Similarity Properties Research Articles

The integrated and local estimations of instability for a class of autonomous delay systems

Abstract The Lyapunov stability of a partly nonlinear delay system is investigated both analytically and numerically for the sake of calculation of (i) integrated and (ii) local estimates. The improvement of numerical scheme for calculation of characteristic exponents is achieved within the integrated analysis and the properties of mutual similarity of the internal product are proved. At the local instabilities investigation, two kinds of instability for the delay system with high-power nonlinearity are detected. The intermittency of the chaotic behavior is also explored numerically and analogy with hydrodynamic turbulence is shown.

LOW BIT-RATE IMAGE COMPRESSION SCHEMES BASED ON VECTOR QUANTIZATION

Three image compression schemes based on vector quantization are proposed in this paper. The block similarity property among neighboring image blocks is exploited in these schemes to cut down the bit rate of the vector quantization scheme. For the first scheme, the correlation among the encoded block to the left and the encoded block directly above the current processing block is exploited. In the second scheme, the relative addressing technique is incorporated into the encoding procedure. Finally, the third scheme introduces a simple technique to reduce the required bit rate with only a slight reduction in image quality. According to the experimental results, it is shown that these proposed schemes not only reduce storage costs but also achieve good reconstructed image quality. Furthermore, the required computational cost for the encoding/decoding procedures of these schemes is less than that of the conventional vector quantization scheme. In other words, these schemes are suitable for the compression of digital images.

Evaluation of six relations of the kinetics of uptake by phytoplankton in multi-nutrient environment using JGOFS experimental results

Abstract The inhibitory effect of ammonium on nitrate uptake, which has received a fair amount of attention, is an example of phytoplankton uptake kinetics in a multi-nutrient environment with nutrient interaction. We examine six relations [Wroblewski, 1977. Journal of Marine Research 35, 357–394; O’Neill et al., 1989. Ecological Modelling 46, 147–163; Walsh and Dugdale, 1971. Deep-Sea Research 22, 201–236; Jamart et al., 1977. Deep-Sea Research 31, 21–37; Frost and Franzen, 1992. Marine Ecology Progress Series 83, 291–303; Yajnik and Sharada, 2003. Current Science 85(8), 1180–1189] governing the uptake of nitrate and ammonium by phytoplankton in the context of the nitrogen dynamics experiments of McCarthy et al. [1999. Nitrogen dynamics during the Arabian Sea northeast monsoon. Deep- Sea Research II 46 (8–9), 1623–1664] in the Indian Ocean. One of the relations [Yajnik and Sharada, 2003. Current Science 85(8), 1180–1189], which is based on the properties of similarity and hyperbolicity, is shown to represent the experimental observations more accurately than others. We then examine the consequences of selection of one of these kinetic relations on 3D simulations of the Indian Ocean ecosystem. The 3D simulations are based on the biological model of Fasham et al. [1990. Journal Marine Research 48, 591–639] coupled to a physical oceanographic model Saramiento et al. [1993. Global Biogeochemical Cycles 7 (2), 417–450] and are performed for three relations [Wroblewski, 1977. Journal of Marine Research 35, 357–394; O’Neill et al., 1989. Ecological Modelling 46, 147–163; Yajnik and Sharada, 2003. Current Science 85(8), 1180–1189]. The values of kinetic parameters are determined from the experiments of McCarthy et al. [1999. Deep- Sea Research II 46 (8–9), 1623–1664]. The spatial variation of annual average primary productivity, especially in the regions of high primary productivity in the northern Indian Ocean, is found to agree most favourably with SeaWiFS data for the relation [Yajnik and Sharada, 2003. Current Science 85(8), 1180–1189] based on similarity and hyperbolicity. The distribution of particle export ratios also appears to be close to present expectations.

