Quantitative Laws Research Articles

Modified Beer's Law – historical perspectives and relevance in near-infrared monitoring of optical properties of human tissue

Studying the interaction of light with human tissue is important in understanding functional changes and oxidative metabolism of tissue (e.g., skeletal muscle, brain). This manuscript focuses on the development of quantitative absorption laws of light energy, from the inception of Bouguer Law to Beer's Law, to gain a perspective on the present application of the absorption concepts in investigating optical properties of light absorbing chromophores of human tissue. Although these absorption laws are applicable to determine the absolute concentration of substances present in solids or solvents, these laws do not take into consideration of either reflection or scattering of incident light that accounts for the loss of transmitted light intensity. Importance of light energy in the near-infrared window of 700–1300 nm compared to that of other regions in the electromagnetic spectrum for determination of optical tissue properties in vivo is emphasized. Since human tissue is a highly scattering non-homogenous medium, limitations of Beer's Law with respect to studying human tissue chromophores are presented. Finally, modifications of Beer's Law to investigate the relationship between changes in absorbency and concentrations of light absorbing chromophores within the medical spectral window (700–900 nm) in human tissue are discussed. Relevance to industry As light propagates through human tissue, concentration of some chromophores varies in time within the medical spectral window, implying physiological changes in the tissue. Utilization of this optical principle in biomedical (non-invasive) research of the health and disease of human tissue has increased in the last two decades. While impressive in clinical applications, researchers in the field of ergonomics and human factors have been slow in exploiting the potential of examining optical properties of tissue relevant to human performance at the workplace.

Experimental Investigation on the Heterogeneous Kinetic Process of the Low Thermal Decomposition of Ammonium Perchlorate Particles

AbstractThe thermal decomposition of ammonium perchlorate has been extensively studied in the past. Nevertheless, the various results published illustrate, on the one hand, significant differences regarding the influence of different parameters on the decomposition and on the other hand, a lack of useful quantitative laws to predict the thermal behaviour of this crystal under a range of conditions (temperature, duration of exposure, presence of confinement).

From Universal Laws of Cognition to Specific Cognitive Models

The remarkable successes of the physical sciences have been built on highly general quantitative laws, which serve as the basis for understanding an enormous variety of specific physical systems. How far is it possible to construct universal principles in the cognitive sciences, in terms of which specific aspects of perception, memory, or decision making might be modelled? Following Shepard (e.g., 1987), it is argued that some universal principles may be attainable in cognitive science. Here, 2 examples are proposed: the simplicity principle (which states that the cognitive system prefers patterns that provide simpler explanations of available data); and the scale-invariance principle, which states that many cognitive phenomena are independent of the scale of relevant underlying physical variables, such as time, space, luminance, or sound pressure. This article illustrates how principles may be combined to explain specific cognitive processes by using these principles to derive SIMPLE, a formal model of memory for serial order (Brown, Neath, & Chater, 2007), and briefly mentions some extensions to models of identification and categorization. This article also considers the scope and limitations of universal laws in cognitive science.

Reflexiones sobre la procedencia y evolución del “ritmo” en la monodia litúrgica y polifonía medieval (I)

El escrito presenta unas “reflexiones” sobre el ritmo y metro en la monodia litúrgica y polifonía medieval, surgidas del contacto con fuentes musicales históricas al interpretar la “música antigua”. La investigación histórica de la notación musical, desde el siglo XIX, fundándose en teóricos mensuralistas del XIII, ha centrado principalmente la atención en el estudio y aplicación “tajante” de leyes métrico-cuantitativas a las figuras musicales (mensura certa), dejando un tanto marginadas otras posibles normas basadas en el acento o impulso del idioma (peso, apoyo, “ritmo oratorio”, “mensura non certa”, “numerose canere”), más difíciles de formular “matemáticamente”. Es muy difícil definir o establecer fronteras entre metro y ritmo. San Agustín decía que “el ritmo es el alma del metro” y que “todo metro es ritmo, pero no todo ritmo es metro”. Este trabajo reflexiona sobre diversas circunstancias, que pudieron condicionar el estudio de las antiguas notaciones europeas, en el siglo XIX, y sobre la necesidad de volver la mirada hacia antiguos escritores griegos y latinos, que pudieran iluminar el problema.

