Properties Of Caustics Research Articles

Anemia hemolítica causada por Ditaxis desertorum (Euphorbiaceae) em bovinos

Ditaxis desertorum Pax et K. Hoffm., planta herbácea da família Euphorbiaceae, causou experimentalmente em bovinos um quadro caracterizado por hemoglobinúria em virtude de sua ação hemolítica, quando administrada por via oral em doses diárias de 1,0 a 2,5 g/kg (planta fresca), a partir do 4° ao 8° dia do experimento. Após um período de 3 a 5 dias em que os animais tiveram hemoglobinúria e anemia acentuadas, apesar de continuarem a receber a planta (durante um total de 12 a 14 dias), em três dos quatro animais esses sintomas desapareceram. Verificou-se nesses casos uma rápida recuperação dos valores hemáticos logo que cessou a hemoglobinúria. O quarto bovino, que recebeu 2,5 g/kg/dia durante 5 dias, morreu no 8° dia, tendo apresentado durante os últimos 4 dias de vida hemoglobinúria e anemia acentuadas. À necropsia e nos exames histopatológicos deste animal foram verificadas nefrose hemoglobinúrica e distrofia hepática com necrose centrolobular do parênquima. Dose de 7,7 g/kg única ou quantidades de 2,5 e 3 g/kg/dia administradas durante 2 dias seguidos, causaram em três outros bovinos quadro clínico de cólica, com morte em questão de horas, verificando-se à necropsia acentuado edema da parede do rúmen e do retículo. Pelos históricos obtidos somente ocorre, sob condições naturais, a intoxicação caracterizada pelo quadro da anemia hemolítica, indicando que possivelmente a ingestão de D. desertorum em quantidades necessárias para causar o quadro com lesões dos proventrículos ser, apesar de sua boa palatabilidade, autolimitada pelo efeito cáustico da planta.

Light caustics of hydrodynamic solitons illuminated by a laser beam

Properties of caustics of plane curves are used for interpretation of optical experiments with hydrodynamic solitons in a one-dimensional water channel. The water-free surface acts as a curvilinear plane mirror for incoming light beams. Experiments with single solitons and with couples of colliding solitons are presented and discussed within the framework of geometrical optics.

Properties of caustics of a plane curve illuminated by a parallel light beam

A geometric procedure allowing graphical construction of the caustic of a plane curve (2D mirror) illuminated by a parallel light beam is reminded. A new geometric variational criterion is given to determine the position of caustic regression points. Parametric equations of the caustic in an arbitrary cartesian coordinate system are calculated. It is proved that the loci of foci corresponding to different slopes of the incident beam form a regular curve.

Ammonia-water volcanism on icy satellites: Phase relations at 1 atmosphere

Icy satellites exhibit an amazing variety of terrains, many of which were formed by extrusions of aqueous solutions. Aqueous ammonia has been implicated on the basis of theoretical and morphological evidence as a probably cryovolcanic agent on some resurfaced icy satellites. Considering the solvent and caustic properties of ammonia-water (pH up to 13) with respect to chondritic rock, and that many other ammonia-water-soluble substances are probably present in satellite ices, it is unlikely that ammonia-water magmas would be pure. Comets and carbonaceous chondrites represent two possible components of icy satellites. Several comets contain ∼ 1 to several percent each of methanol, formaldehyde, and carbon dioxide relative to water, and C1 and C2 carbonaceous chondrites contain up to 10% magnesium sulfate. Carbon dioxide, magnesium sulfate, and formaldehyde sequester ammonia as ammonium carbonate, ammonium sulfate, and the organic salt hexamethylenetetramine (HMT). If these reactions leave excess ammonia, the resulting ices may include water ice, ammonia dihydrate, and methanol monoammoniate in addition to the reaction salts. This mixture melts near 153 K yielding an extremely viscous solution of water, ammonia, methanol, and small amounts of salts. This liquid may resemble the viscous lavas extruded on Triton, Ariel, and Miranda. However, if these reactions sequester all available ammonia, or if ammonia was not initially present in an icy satellite, then melting produces comparatively low-viscosity, ammonia-deficient saline or methanol solutions. Formation of ammonia-rich liquids is possible only if the molar abundance of ammonia N NH3 > (2N CO2 + 2N MgSO4 + sol2 3N H2 CO ) . For instance, direct melting of pure Comet Halley, even though it may contain some ammonia, probably would not yield an ammonia-water liquid. Sulfur-and carbon-bearing constituents in ammonia-water lavas would alter to spectrally important chromophores on irradiated satellite surfaces, possibly explaining geologically correlated variations in the colors and albedos of icy satellites. Many cryovolcanic surfaces have nearly uniform spectrophotometric properties and may be explained as compositionally invariant eutectic or peritectic mixtures. Other cryovolcanic terrains have stark color and albedo contrasts and may be explained as compositionally distinct melt products. Small but important quantities of dissolved potassium-and rubidium-bearing salts are probably sufficient for isotopic dating.

