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A survey is presented of the behavior of transport properties near the gas‐liquid critical point of one component fluids and near the critical mixing point of binary liquids. The paper deals specifically with the shear viscosity and those transport properties, thermal conductivity and thermal diffusivity of gases and binary diffusion coefficient of liquid mixtures, that are related to the critical slowing down of the fluctuations in the order parameter. The experimental data are compared with current theoretical predictions.

It is the author’s hope that this document will help provide the novice with both an understanding of what dynamic aperture is and some insight as to why it is limited. In addition, we hope that this paper will provide information as to the analytical and numerical methods available for the study of dynamic aperture. Finally, we wish to present some interpretations and applications of these concepts and tools by means of examples. Those factors having an impact on the dynamic aperture of circular machines and storage rings will be discussed; applications to two types of machine of current popular interest (namely, large hadron colliders and synchrotron radiation electron storage rings) will be made in order to illustrate the ideas that are presented.

A computational experiment for simulating building performance needs basically three important input data sets, namely the material properties, environmental conditions and initial conditions. As the result of any prediction depends strongly on a considered geographical location, a database of locations and climatic data is required to support any reliable numerical simulation. In this paper, we present an online application for gathering, sharing and processing of climatic data from stations all around the world. An illustrative example confirms the necessity of such a software tool.

This paper reviews recently developed numerical methods for the solution of free‐boundary problems in fluid dynamics. A sample of recent CFD studies from our research is then presented, with the goal of illustrating the potential of ‘‘computational experiments’’ in elucidating the dynamics of bubbles and drops in viscous fluids at both zero and nonzero Reynolds numbers.

The roton‐like excitations identified in many metallic glasses by neutron diffraction experiments and computor simulations have been considered as longitudinal accoustic phonons, since they all seem to lead to the sound waves in an elastic continuum in the long wavelength limit. In this paper, however, we will show that they are in fact optical phonons, by applying both analytical and computational methods to amorphous Mg70Zn30 alloy.

In Part I of this paper, we described a numerical method for nonlinear signal detection and classification which made use of techniques borrowed from dynamical systems theory. Here in Part II of the paper, we will describe an example of data analysis using this method, for data consisting of open ocean acoustic (SONAR) recordings of marine mammal transients, supplied from NUWC sources. The purpose here is two‐fold: first to give a more operational description of the technique and provide rules‐of‐thumb for parameter choices; and second to discuss some new issues raised by the analysis of non‐ideal (real‐world) data sets. The particular data set considered here is quite non‐stationary, relatively noisy, is not clearly localized in the background, and as such provides a difficult challenge for most detection/classification schemes.

This paper is a brief survey of numerical methods for computing bifurcations of generic families of dynamical systems. Emphasis is placed upon algorithms that reflect the structure of the underlying mathematical theory while retaining numerical efficiency. Significant improvements in the computational analysis of dynamical systems are to be expected from more reliance of geometric insight coming from dynamical systems theory.

The present report contains an investigation of the dynamics of thin-foils accelerated by light-ion beams. The experiments were performed at KALIF. Equations of State used in the present calculations is in a simple analytical form. The empirical parameters of this EOS have been adjusted to adequately describe experimental data in one dimensional calculations as well as shock compression data. In this paper we redo these calculations with a moving grid 2D code. 2D computations are much more time consuming then ID especially for problems containing different time and space scales. Efficient numerical algorithms are required to perform these computations. We present in this report 2D applications of Godunov Moving Grid Code to beam-target interaction problems.

Several designs for linear colliders for electron-positron-collisions in the TeV range are currently under discussion. Most of them will use long trains of bunches. Therefore the study of higher order modes excited by previous bunches in a train became even more important for the optimal design of the accelerator components. Many of the designs use long tapered disc-loaded waveguides for acceleration. Numerical reasons hinder the mode analysis of these long structures by discretization methods. In this paper the electromagnetic waves in tapered multi-cell structures with circular cross section are calculated by a modal field matching method in which the scattering matrix formulation is used to calculate the amplitudes of the field expansion. Some remarks on convergence aspects are made. The field distribution of deflecting dipole modes is analyzed for a 180-cell tapered disc-loaded S-Band structure as well as for a 36-cell test structure. For the 36-cell test structure comparisons with a grid-oriented numerical method, an equivalent circuit model and measurements are also presented.