Slumping instabilities of elastic membranes holding liquids and gases

This paper treats the plane-strain free-boundary problem describing the equilibrium of a closed cylindrical non-linearly elastic membrane that contains a heavy liquid and a weightless compressible gas and that sits upon a rigid horizontal plane. The material points of the membrane in contact with the rigid plane, the liquid, and the gas are unknowns of the problem. We carefully formulate the geometrically exact equations, and then show that solutions must have attractive regularity, symmetry, and similarity properties, which are not intuitively obvious. There is an interesting interplay between the material behavior and the live pressure loadings generated by gases and heavy liquids. The properties of the equilibrium states depend crucially on the material behaviour of the membrane. In particular, for certain materials the number of equilibrium states changes abruptly as certain parameters describing the liquid and gas change. Thus the system can suffer instabilities of snapping type (with their attendant hysteresis effects), which we term slumping instabilities.

Proximate causes and fitness consequences of hatching failure in lesser kestrels Falco naumanni

Hatching failure is a pervasive phenomenon in birds, but factors affecting hatchability remain poorly understood. We studied proximate causes and fitness consequences of hatching failure in a long‐monitored population of the colonial lesser kestrel Falco naumanni. We investigated whether hatchability was related to clutch characteristics, parental traits, and social or environmental features. Hatching failure represents a cost for the parents in terms of immediate fitness, since it reduced both their number of young fledged and recruits in the breeding population, even when controlling for clutch size. Hatching failure showed a non‐linear relationship with clutch size, clutches of four eggs showing higher levels of hatching success than larger or smaller clutches. Hatchability could therefore play a role in the evolution of optimal clutch size in this species, at least constraining the maximum number of eggs the parents can afford to incubate. Contrary to most studies, the mean volume of the clutch and the individual egg volume were negatively related to hatching failure, indicating that large eggs have thermoregulatory and/or nutritional advantages. Mean daily maximum temperature during incubation affected hatching success negatively, but only for females in poor condition. This result seems to indicate that females are reluctant to jeopardize their own condition, but instead sacrifice incubation effort by paying the costs of a lower hatching success in circumstances of high temperatures. There was no evidence that hatching failure was related to the intrinsic properties of individuals or genetic similarity between the parents as indicated by low repeatabilities of: (1) males that bred with different females, (2) females that bred with different males, and (3) pairs breeding together in different years. Neither colony size nor subpopulation size affected hatchability. All these findings show how hatching failure is simultaneously influenced by several factors acting in a complex way, which could in part explain the apparently conflicting conclusions of empirical or even experimental studies carried out to date.

Incomplete self-similarity and fatigue-crack growth

The Paris power law, which relates fatigue-crack growth rates to the applied stress-intensity range, is an example of a scaling law with the inherent property of incomplete similarity. Previous considerations of dimensions and self-similarity have suggested that the assumed 'materials constants' in this law are also a function of specimen size. In this note, the question of the size-dependence of the Paris law is re-examined, and through comparison to a larger body of fatigue-crack growth data in steels, physical explanations why such scaling effects may exist are deduced.

The space-time fractional diffusion equation with Caputo derivatives

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order β∈(0, 2] and the first-order time derivative with Caputo derivative of order α∈(0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.

Genetical and Mathematical Properties of Similarity and Dissimilarity Coefficients Applied in Plant Breeding and Seed Bank Management

A proper choice of a dissimilarity measure is important in surveys investigating genetic relationships among germplasm with molecular marker data. The objective of our study was to examine 10 dissimilarity coefficients widely used in germplasm surveys, with special focus on applications in plant breeding and seed banks. In particular, we (i) investigated the genetical and mathematical properties of these coefficients, (ii) examined consequences of these properties for different areas of application in plant breeding and seed banks, and (iii) determined relationships between these 10 coefficients. The genetical and mathematical concepts of the coefficients were described in detail. A Procrustes analysis of a published data set consisting of seven CIMMYT maize populations demonstrated close affinity between Euclidean, Rogers', modified Rogers', and Cavalli-Sforza and Edwards' distance on one hand, and Nei's standard and Reynolds dissimilarity on the other hand. Our investigations show that genetical and mathematical properties of dissimilarity measures are of crucial importance when choosing a genetic dissimilarity coefficient for analyzing molecular marker data. The presented results assist experimenters to extract the maximum amount of information from genetic data and, thus, facilitate the interpretation of findings from molecular marker studies on a theoretically sound basis.

