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The rotation number of orientation-preserving circle maps that are not necessarily surjective nor injective is discontinuous. In this paper we characterize the circle maps that are points of discontinuity of the rotation number and the relationship between its various possible values on a discontinuity. In particular, we show that, for each circle map corresponding to a discontinuity of the rotation number, all orbits are periodic after a fixed number of iterates, and the entire range of possible rotation numbers at each discontinuity is finite.

In this work we suggest that a turbulent phase of the Rayleigh-Taylor instability can be explained as a universal stochastic wave traveling with constant speed in a properly renormalized system. This wave, originating from ordinary deterministic chaos in a renormalized time, has two constant limiting states at both sides. These states are related to the initial discontinuity at large scales and to stationary turbulence at small scales. The theoretical analysis is confirmed with extensive numerical simulations made for a new shell model, which features basic properties of the phenomenological theory for the Rayleigh-Taylor instability., Comment: 22 pages

Viscosity variation of solvent in local regions near a solid surface, be it a biological surface of a protein or an engineered surface of a nanoconfinement, is a direct consequence of intermolecular interactions between the solid body and the solvent. The current coarse-grained molecular dynamics study takes advantage of this phenomenon to investigate the anomaly in a solvated protein’s rotational dynamics confined using a representative solid matrix. The concept of persistence time, the characteristic time of structural reordering in liquids, is used to compute the solvent’s local viscosity. With an increase in the degree of confinement, the confining matrix significantly influences the solvent molecule’s local viscosity present in the protein hydration layer through intermolecular interactions. This effect contributes to the enhanced drag force on protein motion, causing a reduction in the rotational diffusion coefficient. Simulation results suggest that the direct matrix-protein non-bonded interaction is responsible for the occasional jump and discontinuity in orientational motion when the protein is in very tight confinement.

A multi-temperature formal hydrodynamic limit of kinetic equations, based on Grad-type approximation of the distribution functions, is employed for the analysis of the steady shock problem in a binary mixture. The presence of a singular barrier and its effects on the occurrence of either smooth profiles or of weak solutions with a discontinuity is investigated for varying Mach number. Some numerical simulations of mixtures of two noble gases are presented and commented on, with reference also to analogous phenomena in different model descriptions.

The sensor for studying composite materials of the metal-polyethylene-metal type was developed on the basic of the designed ultra-miniature eddy-current transducer. The test of the developed sensor was carried out on standard defects of composite materials in the form of an inhomogeneity defect in the metal and (or) polyethylene layer. This sensor uses the original converter design, produced according to the differential circuit with the ability to localize the contact area of the sensor and the material up to 0.1-0.5 mm2. The measurement procedure for detecting defects in composite materials is also given in the article. The article presents the correlations of the output signal of the developed sensor based on the aluminum-polyethylene-aluminum composite material, in which the defect was located. We also obtained standard images of model defects of a composite such as a layered discontinuity. The images obtained as a result of processing information from the developed sensor make it possible to draw conclusions about the topology of the field near violations of the internal structure, the type of this violation and its localization in layers of material.

The fundamental mode intensity profile is calculated for different points along the transition of an optical fibre taper from standard size (125 μm external cladding diameter and 8 μm core diameter) down to micro (1 μm external fibre diameter) and submicro size (down to 440 nm fibre diameter) at 1550 nm operational wavelength. The first section of the taper was evaluated using weak guidance approximation, the second section was treated as a three-index layer structure (double-clad) and evaluated with eigenvalue equations for three refractive indices. An external medium being a liquid with a refractive index close to silica is being considered. The third and thinnest section of the taper was evaluated with the exact mode eigenvalue equation. The results show that the fundamental mode intensity for the third section show a discontinuity just at the fibre edge with a peak amplitude larger than the optical field at the centre of the fibre. The taper shape that complies with the adiabaticity criterion and how the mode intensity profile and the spot size (Petermann 1 definition) of the fundamental mode change along their position on the taper were determined.

The work is devoted to the problem of the formation of a mathematical model of a smoothbore gun. It is shown that due to the low accuracy of the initial data, the high accuracy of the mathematical model is not rational, and the mathematical model in the adiabatic formulation is quite reasonable. On the other hand, simple methods of numerical integration are excluded due to the discontinuity of functions at the beginning of the combustion phase of gunpowder. Accounting for the rotation of the cannonball, necessary for external ballistics, is possible only for a probabilistic task. Therefore, it will be most convenient to evaluate this parameter through the form factor of the external ballistic calculation.