Semiclassical theory of direct and deep inelastic heavy ion collisions

A sufficiently simple approach is formulated for the quantitative description of direct and multi-step processes in heavy ion collisions with arbitrary (not only small) mass, energy, and angular momentum transfer. The simplification is achieved owing to the use of semiclassical description of the colliding particles relative motion. The semiclassical approximation is used for the three-dimensional (not partial) distorted waves with accounting of all caustic properties, and the channel coupling is simulated by the dissipative forces. The transition amplitude is reduced to the one-dimensional integral along the so-called “transition lines” where the inelastic process is localized. The comparison is done with the experimental data and with exact calculations of some direct reaction cross sections. Heavy-ion-induced multi-step (quasidirect) massive transfer processes with the fast light particle formation are analyzed.

The regular prismatic bar under torsion: A new approach based on caustics

A new approach to the general torsion problem of the regular prismatic bar was introduced, based on extensive and meticulous experimental evidence, indicating that the twisted prismatic bars, except the cylindrical ones, present, a longitudinal warping, following a sinusoidal type of curves for the warping displacements with their extrema displaced towards the corners. As a guide for the establishment of the method the solutions of the elliptical and the equiangular triangular bars were used. It was found that the regions inside the inscribed circles tangent to the sides of their undeformed cross-sections constituted regions whose warped surfaces constitute undulated forms following sinusoidal surfaces. This property was proved exact for the exact solutions for the elliptic and triangular cross-sections and it is assumed by induction valid for any regular cross-section. Comparing the warping displacements along the inscribed circle to a square or regular polygon cross section with the classical Timoshenko solution for the square bar it was found an exact coincidence in these displacements. It was further shown that these circles and all concentric full circles constitute the initial curves of the caustics formed from reflections of the warped cross-sections of the twisted bars. The differences between the stresses and displacements between the existing approximate solutions and the new approach appear in the partly curved triangles lying outside the inscribed circles. For the square cross-section it was shown that thew-displacements between Timoshenko's solution and the present one were less than 5 percent. Experimental evidence with the Moire method and comparison with the exact solution for the equiangular triangular cross section proved that the present approach is closer to reality and therefore presents higher accuracy than any approximate method. Furthermore, it presents the advantage that the full circles inscribed inside the cross-section constitute the initial curves forming caustics in space when a parallel light beam is reflected on the warped cross-section of the twisted bars. interesting properties of caustics, proved in this paper, help down-rightly for a thorough study of the form and properties of the twisted bars.

Gravitational waves in general relativity - XIII. Caustic property of plane waves

We study the effect of a plane gravitational wave of limited duration (‘sandwich wave’) on an infinite set of test particles at relative rest. We prove, at least for waves of fixed polarization, that all the particles strung out in a certain direction will collide after a finite time that is independent of how far apart they were originally. This we call the caustic property. The effect of the wave on null geodesics is such that this phenomenon does not require any particle to move faster than light. Indeed, an observer who has passed through such a wave will within a finite time have seen an infinite spatial volume lying in a space-like half­ hyperplane on the other side of the wave. For a certain (‘bicaustic’) type of wave the whole of that half-hyperplane will have become visible.

Definition of the crack tip as the center of the caustic

The optical caustics developed around singularities in elastic stress fields have usually the shape of generalized epicycloids. The most important caustics in the praxis are created around singularities at crack tips submitted to various types of loading. In this paper an exact geometric construction is presented for defining the exact position of the center of the caustic which coincides with the crack tip. The method based on the properties of caustics is superior to any other approximate method based on hybrid mathematical procedures using data from experiments and defining the centers by elaborate solutions.