Asymptotic analysis of stress singularities in composite laminates by the boundary finite element method

The present contribution contains asymptotic studies of stress singularities which occur in the vicinity of interfaces at straight free edges and also at free corners of composite laminates where two straight free edges intersect. The computations are performed by the boundary finite element method (BFEM) which only requires a boundary discretization and which in essence is a boundary element method solely relying on standard finite element formulations. The BFEM does not require the knowledge of a fundamental solution and reduces the spatial dimension of the discretizational effort by one. Anisotropic material behaviour is incorporated without difficulties. As the BFEM requires certain similarity or scaling properties of the given structural situation and involves the closed-form solution of a system of differential equations for the displacement components with respect to the scaling direction, it can also be characterized as a hybrid or semi-analytical method.

Hierarchical structure description of spatiotemporal chaos

We develop a hierarchical structure (HS) analysis for quantitative description of statistical states of spatially extended systems. Examples discussed here include an experimental reaction-diffusion system with Belousov-Zhabotinsky kinetics, the two-dimensional complex Ginzburg-Landau equation, and the modified FitzHugh-Nagumon equation, which all show complex dynamics of spirals and defects. We demonstrate that the spatial-temporal fluctuation fields in the above-mentioned systems all display the HS similarity property originally proposed for the study of fully developed turbulence [Phys. Rev. Lett. 72, 336 (1994)]]. The derived values of a HS parameter beta from experimental and numerical data in various physical regimes exhibit consistent trends and characterize the degree of turbulence in the systems near the transition, and the degree of heterogeneity of multiple disorders far from the transition. It is suggested that the HS analysis offers a useful quantitative description for the complex dynamics of two-dimensional spatiotemporal patterns.

Local Similarity Properties of the Continuously Turbulent Stable Boundary Layer over Greenland

The concept of local scaling has proven to be a useful tool for the description of turbulence structures in the stable boundary layer (SBL) in mid-latitudes. In the present paper, local similarity properties of the continuously turbulent SBL over the Greenland ice sheet are investigated. The observations were obtained during the aircraft-based experiment KABEG (Katabatic wind and Boundary-layer front Experiment around Greenland) under conditions of strong katabatic winds. For the first time, this dataset allows the study of the turbulence structure in the katabatic wind system over the whole boundary layer and over a horizontal scale of 80 km. Data from six flights during different synoptic conditions are summarized. In all situations, the katabatic flow was associated with a low-level jet, and maximum wind speeds exceed 20 m s−1 in several cases. The strong katabatic winds over the Greenland ice sheet represent conditions of the fully turbulent SBL under strong baroclinicity. Almost all data were collected above the surface layer and can be attributed to the regions of local scaling or z-less scaling. The local scaling concept was found to be valid also for these strong katabatic wind conditions. Profiles of scaled variances and fluxes agree with mid-latitude results, except for the total momentum flux. For the similarity functions and eddy diffusivities of the sensible heat flux, the use of the buoyancy length scale is found to be superior compared to the local Obukhov length.

Global Markov models for eukaryote nucleotide data

We discuss the quite remarkable global Markovian structure of the nucleotides in eukaryotic DNA strands with special emphasis on (i) the similarity property for intra- species chromosomes and (ii) the reversibility property for the two (complementary) strands of a chromosome.

