Infinite Areas Research Articles

Transverse and Longitudinal Harmonic Wave in Layered Structure Made of Hyperelastic Materials

The purpose of paper is to analyze approximate behavior of harmonic wave propagating in a layered composite. The composite was made of materials with hyperelastic Blatz-Ko potential. Using two special cases of constitutive equation of Blatz-Ko material, it was assumed that the layers are filled alternately with foam rubber and homogenous rubber. The two extreme layers are infinite material areas separated by two layers on the lengths d1 and d2. According to the assumptions in the work it was discussed harmonic wave in the form of longitudinal and transverse acoustic wave. Numerical analysis was carried out based on the work [1] using the material constants obtained on the basis of experimental studies in works [2-4].

Statistical Distribution of the Normalized Difference Polarization Index for 3-D Layered Structures With Slightly Rough Interfaces

We determine the probability distribution of the normalized difference polarization index (NDPI) for a stack of slightly rough interfaces illuminated by a plane wave. For infinite surface areas and Gaussian-centered height distributions, we show within the framework of the first-order small perturbation method that the co- and cross-polarized NDPIs are random variables, the probability laws of which depend only on two parameters. Contrary to the intensity ratio which follows a heavy-tailed distribution, the NDPI has finite mean and variance. For a sand layer covering a granite surface and Gaussian correlation functions, we analyze the combined influence of the anisotropy and cross correlation upon the probability laws.

STATISTICAL DISTRIBUTION OF THE LAYERED ROUGH SURFACE INDEX (LRSI)

In this paper we determine the statistical distributions of the co-and cross-polarized Layered Rough Surface Index (LRSI) for three-dimensional layered structures with an arbitrary number of slightly rough interfaces illuminated by an electromagnetic plane wave. For infinite surface areas and Gaussian centered height distributions, we show within the framework of the first-order small perturbation method that the LRSI under a given observation direction is a random variable, whose statistical distribution is only function of two parameters. Contrary to the intensity ratio which follows a heavy-tailed distribution, the LRSI has finite mean and variance. For a structure air/clayey soil/rock, we analyze the influence of a snow layer upon the probability laws in the cases of Gaussian or exponential correlation functions.

The co- and cross-polarized scattered intensity ratios for 3D layered structures with randomly rough interfaces

We determine the statistical distributions for the co- and cross-polarized scattered intensity ratios characterizing three-dimensional layered structures with an arbitrary number of rough interfaces illuminated by a plane wave. Within the framework of the first-order small perturbation method, we show for slightly rough interfaces with infinite surface areas and Gaussian height distributions that the intensity ratio is a random variable, the probability law of which is a function of two parameters. For air/clayey soil/rock structures, we analyze the influence of a snow layer upon the probability laws and we validate the closed-form formulae by comparison with Monte-Carlo simulations.

Industrial Applications of SelectedJFSArticles

Industrial Applications of Selected<i>JFS</i>Articles

Coefficients of Reflection and Transmission of Transverse and Longitudinal Acoustic Wave in the Blatz-Ko Material

Abstract The purpose of this paper is to analyze the propagation of transverse and longitudinal acoustic wave in a composite made of hyperelastic Blatz-Ko material. Composite consists of a homogeneous layer of predetermined thickness d separating two infinite homogeneous material areas. In the paper it is assumed that the middle layer is filled with a homogeneous rubber (ƒ=1), whereas the external areas with foam rubber (ƒ=0). The final effect of paper are graphs of coefficients reflection of transverse and longitudinal acoustic wave, propagating in this composite.

The New Dimension in a Calendar: The Use of Different Senses and Augmented Reality Apps

Augmented reality has arrived, bringing infinite possibilities. This communication tool is applicable to any market or product and is key to understanding the new dimension that print communication is taking on. Augmented reality is capable of recreating a whole virtual universe from a print, to the point that in the not- sodistant, future, printing and augmented reality will not have reason to exist without each other. We are at a turning point, where how we communicate is changing, growing, evolving and opening up new channels of expression. Through the augmented reality applications, print communication takes on a new dimension, grows and is enriched to generate a virtual universe aimed at covering new needs in infinite areas and markets. Two parallel worlds, digital communication and print communication that now converge and are mutually enriched. This year our calendar does an about turn to offer something totally new. Month by month we have conceived a unique calendar so that each print is an exclusive and surprising experience. The prints contain different icons that tell us about new printing experiences. These icons show us whether the print is treated with augmented reality or with different textured finishes, which take printing to another dimension, interacting with our senses. Touch: Explore and discover the print, where you see this icon. Experience the possibilities we can offer through touch. SIGHT: An exclusive example of a textured finish that glows in the dark. SMELL: Find the textured surface and gently rub your finger on it. The print gives off a pleasant smell of grass.

Comment on “Why the `coarse-graining' of Wigner function is always coarse” [Opt. Commun. 178 (2000) 147

Incorrect statements and assumptions undermining the validity of the results presented in the above paper are pointed out and shortly discussed. It is stressed that a proper `coarse graining' of a Wigner phase-space distribution function cannot be in general performed over finite phase-space cells and that any `smearing' over infinite phase-space areas cannot violate the respective uncertainty relations, which furnishes an answer to the question asked in the title.

Absorption by seating and audience—Whose figures, whose measurement method?