Within the last two years a number of highly refined measurements have been performed on H targets which have yielded accurate absolute data for a range of energies and geometries [1] and it would appear that the experimental situation for this, the simplest of atomic targets is now resolved. The theoretical situation is however far from satisfactory and in this paper we will analysis some of the main approaches and characterize their strengths and their weaknesses. We have developed a numerical method which allows us to evaluate triple differential cross sections (TDCS) using the most complex position dependent analytic ansatz wave function and we will present results, using this for low energy (e,2e) processes. We will see that this approach fails when incident channel effects, such as target polarization are likely to be strong.

This paper summarizes a fast numerical technique for solving Poisson’s equation in an axisymmetric Malmberg-Penning trap. The method assumes the charge density qn(r,z) and boundary potentials φ(r=Rw,z) are specified, and solves for the electrostatic potential φ(r,z) within the cylinder. The solution of Poisson’s equation is often an important step in the numerical reconstruction of the nonneutral plasma density profile n(r,z) from the axially integrated measurements of the charge density profile, Q(r)=qAh∫dzn(r,z), where q is the charge and Ah is the effective area of the collimator hole.

Detailed numerical modeling has provided valuable insights into the operation and performance limitations of solar cells for both space and terrestrial applications. Detailed numerical modeling of TPV cells should provide similar benefits. In this paper, a detailed numerical model appropriate for TPV cells is presented.

More than any other NDE method, the remote field effect is subject to various interpretations based on either measured data or on assumed theoretical models which try to explain measured data. Some of these are based on an induction process while others presume a propagation process. All of these models are successful to a certain degree in explaining measured results, but some are not satisfactory from a theoretical point of view and in some cases, contradicting. The current paper attempts to clarify these issues by discussing the various models available, separating those which are theoretically sound and proposing both theoretical and numerical models which are supported by either experiment or valid computation. It is shown that the induction based models are supported by both theory and experiment. The propagation based models, while successful at explaining the phenomena observed are not valid theoretical models and, in fact, have only been used loosely. More specifically, no propagation model has b...

Electricite de France conducts a study on the effects of metallurgical structures of austenitic stainless steel welds on ultrasonic wave propagation for application to ultrasonic nondestructive testing. Two complementary methods are performed: a direct experimental study on various kinds of welds and a theoretical study using ultrasonic simulation tools. This simulation study makes use of two different models. The first, called ULTSON-2D, is a finite element code developed by the EDF Research and Development Division. It is adapted to orthotropic media and heterogeneous structures and takes into account the scattering of waves from flaws such as cracks and holes. The second, called Champ-Sons is a 3D semi-analytical code developed by the French Atomic Energy Commission (CEA) which allows to predict ultrasonic beam radiation into anisotropic and heterogeneous media. Both models deal with broadband excitation pulses since they are time-dependent. The present study aims at evaluating the ability of the two models to predict typical beam distortion effects in complex anisotropic and heterogeneous weld structures as compared to experimental measurements. This study is based on preliminary results of weld structural characterization presented in a companion paper.

An integral equation is formulated for the scattering problem by the planar periodic array of scatterers. In this case, the fundamental solution is in a form of double series and the series may converge very slowly in a certain configuration of periodic scatterers. In this paper, a practical numerical integration based on Ewald method is investigated for the fundamental solution with the double infinite series. In more detail, the fundamental solution is converted into the integral form with rapidly convergent integrand and the Gauss’ numerical integration is performed here to evaluate the integral. The convergence and the efficiency of the method are demonstrated numerically for the integral equation by the planar array of scatterers. The reflection and transmission coefficients are calculated as an application of the present numerical evaluation for the fundamental solution.