Phospholipase D Is a Negative Regulator of Proline Biosynthesis in Arabidopsis thaliana

Accumulation of proline has been observed in a large number of plant species in response to drought and salt stresses, suggesting a key role of this amino acid in plant stress adaptation. Upstream components of the proline biosynthesis signal transduction pathways are still poorly defined. We provide experimental evidence that phospholipase D (PLD) is involved in the regulation of proline metabolism in Arabidopsis thaliana. The application of primary butyl alcohols, which divert part of PLD-derived phosphatidic acid by transphosphatidylation, stimulated proline biosynthesis even without hyperosmotic constraints. Moreover, application of primary butyl alcohols enhanced the proline responsiveness of seedlings to mild hyperosmotic stress. These data indicate that some PLDs are negative regulators of proline biosynthesis and that plants present a higher proline responsiveness to hyperosmotic stress when this regulator is abolished. We clearly demonstrate that PLD signaling for proline biosynthesis is similar to RD29A gene expression and different from the abscisic acid-dependent RAB18 gene expression. Our data reveal that PLDs play positive and negative roles in hyperosmotic stress signal transduction in plants, contributing to a precise regulation of ion homeostasis and plant salt tolerance.

A hybrid 3D thermo-elastic infinite element modeling for area-array package solder joints

In this paper, we present a 3D thermo-elastic infinite element methodology (IEM) for modeling solder joints in area-array packaging. We also propose a new concept which involves converting the IEM into an infinite element (IE). The special element is formulated based on the conventional finite element method (FEM) using the similarity property of stiffness in isoparametric elements and matrix condensation operations. We developed an IE–FE coupling scheme and implemented it using the commercial finite element software ABAQUS so that a complete elastostatic analysis can be conducted. This study investigated out-of-plane thermal deformation (warpage) and its effect on thermal stress distribution in the solder joints of multi-chip module (MCM) BGA assemblies. The proposed model was able to simulate a large number of solder joints for efficient computations. The most susceptible solder joints were identified and replaced by 3D finite element models for thermal elastic–plastic re-analysis. Two types of MCM BGA assemblies with symmetrical and non-symmetrical area-array solder joints are studied.

Three theorems on hierarchical decomposition of similarity linear systems

In this paper the problem of system decomposition of complex linear dynamical systems biy exploiting the similarity property is studied. System decompositions are sought in terms of similarity hierarchical structures. The method for constructing the transformation is derived. The conditions for such decomposition of complex linear systems are given.

Using Origami to Promote Geometric Communication

Rigami has been used frequently in teaching geometry to promote the development of spatial sense; to make multicultural connections with mathematical ideas; and to provide students with a visual representation of such geometric concepts as shape, properties of shapes, congruence, similarity, and symmetry. Such activities meet the Geometry Standard (NCTM 2000), which states that students should be engaged in activities that allow them to “analyze characteristics and properties of twoand three-dimensional geometric shapes and develop mathematical arguments about geometric relationships” and to “use visualization, spatial reasoning, and geometric modeling to solve problems” (p. 41). This article begins with an explanation of the importance of communication in the mathematics classroom and then describes a middle school mathematics lesson that uses origami to meet both the Geometry Standard as well as the Communication Standard.

Sieve mechanism of microfiltration separation

A theoretical model of dead-end microfiltration (MF) of dilute suspensions is proposed. The model is based on a sieve mechanism of MF and takes into account the probability of membrane pore blocking during MF of dilute colloidal suspensions. An integro-differential equation (IDE) that includes both the membrane pore size and the particle size distributions is deduced. According to the suggested model a similarity property is applicable, which allows one to predict the flux through the membrane as a function of time for any pressure, and dilute concentration, based on one experiment at a single pressure and concentration. The suggested model includes only one fitting parameter, β >1, which takes into account the range of the hydrodynamic influence of a single pore. For a narrow pore size distribution in which one pore diameter predominates (track-etched membranes), the IDE is solved analytically and the derived equation is in good agreement with the measurements on different track-etched membranes. A simple approximate solution of the IDE is derived and that approximate solution, as well as the similarity principal of MF processes, is in good agreement with measurements using a commercial Teflon microfiltration membrane. The theory was further developed to take into account the presence of multiple pores (double, triple and so on pores) on a track-etched membrane surface. A series of new dead-end filtration experiments are compared with the proposed initial and modified pore blocking models. The challenge suspension used was nearly monodispersed suspension of latex particles of ∼0.45 μm filtered on a track-etched membrane with similar sized pores ∼0.4 μm. The filtered suspension concentration ranged from 0.00006 to 0.01% (w/w) and the cross-membrane pressures varied from 1000 to 20,000 Pa. Three stages of microfiltration have been observed. The initial stage is well described by the proposed pore blocking model. The model required only a single parameter that was found to fit all the data under different experimental operational conditions. The second stage corresponds to the transition from the blocking mechanism to the third stage, which is cake filtration. The latter stage occurred after approximately 10–12 particle layers were deposited (mass = 0.006 g) on the surface of the microfiltration membrane.