Buckling instabilities of subducted lithosphere beneath the transition zone

A sheet of viscous fluid poured onto a surface buckles periodically to generate a pile of regular folds. Recent tomographic images beneath subduction zones, together with quantitative fluid mechanical scaling laws, suggest that a similar instability can occur when slabs of subducted oceanic lithosphere encounter enhanced resistance to penetration at 660 km depth. Beneath subduction zones such as Central America and Java, the fast anomalies in elastic wavespeed are too broad (≥400 km) to be explained by simple compressional thickening of subducted lithosphere that is initially 50–100 km thick. By contrast, a periodic buckling mechanism can account for both the characteristic ‘wedge’ shapes of the anomalies and for their widths, which agree closely with those predicted by the scaling laws. In addition to providing a plausible physical interpretation of tomographic observations beneath some subduction zones, buckling instabilities have important consequences for other aspects of global geodynamics such as tectonic plate reconstructions, interpretation of geoid anomalies, and modeling of secular changes in Earth's moment of inertia.

Urgent problems of groundwater quality

The book under review is a fundamental study of important problems of present-day hydrochemistry and hydrogeology. One of these is the problem of the quality of groundwater used for drinking. It is solved with the use of the up-to-date methods of physicochemical modeling of geochemical processes. The authors reasonably assume these processes to be governed by the quantitative laws of exact basic sciences (physics and chemistry), while the ambient geological environment determines the boundary conditions for the implementation and proceeding of these processes. This is the basis the authors use to carry out an important generalization of the geochemical properties of the standardized elements and substances and summarize everything that is needed to assess the quality of groundwater used for drinking water supply. The geochemistry of the elements Be, Sr, Cu, Pb, Hg, Ra, Ru, Al, P, S, As, Se, Cr, Mn, F, Mo, Fe, Co, and Ni and toxic substances such as phenols, dioxins, pesticides, surfactants, various oil products, and others in groundwater is considered in detail. The analysis of their geochemistry is based on the present-day notions of their migration forms in groundwater and changes in these forms depending on changes in the geochemical environment. The problems of assessment of groundwater quality and its medical‐ecological state cannot be solved without the use of the migration forms of chemical elements. A special theoretical chapter of the book is devoted to the formation of the migration forms of elements in various geochemical types of groundwater.

The Impact of Mechanical Defects on the Reliability of Solar Cells in Aerospace Applications

A stable supply of electrical power is crucial for the success of space missions. Photovoltaic arrays are the most common means of in-orbit energy generation. Mechanical solar cell defects have the potential to impact their reliability considerably. In order to address this question, the environmental loads encountered in space were simulated experimentally. Five miniature solar arrays, featuring a total of ap200 cells with representative mechanical defects, were built and subjected up to 12 000 simulated eclipse phases. ap400 cell cracks on actual flight panels were monitored throughout sine vibration and acoustic noise testing to cover the mechanical loads during launch of a solar array. Electroluminescence imaging and pulsed solar simulator measurements were used to record crack patterns, to track their evolution and to quantify their electrical impact. The original size of the crack and the number of thermal cycles were identified as the main factors that determine crack growth. The number of crack growth events (CGE) per cycle was found to follow a power law dependence with an exponent of -0.85 on the number of thermal cycles and the total number of CGE accumulated over 2000 cycles showed a linear dependence on the size of the crack. A preferential crack growth direction along the short cell edge was found and attributed to the particular coupling between the cells and their carbon fiber support structure. Sine vibration and acoustic-noise testing did not result in any crack propagation. The electrical impact of mechanical defects originated predominantly from the interruption of the contact network on the cell front side. Cell area is electrically isolated either by a propagating crack that separates the singular electrical connection of a particular area, or along the original path of the crack. The quantitative laws derived allow to predict the propagation and the electrical impact of a given mechanical defect during 15 years in a geostationary-orbit environment

ACTIVE WALKS: THE FIRST TWELVE YEARS (PART II)

Active Walk (AW) is a paradigm for self-organization and pattern formation in simple and complex systems, originated by Lam in 1992. In an AW, the walker changes the deformable landscape as it walks, and is influenced by the changed landscape in choosing its next step. Active walk models have been applied successfully to various biological, physical, geological and economic systems from both the natural and social sciences. More recently, it has been used to model human history. In Part I of this review, the birth of the AW paradigm, its basic concepts and formulations, a solvable two-site model, and the experiments and AW modeling of surface-reaction filamentary patterns are presented. Part II here continues with properties of AW, and applications of AW in nonliving and living systems — including those from the social sciences and human history. (In particular, unsuspected quantitative laws and a prediction about the Chinese history are given.) A comment on the relationship between physics, social science and complex systems is provided. The review concludes with open problems in the form of workable research projects and general discussions.

