Kinds Of Diagrams Research Articles

Numerical simulation of the soft contact dynamics of an impacting bilinear oscillator

Systems constituted by moving components that make intermittent contacts with each other can be modelled by a system of ordinary differential equations containing piecewise linear terms. We consider a soft impact bilinear oscillator for which we obtain bifurcation diagrams, Lyapunov coefficients, return maps and phase portraits of the response. Besides Lyapunov coefficients diagrams, bifurcation diagrams are represented in terms of both non-dimensional time instants of contact (when the mass impacts the obstacle) and of portions of contact duration (the percentage-time interval when the material point is inside the obstacle) vs. non-dimensional external force frequency (or amplitude). The second kind of diagrams is needed because the contact duration (or the complementary flight time duration) are quantities that can easily be measured in an experiment aiming at confirming the validity of the present model. Lyapunov coefficients are evaluated converting the piecewise linear system of ordinary differential equations into a map, the so-called impact map, where time and velocity corresponding to a given impact are evaluated as functions of time and velocity corresponding to the previous impact. Thus, the usual methods related to this last map are used. The trajectories are represented in terms of return maps (all points in the time-velocity plane involved in the impact events) and phase portraits (the trajectory-itself in the displacement-velocity plane). In the bifurcation diagrams, transition between different responses is evidenced and a perfect correlation between chaotic (periodic) attractors and positive (negative) values of the maximum Lyapunov coefficient is found.

Invariant based programming: basic approach and teaching experiences

Abstract Program verification is usually done by adding specifications and invariants to the program and then proving that the verification conditions are all true. This makes program verification an alternative to or a complement to testing. We describe here another approach to program construction, which we refer to as invariant based programming , where we start by formulating the specifications and the internal loop invariants for the program, before we write the program code itself. The correctness of the code is then easy to check at the same time as one is constructing it. In this approach, program verification becomes a complement to coding rather than to testing. The purpose is to produce programs and software that are correct by construction. We present a new kind of diagrams, nested invariant diagrams , where program specifications and invariants (rather than the control) provide the main organizing structure. Nesting of invariants provide an extension hierarchy that allows us to express the invariants in a very compact manner. We have studied the feasibility of formulating specifications and loop invariants before the code itself has been written in a number of case studies. Our experience is that a systematic use of figures, in combination with a rough idea of the intended behavior of the algorithm, makes it rather straightforward to formulate the invariants needed for the program, to construct the code around these invariants and to check that the resulting program is indeed correct. We describe our experiences from using invariant based programming in practice, both from teaching programmers how to construct programs that they prove correct themselves, and from teaching invariant based programming for CS students in class.

Adding inverses to diagrams encoding algebraic structures

We modify a previous result, which showed that certain diagrams of spaces are essentially simplicial monoids, to construct diagrams of spaces which model simplicial groups. Furthermore, we show that these diagrams can be generalized to models for Segal groupoids. We then modify Segal’s model for simplicial abelian monoids in such a way that it becomes a model for simplicial abelian groups. Much research has been done on various structures equivalent to topological or simplicial groups. Classical examples include Thomason’s work with delooping machines [27] and Stashefi’s group-like A1-spaces [26], while more modern examples make use of the structure of algebraic theories [1], [2]. In [7], we focus instead on simplicial monoids. In particular, we consider diagrams of spaces which essentially give one of the spaces the structure of a monoid. While such a structure is given when the diagram is the theory of monoids, we obtain a simpler diagram which, from the viewpoint of homotopy theory, encodes the same structure. Here we return to the original situation and ask if this construction can be modifled to obtain a diagram encoding the structure of a simplicial group rather than a simplicial monoid. After all, we need only to flnd a way to include inverses. In this paper, we show that indeed we can represent simplicial groups in this manner. Furthermore, as the construction for simplicial monoids generalizes to the manyobject case of simplicial categories, we can obtain models for simplicial groupoids as well. In doing so, we extend a result relating simplicial categories to Segal categories (essentially categories with composition only given up to higher homotopy) to one relating simplicial groupoids to Segal groupoids. One might ask, then, if there are other algebraic structures which can be modelled in a similar way, in particular by some kind of diagram which is simpler than the one given by the corresponding algebraic theory. An answer for the case of simplicial abelian monoids is given by Segal’s category i [24], although it does not provide the