Measuring the absorption coefficients of seating and audience is no easy matter because of the difference in size between auditoria and standard test chambers. An optimum test method remains still to be established. Two authors have published papers on this issue recently in the Journal of the Acoustical Society of America. The designer, though, is left confronted by contradicting figures and test proposals. Bradley (1992, 1996) has proposed a technique which involves measuring about five different configurations of seats to establish the absorption of infinite seat areas and absorption by the perimeter. Davies et al. (1994) deal with the perimeter absorption by testing with and without barriers placed over the front and sides of a test block of seating. Neither method is ideal; Bradley’s depends on extrapolation to the smaller ratios of perimeter to area found in real auditoria, while Davies’ method assumes that the barriers do not introduce any new problems of their own. Beranek in his new book (1996) has reanalyzed measured data from full-size concert halls to produce revised absorption figures. This paper seeks to find what common ground there is between the measurement methods and published data. It will draw on results of some tests on model seating in a model test chamber.

A contribution to shape theory for the ising model at low temperature

We consider low temperature limits of Gibbs states of the ferromagnetic nearest-neighbour Ising Hamiltonian in the positive orthant of the lattice ℤ d ,d=1, 2,..., under a negative boundary condition and a small positive external fieldh that decreases linearly with the temperatureT. It is shown that positive and negative spins are separated by a “staircase-shaped” random boundary. Its explicit distribution is computed in the case that the ratio α=h/T exceeds some positiveα0. Forα <α0, our results do not rule out infinite negative areas.

Solder Joint Formation in Surface Mount Technology—Part I: Analysis

An analytical model of solder joint formation during a surface mount reflow process is developed in the present paper, and the solution is obtained in an explicit integral form. For two limiting cases—infinitesimal and infinite solder areas—the solution is expressed in closed form. Numerical results illustrate the influence of the process parameters (surface tension, density, and cross-sectional area of the molten solder, and the contact angles between the solder andpretinning) on joint shape and overall fillet dimensions. Comparisons between theoretical predictions and laboratory data show excellent agreement.

Point-to-Point Kernel Analysis of an Experiment to Determine Wall Penetration of a Squarebased Concrete Structure by Gamma Radiation

An analysis was made of shielding data obtained from an experiment designed to determine the wall attenuation properties against residual gamma radiation of a simple 12 ft × 12 ft × 8 ft concrete blockhouse for three different wall thicknesses (48, 93.7 and 139 lb/ft2). Roof thickness was chosen so that radiation scattered through the roof could be considered negligible. A plane source was simulated by successively positioning point isotropic Co60 and Cs137 sources on the ground surrounding the structure. The experiment was designed to obtain experimental evidence for the validity of certain aspects of L. V. Spencer's Theory of Structure Shielding against Fallout Radiation as presented in NBS Monograph 42. From analysis of a total of 9700 measurements, a point-to-point kernel was developed which permits calculation of the dose rate at any point within the structure from a point isotropic source on the ground outside. Doses calculated from the kernel differ less than 10 to 50 per cent from the experimental doses, except at extreme angles of incidence where the error can exceed a factor of 2. A computer program has been written which integrates the point-to-point kernel over infinite or finite rectangular areas. The kernel was integrated over an infinite area and results were compared with those obtained from Spencer's theory. It was found that the difference in reduction factor D/D0 from ‘experimental’ point-to-point kernel data and Spencer's theory did not exceed 40 per cent. Free-field (unshielded detector) dose rates obtained from integrating the point-to-point kernel over Co60 and Cs137 infinite-plane isotropic sources have been compared with those obtained experimentally by Rex-road and Schmoke. The difference was found to be 9 and 7 per cent respectively for the Co60 and the Cs137 source fields.

Non-Euclidean Geometry

MR. FRANKLAND (NATURE, September 7) has raised the old problem of Bertrand's proof of the parallel-axiom by a consideration of infinite areas. This is perhaps the most subtle and the most specious of all the attempted proofs, and this character it owes to the fact that a process of reasoning which is sound for finite magnitudes is extended to a field which is beyond our powers of comprehension—the field of infinity. The fallacy which underlies Bertrand's proof becomes more apparent in Legendre's simpler device (“Elements de Geometrie, ” 12 ed., Note ii.). A straight line divides a plane in which it lies into two congruent parts—;this, of course, has no real meaning, since we are dealing with infinite areas, but such is the argument—;and two rays from a point enclose an (infinite) area which is less than half the whole plane. Hence, if two intersecting lines are both parallel to the same straight line, the area of half the plane can be enclosed within an area which is less than half the plane.

Note on Legendre's and Bertrand's Proofs of the Parallel-Postulate by Infinite Areas

One of the most plausible of the host of “proofs” that have ever been offered for Euclid's parallel-postulate is that known as Bertrand's, which is based upon a consideration of infinite areas. The area of the whole plane being regarded as an infinity of the second order, the area of a strip of plane surface bounded by a linear segment AB and the rays AA′, BB perpendicular to AB is an infinity of the first order, since a single infinity of such strips is required to cover the plane. On the other hand, the area contained between two intersecting straight lines is an infinity of the same order as the plane, since the plane can be covered by a finite number of such sectors. Hence if AP is drawn making any angle, however small, with AA′, the area A′AP, an infinity of the second order, cannot be contained within the area A′ABB′, an infinity of the first order, and therefore AP must cut BB′. And this is just Euclid's postulate.