Genetic code, attributive mappings and stochastic matrices

In this paper we construct three primitive mappings based on three kinds of genetic attribute equivalences. We then apply the mappings and basic addition operation to the universal genetic code to generate three square matrices. We show that these square matrices are stochastic in nature. They demonstrate some fractal similarity properties and resemble the similar properties to the original stochastic matrices.

Generalized periodically focused beams and multiple on-axis lens imaging

A class of periodically focused propagation-invariant monochromatic beams with sharp central peak is extended to the beams, of which the patterns of intensity at discrete transverse planes regularly spaced along the propagation axis may have an arbitrary, but the same, form. It is shown that the wave field of such beams in free space may be represented as a discrete set of nonuniform phase-distorted spherical wavelets converging to the vicinities of axial points at the indicated transverse planes and possessing the property of mutual similarity. High-order azimuth angular constituents of these wavelets are shown to have phase singularities appearing in the transverse planes as dark coaxial spots with bright rims. Hybrid refractive–diffractive systems are proposed, which are suited both for the direct high efficient production of the beams considered and for the multiple imaging of arbitrary plane objects. The results of numerical simulations are given for two cases of multiple reproduction of rings with large and small radii.

The repugnant and the mature in phylogenetic inference: atemporal similarity and historical identity

AbstractThe significance of “being similar” in the inference of species relationships is refuted once again (see also Hennig, 1966, Phylogenetic Systematics, Univ. of Illinois Press, Urbana, IL). Without merit is Rieppel and Kearney's (Biol. J. Linn. Soc., 2002, 75, 59–82) claim that submitting the relational property of topological similarity, their preferred definition of character, to falsifying tests of similarity benefits that kind of inference. Such a priori uses of similarity, in character analysis, are consistent with observational theory, where a character is defined intensionally in terms of immutable properties. However, the induced hypotheses that follow from this theory, not the deductive test that Rieppel and Kearney wanted, remain controversial, because their predictability is a consequence of circular reasoning, and their projectabality fails empirically from incongruent observation reports. Further, a category mistake is made when the abstract, similarity‐defined, group of organisms is reified, as a part of history. In addition, Rieppel and Kearney failed to provide a special theory for similarity, which renders similarity scientifically repugnant (Quine, 1969, Ontological Relativity and Other Essays, Columbia Univ. Press, New York). A return to Hennig's (1966) evolutionary concept of evidence, as transformation series, is urged, and from which a testable character hypothesis can be formulated. There is no one operation for determining character states in this system—it can be anything that leads to the testable hypothesis of synapomorphy, as an historical identity relation. Character compatibility and conjunction, but not similarity, provide a priori tests in phylogenetic character analysis. In turn, the phylogenetic system of inference leads to explanations of homology, as historical identities, which exemplifies the goal of achieving a mature state of historical knowledge (not of Quine, 1969). Such maturity obtains from attempts to falsify hypotheses of species relationships with severely tested evidence, not from induction of “the” observation statement that Rieppel and Kearney sought to justify their true belief in a hypothesis of relationships.