The term “overdriven detonation” refers to detonation process in which the main detonation parameters, such as detonation pressure and propagating velocity, exceed the corresponding Chapman-Jouguet (C-J) values. This kind of detonation state can be realized by the impingement of a high velocity object upon the explosive. This paper presents our initial survey on the occurrence of overdriven detonation in high explosive. The HMX-based PBX is used to accelerate the metal plate being used as the impactor. The target explosive is the so-called SEP, simplified from the term of the ‘safety explosive,’ with the composition of PETN wt.65% and paraffin 35 wt.%. By changing the thickness of the metal plate under an unvaried amount of donor explosive, the different impinging velocities are yielded. The propagation of the detonation wave grown from the impingement of metal plate is recorded by the high-speed streak camera owing to the self-luminosity of detonation. The higher detonation velocity is found from the experimental results. Meanwhile, the impacting velocities of the metal plate are determined by one-dimensional Lagrangian numerical method enabling to estimate the initial input pressure into the target explosive by the impedance matching method. The obtained input pressures are of larger values than the C-J pressure.

Nonparametric Bayesian approaches to density estimation (“Bayesian field theories”) have typically to be solved numerically on a lattice. This is often numerically quite expensive. The Paper wants to show that such numerical calculations are nowadays feasible for some interesting problem classes. In particular, Bayesian field theories are defined by 1. a likelihood model, being a probabilistic description of the measurement process of observational data. and 2. a prior model, determining the generalization behavior of the theory by implementing available a priori knowledge. In this Paper some variations of prior and likelihood models are discussed: First, the implementation of approximate symmetries with Gaussian process priors is demonstrated for approximate periodic and for approximate fractal functions. Second, besides a discussion of the classical likelihood models of general density estimation and regression, special emphasis is put on the likelihood model of quantum theory to treat the inverse probl...

A novel numerical procedure is presented in this paper to study wave scattering problem by circumferential cracks in steel pipes. The study is motivated by the need to develop a quantitative ultrasonic technique to characterize properties of cracks in pipes. By employing wave function expansion in axial direction and decomposing the problem into a symmetry problem and an antisymmetry problem, a three-dimensional wave scattering problem is then reduced into two quasi-one-dimensional problems. This simplification greatly reduces the computational time. Numerical results for reflection and transmission coefficients of different incident wave modes are presented here for a steel pipe with cracks (may have arbitrary circumferential crack length and radial crack depth) and they are shown to agree quite closely with available but limited experimental data.

Integral equation (IE)-based techniques have been widely used for computing the magneto-static field in both the linear and non-linear regime. One disadvantage of IE-based techniques is that they result in dense matrices, the solution of which is computationally prohibitive. Indeed, both the computational time and memory scale as O(N2), where N is the number of spatial unknowns that the body is discretized into. The computational complexity has been the primary hurdle towards the popularity of such solvers. Our goal is to develop a fast solution scheme for magneto-static field computations. In this paper, a novel integral equation formulation has been used and a version of the fast multipole algorithm has been incorporated in the overall solution procedure.

The interaction of an incident monochromatic bounded beam with an anisotropic multilayered plate immersed in an external fluid has been modelled, using the decomposition method into monochromatic plane waves and the transfer matrix method, in a 3D configuration. The subject of this paper is the study of the deviation of a monochromatic Lamb wave beam due to the anisotropy of the structure. Comparisons between some theoretical, numerical and experimental results are given.

Two important application of electrodynamic tethers, among others, are those of using them for deorbiting and/or propulsion. A crucial issue for both of the above applications is the dynamic stability of the tether system. The electrodynamic forces on the tether couple in fact in plane and out of plane oscillations and, especially for light systems, can drive the tethers unstable as has been shown in several numerical simulations. In both the applications of deorbiting and propulsion, the tether system is supposed to operate for long intervals of time (months) so that a crucial issue, in view of the fact that the system is potentially unstable, is that of analyzing the constraints, in terms of average current, ensuring long term safe operations (i.e. with the tether oscillation amplitudes below certain limits). In this paper we consider this issue referring, in particular, to the tether lateral oscillations which (from numerical simulations), appear the ones for which instability develops. We refer theref...