Soil drilling operation has become one of the most important interests to researchers due to its many applications in engineering systems. Such as construction industry, soil samples for geological sciences and space sampling. The dominant factor in determining drilling parameters based on drilling operations experience or in some times based on proposed modelling techniques. As a result, soil drilling process using auger drilling is studied to obtain drilling parameters and then optimize these parameters to improve drilling performance which enables proper selection of machine for a required job. One of the main challenges that faces researchers during using modelling techniques to define the soil drilling problem is the complex nonlinear behaviour of the drilled medium itself due to its discontinuity and heterogeneous formation. This paper presents a developed apparatus that has been designed and manufactured to be used in measuring and recording the total torque required during soil drilling operation. A simplified auger drilling machine is built in soil-tool interaction laboratory, Military Technical College, to obtain experimental results that can be used to verify the presented models. Data acquisition measuring system is established to analyse experimental results using a. The Labview® program enables recording and displaying the output data collected mainly from sensors planted in the test rig. Results of both analytical and numerical models are then compared to experimental results to aid in developing the presented parametric study that can be used to define the working parameters during drilling operations in different types of soils.

The paper 'A detailed comparison of two continuous GPS carrier-phase time transfer techniques' (Yao et al 2015 Metrologia 52 666) presents the revised RINEX-shift (RRS) method, a technique using 'classical precise point positioning (PPP)' solutions on sliding batches and aiming at providing continuous time links. The authors claim the superiority of the RRS technique with respect to 'classical PPP' in terms of frequency stability and solving for discontinuities due to data gaps. It is shown here that these conclusions do not rely on physical principles, and are erroneous as they are driven by misinterpreted or corrupted PPP solutions. Using state-of-the-art PPP computation on the same data sets used in Yao et al's paper (2015 Metrologia 52 666), we show that the stability of RRS is at best similar to that of 'classical PPP' (within statistical uncertainties). Furthermore, the RRS method of removing discontinuities in case of data gaps by interpolating the phase data should not be applied systematically as it can cause erroneous clock solutions when the data gaps are associated with a true phase discontinuity.

Conceptual climate models provide an approach to understanding climate processes through a mathematical analysis of an approximation to reality. Recently, these models have also provided interesting examples of nonsmooth dynamical systems. Here we develop a new conceptual model of glacial cycles consisting of a system of three ordinary differential equations defining a discontinuous vector field. Our model provides a dynamical systems framework for a mechanism previously shown to play a crucial role in glacial cycle patterns, namely, an increased ice sheet ablation rate during deglaciations. We use ad hoc singular perturbation techniques to prove the existence of a large periodic orbit crossing the discontinuity boundary, provided the ice sheet edge moves sufficiently slowly relative to changes in the snow line and temperature. Numerical explorations reveal the periodic orbit exists when the time constant for the ice sheet edge has more moderate values.

We study the bootstrap and diffusion percolation models in the simple-cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices using the Newman-Ziff algorithm. The percolation threshold and critical exponents were calculated through finite-size scaling with high precision in the three lattices. In addition to the continuous and first-order percolation transitions, we found a double transition, which is a continuous transition followed by a discontinuity of the order parameter. We show that the continuous transitions of the bootstrap and diffusion percolation models have the same critical exponents as the classical percolation within error bars and they all belong to the same universality class., 10 pages, 3 figures

Decisions made by two (or more) independent players in a dynamical system can result in an indeterminable, yet non-stochastic, outcome. The mechanism can be presented as a thought experiment in which two pilots attempt to steer a spacecraft but, in stabilizing its pitch and yaw, lose all knowledge of its forward motion. It is useful to think of this pilots’ dilemma as a classical analogue of Schrödinger’s ‘cat in a box’ thought experiment. In both, the outcome of a life or death scenario is indeterminate until it is directly observed, but in place of the probabilistic radioactive source in Schrödinger’s problem, the discontinuous action of the pilots’ decisions create the classical indeterminacy. We discuss the wider implications of the phenomenon, such as predicting indeterminate scenarios in optimal transport or other network problems. The behaviour only becomes apparent when a system’s dynamics is sufficiently taken into account.

