating flow in the vessel. The detailed flow structure near the edge as well as along the plate is clarified.

The non-destructive testing of materials can be conducted by various techniques. Amongst these, method based on ultrasonic waves is one of the most common one. Of these ultrasonic waves Lamb waves are of particular interest for the inspection of large structures for various reasons. Scattering of Lamb waves from flaws has generated a considerable amount of research over last couple of decades. Most of the work has been done using computational tools like Finite Element Methods and experimental technique. In this paper an analytical approach is presented to develop a fundamental understanding of the scattering of Lamb waves from geometric discontinuities in 2 dimensions. We have considered simplest of all geometric discontinuity – a step, as this fundamental understanding can easily be extended to corrosion or crack.

We discuss the problem of approximating the length of a curve γ in arbitrary euclidean space En, from e-uniformly sampled reduced data Qm={qi}i=0m, where γ(ti) = qi. The interpolation knots {ti}i=0m are assumed in this paper to be unknown (the so-called non-parametric interpolation). We fit Qm with the piecewise-quadratic interpolant γ^2 based on the so-called exponential parameterization (depending on parameter λ ∈ [0, 1]) which estimates the missing knots {ti}i=0m≈{t^i}i=0m.The asymptotic orders βe (λ) for length estimation d{γ}≈d{γ^2} in case of λ = 0 (uniformly guessed knots) read as βe (0) = min{4,4e} (for e>0) - see [1]. On the other hand λ = 1 (cumulative chords) yields βe (1) = min{4,3+e} (see [2]). This paper establishes a more general result holding for all λ ∈ [0,1] and e-uniform samplings - see Th. 5. More specifically the respective convergence orders amount to βe (λ) = min{4,4e} for λ ∈ [0,1). Consequently βe (λ) are independent of λ ∈ [0,1) and the discontinuity in asymptotic orders βe (λ) ...

A computational analysis of a hypersonic flow over a combined gap/step configuration at zero degree angle of attack, in chemical equilibrium and thermal non-equilibrium is presented in this work. Effects on pressure and heating loads due to changes on the freestream Mach number and on the step frontal-face height have been investigated by employing the Direct Simulation Monte Carlo (DSMC) method. The work focuses the attention of designers of hypersonic configurations on the fundamental parameter of surface discontinuity, which can have an important impact on even initial design. The analysis showed that heating and pressure loads increased with increasing not only the step height but also with the freestream Mach number. In addition, peak values for both loads took place at the vicinity of the step convex corner, a similar behavior observed for a forward-facing step configuration. It was also found that these loads for the gap/step configuration are slightly smaller than those for a forward-facing step.

Analysis of travelling waves in elastic waveguides with complex cross-sections, such as train rails, can only conveniently be performed numerically. The semi-analytical finite element (SAFE) method has become a popular tool for performing such analyses. This paper employs a hybrid SAFE-3D FE method to investigate the scattering of guided waves at discontinuities such as welds or cracks, in continuous welded train rails. The aim of the analysis is to predict transmission and reflection coefficients for a given incident wave and known discontinuity. This characterisation is useful for predicting the long-range transmission characteristics of transducers in non-destructive evaluation (NDE) and monitoring systems, such as the ultrasonic broken rail detector (UBRD) system developed by the Institute for Maritime Technology (IMT) and the Council for Scientific and Industrial Research (CSIR). Furthermore, we investigate an extension of the current UBRD system to detect cracks before complete breaks occur, which will require distinguishing between reflections from cracks and other reflectors such as welds, in order to avoid false alarms.