Formal notations are diagrams: Evidence from a production task

Although a general sense of the magnitude, quantity, or numerosity of objects is common in both untrained people and animals, the abilities to deal exactly with large quantities and to reason precisely in complex but well-specified situations--to behave formally, that is--are skills unique to people trained in symbolic notations. These symbolic notations typically employ complex, hierarchically embedded structures, which all extant analyses assume are constructed by concatenative, rule-based processes. The primary goal of this article is to establish, using behavioral measures on naturalistic tasks, that some of the same cognitive resources involved in representing spatial relations and proximities are also involved in representing symbolic notations--in short, that formal notations are a kind of diagram. We examined self-generated productions in the domains of handwritten arithmetic expressions and typewritten statements in a formal logic. In both tasks, we found substantial evidence for spatial representational schemes even in these highly symbolic domains.

Studies on the Middle‐phase Microemulsion of Lauric‐N‐methylglucamide

AbstractThe phase behaviour of the middle‐phase microemulsion for the quaternary system lauric‐N‐methylglucamide (MEGA‐12)/n‐butanol/alkane/water has been studied with Winsor type, δ‐γ fishlike and novel ε‐β fishlike phase diagrams. A series of phase inversions Winsor I ($\underline {2}$)→III (3)→II ($\overline {2}$) were observed for the three kinds of phase diagrams. The phase types, the phase volumes and the range of alcohol concentrations from the beginning to the end of the middle‐phase microemulsion were obtained from Winsor phase diagram. From δ‐γ fishlike phase diagram, the physicochemical parameters, such as the mass fraction of n‐butanol in the hydrophile‐lipophile balanced interfacial layer, AS, the coordinates of the start and end points of the middle‐phase microemulsion, and the solubilities of MEGA‐12 and n‐butanol in alkane phase were calculated. The novel ε‐β fishlike phase diagram was also presented. From this kind of diagram, the above experimental phenomena were observed and the physicochemical parameters were calculated precisely. The novel fishlike phase diagram has advantages over the Winsor and δ‐γ fishlike phase diagrams in the evaluation of the solubilization power of the microemulsion and calculation of the related physicochemical parameters.

Response to loading and stiffness of coated substrates indented by spheres

Simulations of spherical indentation of a substrate coated with a protective layer have been performed in the elastic deformation range. They provide key responses that can be used to examine the load resistance of a coated substrate. The key responses result in diagrams indicating whether yielding or fracture occurs first. In this kind of diagram, the ratio of coating fracture strength to substrate yield is related to the contact radius in indentation. As it is difficult to determine the contact radius experimentally, the latter has been found numerically and has also been approximated analytically. The analytical approximation plays an important role as it identifies the general loading condition for various sphere radii. This approximation can be extended to predicting the unloading curve which allows the elastic properties of a coated substrate to be determined.

String interactions in appwave from N = 4 super Yang-Mills theory

We consider nonplanar contributions to the correlation functions of Berenstein-Maldacena-Nastase (BMN) operators in free N = 4 super Yang-Mills theory. We recalculate these nonplanar contributions from a different kind of diagram and find some exact agreement. The vertices of these diagrams are represented by free planar three-point functions; thus, our calculations provide some interesting identities for correlation functions of BMN operators in N = 4 super Yang-Mills theory. These diagrams look very much like loop diagrams in a second quantized string field theory; thus these identities could possibly be interpreted as natural consequences of the $\mathrm{pp}$-wave/conformal field theory correspondence. For convenience we will call these diagrams ``string theory diagram,'' although there are reasonable doubts as to whether these calculations are truly string theory calculations since it is not known how to compute general loop amplitudes in a second quantized string theory.