Elastic Surface Rayleigh Wave (R-wave) based non-destructive test (NDT) techniques have been studied broadly for concrete surface crack assessment in the past few decades. However, the effect of environment factors on the accuracy of R-wave NDT results are often being neglected. Sand and dust are ones of them that easily accumulate within the surface cracks of concrete structures, which potentially affect the characteristics of R-waves propagation when it travels through the concrete medium that containing cracks. This study is aimed to investigate the effect of concrete surface crack filling conditions to the dominant frequency of R-wave. Numerical simulations were conducted to study the changes of R-wave waveform when it propagated through a cracked concrete model with two various filling conditions, namely fine sand and charcoal powder. Fast Fourier Transform (FFT) for post-signal-processing (PSP) of raw R-wave signals to determine its dominant frequency. The results of numerical simulations were then justified by experimental measurements. It was found that the dominant frequency of R-wave is independent to the volume and the type of filling materials, but sensitive to the surface discontinuity of the concrete.

Diffusive Kerr-type interfaces separating media that differ only in the diffusion strength are studied within the Helmholtz framework. We obtain an analytical expression for a soliton effective nonlinear refractive index that takes into account diffusion. A discontinuity in this coefficient makes a soliton undergo external refraction after entering a second medium with a higher diffusion strength. Our theory also predicts total internal reflection and giant Goos H\"anchen shifts when the diffusion is higher in the first medium. Numerical simulations are used to test the validity of the model showing an excellent agreement with theoretical predictions.

Global positioning system (GPS) carrier-phase time transfer, as a widely accepted high-precision time transfer method, frequently shows a data-batch boundary discontinuity of up to 1 ns, because of the inconsistency of the phase ambiguities between two consecutive data batches. To eliminate the data-batch boundary discontinuity, several techniques have been proposed in recent years. The question is how much the solutions of these techniques differ from each other and how well the solutions are faithful to clocks. To answer these questions, this paper chooses two techniques to study: revised RINEX-shift (RRS) technique [1, 2], and phase integer common-view (Phase-CV) technique [3]. This paper shows that the time deviation of the difference between the two techniques is below 100 ps, for an averaging time of less than 10 d. Especially, for an averaging time of less than 1 d, the time deviation is less than 30 ps. We also find that both RRS and Phase-CV match TWSTFT (two-way satellite time and frequency transfer) and TWOTFT (two-way optical-fiber time and frequency transfer) quite well. Especially, the difference between RRS/Phase-CV and TWOTFT is less than ±0.25 ns for more than 20 d, for a baseline of 268 km. These results show that both RRS and Phase-CV agree very well, and they are both faithful to clocks. However, this is based on the assumption that there is no obvious change in the GPS receiver reference time. When there is a sudden change in the reference time, Phase-CV cannot follow the time change. In contrast, RRS still follows the time change and represents the clock well.

Monotonic maps with a single discontinuity arise in a variety of situations. We describe the infinite sets of periods for such maps on the boundary of chaos; this gives a sense of the routes to chaos in such maps. The description involves an explicit subshift of finite type which describes the sequences of different renormalizations possible in these maps.

In this paper, an 8th order Upwinding Compact Scheme is derived by using the idea of the nth order polynomial. Also, the dissipation and dispersion analysis of the scheme is obtained by Fourier analysis after getting the wave number of the scheme. When applying the proposed scheme on continuous functions, high order of accuracy is achieved with high resolution due to the properties of compact schemes. The idea of WENO smoothness indicator is used to detect discontinuity locations. To overcome the global dependency issue, which causes problems near discontinuities in compact schemes, the technic of the decoupling system is used to switch into a local dependency in non-smooth regions. In this work, the promise and success of the proposed scheme is verified by gaining high order, high resolution, and non-oscillation from various numerical examples. Additionally, there is a plan to confirm the achievement of the present scheme when applying it to multidimensional flows with shock-turbulence interaction problems from Computational Fluid Dynamics (CFD).

The space-time conservation element and solution element (CESE) method is one of the recent advancements in CFD. This paper attempts to review various schemes along with their limitations starting with a non-dissipative a -scheme. The following a- e scheme has an added numerical dissipation term. This numerical dissipation is capable of damping out numerical instabilities that arise only from the smooth region of the solution but fails to suppress numerical wiggles. The a-e-α-β scheme is augmented with the ability to suppress the wiggles introduced due to discontinuities, using another added term to the solution. Hence a-e-α-β scheme is capable of capturing both small disturbances and sharp discontinuities simultaneously. Its advantage over a-e scheme as well as the suppression of numerical wiggle at the discontinuity will be demonstrated using Sod's shock tube problem. All of these CESE schemes described so far become excessively diffusive at low Courant number and Mach number. Hence the construction of a Courant number insensitive scheme which has a weighted average sense. Its advantage over a-e-α-β in terms of stability will be explained further in the paper using Sod's shock tube problem as an example and its ability to resolve contact discontinuities without any ad-hoc parameter over CFL number ranging from one to close to 0.001