The thick gravitational lens - A lens composed of many elements at different distances

view Abstract Citations (64) References (40) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Thick Gravitational Lens: A Lens Composed of Many Elements at Different Distances Kovner, Israel Abstract This paper presents a theory of transparent gravitational lenses in the Newtonian limit (the perturbations of the gravitational field by mass inhomogeneities in the universe are assumed weak both on the cosmological and on local scales). In a partially evacuated cosmic "bottle" the light-ray trajectory is derived in a simple manner, suitable for use in a lens theory. The theory is presented in a simple form, applicable to single-redshift as well as to multiredshift lenses. The simplified case of a "nonlinear telescope", composed of many elements at different distances, is analyzed in detail. The universal properties of caustics of an almost spherical lens with a weak quadrupole (tidal) component are analyzed. Publication: The Astrophysical Journal Pub Date: May 1987 DOI: 10.1086/165179 Bibcode: 1987ApJ...316...52K Keywords: Gravitational Lenses; Relativity; Astronomical Models; Gravitation Theory; Quasars; Astrophysics; COSMOLOGY; GALAXIES: GENERAL; GRAVITATION; QUASARS; RELATIVITY full text sources ADS |

Caustics and focusing produced by sedimentary basins: applications of catastrophe theory to earthquake seismology

Summary. As high-frequency elastic waves propagate through real media, it is common for caustics and focusing to occur. Typically, rays may envelop a caustic surface in space, or exceptionally they may all coalesce at a focal point. In strong motion seismology, the observed large fluctuations in peak acceleration and intensity of ground shaking may just be a consequence of focusing and caustics created by waves propagating through irregularly shaped sedimentary basins. These basins, acting as deformed optical lenses, are capable of producing a complex network of patches and seemingly isolated pockets of intensified damage or high intensity shaking where the caustic intersects the ground surface. We adapt methods from optics and catastrophe theory to study the properties of caustics induced by typical sedimentary basins. Several hypothetical examples are shown that reflect the fact that these properties are useful to assess quantitatively the degree of wavefield amplification to be expected. A good correlation is found between actual damage patterns and caustic locations computed for the Caracas, Venezuela earthquake of 1967.

Caustics in Extended Euclidean Space

This paper is one of a series in which the authors investigate genericity properties of caustics by reflexion from smooth mirrors. Here, the mirror is a smooth surface in $\mathbb{R}^3 $, and two related problems are considered: (1) what is the form of the caustic at infinity (the caustic in the “far field”), generically, with a finite light source; (2) what is the form of the caustic generically when the light source is at infinity? For (1) both “mirror genericity,” where deformations of the mirror are allowed, and “source genericity,” where only the source may be moved, are considered. With some assumptions on M it is shown that the caustic can be made generic in either of these two ways. (In the latter case, only a local result is proved.) For (2), only mirror genericity is considered, and it is shown that there is an obstruction to proving a result of this kind, caused by an inherent lack of genericity in wavefronts arising from parallel light reflected from a mirror in $\mathbb{R}^3 $. It is proved, ...

Generalized Curvilinear Diffraction Gratings: II. Generalized ray equations and caustics

This paper is the second in a series [1] of papers on the diffraction and imaging properties of generalized curvilinear diffraction gratings. In this article, a set of generalized ray equations is derived and applied to the calculation of the caustic properties of generalized gratings. No restriction is placed on the form of the ruling pattern or on the shape of the grating surface. For generalized uncrossed and off-axis plane gratings, the ruling pattern may be regarded as a contour map of some abstract surface. In this case, it is shown that the far-field caustic properties of the grating are determined by the regions of vanishing gaussian curvature on the abstract surface. As an application of the theory, a new method for laser material processing is discussed.

Some further properties of caustics useful in mechanical applications

The caustics created from reflections of light rays at the vicinity of stress singularities and other stress concentrations in an isotropic and elastic plate submitted to a plane-stress mode of deformation yield important information concerning the order of singularity of the stress intensity or concentration factor at these particular points of a stress field. All information was extracted from particular measurements of the longitudinal or transverse diameters of the caustics, based on basic properties of caustics. In this paper some further properties were found, which are very useful in evaluating the stress field creating the caustic, which make the respective measurements independent of the angle of orientation of the caustic and more reliable than previously.

Nutrition and gastric cancer.

Gastric cancer (Gc) is generally conceived as having a multifactorial origin. Different genetic factors, soil, nutritional and socioeconomic factors have all been mentioned in the literature as possible causes. Further research on the causation of Gc has, in fact, been hampered by the large number of hypotheses. A strong geographic association between gastric cancer and stroke mortality was found by chance in 1964; this association could be spurious, but the quantitative analysis of the data showed similar relationships both between countries and within countries (e.g., in countries as different as the US and Japan), a very unlikely situation if due to chance. The same quantitative relationship was maintained using multiple regression analysis of stroke mortality. All this was observed for each sex separately and for both sexes combined. The working hypothesis was set forth in 1965 that salt intake was the predominant linking factor for both types of mortality. Stroke would then be influenced by the relationship between salt and blood pressure; Gc would result from the delaying and caustic properties of a hypertonic stomach content. The latter condition could produce atrophic gastritis, a common problem in Japan, Chile and Columbia. Atrophic gastritis favors the synthesis of endogenous nitrites and, henceforth, of nitroso-carcinogens. The salt hypothesis can give an explanation for the geographical and time behavior of Gc and stroke mortality and for the socioeconomic gradient of both diseases. Gc mortality can also be used to provide a rough estimate of the salt intake in a given country and year. The hypothesis was tested in Belgium through a deliberate attempt to lower the salt intake of the population. The observed decreases in Gc and stroke mortality were consistent with the measured decrease in salt excretion. Further research is urgently needed through the monitoring of 24-hour salt and creatinine excretion in different countries and over many years.

