891 resultados para Difference Equations with Maxima
Resumo:
Normative influences on road user behaviour have been well documented and include such things as personal, group, subjective and moral norms. Commonly, normative factors are examined within one cultural context, although a few examples of exploring the issue across cultures exist. Such examples add to our understanding of differences in perceptions of the normative factors that may exert influence on road users and can assist in determining whether successful road safety interventions in one location may be successful in another. Notably, the literature is relatively silent on such influences in countries experiencing rapidly escalating rates of motorization. China is one such country where new drivers are taking to the roads in unprecedented numbers and authorities are grappling with the associated challenges. This paper presents results from qualitative and quantitative research on self-reported driving speeds of car drivers and related issues in Australia and China. Focus group interviews and questionnaires conducted in each country examined normative factors that might influence driving in each cultural context. Qualitative findings indicated perceptions of community acceptance of speeding were present in both countries but appeared more widespread in China, yet quantitative results did not support this difference. Similarly, with regard to negative social feedback from speeding, qualitative findings suggested no embarrassment associated with speeding among Chinese participants and mixed results among Australian participants, yet quantitative results indicated greater embarrassment for Chinese drivers. This issue was also examined from the perspective of self-identity and findings were generally similar across both samples and appear related to whether it is important to be perceived as a skilled/safe driver by others. An interesting and important finding emerged with regard to how Chinese drivers may respond to questions about road safety issues if the answers might influence foreigners’ perceptions of China. In attempting to assess community norms associated with speeding, participants were asked to describe what they would tell a foreign visitor about the prevalence of speeding in China. Responses indicated that if asked by a foreigner, people may answer in a manner that portrayed China as a safe country (e.g., that drivers do not speed), irrespective of the actual situation. This ‘faking good for foreigners’ phenomenon highlights the importance of considering ‘face’ when conducting research in China – a concept absent from the road safety literature. An additional noteworthy finding that has been briefly described in the road safety literature is the importance and strength of the normative influence of social networks (guanxi) in China. The use of personal networks to assist in avoiding penalties for traffic violations was described by Chinese participants and is an area that could be addressed to strengthen the deterrent effect of traffic law enforcement. Overall, the findings suggest important considerations for developing and implementing road safety countermeasures in different cultural contexts.
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In this article, we analyze the three-component reaction-diffusion system originally developed by Schenk et al. (PRL 78:3781–3784, 1997). The system consists of bistable activator-inhibitor equations with an additional inhibitor that diffuses more rapidly than the standard inhibitor (or recovery variable). It has been used by several authors as a prototype three-component system that generates rich pulse dynamics and interactions, and this richness is the main motivation for the analysis we present. We demonstrate the existence of stationary one-pulse and two-pulse solutions, and travelling one-pulse solutions, on the real line, and we determine the parameter regimes in which they exist. Also, for one-pulse solutions, we analyze various bifurcations, including the saddle-node bifurcation in which they are created, as well as the bifurcation from a stationary to a travelling pulse, which we show can be either subcritical or supercritical. For two-pulse solutions, we show that the third component is essential, since the reduced bistable two-component system does not support them. We also analyze the saddle-node bifurcation in which two-pulse solutions are created. The analytical method used to construct all of these pulse solutions is geometric singular perturbation theory, which allows us to show that these solutions lie in the transverse intersections of invariant manifolds in the phase space of the associated six-dimensional travelling wave system. Finally, as we illustrate with numerical simulations, these solutions form the backbone of the rich pulse dynamics this system exhibits, including pulse replication, pulse annihilation, breathing pulses, and pulse scattering, among others.
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In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction-diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions. A mathematical analysis of pulse interactions is based on detailed information on the existence and stability of isolated pulse solutions. The existence of these isolated pulse solutions is established in previous work. Here, the pulse solutions are studied by an Evans function associated to the linearized stability problem. Evans functions for stability problems in singularly perturbed reaction-diffusion models can be decomposed into a fast and a slow component, and their zeroes can be determined explicitly by the NLEP method. In the context of the present model, we have extended the NLEP method so that it can be applied to multi-pulse and multi-front solutions of singularly perturbed reaction-diffusion equations with more than one slow component. The brunt of this article is devoted to the analysis of the stability characteristics and the bifurcations of the pulse solutions. Our methods enable us to obtain explicit, analytical information on the various types of bifurcations, such as saddle-node bifurcations, Hopf bifurcations in which breathing pulse solutions are created, and bifurcations into travelling pulse solutions, which can be both subcritical and supercritical.