During the development of full scope simulator (FSS) in nuclear power plant, it is difficult to satisfy with high precision and efficiency of the 3D distribution calculation of reactor power. The accuracy of conventional coarse mesh finite difference method (CMFD) cannot meet the requirement if the nodal size is large. According to the generalized equivalence theory (GET), the finite difference solution of diffusion equation based on discontinuity factor correction was deduced, the calculation method of the discontinuity factor and boundary albedo are presented through the process of assembly homogenization. Through the calculation of typical LMW benchmark problem, the simulation results showed that using CMFD with discontinuity factor ratio (CMFD-DFR) to solve the time-dependent neutron kinetic equation, can not only improve the simulation precision, and can keep the calculation speed, and can meet the requirement of reactor core real-time model of FSS.

In this paper wave scattering from an asymmetrical change of cross-sectional area in a beam is numerically studied. Incident symmetric and antisymmetric Lamb waves are considered and multiple wave mode conversion due to interaction with the discontinuity are investigated up to high frequency (above the cut-off of the second symmetric Lamb wave mode, S 2). Results are presented in terms of transmission power coefficients, kinetic energy, and energy velocity. These are evaluated using the Wave Finite Element method to predict the wave modes from FE cross-sectional nodal displacements and nodal forces. It is shown that the methodology proposed can give an insight into wave scattering and multiple converted Lamb wave modes, which can be useful in Structural Health Monitoring.

The present paper contains the results of the aerodynamics and gas dynamics calculations of HB–1 standard ballistic model performed by the UST3D code. There were the following test cases for the numerical simulations. At first, the computations were conducted for the different Mach numbers at the various angles of attack. At second, the effect of the tetrahedron grid elements number on the flow field and aerodynamics coefficients was estimated. At last, the different approaches to the decay of discontinuity investigation were applied. The comparisons between the experimental data and results of calculations are also presented.

International audience; Mixed order transitions are those which show a discontinuity of the order parameter as well as a divergent correlation length. We show that the behaviour of the order parameter correlation function along the transition line of mixed order transitions can change from normal critical behaviour with power law decay, to fluctuation-dominated phase ordering as a parameter is varied. The defining features of fluctuation-dominated order are anomalous fluctuations which remain large in the thermodynamic limit, and correlation functions which approach a finite value through a cusp singularity as the separation scaled by the system size approaches zero. We demonstrate that fluctuation-dominated order sets in along a portion of the transition line of an Ising model with truncated long-range interactions which was earlier shown to exhibit mixed order transitions, and also argue that this connection should hold more generally.

A one-dimensional TVD correction scheme is described, which can be successfully applied not only in 1D calculations, but also in 2D - 3D modeling [1-2]. The advantage of the proposed scheme is the lack of solving matrix equations. The implementation of the scheme in conjunction with the large particle method was tested on the problems of arbitrary discontinuity breakup and strong point explosion. The modeling of acetylene combustion in a shock tube and its transition to detonation was performed depending on the conditions set on the surface of the tube, and the parameters of the problem.

The behavior of unstable relativistic shock waves is studied with the use of specially developed model equation of state (EOS). The EOS admits the Taub-Hugoniot adiabats with segments on which the criteria of the relativistic shock wave stability are violated. The instability segments are overlapped by the regions with ambiguous representation of the shock-wave discontinuity. The simulations are fulfilled for L (1 + 2M + v 0 v 1)/(1 − v 0 v 1) instability conditions, where L is relativistic analog of Dyakov parameter, M is post-shock Mach number, v0 and v 1 are pre- and post-shock velocities in the shock attached reference frame. Under the condition of ambiguous representation of the shock-wave discontinuity in the former case the splitting of the unstable shock with formation of a composite compression wave with Lorentz factor dependent structure is observed. It is shown that the latter condition leads to two-dimensional non-stationary solutions characterized by presence of strong transverse waves.