We describe a ∼4 hour-long solar wind transient observed by the Wind spacecraft, in which is embedded a pressure-balanced structure. Minimum variance analysis on high resolution (∼11 Hz) magnetic field data shows it to be planar to an excellent approximation (ratio of intermediate-to-minimum eigenvalues = 83). The structure starts with a very sharp discontinuity whose orientation coincides within four degrees with that of the structure itself. We find that this discontinuity has a bifurcated magnetic field and plasma flow structure. There is also a velocity depression coextensive with it. Applying a tangential stress balance test (Walen relation) to the discontinuity, we find good agreement of predictions with observations. We show directly the presence of two Alfven waves propagating in opposite directions. The observation is consistent with the presence of a reconnection region in a hitherto unexplored configuration within a small solar wind transient.

When two continuous bodies are in contact and subjected to relative motion, both particle detachment and dynamic instabilities naturally occur. To properly model such interacting phenomena, it is required to take account for the discontinuity of the interfacial layer (usually modeled with Discrete Element Model) as well as the continuity of the bodies in contact (usually modeled with Finite Element Model). For that, the present paper aims at validating experimentally the coupled FEM-DEM method. The experimental set-up aims at modeling the frictional behavior between a holed disk, tied on its exterior side and made of transparent polymer with birefringence property, and an inner rotating cylinder, made of steel. This last is statically enlarged to reach the wanted contact pressure and then animated with constant angular velocity. The birefringence property of the disk is used to dynamically visualize the evolution of stresses in the disk at both contact scale and body scale. Based on the same principle with the same boundary conditions, the numerical model coupled the modeling of a deformable disk, a pseudo-rigid cylinder and wear particles by a combination of a finite element method and a discrete element method. Parametrical study has been numerically made to study the influence of particle morphology on stress evolution in the disk. A good agreement is showed between the numerical results obtained with particles artificially introduced in the contact and the experimental results obtained with wear particles naturally produced in the contact.

Corrugation instabilities of the Riemann problem in relativistic hydrodynamics are investigated numerically in the case of nonvanishing velocities tangent to the initial discontinuity. Three dimensional simulations are performed for the ultrarelativistic and the perfect gas equations of state for moderately relativistic speeds. The results agree qualitatively for both equations of state. Shock waves and rarefaction waves behave in a stable way, and a Kelvin–Helmholtz type instability develops near the contact discontinuity.

Typical ultrasonic methodology for nondestructive scanning evaluation uses systematic scanning paths. In many cases, this approach is time inefficient and also energy and computational power consuming. Here, a methodology for the scanning of defects using an ultrasonic echo-pulse scanning technique combined with chaotic trajectory generation is proposed. This is implemented in a Cartesian coordinate robotic system developed in our lab. To cover the entire search area, a chaotic function and a proposed mirror mapping were incorporated. To improve detection probability, our proposed scanning methodology is complemented with a probabilistic approach of discontinuity detection. The developed methodology was found to be more efficient than traditional ones used to localize and characterize hidden flaws.

The singularity in the energy band‐structure which is the zero‐gap state (Dirac point) in the HgCdTe or ZnHgTe alloys, causes a discontinuity in the temperature dependence of the transverse optical phonon frequency, as shown in the optical reflectivity experiments.

In this work a discontinuous boundary‐value problem with retarded argument which contains spectral parameters in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions.

A nonlinear model for contact acoustic nonlinearity (CAN) of closed crack was proposed and analyzed to investigate the nonlinear characteristics of transmitted wave for normal incident wave. Closed crack was modeled as an imperfectly jointed interface that has nonlinear discontinuity in displacement across its boundary. Based on the interfacial stiffness of contact interface, a nonlinear parameter was defined as the ratio of second harmonic component to first harmonic, and derived in terms of discontinuous displacements across the interface. It is found that the amplitude of second order harmonic wave is highly dependent on interfacial stiffness. This was verified by experiments for a real crack. For this, a CT fatigue specimen of Al6061 with V‐notch was prepared to initiate the crack, and the amplitude of second order harmonic was measured by scanning along the crack direction. From the results of pre‐test to evaluate the contact condition of crack interfaces by monitoring the amplitudes of echo and through transmission, the crack was regarded as gradually closed. It could be observed that the harmonic amplitude had a good correlation with the crack closure and agreed well with the theoretical expectation.