The objectives of this paper are to detect and identify flaws in conducting tubes surrounded partially by subsurface structures. Signals from eddy current sensors are frequently contaminated by noise due to the presence of such elements. When employing single frequency systems it is very difficult to discriminate between various factors, which cause signal changes. To deal with this problem, application of the multi-frequency system and restoration procedure is proposed. Numerical simulations and experiments with various interfering structures were performed.

The paper is devoted to experimental and theoretical investigation of two types of one-sectional generators with overmoded slow-wave structures (SWS). Numerical analysis was made by means of a computer code MULTIWAVES-5.2. Comparison and discussion of obtained results that can be used at development of multiwave Cerenkov generators were made.

Since the first observation of ultracold molecules in Orsay, investigation of new ways of creating ultracold molecules inside cold atom traps is a challenging task for both theoretical and experimental groups. In this paper, we review some of our recent results on formation processes using cw laser photoassociation of cold atoms, involving population of long‐range molecular potential wells, or resonant coupling. We implemented accurate numerical methods based on a mapped Fourier grid approach, to solve time‐independent Schrodinger equation, in order to obtain quantitative predictions for ultracold molecule formation rates and detection efficiency.

In this paper we describe a DSMC algorithm for the Uehling‐Uhlenbeck‐Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi‐Dirac and Bose‐Einstein cases. By numerical experiments we study the sensitivity of the algorithm to the number of simulation particles and to the discretization of the velocity space, when approximating the steady state distribution.

The high‐β magnetically confined plasmas in spherical tori (ST), like NSTX and MAST, provide a unique opportunity for a wide variety of applications of electron Bernstein waves (EBW). These applications range from heating of the ST plasma to modifying and controlling its current profile. Using the fully relativistic dielectric tensor for a Maxwellian distribution function, this paper presents initial results illustrating the effect of relativity on the dispersion characteristics of EBWs. It is found that, even at temperatures relevant to present STs, the relativistic dispersion properties of EBWs are significantly different from their non‐relativistic counterpart.

The paper discusses current challenges and problems pertaining to the development and application of the direct simulation Monte Carlo method. The attention is paid to the issues related to the efficiency and accuracy of the method in the near‐continuum regime, as well as its use for modeling of rarefied flows with real gas effects.

In the last two decades considerable progress has been made in numerical modeling of isothermal and non‐isothermal cavities by the Monte Carlo method, in particular, by the use of the uniform specular‐diffuse reflection model and backward ray tracing techniques. However, this technique has no essential theoretical foundation. In the present paper a comparative numerical analysis of forward and backward ray tracing algorithms shows agreement with earlier analytical results. Numerical experiments show that the use of uniform specular‐diffuse reflection model, which obeys the reciprocity principle, leads to excellent agreement between effective emissivities, computed by forward and backward ray tracing. At the same time, results obtained for the non‐reciprocal Phong’s model demonstrate substantial discrepancies.

A steady state of a binary mixture of hard‐sphere gases in the near continuum regime, where the Knudsen number is small, is considered in the case where the density and temperature variations are large, but the Mach number of the flow is as small as the Knudsen number. Thus, the flow vanishes in the continuum limit where the Knudsen number goes to zero. The set of fluid‐dynamic‐type equations in this case was derived by Takata and Aoki [Transp. Theor. Stat. Phys. 30, 205 (2001)] by means of a systematic asymptotic analysis of the Boltzmann equation. This set gives the correct behavior of the mixture in the continuum limit, i.e., it describes the ghost effect discovered by Sone et al. for a single‐component gas [Phys. Fluids 8, 628 (1996)]. The set contains various transport coefficients that depend on the local properties of the gas. In particular, their dependence on the local concentration of one of the components cannot be obtained explicitly. In this paper, this unknown dependence is established numerically by a direct numerical analysis of the basic integral equations, and a database that provides the numerical values of the transport coefficients immediately for an arbitrarily specified local state of the mixture is constructed. The database makes the fluid‐dynamic‐type equations applicable to practical problems.