This paper presents an experimental validation of an analytical method called complex mode expansion with vector projection (CMEP), which is used to calculate the scattering coefficients (amplitude of the out-of-plane velocity) of Lamb wave modes from geometric discontinuities. For a test case, a plate with a thickness step change type geometric discontinuity is considered in this paper. The scattered wave fields from the discontinuity are expanded in terms of complex Lamb wave modes with unknown scatter coefficients. These unknown coefficients are obtained by projecting the stress or displacement boundary conditions on the displacement or stress boundary conditions utilizing the power expression. In the analytical analysis, complex-valued scatter coefficients are calculated with frequency-thickness product from 50 to 1500 kHz mm for A0 incident wave. A parametric study was conducted using CMEP to find the optimized step depth ratio for the experiment. For incident A0 mode at step depth ratio of 0.6, the scattering coefficients of reflected and transmitted S0 modes are maximum. A plate of thickness 4.86 mm with a step depth ratio of 0.6 was chosen for experimental study. Long piezoelectric wafer active sensors (PWAS) were used to create straight crested Lamb wave modes. Antisymmetric Lamb wave mode selectively excited by using two PWAS in out of phase on opposite sides of the plate. Scanning laser Doppler vibrometer was used to measure the out-of-plane velocity of scattered Lamb wave fields on the plate. Scatter coefficients were calculated from Fourier transform of the time domain signal. The obtained experimental results agree well with the CMEP analytical predictions.

We present three open problems in the mathematical modelling of the flow of non-Newtonian fluids. The first problem is rather long standing: a discontinuity in the dependence of the rise velocity of a gas bubble on its volume. This is very well characterized experimentally but not, so far, fully reproduced either numerically or analytically. The other two are both instabilities. The first is observed experimentally but never predicted analytically or numerically. In the second instability, numerical studies reproduce the experimental observations but there is as yet no analytical or semi-analytical prediction of the linear instability which must be present.

The max-min approach is applied to mathematical models of some nonlinear oscillations. The models are regarding to three different forms that are governed by nonlinear ordinary differential equations. In this context, the strongly nonlinear Duffing oscillator with third, fifth, and seventh powers of the amplitude, the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration. The obtained results via the approach are compared with ones achieved utilizing other techniques. The results indicate that the approach has a good agreement with other well-known methods. He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.

The one-dimensional finite well is a textbook problem. We propose approximate approaches to obtain the energy levels of the well. The finite well is also encountered in semiconductor heterostructures where the carrier mass inside the well (mi) is taken to be distinct from mass outside (mo). A relevant parameter is the mass discontinuity ratio ? = mi/mo. To correctly account for the mass discontinuity, we apply the BenDaniel?Duke boundary condition. We obtain approximate solutions for two cases: when the well is shallow and when the well is deep. We compare the approximate results with the exact results and find that higher-order approximations are quite robust. For the shallow case, the approximate solution can be expressed in terms of a dimensionless parameter ?l = 2moV0L2/2 (or ? = ?2?l for the deep case). We show that the lowest-order results are related by a duality transform. We also discuss how the energy upscales with L (E?1/L?) and obtain the exponent ?. Exponent ? ? 2 when the well is sufficiently deep and ? ? 1. The ratio of the masses dictates the physics. Our presentation is pedagogical and should be useful to students on a first course on elementary quantum mechanics or low-dimensional semiconductors.

An approximate analytical solution is obtained for the shock tube problem in a rectangular channel with an array of rectangular grooves in the lower wall. The analytical solution is based on the approximate quasi-1D shock adiabat for a shock wave that propagates in a channel with periodically located barriers. This problem is also studied numerically. It is found that the approximate analytical solution correctly predicts the propagation velocity of the leading discontinuity and the flow parameters at this discontinuity. The leading gas-dynamic discontinuity is followed by a relaxation zone in which there are long-wave and short-wave flow oscillations. These oscillations are caused by waves arising from the interaction of the flow behind the leading shock wave with the side and bottom walls of the grooves. An approximate analytical solution allows one to obtain the values of the flow parameters at the end of the relaxation zone. These values are in good agreement with the numerical calculation.

The multi-cusped field thruster is a novel electrostatic thruster with significant performance merits in spacecraft propulsion. In this paper, the ion energy distribution function (IEDF) in the plume region and its changing characteristics with anode voltage are tested to study the ionization regions in a two-stage cusped field thruster. Firstly, the IEDFs in two different operating modes are studied, the test result indicates that the plume region could be divided into three angle zones by the discontinuity of IEDFs. Secondly, the changing characteristics of IEDF in each angle zone are studied to analyze the location and the forming process of the corresponding ionization regions. The results show that the two-stage cusped thruster contains three ionization regions. The ions in zone II (from 15 to 40 degrees) are generated in columnar ionization region in discharge channel. The ions in zone III (above 40 degrees) are generated in the exit ionization region. The ions near axis in zone I (from 0 to 15 degrees) are generated in two significant different ionization regions. The high-energy ions are generated in the exit ionization region and the low-energy ions are generated in the plume ionization region. In this study, the number of the ionization regions is validated and the relationships between ion current in plume zones and ionization regions are specified, which is helpful to clarify the complicated ionization processes in the multi-cusped thruster.