Light elements synthesized in the He-layer and the H-rich envelope of a type II supernova, II, —Influence of initial chemical compositions—

This is the second paper of a series of our studies, in which we have investigated the light element synthesis (Li, Be, B, and the CNO-elements) in the He-layer and the H-rich envelope of supernovae and the aim of this paper is to see the sensitivity of the element synthesis to the chemical compositions in the presupernova stage. First, we deduced the probable range of the chemical composition in the presupernova stage on the basis of the previous studies of stellar evolution as well as the observational studies of stellar chemical compositions. Secondly, we pursued the explosive nucleosynthesis by using artificially modeled chemical compositions composed of only four elements (1H, 4He, 12C, and 16O). Combining these results, we constructed five kinds of diagrams between two isotopic/elemental ratios which are useful for distinguishing presolar grains of supernova origin: 6Li/16O and 9Be/16O to 7Li/16O, and 11B/7Li, 14N/15N, and 16O/17O to 12C/(13C. In conclusion, the uncertainties in the chemical compositions in the presupernova stage brought smaller varieties in the isotopic/elemental ratios of the light elements compared with the varieties investigated in our first paper about the neutrino emission models.

Characterization of the Porous Medium Diffusivity by Use of Isotopic Tracing. Application to Gas Darceo-Diffusive Transport in Sedimentary Basins

The importance of diffusion phenomenon in losses of gases in sedimentary basins leads to study the quantification of the diffusive flow which requires the knowledge of the diffusivity value. This geometric parameter is defined as the ratio of a gas diffusion coefficient in the water filling the porous medium to the same gas diffusion coefficient in pure water; it is at first sight linked to the tortuosity of the porous medium. However, this parameter is generally not measured and its variations with the different characteristics of the medium are poorly known. As a consequence, some authors often disagreed on estimations of residence time of gas in a structure (Krooss et al., 1992; Nelson et al., 1992). Therefore, the aim of this study is to improve the understanding of diffusivity and its variations by measuring directly its value for some porous media of various porosity, for different diffusing gas species and by determining isotopic fractionations. It has already been shown that isotopic ratios of hydrocarbons are affected in some ways by transport (like diffusion through water). A previous study carried out in this laboratory, pointed out that hydrocarbon diffusion in shale may entail some isotopic fractionation (Pernaton et al., 1996). This study, hence, will allow us to examine how far isotopic fractionations, when they occur, depend on the medium and its geometry. The results of our work will allow us to model the diffusivity as a function of the porous medium parameters. To carry out the experiments, we used a diffusion cell (fig. 1) made of two gas reservoirs separated by a water-saturated porous mediuln. The gas reservoirs were respectively filled with different gases (hydrocarbons, nitrogen) and were kept at the same pressure in order to avoid any darcean flow. The porous medium used was a water-saturated, reconstituted sandstone, of measured thickness and porosity. Gas samples were collected during the course of the experiment to monitor the progress of the diffusion process. Those samples were analysed by a Toepler line, gas chromatography and mass spectrometry (GC-C-IRMS) in order to get chemical proportions and isotopic ratios for carbon (813C) and hydrogen (SD). From gas analysis, we could plot two kinds of diagrams: migrated gas production curve which represents the diffused gas amount versus time and migrated gas isotopic fractionation curve which represents the difference between the isotopic ratios of migrated and initial gases versus time. Then we used a numerical model to determine diffusivity values. This model simulates the transport of gas molecules in the cell (Schneider et al., 1995) : each part of the cell is described by a physical law (Fick's law and a solubilisation law at the gas-water interfaces). Model results are adjusted on experimental ones. The model adjusting parameter is called the migration rate. In its expression each parameter is known except diffusivity. Then from the value of the migration rate given by the model, we can deduce the diffusivity value. So far, three experiments have been carried out at different porosities (30 to 45%), in order to study compaction influence on diffusivity. The diffusing gaseous species studied for the two first experiments were methane and nitrogen as counter-gas. In the third experiment, as we wanted to study the influence of the diffusing gas species, we used a mixture of three hydrocarbons: methane, ethane and propane, the counter-gas used was still nitrogen. Experimental conditions were the same for all the experiments: gas pressure at 25 bars in both chambers of the cell, and ambient temperature. The porous medium used was also the same in the three exper iments : a Fontainebleau sand of 100 pm compacted, and saturated with water to form a reconstituted sandstone. Comparisons of our results in sandstones with those of a previous work using reconstituted and natural shales (Pernaton el aL, 1996) allowed us to study the influence of the medimn lithology.

