Miracle-dz/UniFAR-FTUs huggingface dataset:
Error Estimates for a Combined Finite Volume--Finite Element Method for Nonlinear Convection--Diffusion Problems

The subject of this paper is the analysis of error estimates of the combined finite volume--finite element (FV--FE) method for the numerical solution of a scalar nonlinear conservation law equation with a diffusion term. Nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume mesh dual to a triangular grid, whereas the diffusion term is discretized by piecewise linear conforming triangular finite elements. Under the assumption that the exact solution possesses some regularity properties and the triangulations are of a weakly acute type, with the aid of the discrete maximum principle and a priori estimates, error estimates of the method are proved.
A preliminary model of ion beam neutralization

A theoretical model of neutralized thruster ion beam plasmas has been developed. The basic premise is that the beam forms an electrostatic trap for the neutralizing electrons. A Maxwellian spectrum of electron energies is maintained by collisions between trapped electrons and by collective randomization of velocities of electrons injected from the neutralizer into the surrounding plasma. The theory contains the observed barometric law relationship between electron density and electron temperatures and ion beam spreading in good agreement with measured results.
Development of plasma cathode electron guns

The status of experimental research and ongoing development of plasma cathode electron guns in recent years is reviewed, including some novel upgrades and applications to various technological fields. The attractiveness of this kind of e-gun is due to its capability of creating high current, broad or focused beams, both in pulsed and steady-state modes of operation. An important characteristic of the plasma cathode electron gun is the absence of a thermionic cathode, a feature which leads to long lifetime and reliable operation even in the presence of aggressive background gas media and at fore-vacuum gas pressure ranges such as achieved by mechanical pumps. Depending on the required beam parameters, different kinds of plasma discharge systems can be used in plasma cathode electron guns, such as vacuum arcs, constricted gaseous arcs, hollow cathode glows, and two kinds of discharges in crossed E×B fields: Penning and magnetron. At the present time, plasma cathode electron guns provide beams with transvers.
ABAKO: A new code for population kinetics and radiative properties of plasmas under NLTE conditions

In this work we present ABAKO, a new computational code based on analytical models and developed to study the population kinetics of steady-state plasmas. The tool ABAKO can be applied to low-to-high Z ions under a wide range of laboratory plasma conditions: coronal, LTE or NLTE, optically thin or thick plasmas. Autoionizing states are explicitly included. The results obtained with ABAKO are competitive with more elaborated, but also time-consuming codes. Our code provides satisfactory charge state distributions (CSD) and reasonable estimations of spectroscopic observables of high-Z plasmas, as it can be seen through comparison with experimental data.
Turbulent flow in the bulk of Rayleigh–Bénard convection: aspect-ratio dependence of the small-scale properties

Abstract Geometrical confinement of turbulent Rayleigh–Bénard convection (RBC) in Cartesian geometries is found to reduce the local Bolgiano length scale in the centre of the cell $L_{B,centre}$ and can therefore be used to study cascade processes in the bulk of RBC. The dependence of $L_{B,centre}$ versus $\varGamma $ suggests a cut-off to the local $L_B$ , which depends on the Prandtl number $Pr$ and is of the order of the cell’s smallest dimension. It is also observed that geometrical confinement changes the topology of the flow, causing the turbulent kinetic energy dissipation rate and the temperature variance dissipation rate (averaged over the centre of the cell and normalized by their respective global averages) to exhibit a maximum at a certain $\varGamma $ , which roughly coincides with the aspect ratio at which the viscous and thermal boundary layers of the two opposite lateral walls merge. As a result the mean heat flux through the core region also exhibits a maximum. Unlike in the cubic case, we find that geometrical confinement of the flow results in a local balance of the heat flux and the turbulent kinetic energy dissipation rate for $Pr= 4.38$ for all values of the Rayleigh number $Ra$ (up to $10^{10}$ ), while no balance is observed for $Pr= 0.7$ . The need for very high bulk resolution to accurately resolve the gradients of the flow field at high $Ra$ is shown by analysing the second-order structure functions of the vertical velocity and temperature in the bulk of RBC. Under-resolution of the temperature field yields a large error in the dissipative range scaling, which is believed to be an effect of intermittently penetrating thermal plumes. The resolution contrast resulting from the requirement to resolve the thermal plumes and the homogeneous and isotropic background turbulence scales as $\delta _T / \langle \eta _k \rangle _{centre} \sim Ra^{0.1}$ and should therefore be taken into account when tackling very high $Ra$ . In the case studied here, under-resolution can have a significant effect on the local heat flux through the centre of the cell.
General theory of a vibrating magnetometer with extended coils