The risk forecasting and modeling during the construction period of water conservancy and hydropower projects are solved by including early warning of risk in the grey system problem. In order to mitigate the problem of modeling difficulties caused by short sequence and lack of information, change in the parameter function of the data sequence, mutation and discontinuity of the original monitoring data have been overcome. In addition, the traditional grey prediction model is upgraded to increases the focus on new interest so that the system change trend reflected by modified model is investigated profoundly. Similarly, modified model is built based on time-varying parameters that greatly enhanced the fitting and accuracy of the forecasting model. Its application realms prove that the method is effective and reasonable.

The longitudinal-random-field mixed Ising model consisting of arbitrary spin values has been studied by the use of an effective field theory with correlations (EFT). The phase diagrams of systems with mixed spins: σ = 1/2, S = 1; σ = 1/2, S = 3/2 are plotted. Not only the discontinuity at T = 0 K, is found when both longitudinal fields are trimodal distributed, but also the tricritical behavior is observed in these phase diagrams between the bimodal and trimodal distributions of longitudinal fields, which is different from the single-spin one. The appearance of tricritical point is independent of the coordination number and spin values.

In the definition of , it was assumed that the interval [a, b] was finite. However, in many application in physics, engineering, economics, and probability we wish to allow a or b (or both) to be infinite or for the other case when f has an infinite discontinuity in [a, b]. In either case the integral is called improper integral. Definition of improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or −∞ or, in some cases, as both endpoints approach limits. Many of the first-year students in ITERA learning about improper integrals make an abuse notation like written improper integral just like standard definite integral. Based on this situation, we tried to change the habits of the students in the writing of improper integrals by providing sufficient understanding and considerable exercises. It turns out this way gives good result, based on the percentage of the value of the midterms to the problem of improper integrals give a fairly good percentage value.

We studied quantitatively the effects of the discontinuity introduced in an otherwise homogeneous background by the cold walls of the standard spherical glass inserts commonly used in phantom measurements for calibration of threshold-based approaches to volumetric evaluation of PET investigations. We concentrated especially on the question of threshold-based volume determination. We computed analytically the convolution of an isotropic Gaussian point-spread function with the insert geometry (hot sphere + cold wall + warm background) and derived the theoretical background dependence of the volume reproducing threshold. This analysis shows a clear wall-related reduction of the optimal threshold with increasing background. The predictions of our theoretical analysis were verified in phantom measurements at background fractions between 0 and 0.29. Defining the background-corrected relative threshold T = Tabs−B ./. A−B (Tabs: absolute volume reproducing threshold, A: measured activity at centre, B: background), we find that for a wall-less sphere T is independent of the background level. In the presence of cold walls, T drops (for not too small spheres, where recovery at the centre approaches 100%) from about 43% at B/A = 0 to about 25% at B/A = 0.5. Applying these thresholds towall-less spheres leads to sizeable overestimates of the true volumes (43% at B/A = 0.5 for a sphere of 6 ml volume). We conclude that phantom measurements with standard sphere inserts for calibration of optimal thresholding algorithms introduce a systematic bias if performed at finite background levels. The observed background dependence is an artefact of the measurement procedure and does not reflect the conditions present in actual patient investigations.

The effects of atomic-level mixing are systemically investigated in a multifluid interpenetration mix model, and results are compared with the single-fluid model's simulations and experimental data. It is shown that increasing the model free parameter α, shock Mach number, and the initial density discontinuity makes the mix length and fraction of mixing particle increase, resulting in the lower shock temperatures compared with the results of single-fluid model without mixing. Recent high-compressibility direct-drive spherical implosions on OMEGA are simulated by the interpenetration mix model. The calculations with atomic mixing between fuel and shell match quite well with the observations. Without considering any mixing, the calculated neutron yields and ion temperatures are overpredicted; while inclusion of the interpenetration mix model with the adjustable parameter α could fit the simulated neutron yields and ion temperatures well with experimental data.