Resumo:
An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variable effective diffusivity. In order to test the model, experimental data was collected for the drying of green peas in a fluidised bed at three drying temperatures. Through fitting three equation types for effective diffusivity to the data, it was found that a linear equation form, in which diffusivity increased with decreasing moisture content, was most appropriate. The final model accurately described the drying curves of the three experimental temperatures, with an R2 value greater than 98.6% for all temperatures.
Resumo:
Purpose: Changes in pupil size and shape are relevant for peripheral imagery by affecting aberrations and how much light enters and/or exits the eye. The purpose of this study is to model the pattern of pupil shape across the complete horizontal visual field and to show how the pattern is influenced by refractive error. Methods: Right eyes of thirty participants were dilated with 1% cyclopentolate and images were captured using a modified COAS-HD aberrometer alignment camera along the horizontal visual field to ±90°. A two lens relay system enabled fixation at targets mounted on the wall 3m from the eye. Participants placed their heads on a rotatable chin rest and eye rotations were kept to less than 30°. Best-fit elliptical dimensions of pupils were determined. Ratios of minimum to maximum axis diameters were plotted against visual field angle. Results: Participants’ data were well fitted by cosine functions, with maxima at (–)1° to (–)9° in the temporal visual field and widths 9% to 15% greater than predicted by the cosine of the field angle . Mean functions were 0.99cos[( + 5.3)/1.121], R2 0.99 for the whole group and 0.99cos[( + 6.2)/1.126], R2 0.99 for the 13 emmetropes. The function peak became less temporal, and the width became smaller, with increase in myopia. Conclusion: Off-axis pupil shape changes are well described by a cosine function which is both decentered by a few degrees and flatter by about 12% than the cosine of the viewing angle, with minor influences of refraction.
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In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, center-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.
Resumo:
An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variable effective diffusivity. In order to test the model, experimental data was collected for the drying of green peas in a fluidised bed at three drying temperatures. Through fitting three equation types for effective diffusivity to the data, it was found that a linear equation form, in which diffusivity increased with decreasing moisture content, was most appropriate. The final model accurately described the drying curves of the three experimental temperatures, with an R2 value greater than 98.6% for all temperatures.
Resumo:
The charge of an isolated dust grain and ion drag forces on the grain in a collisionless, high-voltage, capacitive rf sheath are studied theoretically. The studies are carried out assuming that the positive ions are monoenergetic, as well as in more realistic approximation, assuming that the time-averaged energy distribution of ions impinging on the dust grain has a double-peaked hollow profile. For the nonmonoenergetic case, an analytical expression for the ion flux to the dust grain is obtained. It is studied how the dust charge and ion drag forces depend on the rf frequency, electron density at plasma-sheath boundary, electron temperature and ratio of the effective oscillation amplitude of rf current to the electron Debye length. It is shown that the dust charge and ion drag forces obtained in the monoenergetic ion approximation may differ from those calculated assuming that the ions are nonmonoenergetic. The difference increases with increasing the width of the ion energy spread in the ion distribution. © 2009 American Institute of Physics.
Resumo:
To reduce the natural convection heat loss from enclosures many researchers used convection suppression devices in the past. In this study a single baffle is used under the top tip to investigate numerically the natural convection heat loss in an attic shaped enclosure which is a cost effective approach. The case considered here is one inclined wall of the enclosure is uniformly heated while the other inclined wall is uniformly cooled with adiabatic bottom wall. The finite volume method has been used to discretize the governing equations, with the QUICK scheme approximating the advection term. The diffusion terms are discretized using central-differencing with second order accuracy. A wide range of governing parameters are studied (Rayleigh number, aspect ratio, baffle length etc.). It is observed that the heat transfer due to natural convection in the enclosure reduces when the baffle length is increased. Effects of other parameters on heat transfer and flow field are described in this study.