The modeling of transport phenomena between homogeneous regions requires the derivation of jump boundary conditions. These conditions account for the rapid spatial variations of the transport properties taking place near the dividing surface of the media. There has been a long debate in the literature about whether the discontinuity should apply to the fields (e.g., velocity, temperature, concentration) or to their fluxes. In this work, a general methodology giving rise to jump conditions for both the fields and the fluxes is proposed. This method, besides using a microscopic closure, introduces macroscopic deviation fields that lead to closure schemes for both jump conditions. The methodology is applied first to the diffusive mass transport of a passive solute between a porous medium and a plain fluid and second to the classical problem of momentum transport in a channel partially filled with a porous medium. In both cases, it is required to account for the spatial variations of effective transport coeff...

This paper describes the development of free surface capturing method on Cartesian cut cell mesh to water entry problem for free‐falling bodies with body‐fluid interaction. The incompressible Euler equations for a variable density fluid system are presented as governing equations and the free surface is treated as a contact discontinuity by using free surface capturing method. In order to be convenient for dealing with the problem with moving body boundary, the Cartesian cut cell technique is adopted for generating the boundary‐fitted mesh around body edge by cutting solid regions out of a background Cartesian mesh. Based on this mesh system, governing equations are discretized by finite volume method, and at each cell edge inviscid flux is evaluated by means of Roe’s approximate Riemann solver. Furthermore, for unsteady calculation in time domain, a time accurate solution is achieved by a dual time‐stepping technique with artificial compressibility method. For the body‐fluid interaction, the projection m...

The non‐linear analysis of the plane shock wave stability in media with arbitrary equation of state has been carried out in a systematic way. The one and multi‐dimensional computations have been conducted in the inviscid and viscous formulations. The real and properly constructed model equations of state have been used. The behavior of shocks in the regions of their ambiguous representation overlapping the Hugoniot segments that meet the linear criteria of the shock wave instability has been studied. The evolution of shock waves being neutrally stable in keeping with the results of the linear analysis has been also simulated. The results obtained indicate basic distinctions from the linear theory predictions.

Density functional theory using accepted semi‐local exchange‐correlation functionals is generally successful for structural properties. However, for electrical response calculations of extended molecular systems, like e.g. polyacetylene, they make large errors; for the hyperpolarizability the error can be several orders of magnitude. The errors can be traced to qualitative differences between the exchange potentials of semi‐local and exact exchange methods. A recent effort has been successful in using a corrective term based on semi‐local quantities to introduce the missing features directly into the exchange potential (as opposed to modeling the exchange‐correlation energy). The resulting potential reproduces the derivative discontinuity, step structure, and counteracting field slope of exact exchange. It gives the polarizability of hydrogen chains with similar accuracy as exact exchange methods.

We study some properties of piecewise‐linear differential systems describing gene regulatory networks, where the dynamics is governed by sigmoid‐type nonlinearities which are close to or coincide with the step functions. To overcome the difficulty of describing the dynamics of the system near singular stationary points (i.e. belonging to the discontinuity set of the system) we use the concept of Filippov solutions. It consists in replacing differential equations with discontinuous right‐hand sides with differential inclusions with multi‐valued functions. The global existence and some basic properties of Filippov solutions such as continuous dependence on parameters are studied. We also study uniqueness and non‐uniqueness of the Fillipov solutions in singular domains. The concept of Filippov stationary point is extensively exploited in the paper. We compare two approaches in defining the singular stationary points: based on Fillipov theory and based on replacing step functions by steep sigmoids and investi...