Non-equilibrium diagrams of phase growth for smart materials

Abstract A new kind of diagram is proposed to analyse the rates of phase transitions in ferroelectric smart materials. These diagrams give a convenient graphical representation of the kinetics of phase growth under changing thermodynamic parameters as well as under the influence of an external magnetic field.

A process model for active brazing of ceramics: Part II Optimization of brazing conditions and joint properties

In the present investigation, the process model developed in Part I has been applied to evaluate the microstructure and strength evolution during active brazing of ceramics. As a starting point, reaction-layer growth is assumed to occur isothermally with no restrictions in the supply of reactive element. Different kinds of diagrams are then constructed to show how specific process variables (e.g. the heating and cooling period, the limiting layer thickness, and the diffusion mechanism) affect the growth kinetics. It is concluded that the key to improved joint properties lies in control of the reaction-layer thickness through optimization of the brazing conditions, and an illustration of this is given.

A similarity retrieval method of drawings based on graph representation

AbstractAn efficient method to retrieve necessary information from drawings for plant diagrams, logic circuit diagrams, etc. stored in a database is presented. In the image information retrieval systems currently in use, a keyword is assigned to each diagram and information is retrieved by the user by giving the keyword. When the features of the desired image are not registered as a keyword, however, its retrieval becomes difficult. In this paper a method is proposed in which the user shows features of the desired diagram using a sample diagram and a section similar to the sample diagram is retrieved. In this research, diagrams consisting mainly of symbols and connecting lines are considered. This kind of diagram is represented by a graph and similarities in topological features between the sample graph and graph representations of the diagrams in the database are evaluated. The retrieval is then performed based on the value obtained. The results of an experiment conducted using plant diagrams show that similar diagrams can be retrieved using this method.

Epsilon -type contribution to baryon asymmetry from colored Higgs triplets.

In scenarios where the cosmological baryon asymmetry is generated in the decay of heavy colored Higgs triplets at the one-loop level (at least two triplets are needed), it is shown that in addition to the conventional triangle loop (\ensuremath{\epsilon}'-type effect), a new kind of diagram must be considered. This new type of diagram has its origin in the mixing of the two Higgs fields (\ensuremath{\epsilon}-type effect). The mixing of the two Higgs fields violates CP provided they have at least two common decay channels. For small mixing angles, the new contribution can be bigger than the conventional one.

The relation between reduction potential and solvation energy for some arylmethylium ions

The polarographic half-wave potentials, E½, of arylmethylium ions in MeSO3H range from –0.275 V for Ph2HC+ to –0.955 V for (4-McOC6H4)3C+, against the Hg/HgSO4/98% H2SO4 electrode. The narrowness of this span, equivalent to ca. 70 kJ mol–1, is explained in terms of the ionization potentials Ei of the corresponding radicals and the solvation enthalpies ΔHS⊖ of the ions. Since the factors which increase Ei also diminish ΔHS⊖ the sum of Ei and ΔHS⊖, which determines E½, does not change much from one extreme of the array of ions to the other, although both terms may vary over a much greater range. A comparison of E½ for the three triarylmethylium ions in McSO3H and CH2Cl2 shows that (a) as the charge becomes more diffuse, the difference between E½ for any one ion in the two solvents I and II,I–IIΔE½(R+), becomes smaller; and (b) the difference in E½ between two ions, A – BΔE½ becomes smaller for a given solvent, the more polar that solvent. The value of E½ obtained in different solvents can be correlated by a new kind of diagram in which the origin of the axes represents the E½ of Ph3C+. For each of three very different ions the E½ values are almost identical in CH2Cl2 and MeCN; this can be attributed to the fact that E½ is not that of a free cation, but of a cation which is part of an ion pair or a higher aggregate, formed from the abundant supporting electrolyte.