A general theory of a vibrating magnetometer pick-up system employing extended circular coils is outlined in the point magnetic dipole approximation. Systems based upon cylindrical and toroidal coils are discussed in more detail with some attention focused on the ability of the systems to measure simultaneously all components of the magnetic moment. The EMF detectability limits due to overall sensitivity, thermal noise and sample displacement are analysed for several existing and proposed coil arrangements. A Smith-type arrangement has been found which is very stable with respect to axial displacement. The tables essential for the rapid computation of the vectorial geometry factor (VGF) for arrangements composed of cylindrical coils have been compiled.
Expander Graphs and their Applications

A major consideration we had in writing this survey was to make it accessible to mathematicians as well as to computer scientists, since expander graphs, the protagonists of our story, come up in numerous and often surprising contexts in both fields. But, perhaps, we should start with a few words about graphs in general. They are, of course, one of the prime objects of study in Discrete Mathematics. However, graphs are among the most ubiquitous models of both natural and human-made structures. In the natural and social sciences they model relations among species, societies, companies, etc. In computer science, they represent networks of communication, data organization, computational devices as well as the flow of computation, and more. In mathematics, Cayley graphs are useful in Group Theory. Graphs carry a natural metric and are therefore useful in Geometry, and though they are “just” one-dimensional complexes, they are useful in certain parts of Topology, e.g. Knot Theory. In statistical physics, graphs can represent local connections between interacting parts of a system, as well as the dynamics of a physical process on such systems. The study of these models calls, then, for the comprehension of the significant structural properties of the relevant graphs. But are there nontrivial structural properties which are universally important? Expansion of a graph requires that it is simultaneously sparse and highly connected. Expander graphs were first defined by Bassalygo and Pinsker, and their existence first proved by Pinsker in the early ’70s. The property of being an expander seems significant in many of these mathematical, computational and physical contexts. It is not surprising that expanders are useful in the design and analysis of communication networks. What is less obvious is that expanders have surprising utility in other computational settings such as in the theory of error correcting codes and the theory of pseudorandomness. In mathematics, we will encounter e.g. their role in the study of metric embeddings, and in particular in work around the Baum-Connes Conjecture. Expansion is closely related to the convergence rates of Markov Chains, and so they play a key role in the study of Monte-Carlo algorithms in statistical mechanics and in a host of practical computational applications. The list of such interesting and fruitful connections goes on and on with so many applications we will not even
Theory of Long-Range Interatomic Forces. I. Dispersion Energies between Unexcited Atoms

A general theory of second-order dispersion forces between atoms in nondegenerate ground states is first developed by using an irreducible tensor formalism and the theory of angular momentum. This forms the basis for calculations of forces between excited systems. Attention is given to the interaction of two noble gas atoms where it is assumed that each electron oscillates with simple harmonic motion, and the interaction between two alkali atoms is calculated by considering the electrons to be moving in a Coulomb field. The dominant terms of the dispersion energy between a number of atoms and molecules are tabulated. The results indicate that the hitherto neglected dipole- octupole contributions are in many cases larger than the quadrupole-quadrupole terms. (auth)
Nonlinear optimization of the shape function in the finite element method when determining cutoff frequencies of waveguides of arbitrary cross section

The authors studied the k optimization process of the finite-element method when solving eigenvalue problems. The optimization process is then applied to the determination of the fundamental cutoff frequency of a waveguide of cardiodal cross section. It is shown that a considerable reduction in computer memory and/or CPU time is achieved by this process. >
Sound propagation in liquid He in impurity–helium solids

The observed features of the attenuation of ultrasound in Im–He samples created after the introduction of impurity particles (D2,N2, Ne, Kr) in a volume of helium II show that a porous substance consisting of a loosely interconnected continuous network is created. It is formed by impurity particles encapsulated in solidified helium. The propagation of ordinary sound in these porous samples is similar to the fast sound mode in light aerogels. The temperature dependence of the attenuation for different Im–He samples is investigated. It is established that the character of the attenuation in D2–He samples is considerably different from that in heavier Im–He solids (Im=N2, Ne, Kr). Analysis of the attenuation leads to the conclusion that Im–He samples have a wide distribution of pores, from 8 nm to 800 nm. The study of ultrasound in helium in Im–He samples near the λ point shows the presence of broadening in the attenuation peak as compared with bulk liquid helium. The suppression of Tc is very small, ⩽ 0.2 mK.
Accurate Atomic Data and Solar Photospheric Spectroscopy