Geometric modeling of force equilibria in crystals: the “equal distance – equal force” formalism (EDEF)

Abstract For a broad class of symmetric compounds a formalism is presented which allows detection and proof of physical force equilibria on the basis of purely geomet ric considerations. To represent the atomic interactions be tween structural fragments, the traditional concept of coor dination is generalized by means of the Cartesian product of the sets of atomic coordinates of the fragments. If the physical forces between the atom pairs in the generalized coordination shells are of the same kind, translational and rotational equilibrium between fragments can be read from the geometric directions of the interactions rather than from quantitative physical laws. Partial force equilibrium, as a weaker notion of total force equilibrium, opens up a way to qualitative considerations of dynamic phenomena. Here the basic concepts of this “EDEF model” are defined and il lustrated. We also study the relationship between the EDEF formalism and the underlying symmetry and prove condi tions which are sufficient to conclude EDEF equilibria from the common symmetry elements of the fragments involved. The geometric model enables us to consider the structure of crystals from the point of view of their inner forces.

Two New Practical Models for Estimating Reliability-Based Fatigue Strength of Composites

This paper outlines two new practical models to evaluate fatigue residual strength and the overall range of life for reliability-based design. A new fatigue-driven residual strength surface model with four parameters is derived based on an expression form of power function product to estimate the parameters more easily and expediently, and logically characterize the physical characteristics and the phenomenological quantitative laws. A more appropriate S-N curve formulation with four parameters is presented to cover overall life range. By means of the likelihood principle and the linear regression, the parameter determination formulae of these two models are respectively established to deal with the test data effectively and easily. The probability distributions for these two models are also given. Finally, the models are applied to two sets of experimental data, demonstrating the practical and effective use of the proposed models. It is shown from these examples that fatigue-driven residual strength and the overall range of life can be obtained realistically according to the small sample test data using the new formulae.

The Quantitative states laws in mechanics of fracture

The analisis of energetical critcrions was made in mechanics of fracture. The generalized energetical Law of quantitative state of material was offered, which allows to create energetical criterions of quantitative state of material in separate cans

Computational gestalts and perception thresholds

In 1923, Max Wertheimer proposed a research programme and method in visual perception. He conjectured the existence of a small set of geometric grouping laws governing the perceptual synthesis of phenomenal objects, or “gestalt” from the atomic retina input. In this paper, we review this set of geometric grouping laws, using the works of Metzger, Kanizsa and their schools. In continuation, we explain why the Gestalt theory research programme can be translated into a Computer Vision programme. This translation is not straightforward, since Gestalt theory never addressed two fundamental matters: image sampling and image information measurements. Using these advances, we shall show that gestalt grouping laws can be translated into quantitative laws allowing the automatic computation of gestalts in digital images. From the psychophysical viewpoint, a main issue is raised: the computer vision gestalt detection methods deliver predictable perception thresholds. Thus, we are set in a position where we can build artificial images and check whether some kind of agreement can be found between the computationally predicted thresholds and the psychophysical ones. We describe and discuss two preliminary sets of experiments, where we compared the gestalt detection performance of several subjects with the predictable detection curve. In our opinion, the results of this experimental comparison support the idea of a much more systematic interaction between computational predictions in Computer Vision and psychophysical experiments.

Simultaneous generation of hotspots and superswells by convection in a heterogeneous planetary mantle

Mounting evidence indicates that the Earth's mantle is chemically heterogeneous. To understand the forms that convection might take in such a mantle, I have conducted laboratory experiments on thermochemical convection in a fluid with stratified density and viscosity. For intermediate density contrasts, a ‘doming’ regime of convection is observed, in which hot domes oscillate vertically through the whole layer while thin tubular plumes rise from their upper surfaces. These plumes could be responsible for the ‘hot spots’ and the domes themselves for the ‘superwells’ observed at the Earth's surface. In the Earth's mantle, the doming regime should occur for density contrasts less than about 1%. Moreover, quantitative scaling laws derived from the experiments show that the mantle might have evolved from strictly stratified convection 4 Gyr ago to doming today. Thermochemical convection can thus reconcile the survival of geochemically distinct reservoirs with the small amplitude of present-day density heterogeneities inferred from seismology and mineral physics.