In the problems of detonation we are going to present here, the capture of shocks is crucial, since from its accuracy depends the very physical relevance of the whole solution. We already obtained some improvements in the capture of detonation fronts on underresolved grids in the one‐dimensional case thanks to Harten’s artificial compression [1], [2], and we now turn to two‐dimensional cartesian grids. In two space dimensions, the complexity of the discontinuity implies not only the location and speed of the front, but also its shape. These three aspects will be explored here, for the ZND detonation model, based on Euler’s system. We will use two‐dimensional central schemes for main computations, namely the classical “Lax‐Friedrichs” first order scheme and the second order “Jiang‐Tadmor” scheme [3]. To each of these methods, we will add two different versions of ACM (Artificial Compression Method), one that uses space splitting, and the other based on directional differencing [4]. Finally, as ACM require a good knowledge of the regions of the solution potentially carrying discontinuities, it will be assisted by a DoD (Detector of Discontinuities) based on the entropy production rate.

When seismic isolator devices are moving large deformations appear and their possible failure can be delamination phenomenon. Mathematically speaking the problem is individualized within the framework of the unilateral contact with adhesion. Therefore, formulating the analytical characterization by means of the variational approach, we see in the equilibrium equation set one or more inequality condition. We investigate about equilibrium conditions after delamination considering the problem with variational approach. Applying the theory of functions of bounded variations and developing it as free‐discontinuity problem we find approximate solutions about the sharp energy variation when displacements discontinuity appears.

In design practice of many countries, seismic analysis and proportioning of structures are usually based upon linear elastic analysis due to reduced seismic forces by response coefficient; R. Setback structures are one of the most popular shapes of the constructed buildings. In setback structures, the shape and proportions of the building have a major effect on distribution of earthquake forces as they work their way through the building. On the other hand, geometric configuration has a profound effect on the structural-dynamic response of a building. Therefore, when a building has irregular features, such as asymmetric in height or vertical discontinuity, the traditional assumptions used in development of seismic criteria for regular buildings may not be applicable. Inelastic seismic behavior of these types of structures seems to be quite different from the regular steel moment resisting structures in which the overall ductility is localized at beam-ends.In order to investigate the seismic behavior and estimate the Response Coefficient of those structures, nonlinear static analysis (pushover) are used for three categories of setback structures namely low rise, medium rise and high rise buildings with different setbacks in their height. The Response Coefficient are calculated and compared with those taken from regular type ofmore » moment frame structures.« less

A theorem of equivalence regarding the discontinuity of the solution u (ũ(1),ũ(2),…,ũ(n),ũ) of an underdetermined system of n quasi‐linear partial differential equations in one spatial dimension is proven. It is also included in the proof that all the thicknesses of the discontinuities of ũ(i) (i = 1,2,…,n+1) are the same. Unsteady state Rankine‐Hugoniot (RH) jump conditions are derived from the system through its integration over the thickness. The jump conditions suggest a possibility that the jumps in u evaluated from the conditions can differ significantly from those from the RH jump conditions. The significant differences in evaluation between both jumps can be illustrated by demonstrating that infinitely large jumps in the particle velocity and stress across a spherical wave front are caused by an extremely intense explosion.

We have shown that if one relaxes the constraint that the quarks in a heavy quarkonium are at rest and on-shell, new contributions to the discontinuity of the production amplitude appear. These can be seen as a s-cut in the amplitude and are on the same footage as the classical cut of the Colour-Singlet Model (CSM), where the heavy quarks forming the quarkonium are put on-shell by hypothesis. We treat this cut in a gauge-invariant manner by introducing necessary new 4-point vertices, suggestive of the colour-octet mechanism. We have further shown that this cut contributes at least as much as the LO CSM at large P_T. However, the 4-point vertices cannot be totally constrained and an ambiguity remains to what concerns their actual contribution. Theoretical insights from meson photoproduction are discussed in that context., Comment: Presented at the 7th International Conference on Quark Confinement and Hadron Spectrum (QCHS7), September 2-7 2006, Ponta Delgada, Portugal and at the 4th Meeting of the Quarkonium Working Group, June 27-30 2006, BNL, USA, 4 pages, 3 figures, LaTeX, uses aip-6s.clo, aipproc.cls and aipxfm.sty (included)