Phase Equilibrium and Martensitic Transformation in Lanthana‐Doped Zirconia

The system ZrO2‐La2O3 has been studied in the 0 to 15 mol% La2O3 range using X‐ray diffraction and thermal analysis. Two kinds of diagrams were elaborated: First is a phase equilibrium diagram where the eutectoid decomposition of ZrO2,ss(T) → ZrO2,ss(M) + Pyss occurs at 1100°C and 0.75 mol% La2O3 (Py is the pyrochlore compound Zr2La2O7). The maximum solubility of La2O3 in ZrO2,ss(M) is 0.5 mol% at room temperature. Second, a nonequilibrium diagram is determined showing the correlations between grain size, La2O3 content, and the martensitic transformation temperature start (Ms).

A graphical approach to redox titrations

A method for drawing a logarithmic diagram which gives a correct representation of the equilibrium concentrations of the various species taking part in a redox titration is described. The use of this kind of diagrams for evaluating the titration error and for calculating the titration curve is illustrated. The symmetry properties of titration curves and the linearity range of Gran plots are also discussed on the basis of the logarithmic diagrams.

Constant Rate of Strain Consolidation for very Soft Clayey Soils

ABSTRACT In order to predict the consolidation constants for very soft soils with high water contents, the constant rate of strain consolidation test method has been proposed together with a new interpretation of the test results. Three kinds of diagrams are constructed on the basis of the finite difference solutions for the basic equation of consolidation including the large strain effects. It has been found that using such diagrams, the consolidation constants of very soft clays in the pressure range required for practice can be accurately determined from consolidation tests under constant rates of strain.

A proposed new characterization of particle shape and its application

In order to identify particles morphologically nine new shape indices, using three kinds of powder particles which include circularity and elongation as reltionships between characteristic diameters, have been defined. Shape indices have been examined on their numerical lines. The nine shape indices were divided into three groups which characterize the concavities and/or convexities of a particle, mainly characterize slimless and do not characterize specific shape. Shape identification has been tried on two kinds of diagrams which were obtained by combining shape indices of different character. Particle shape without surface texture is characterized on the diagrams and it is also suggested that morphological identification of powder particles is possible with statistical treatment.

Partition coefficients of alkali and alkaline-earth elements between alkali feldspar phenocrysts and their lava matrix

SummaryPlots of partition coefficients (mineral/ matrix) against ionic radius of the alkali and alkaline earth elements in forty-four alkali feldspars from rhyolites and trachytes show two kinds of diagram, one for homogeneous alkali feldspars with a single peak, and the other for cryptoperthites with a wide spread of points, which cannot represent a single peak, but may probably be explicable in terms of two peaks. The difference in behaviour does not seem to be due to the chemical composition, but is apparently related to the crystallo-graphic features of the alkali feldspar structures. In particular the presence of two peaks in the diagrams of the cryptoperthites seems to be due to the existence of lattice positions suited to receive bigger ions (K, Ba, Rb) and smaller ions (Na, Ca, Sr) in the potassic and sodic domains.

Distribution of residual macrostresses arising in process of surface plastic deformation of steel parts

As is well known, with surface plastic deformation of articles (rolling with rollers or a ball, stamping, blasting with shot, etc.) there arise residual compressive stresses, characterized mainly by two kinds of diagrams: the first with a maximum of the compressive stresses at the surface and the second with a drop in these stresses near the surface. In the first case, the stress distribution is considered more favorable for an increase in the fatigue strength. There are different opinions as to the reason for the appearance of two kinds of diagrams. Many investigators have come to the conclusion that the drop in the stresses is the result of the effect of the temperature, arising in the deformation process [1-3]; some explain this drop by the existence of different deformation schemes: contactshear and pure contact [4]. For example, with rolling by a ball there is a purely contact scheme of the deformation, and with rolling by a roller there is contact-shear deformation. The authors of [5] explain the drop in the residual stresses by a different scheme of surface plastic deformation, in accordance with which the second kind of diagram must occur more frequently for peripheral stresses than for axial stresses. However, it is not clear why under identical conditions for one steel there is a drop in the stresses, while for another steel there is not.