The paper is focused on numerical investigation of the gasdynamic processes accompanying laser beam energy deposition in nozzle of the laser propulsion engine (LPE). Various gasdynamic models were implemented in order to compare their applicability for simulation of the phenomena: (a) perfect ideal gas; (b) equilibrium plasma; (c) non‐equilibrium multi‐temperature plasma, and (d) two‐phase mixture. Numerical method of the simulation is based on high‐resolution Godunov‐type scheme and unstructured adaptive grid technique. Two types of LPE nozzles were considered: parabolic and “toroidal” parabolic. Non‐stationary gasdynamic function distribution and the thrust of the LPE were obtained. Time of gasdynamic parameter relaxation in the nozzle was estimated.

Three‐dimensional mathematical models of band cold rolling from steel feed with a wedge cross‐section and band flattening have been constructed. In accordance with the first model in the case of rolling a considerable transverse deformation takes place. The second model makes it possible to describe the process of band flattening in horizontal and vertical rolls and in tuck head. In the presented paper original results are given under consideration. They played an important in the introduction of new technologies.

This paper introduces a new methodology from which better material parameters may be identified. The method will account for both non‐repeatability of test data (by means of signal‐to‐noise weighting factors) and potential discrepancies between material parameters in different deformation modes (by means of a multi‐objective optimization process). Finally, to show the application of the method, test data for a 2×2 twill weave fabric from different modes (namely, uniaxial extension and bias‐extension) are selected to identify the model parameters of an orthotropic material model. The procedure may be applied to other material models and applications.

Wave propagation in a granular bed is a complicated, highly nonlinear phenomenon. Yet studies of wave propagation provide important information on the characteristics of these materials. Fundamental nonlinearities of the bed include those in the particle contact model and the fact that there exists zero applied force when grains are out of contact. The experimental work of Liu and Nagal showed the strong dependence of wave propagation on the forming and breaking of particle chains. As a result of the nonlinearities, anomalous behavior such as solitary waves and sonic vacuum have been predicted by Nesterenko. In the present work we examine wave propagation in a granular bed subjected to vertical agitation. The agitation produces continual adjustment of force chains in the bed. Wave propagation speed and attenuation measurements were made for such a system for a range of frequencies considerably higher than that used for the agitation. Both laboratory experiments and simulations (using a two-dimensional, discrete soft-particle model) have been used. The present paper is a progress report on the simulations.

This work is part of a project dedicated to find accurate and reliable tools for prediction of welding and post weld heat treatment. In other parts of the project, a simulation method for combined welding and heat treatment simulations of the component was developed and different plastic/viscoplastic material models have been compared, these models included effects of phase changes. These simulations were made using an axisymmetric finite element model. The current paper presents welding and heat treatment simulations of the same aerospace component but now using a three‐dimensional shell model. The results are compared with the previously used axisymmetric model. The simulations revealed that the two first welds have the greatest influents on a ‘key dimension’. From the simulation, it can be concluded that the three‐dimensional model give better prediction of the dimension based on measurement performed but not presented here.

A method of optimal control of the thermomechanical parameters during hot strip rolling processes, based on the modern optimal control theory, is presented in the paper. Optimal parameters are defined from the desired final grain size. The austenite grain size is the criterion of optimization. A state‐space model with physical constraints is described. The model is based on the models of rolling process, recrystallization and grain growth, developed for 304L steel. The optimal discrete trajectories for such control parameters as the initial temperature, reductions and interpass time, are to be found. The rolling constrains are applied to the control trajectories (reduction, interpass time) and to state‐space trajectories (temperature, rolling force and moment). The results of calculations allow for the design of the optimal rolling schedule.