Shell elements are commonly used in simulations of sheet metal forming using finite element analysis. Element matrices, due to their complexity, cannot conveniently be calculated in a closed form and therefore numerical integration is employed. The most commonly used rules for through-thickness integration in shell elements are Gauss quadrature and rules based on the Newton-Cotes formula. Considering the integrand in the expression for the internal force vector, one may state that it is smooth only if during a finite element analysis the material remains in the elastic regime. When the material is in the elastic-plastic regime the integrand becomes non-smooth in, for example, out-of-plane direction since the stress profile may have a point of discontinuity at the surface that separates the elastic and plastic regions. The traditional numerical schemes do not perform well when integrating a non-smooth function and integration error may increase significantly. Therefore, if a shell element is in the elastic-plastic regime, the error due to numerical integration may be large and has to be dealt with. A large number of sampling points in thickness direction may decrease the error due to numerical integration at the cost of increased computation time. Alternatively, the in- tegration error can be decreased without a drastic increase in the computation time by using an adaptive through-thickness integration. A distinguishing feature of this integra- tion scheme is that the location and/or the number of the sampling points is adapted to the through-thickness stress profile, leading to accurate numerical integration at minimal costs. An adaptive through-thickness integration strategy for shell elements is developed in this report. The strategy consists of several algorithms that locate points of discontinuity in the out-of-plane stress profile, adapt sampling points, update values of internal variables and perform numerical integration. Performance of the integration strategy is evaluated using a problem of bending of a beam under tension. It is shown that with adaptive integration it is possible to obtain accurate results with a very low number of sampling points.

A method to study asymptotic properties of solutions to systems of differential equations with distributed time‐delays and Boolean‐type nonlinearities (step functions) is offered. Such systems arise in many applications, but this paper deals with specific examples of such systems coming from genetic regulatory networks. A challenge is to analyze stable stationary points which belong to the discontinuity set of the system (thresholds). The paper describes an algorithm of localizing stationary points in the presence of delays as well as stability analysis around such points. The basic technical tool consists in replacing step functions by the so‐called “logoid functions” and investigating the smooth systems thus obtained.

In this paper we present a hybrid eXtended Finite Element/Level Set Method to simulate a two dimensional moving interfaces. The discrete discontinuity (material interfaces) is treated by the extended finite element method (X‐FEM), in the partition of unity concept, whereby interface discontinuities are completely independent of the mesh. In this context, the discontinuity is represented without explicitly meshing its shape and the moving interface simulations are carried out without any re‐meshing. Enriched approximations to the velocities and deformation fields are developed in the context of the eXtended Finite‐Element Method, and the level‐set representation of the interface was used to model the evolution of the discontinuity interface in time. The X‐FEM utilizes the partition of unity property, of the finite element shape functions to incorporate arbitrary enrichment functions into the approximation. An explicit Newmark algorithm and one‐point integration scheme with hourglass mode control is used to...

Most of today's tokamak experiments rely on auxiliary heating of the plasma for achieving reactor‐relevant temperatures. On top of the theoretical efforts to estimate the power deposition profiles of the various adopted heating schemes (NBI, ICRH or ECRH) by numerical modelling, there are various techniques used to infer the power profiles experimentally, usually based on electron/ion temperature data. Amongst these methods, the break‐in‐slope (BIS) and the Fast Fourier Transform (FFT) analyses of the experimental temperature signals responding to a discontinuity (or modulation) on the applied power have been systematically used in JET in the last years. The FFT method requires a periodic modulation of the auxiliary power and provides information on both the power deposition profile and the diffusive heat transport. The standard BIS (linear fit), a priori, does not distinguish between local power deposition and heat transport, but has the advantage of needing only a single discontinuity on the auxiliary power level. In this work we present an improved BIS procedure that not only considers the time delays between the RF power change and the respective temperature responses at the several plasma radii, but also extends the original linear fit of the experimental signals to an exponential one, in a tentative to capture part of the transport phenomena. The results of the improved BIS analysis are compared with the FFT results and the main advantages/restrictions of the two methods are discussed.