In this review we present further requests to atomic spectroscopists for very accurate atomic data, which should "provide a new tool for the investigation of the solar atmosphere". We insist upon the necessity of using very accurate wavelengths, ionization potentials, partition functions, damping constants and transition probabilities in solar photospheric spectroscopy studies in order to refine our knowledge of the physical conditions, physical processes and abundances of the elements in the solar photosphere. In Table I, we summarize the present solar abundances of all the elements and we compare these data with the meteoritic values.
Two modified crossover and mutation operators for image segmentation by genetic algorithms

Segmentation of an image refers to partitioning the image into several subimages such that each subimage forms a connected component representing a logical entity present in the scene, and all the segments as a whole produce a meaningful interpretation of the scene being studied. The problem is inherently of NP nature and it is as hard as the simplest possible NP- complete problem called partition. Existence of the unique solution (the truly optimal segmentation) and its sensitivity to the sampling process is yet to be studied thoroughly. The formulation and implementation of a randomized search approach to segment an image, using genetic algorithms, is presented in this paper. A state space representation of partially segmented image using binary strings is considered. The dominant substrings are easily explained in terms of chromosomes. Also the operations such as crossover and mutations are easily abstracted. A modified crossover operator using boundary interaction and region adjacency graph (BIRAG) has been adopted to improve the performance. Also, a simplified mutation operator called `switch' has been devised using the BIRAG. In particular, the specific data structure used in this scheme also facilitates a means for accommodating pixel- level feed back, and model based bias for model based segmentation of images. Images from two different scenes are segmented using this approach to illustrate the applicability of such a system.
Grouping corrections and maximum likelihood equations

1. Any mention of the word ‘grouping’ immediately brings to a statistician's mind the Sheppard corrections. These are usually used to make inferences about the underlying ungrouped population from observations made on the grouped population, but it is important to realize that, as stated and proved, they have nothing to do with sampling or inference and are merely expressions for the moments of one population in terms of the moments of another population derived from it. They can only be used for the inference problem when allied to the method of moments. This method, as formulated by K. Pearson, consists in taking for θ* the estimate of the population parameter θ, the same function of the sample moments mi that θ is of the population moments μi, each mi being an estimate of the corresponding μi. If the population is grouped the mi are estimates of the , the grouped population moments, so we require θ as a function of the to apply Pearson's method. This can be done since θ is known as a function of the µi and the µi are known as functions of the by the corrections. Use of the Sheppard corrections with any other inference method, even when this method, when applied to the continuous population, yields an estimate which is a sample moment, so far as I am aware, has not been examined except for the normal curve.
Laser interferometry by induced modulation of cavity field

The field backscattered from a remote surface into the laser cavity induces an efficient modulation, both in amplitude and frequency, of the cavity field. The modulating signals are the interferometric components (sin and cos) of object optical path length, which can be recovered by heterodyne detection through a separate reference‐frequency mode. Using a dual polarization Zeeman stabilized He‐Ne laser, a compact self‐aligning interferometer is developed.
On the Power of Fisher's Combination Test for Two Stage Sampling in the Presence of Nuisance Parameters

Combination tests for p-values are used in meta-analysis and in multistage testing with adaptive designs (Bauer & Kohne, 1993). The well known combination test due to Fisher is based on the products of p-values. The power of this test applied to p-values found from stochastically independent samples at two stages of an experiment is calculated. The probability models assumed correspond to the classical t-tests for paired comparisons and parallel groups. The loss of power as compared to the optimal t-tests in the pooled sample is small even for moderate sample sizes differing over stages, however, with one exception: If in the case of parallel groups the sample sizes are substantially unbalanced over treatments, then the combination of two tests with a nonoptimal sample size allocation exaggerates the loss of power.
Structural design of broken contact doublets with prespecified aberration targets using genetic algorithm

This paper presents an implementation of a genetic algorithm in the structural design of broken contact doublets according to a prespecified set of Gaussian characteristics and primary aberration targets. The objective of this study is to investigate the effectiveness of the algorithm in finding out global as well as useful local optima and its dependence on some parameters characterizing the genetic operators. Actual glasses are taken as variables. Some illustrative examples are given.
Transfer function estimation from noisy input and output data

Two new types of bias-eliminated least-squares (BELS) based algorithms are proposed for consistent identification of linear systems with noisy input and output measurements. It is shown that estimation of the noise variances can be implemented through one-dimension over-parametrization of the system transfer function. The two modified BELS algorithms are attractive and meaningful in that noisy data are used directly in identification with no prefiltering and a direct estimate of system parameters is given without any parameter transformation. Simulation examples are included to demonstrate the effectiveness of the two proposed algorithms. © 1998 John Wiley & Sons, Ltd.
Quantum gravity and path integrals