Biological grand universality and its physical challenge

Presented quantitative laws of metabolism, mortality and evolution are valid for animals from bacteria to mammals and demonstrate grand universality in biology. Its microscopic origin may be a physical and mathematical challenge. Natural evolution is accurately reduced to the continuous one, “weak” and “strong” Gould-Eldredge spurts. The discovery of writing, i.e. non-genetic, long range, collective information transfer from generation to generation with human rather than natural selection, leads to post-evolution. Technological post-evolution is exponentially rapid and may lead to the extinction of a civilization. This might resolve the Fermi-Hart paradox: if extra-terrestrial intelligence exists, why it cannot be contacted?

"More Men than Corn": Malthus versus the Enlightenment, 1798

“More Men than Corn”: Malthus versus the Enlightenment, 1798 Rudolph Binion (bio) “More men than corn is a fearful pre-eminence”: this pithy truth was uttered by Mr. Fax, a facsimile of Malthus in Thomas Love Peacock’s spoof Melincourt of 1817. Malthus himself in An Essay on the Principle of Population of 1798 posited that “fearful pre-eminence” in pseudomathematical terms as an insuperable fact of nature. “I think I may fairly make two postulates,” he claimed in that philosophical shocker. “First, That food is necessary to the existence of man. Secondly, That the passion between the sexes...will remain nearly in its present state” as far as can be foreseen. 1 And on the strength of these postulates he pursued: “Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio.” 2 [End Page 564] Nor was this predicament peculiarly human: “Through the animal and vegetable kingdoms, nature has scattered the seeds of life abroad with the most profuse and liberal hand. She has been comparatively sparing in the room and the nourishment necessary to rear them...Necessity, that imperious all-pervading law of nature, restrains them within the prescribed bounds. The race of plants and the race of animals shrink under this great restrictive law. And the race of man cannot, by any effort of reason, escape from it. Among plants and animals its effects are waste of seed, sickness, and premature death. Among mankind, misery...is an absolutely necessary consequence.” 3 To this “absolutely necessary consequence” among mankind, “misery,” Malthus in his Essay of 1798 allowed a single alternative, namely “vice,” by which he appears to have meant infanticide, abortion, and—equally abhorrent to him—intentionally sterile sex. 4 By “misery” itself he meant both what he called the “positive checks” on the “power of population”—primarily malnutrition or outright starvation, secondarily pestilence and warfare—and what he termed the “preventive check,” or “every the slightest check to marriage” for economic reasons. 5 In 1803 he published a second, revised Essay on the Principle of Population that promoted the “preventive check,” now renamed “moral restraint,” as a lesser, virtuous misery. His euphemistic definitions and classifications were fuzzy and slippery in the second Essay as in the first, and right through all its further editions, the last of them dated 1826. 6 For its part, his law of the geometric as against the arithmetic progression held steady until the last reedition inclusive, with its assumption of a mankind perpetually overbreeding and hence agonizing out of a barely and rarely resistible animal craving to copulate however miserable the consequences. Reducing human behavior to laws of nature expressible in mathematical terms was a common ambition of the philosophes throughout the Enlightenment, overawed as they were by the example of the natural scientists of the seventeenth century who had seemingly reduced all physical phenomena to a few simple and elegant mathematical formulae—or rather, who had purportedly detected those simple and elegant formulae encoded in nature. Attempts by humanists to frame such nifty basic laws in their own moral province—or, as they hoped, to discern them there—had ranged from dubious mimicry to meretricious analogy. For dubious mimicry of the quantitative laws of physical science, Jeremy Bentham’s “Moral Arithmetic” is hard to beat, with its reduction of right and wrong to sums of pleasure and pain. As for meretricious analogies between physical and moral law, one of my favorites is Alexander Pope’s reconciliation of self-serving with benevolence in human nature: “On their own axis as the planets run, / Yet make at once their circle round the sun: / So two consistent motions act the soul; / And one regards itself, and one the whole.” 7 Another of my favorites is a rationale for reciprocity in ethics which Immanuel Kant tucked away in a footnote half a century later: “I never can do anything to another man without giving him a right to do the same to me on the same conditions; just as no body can act with its moving force on another body without thereby causing the other to react equally against it.” 8 As for Malthus’s pseudomathematical “principle of population,” it...