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We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.
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In this thesis a new approach for solving a certain class of anomalous diffusion equations was developed. The theory and algorithms arising from this work will pave the way for more efficient and more accurate solutions of these equations, with applications to science, health and industry. The method of finite volumes was applied to discretise the spatial derivatives, and this was shown to outperform existing methods in several key respects. The stability and convergence of the new method were rigorously established.
Resumo:
Abstract: Over the years bioelectrical impedance assay (BIA) has gained popularity in the assessment of body composition. However, equations for the prediction of whole body composition use whole body BIA. This study attempts to evaluate the usefulness of segmental BIA in the assessment of whole body composition. A cross sectional descriptive study was conducted at the Professorial Paediatric Unit of Lady Ridgeway Hospital, Colombo, involving 259 (M/F:144/115) 5 to 15 year old healthy children. The height, weight, total and segmental BIA were measured and impedance indices and specific resistivity for the whole body and segments were calculated. Segmental BIA indices showed a significant association with whole body composition measures assessed by total body water (TBW) using the isotope dilution method (D2O). Impedance index was better related to TBW and fat free mass (FFM), while specific resistivity was better related to the fat mass of the body. Regression equations with different combinations of variables showed high predictability of whole body composition. Results of this study showed that segmental BIA can be used as an alternative approach to predict the whole body composition in Sri Lankan children.
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In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode
Resumo:
We report a circuit technique to measure the on-chip delay of an individual logic gate (both inverting and non-inverting) in its unmodified form using digitally reconfigurable ring oscillator (RO). Solving a system of linear equations with different configuration setting of the RO gives delay of an individual gate. Experimental results from a test chip in 65nm process node show the feasibility of measuring the delay of an individual inverter to within 1pS accuracy. Delay measurements of different nominally identical inverters in close physical proximity show variations of up to 26% indicating the large impact of local or within-die variations.
Resumo:
This dissertation studies the language of Latin letters that were written in Egypt and Vindolanda (in northern Britain) during the period 1st century BC 3rd century AD on papyri, ostraca, and wooden tablets. The majority of the texts is, in one way or another, connected with the Roman army. The focus of the study is on syntax and pragmatics. Besides traditional philological methods, modern syntactic theory is used as well, especially in the pragmatic analysis. The study begins with a critical survey of certain concepts that are current in the research on the Latin language, most importantly the concept of vulgar Latin , which, it is argued, seems to be used as an abstract noun for variation and change in Latin . Further, it is necessary to treat even the non-literary material primarily as written texts and not as straightforward reflections of spoken language. An examination of letter phraseology shows that there is considerable variation between the two major geographical areas of provenance. Latin letter writing in Egypt was influenced by Greek. The study highlights the importance of seeing the letters as a text type, with recurring phraseological elements appearing in the body text as well. It is argued that recognising these elements is essential for the correct analysis of the syntax. Three areas of syntax are discussed in detail: sentence connection (mainly parataxis), syntactically incoherent structures and word order (the order of the object and the verb). For certain types of sentence connection we may plausibly posit an origin in spoken Latin, but for many other linguistic phenomena attested in this material the issue of spoken Latin is anything but simple. Concerning the study of historical syntax, the letters offer information about the changing status of the accusative case. Incoherent structures may reflect contaminations in spoken language but usually the reason for them is the inability of the writer to put his thoughts into writing, especially when there is something more complicated to be expressed. Many incoherent expressions reflect the need to start the predication with a thematic constituent. Latin word order is seen as resulting from an interaction of syntactic and pragmatic factors. The preference for an order where the topic is placed sentence-initially can be seen in word order more generally as well. Furthermore, there appears a difference between Egypt and Vindolanda. The letters from Vindolanda show the order O(bject) V(erb) clearly more often than the letters from Egypt. Interestingly, this difference correlates with another, namely the use of the anaphoric pronoun is. This is an interesting observation in view of the fact that both of these are traditional Latin features, as opposed to those that foreshadow the Romance development (VO order and use of the anaphoric ille). However, it is difficult to say whether this is an indication of social or regional variation.