The path-integral method seems to be the most suitable for the quantization of gravity. One would expect the dominant contribution to the path integral to come from metrics which are near background metrics that are solutions of classical Einstein equations. The action of these background metrics gives rise to a new phenomenon in field theory, intrinsic quantum entropy. This is shown to be related to the scaling behavior of the gravitational action and to the topology of the gravitational field. The quadratic terms in the Taylor series of the action about the background metrics give the one-loop corrections. In a supersymmetric theory the quartic and quadratic but not the so-called logarithmic divergences cancel to give a one-loop term that is finite without regularization. From the one-loop term one can obtain the effective energy-momentum tensor on the background metric. In the case of an evaporating black hole, the energy-momentum tensor will be regular on the future horizon. The usual perturbation expansion breaks down for quantum gravity because the higher (interaction) terms in the Taylor series are not bounded by the quadratic (free) ones. To overcome this I suggest that one might replace the path integrals over the terms in the Taylormore » series by a discrete sum of the exponentials of the actions of all complex solutions of the Einstein equations, each solution being weighted by its one-loop term. This approach seems to give a picture of the gravitational vacuum as a sea of virtual Planck-mass black holes. « less
Fabrication and evaluation of a grayscale mask for x-ray lithography using MEMS technology

We propose a new fabrication method of an x-ray grayscale mask using micro-electro-mechanical-systems MEMS technologies, and also report on successful fabrication of three-dimensional 3D mi- crostructures on a polymethylmethacrylate PMMAsheet by using only a single x-ray exposure. We showed that silicon can be diagonally etched by optimizing the etching condition in a reactive-ion-etching RIE pro- cess. It is well known that the absorbers of an x-ray mask can be made into 3-D shapes. Here, we describe how this process can be extended to fabricate an x-ray grayscale mask by using a tapered-trench-etching technique. With such a mask, we carried out experiments on x-ray lithog- raphy XRL using a beam line BL-4 in the synchrotron radiation facility TERAS of National Institute of Advanced Industrial Science and Technol- ogy AIST. The dose energy used for the exposure was 150 mA·h, and the subsequent resist development was done by a GG developer at room temperature for 16 h. The sidewalls in the upper part of the PMMA resist structure were inclined and rounded. In particular, the shape of the PMMA resist structure of the lines with 20-m width also referred as 20-m lines could be processed to achieve a halberd-like shape. Thus, the effectiveness of the grayscale mask in adjusting to the varying thick- nesses of absorber was confirmed by XRL experiments. Moreover, we showed that the final shape of PMMA resist structures after XRL was predictable by calculations. © 2008 Society of Photo-Optical Instrumentation Engi-
Ultra-Low Profile High-Gain Fabry-Perot Resonant Antennas With Fishnet Superstrate

Abstract In this paper, a new metamaterial superstrate is proposed to design an ultra-low profile and high-gain antenna. According to the theory of Fabry-Perot (F-P) resonant cavity, the F-P resonant antenna is composed of a fishnet superstrate and a printed patch antenna with a solid ground plane. By designing a negative reflection phase and a high reflection magnitude of the fishnet superstrate, we can obtain the F-P resonant antenna with a low profile. Furthermore, by optimizing the superstrate with a suitable reflection phase value, the distance between the superstrate and the patch antenna can be reduced to zero while still maintaining a high gain.
Illusion Devices with Internal or External Circular Objects Designed by the Coordinate Transformation Method

The coordinate transformation method allows to generate an illusion such that an object appears like another one, the issue being simply termed as illusion optics. It has been demonstrated numerically by the finite element method, and more recently, the practical realization was reported. Illusion devices are approached analytically in this paper for internal and external circular objects in the cylindrical coordinate system. The correlations between the three principal elements of an illusion device — the invisibility cloak, real object, and illusion object — are clearly detailed with examples. The fields are expressed analytically, and the scattering patterns are shown comparatively for the real object, illusion device, and illusion object itself.
Helicity dissipation in planar periodic geometries

Topological problems associated with magnetic merging in periodic geometries are considered. It is pointed out that although magnetic reconnection at a single site in a periodic ensemble of null points appears physically well defined, there is some difficulty in interpreting magnetic helicity. We investigate numerically the thought experiment of Berger [1997], in which he claims a periodic assemblage of flux tubes may be turned inside out in weakly resistive plasmas, thereby violating Taylor's conjecture that the helicity (or handedness) of the tubes should be approximately invariant. A concrete demonstration confirms the reversal of the flux tubes, and Berger's suggested periodic helicity measure also changes sign. We conclude that helicity is not approximately conserved in weakly resistive periodic plasmas and therefore that topological fidelity cannot be guaranteed. We go on to suggest that unlike their doubly periodic counterparts, magnetic merging experiments in singly periodic geometries may admit well-defined topological invariants.