Hybrid functionals non-local exchange-correlation potential contains a derivative discontinuity that improves on standard semi-local density functional theory (DFT) band gaps. Moreover, by careful parameterization, hybrid functionals can provide self-interaction reduced description of selected states. On the other hand, the uniform description of all the electronic states of a given system is a known drawback of these functionals that causes varying accuracy in the description of states with different degrees of localization. This limitation can be remedied by the orbital dependent exact exchange extension of hybrid functionals; the hybrid-DFT + V-w method (Ivady et al 2014 Phys. Rev. B 90 035146). Based on the analogy of quasi-particle equations and hybrid-DFT single particle equations, here we demonstrate that parameters of hybrid-DFT + V-w functional can be determined from approximate theoretical quasi-particle spectra without any fitting to experiment. The proposed method is illustrated on the charge self-consistent electronic structure calculation for cerium dioxide where itinerant valence states interact with well-localized 4f atomic like states, making this system challenging for conventional methods, either hybrid-DFT or LDA + U, and therefore allowing for a demonstration of the advantages of the proposed scheme. Funding Agencies|Knut and Alice Wallenberg Foundation; Ministry of Education and Science of the Russian Federation [14.Y26.31.0005]; Hungarian Academy of Sciences

The hierarchical reconstruction (HR) (Liu et al 2007 SIAM J. Numer. Anal. 45 2442–67) can effectively reduce spurious oscillations without local characteristic decomposition for numerical capturing of discontinuous solutions. However, there are still small remaining overshoots/undershoots in the vicinity of discontinuities. HR with partial neighbouring cells (Xu et al 2009 J. Comput. Phys. 228 2194–212) essentially overcomes this drawback for the third order case, and in the mean time further improves the resolution of the numerical solution. Extending the technique to higher order cases we observe the returning of overshoots/undershoots. In this paper, we introduce a new technique to work with HR on partial neighbouring cells, which lowers the order of the remainder of the polynomial in the current cell while maintaining the theoretical order of accuracy, essentially eliminates overshoots/undershoots for the fourth and fifth order cases and reduces the numerical cost.

We present a highly efficient lattice Boltzmann model for simulating compressible flows. This model is based on the combination of an appropriate finite difference scheme, a 16-discrete-velocity model [Kataoka and Tsutahara, Phys. Rev. E 69 (2004) 035701(R)] and reasonable dispersion and dissipation terms. The dispersion term effectively reduces the oscillation at the discontinuity and enhances numerical precision. The dissipation term makes the new model more easily meet with the von Neumann stability condition. This model works for both high-speed and low-speed flows with arbitrary specific-heat-ratio. With the new model simulation results for the well-known benchmark problems get a high accuracy compared with the analytic or experimental ones. The used benchmark tests include (i) Shock tubes such as the Sod, Lax, Sjogreen, Colella explosion wave, and collision of two strong shocks, (ii) Regular and Mach shock reflections, and (iii) Shock wave reaction on cylindrical bubble problems. With a more realistic equation of state or free-energy functional, the new model has the potential tostudy the complex procedure of shock wave reaction on porous materials.

Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-11, period-6, chaotic band-12 and band-6 attractors. They are induced by different mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.

In engineering fields there have recently been a number of studies that have applied the finite-difference time-domain (FDTD) numerical method to elastodynamic problems. These studies include those of ultrasonic transducers and electro-mechanical devices. In FDTD formulations, the first-order set of partial differential equations given by the constitutive equations are discretized using a leap-frog finite-difference scheme. When a high-contrast discontinuity, especially a free surface, is present, some difficulties arise due to the spatially staggered nature of the grid of the FDTD approach, with neither all the velocity variables nor all the stress variables appearing on the same grid lines. The present study considers the following modifications to the FDTD approach: a standard staggered grid for anisotropic elastic wave fields is rotated so that the diagonal directions of the standard grid lie parallel to the axes of the analysis region. This configuration, called the diagonally staggered grid (DSG), improves the accuracy of the implementation of free boundaries without requiring virtual grids in a vacuum area. The effectiveness of DSG was verified by applying this method to model problems of isotropic and anisotropic solid materials.

The excitation and stability of surface waves on the interface of two compressible fluids moving with respect to each other in a two-dimensional channel is investigated. It is shown that in this case surface waves are always unstable. On the other hand, in this case the dispersion relation in the short and the long wavelength limits coincides with the dispersion relation in the compressible and the incompressible infinite fluid, respectively. Furthermore, surface wave excitation under resonant condition is investigated. It is concluded that due to the Cerenkov-like emission mechanism a sound wave propagates in the fluid at rest. In this case, the growth rate of the Cerenkov-like instability is compared with the growth rate of the instability for the excitation of the tangentially discontinuous surface wave. Likewise, using fluent software, surface wave excitation in two dimensions is simulated.