Infinitesimal Steps

Reasoning with the Infinite From the Closed World to the Mathematical Universe. Michel Blay. University of Chicago Press, Chicago, 1998. 226 pp. $30, £25.95. ISBN 0-226-05834-4. The French historian Blay's examination of the emergence of a mathematical physics (the analysis of nature in terms of quantitative laws that allow predictions based on mathematical reason) focuses on lesser known figures (Fontenelle, Wronski) rather than on the more successful efforts of more influential practitioners (Euler, Lagrange, Laplace, Cauchy).

Nouvelles réflexions sur les lois qualitatives du monde végétal et leur valeur heuristique

Summary As in quantitative laws of classic physics, the qualitative laws of the vegetal world (botany, plant sociology) constitute preferential bridges between some areas a priori without report (flora, vegetation on one hand, ecology, geography, dynamics…on the other hand). One gives an inventory of these multiple laws and one shows how it is possible to use them to acquire various informations from limited data. These laws have therefore a high heuristic value, intervening for example in the elaboration of synsystematic keys and in «paleo-plant sociology».

Discovering dynamics: From inductive logic programming to machine discovery

Machine discovery systems help humans to find natural laws from collections of experimentally collected data. Most of the laws found by existing machine discovery systems describe static situations, where a physical system has reached equilibrium. In this paper, we consider the problem of discovering laws that govern the behavior of dynamical systems, i.e., systems that change their state over time. Based on ideas from inductive logic programming and machine discovery, we present two systems, QMN and LAGRANGE, for discovery of qualitative and quantitative laws from quantitative (numerical) descriptions of dynamical system behavior. We illustrate their use by generating a variety of dynamical system models from example behaviors.

The performance of light stabilizers in accelerated and natural weathering

The performance of different classes of light stabilizers is compared in polyolefins. The evolution of stabilization in the past quarter century is illustrated with data generated with polyolefin tapes, multifllaments, films and plaques. The state-of-the-art, based on combinations of light stabilizers, mainly combinations of hindered amine light stabilizers (HALS) is discussed. The light stability data are generated either in various accelerated weathering devices or outdoors in various climates. Correlation between the various accelerated devices on the one hand and between accelerated and natural weathering data on the other hand was the subject of many publications. It is still one of the major problems encountered in assessing the durability of plastic materials for outdoor use. It is found that, even with adequate precautions concerning the light source and its intensity as well as sample temperature, correlation between natural and artificial weathering is the exception rather than the rule. Therefore, another model for lifetime forecasting is proposed. It is based on the quantitative laws deduced for HALS performance in polyolefins. They are, linear increase of performance with HALS concentration in PP and linear increase with the square root of HALS concentration in PE-HD. Then, the knowledge of the effect of one HALS concentration on outdoor weathering with a given polymer and sample form allows prediction of the lifetime with other HALS concentrations. As a consequence, the problem of lifetime forecasting is reduced to an analytical problem, i.e. determination of the stabilizer system.

Numbers as Quantitative Relations and the Traditional Theory of Measurement

The thesis that numbers are ratios of quantities has recently been advanced by a number of philosophers. While adequate as a definition of the natural numbers, it is not clear that this view suffices for our understanding of the reals. These require continuous quantity and relative to any such quantity an infinite number of additive relations exist. Hence, for any two magnitudes of a continuous quantity there exists no unique ratio. This problem is overcome by defining ratios, and hence real numbers, as binary relations between infinite standard sequences. This definition leads smoothly into a new definition of measurement consonant with the traditional view of measurement as the discovery or estimation of numerical relations. The traditional view is further strengthened by allowing that the additive relations internal to a quantity are distinct from relations observed in the behaviour of objects manifesting quantities. In this way the traditional theory can accommodate the theory of conjoint measurement. This is worth doing because the traditional theory has one great strength lacked by its rivals: measurement statements and quantitative laws are able to be understood literally.