Nutrition and gastric cancer.

Gastric cancer (Gc) is generally conceived as having a multifactorial origin. Different genetic factors, soil, nutritional and socioeconomic factors have all been mentioned in the literature as possible causes. Further research on the causation of Gc has, in fact, been hampered by the large number of hypotheses. A strong geographic association between gastric cancer and stroke mortality was found by chance in 1964; this association could be spurious, but the quantitative analysis of the data showed similar relationships both between countries and within countries (e.g., in countries as different as the US and Japan), a very unlikely situation if due to chance. The same quantitative relationship was maintained using multiple regression analysis of stroke mortality. All this was observed for each sex separately and for both sexes combined. The working hypothesis was set forth in 1965 that salt intake was the predominant linking factor for both types of mortality. Stroke would then be influenced by the relationship between salt and blood pressure; Gc would result from the delaying and caustic properties of a hypertonic stomach content. The latter condition could produce atrophic gastritis, a common problem in Japan, Chile and Columbia. Atrophic gastritis favors the synthesis of endogenous nitrites and, henceforth, of nitroso-carcinogens. The salt hypothesis can give an explanation for the geographical and time behavior of Gc and stroke mortality and for the socioeconomic gradient of both diseases. Gc mortality can also be used to provide a rough estimate of the salt intake in a given country and year. The hypothesis was tested in Belgium through a deliberate attempt to lower the salt intake of the population. The observed decreases in Gc and stroke mortality were consistent with the measured decrease in salt excretion. Further research is urgently needed through the monitoring of 24-hour salt and creatinine excretion in different countries and over many years.

On Caustics and Singularities in General Relativity

AbstractComparing gravitational converging effects with self‐focussing and lense effects in ordinary optics, we consider some physical properties of caustics in General Relativity. The resulting relations between geometrical and physical features of caustics are used to discuss the power asymptotes of homogeneous cosmological models in more detail.

Intensity, slope and curvature discontinuities in loading distributions at the contact of two plane bodies

The optical method of caustics was used for the evaluation of intensity, slope and curvature discontinuities of the most general load distribution along a straight boundary in a semi-infinite plane simulating the elastic contact of two bodies under conditions of generalized plane stress. The load distribution was assumed as composed of normal as well as tangential loads. A simple procedure based on the geometric properties of caustics formed at the vicinity of such discontinuities in loading was developed, which yielded all the necessary information for the evaluation of such discontinuities. Interesting properties related to the shape, position and orientation of the caustics were established. Thus, a simple experimental procedure was developed for measuring the influence of friction along the contact area of two bodies.

Properties of caustics from conic reflectors 1: Meridional rays

General relations for the caustic surfaces obtained by illuminating an ellipsoid, paraboloid, or hyperboloid reflector by a point-light source, lying along the principal axis of the reflector, were derived. A thorough study of the evolution of caustics with the particular type of reflector, as well as with the relative position of the point-light source and the reflector, was undertaken. Interesting laws for the shape, position, and properties of the caustics were derived, depending on the shape of the particular reflector used, its aperture, and the relative position of the light source and the reflector. These properties may be useful for the creation of wide angle all-reflective multimirror systems designed for definite limits of distances and which, by adjacent pairs of reflectors, present only a limited and reduced amount of third-order aberrations.

Postmortem Bile Damage to Rainbow Trout (Salmo gairdneri) Livers

Peripheral liver necrosis in rainbow trout (Salmo gairdneri) was shown to result from pre- or postmortem exposure to bile. Accidental spillage of bile onto the liver during sampling or intentional submersion of liver tissue into bile resulted in a time-dependent destruction of liver tissue. Awareness of this caustic property of bile should prompt extreme care in the collection of trout livers for histology.

Upper digestive tract burns caused by Denalan denture cleanser powder.

Denture cleansers are ubiquitous compounds frequently found in the household. Severe oral cavity burns were clinically observed in a two-year-old female who accidentally ingested a denture cleanser powder, Denalan. Experimental studies were carried out to investigate the caustic, chemical and histopathological properties of this compound. Denalan was found to be a powerful alkali agent which caused severe upper digestive tract burns.