In this paper, we present a method for solving inverse Sturm–Liouville problems by generalizing a Rundell–Sacks algorithm. The method is extended to deal with a general reference potential which can be adapted, e.g., to estimations of the jump-discontinuity points of the unknown potential. Moreover, its convergence properties are investigated. Numerical examples show that this modification can achieve more precise results from a given data set than the earlier method in using only the null reference potential and, therefore, the L2- and L∞-error can be reduced significantly.

We prove that in dimension one the combined jumps and singularities of the unknown functions appearing in the nonlinear Schrodinger equation can be recovered using the Born approximation. The result is based on accurate determination of the first nonlinear term of the Born sequence. Numerical examples illustrate the feasibility of this technique.

Wave propagation modelling is important for reliable damage detection based on Lamb waves. A number of different numerical computational techniques have been developed for wave propagation studies. The local interaction simulation approach, used for modelling sharp interfaces and discontinuities in complex media, has been applied effectively for numerical simulations of elastic wave interaction with structural damage. The paper builds upon this experience and reports numerical investigations of Lamb wave propagation modelling for damage detection in metallic structures. The ultimate objective of the investigations is to demonstrate that numerical simulations can significantly ease the monitoring strategy used for damage detection with Lamb waves. The interaction of fundamental Lamb wave modes with a rectangular damage slot in an aluminium plate is investigated as an example. For the sake of completeness, the first part of the paper forms an introduction to wave propagation studies for damage detection. The local interaction simulation approach is implemented. This is followed by a series of two-dimensional studies of wave interaction with damage.

Wave propagation modelling is important for reliable damage detection based on Lamb waves. A number of different numerical computational techniques have been developed for wave propagation studies. The local interaction simulation approach, used for modelling sharp interfaces and discontinuities in complex media, has been applied effectively for numerical simulations of elastic wave interaction with structural damage. The paper builds upon this experience and reports numerical investigations of Lamb wave propagation modelling for damage detection in metallic structures. The ultimate objective of these investigations is to demonstrate that numerical simulations can significantly ease the monitoring strategy used for damage detection with Lamb waves. The interaction of fundamental Lamb wave modes with a rectangular damage slot in an aluminium plate is investigated as an example. The second part of the wave propagation studies focuses on the monitoring strategy for damage detection. The effect of sensor position on the amplitude and time of flight of Lamb waves is investigated and discussed for various severities of damage. The results are validated experimentally.

We consider ordinary Differential equations with a Preisach operator under the derivative. A special case when the right-hand side has discontinuities in time is studied. We present theorems about the existence and uniqueness of solutions. We also prove a theorem which describes the behavior of a solution at the points of discontinuity of the right-hand side.

This paper presents a theory on accurately analysing the dispersion relation and the interaction impedance of electromagnetic waves propagating through a helical groove waveguide with arbitrary groove shape, in which the complex groove profile is synthesized by a series of rectangular steps. By introducing the influence of high-order evanescent modes on the connection of any two neighbouring steps by an equivalent susceptance under a modified admittance matching condition, the assumption of the neglecting discontinuity capacitance in previously published analysis is avoided, and the accurate dispersion equation is obtained by means of a combination of field-matching method and admittance-matching technique. The validity of this theory is proved by comparison between the measurements and the numerical calculations for two kinds of helical groove waveguides with different groove shapes.

A generalization is considered of Williams's well-known model of the attractor in the Lorenz system, the inverse limit of semiflows on branched manifolds that are suspensions over a discontinuous expanding map of a closed line interval. The generalization consists in the consideration of maps with several, rather than one, discontinuity points. A cardinal-valued topological invariant L-manuscript is constructed, which distinguishes a continuum of non-homeomorphic generalized models. A topological invariant distinguishing a continuum of non-homeomorphic geometric Lorenz attractors is obtained as a consequence.

An estimation of the current source in integrated circuits using a SQUID microscope can be made by the magnetic inverse technique, if the current is located at the thin sheet. The estimated current distribution deviates from the original one because of the discontinuity in the data at the edge of the sheet. A window function is introduced to solve this problem. A simulation on estimating a meandering current path was investigated. The error of the current estimated without the window function was about 30% from the original one in whole region. However, when the window function was used for the simulation, the error became less than 1% at all meander lines except in the edge area.