Spatial variations of the electron temperature are calculated in the linear‐response regime in a quantum Hall system with a potential discontinuity in the current direction. It is shown that the sign of the induced deviation of the electron temperature from the lattice temperature exhibits quantum oscillations.

The processes in the tail region of the interaction of the solar wind with the partially ionized local interstellar medium are investigated in a framework of the self‐consistent kinetic gas dynamic model. It is shown that charge exchange of the hydrogen atoms with the plasma protons leads to suppression of the gas dynamic instabilities and disappearance the contact discontinuity at sufficiently large distances from the Sun. It is shown that the solar wind plasma temperature decreases and, ultimately, the parameters of the plasma and hydrogen atoms approach to the corresponding parameters of the pristine interstellar medium at large heliocentric distances.

We consider the dispersion relation for waves in a cosmic ray modified plasma for the case when the background flow consists of a cosmic ray pressure balance structure, in which pg+pc=const. where pc and pg denote the cosmic ray and thermal gas pressures respectively. The stability analysis shows that waves at an arbitrary point in the flow may be driven unstable if the cosmic ray pressure gradient is sufficiently large to overcome wave damping due to cosmic ray diffusion. Following S. Chalov’s work (1) we analyze the instability of a cosmic ray modified tangential discontinuity. Chalov considered the case where pc=const. throughout the structure, whereas in our analysis both pc and pg vary in the direction perpendicular to the surface separating two flow regions. Predictions of the linear theory are compared to numerical simulations. Applications to the stability of the heliopause are discussed.

Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA code, (2) UNICORN code, (3) Schulz hydro, and (4) modified TVD scheme. The first two codes are written in Eulerian coordinates, whereas methods (3) and (4) are in Lagrangian coordinates. MESA and UNICORN codes are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. Code (3) uses typical artificial viscosity for inviscid flow, whereas code (4) uses a modified TVD scheme. The test problem is a strong shock tube problem with a pressure ratio of 109 and density ratio of 103 in an ideal gas. For no mass-matching case, Schulz hydro is better than TVD scheme. In the case of mass-matching, there is no difference between them. MESA and UNICORN results are nearly the same. However, the computed positions such as the contact discontinuity (i.e. the material interface) are not as accurate as the Lagrangian methods.

Push on something. It will move. Push a little bit harder and it will move a little bit more. But occasionally a little extra push will produce an extra large response. Such extra responses are called ‘‘catastrophes.’’ This kind of behavior is summarized by the phrase ‘‘... the straw that broke the camel’s back.’’ Situations in which a gradually increasing force leads to a gradually increasing response, followed by a sudden catastrophic jump to a qualitatively different state, are all too common. They are seen, for example, in the collapse of a bridge, dam, or building; the loss of stability of an aircraft or ship; phase transitions in fluids or solids; ignition of a laser; sudden changes in the earth’s climate. In each of the instances above, and very many others besides, it is possible to see a smooth response and a discontinuous response to a smoothly changing force. It might seem that ‘‘Every smooth response is the same, each discontinuous response is discontinuous in its own fashion.’’ In fact, every smooth process is conveniently described by a linear response function or tensor. However, it is not true that every discontinuity is different. Discontinuities are described by mathematical functions called catastrophe functions. Only a relatively small number of such functions exist. These have been extensively studied. They can be constructed for any physical system. The simplest of these have been studied extensively. The result is that only a handful of different types of discontinuities are typically encountered, and each of these exhibits a characteristic set of properties. A parallel realization that a relatively small number of features characterizes the complex behavior exhibited by nonlinear dynamical systems (sets of ordinary differential equations) has catalyzed the rapid growth of interest in such systems in the last two decades. In the following sections we describe catastrophe theory. In particular, we describe what it is, why it exists, and how it works.