980 resultados para Rate equation


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Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.

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In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

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Many interesting phenomena have been observed in layers of granular materials subjected to vertical oscillations; these include the formation of a variety of standing wave patterns, and the occurrence of isolated features called oscillons, which alternately form conical heaps and craters oscillating at one-half of the forcing frequency. No continuum-based explanation of these phenomena has previously been proposed. We apply a continuum theory, termed the double-shearing theory, which has had success in analyzing various problems in the flow of granular materials, to the problem of a layer of granular material on a vertically vibrating rigid base undergoing vertical oscillations in plane strain. There exists a trivial solution in which the layer moves as a rigid body. By investigating linear perturbations of this solution, we find that at certain amplitudes and frequencies this trivial solution can bifurcate. The time dependence of the perturbed solution is governed by Mathieu’s equation, which allows stable, unstable and periodic solutions, and the observed period-doubling behaviour. Several solutions for the spatial velocity distribution are obtained; these include one in which the surface undergoes vertical velocities that have sinusoidal dependence on the horizontal space dimension, which corresponds to the formation of striped standing waves, and is one of the observed patterns. An alternative continuum theory of granular material mechanics, in which the principal axes of stress and rate-of-deformation are coincident, is shown to be incapable of giving rise to similar instabilities.

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It has been suggested that the Internet is the most significant driver of international trade in recent years to the extent that the term =internetalisation‘ has been coined (Bell, Deans, Ibbotson & Sinkovics, 2001; Buttriss & Wilkinson, 2003). This term is used to describe the Internet‘s affect on the internationalisation process of the firm. Consequently, researchers have argued that the internationalisation process of the firm has altered due to the Internet, hence is in need of further investigation. However, as there is limited research and understanding, ambiguity remains in how the Internet has influenced international market growth. Thus, the purpose of this study was to explore how the Internet influences firms‘ internationalisation process, specifically, international market growth. To this end, Internet marketing and international market growth theories are used to illuminate this ambiguity in the body of knowledge. Thus, the research problem =How and why does the Internet influence international market growth of the firm’ is justified for investigation. To explore the research question a two-stage approach is used. Firstly, twelve case studies were used to evaluate key concepts, generate hypotheses and to develop a model of Internetalisation for testing. The participants held key positions within their firm, so that rich data could be drawn from international market growth decision makers. Secondly, a quantitative confirmation process analysed the identified themes or constructs, using two hundred and twenty four valid responses. Constructs were evaluated through an exploratory factor analysis, confirmatory factor analysis and structural equation modelling process. Structural equation modelling was used to test the model of =internetalisation‘ to examine the interrelationships between the internationalisation process components: information availability, information usage, interaction communication, international mindset, business relationship usage, psychic distance, the Internet intensity of the firm and international market growth. This study found that the Internet intensity of the firm mediates information availability, information usage, international mindset, and business relationships when firms grow in international markets. Therefore, these results provide empirical evidence that the Internet has a positive influence on international information, knowledge, entrepreneurship and networks and these in turn influence international market growth. The theoretical contributions are three fold. Firstly, the study identifies a holistic model of the impact the Internet has had on the outward internationalisation of the firm. This contribution extends the body of knowledge pertaining to Internet international marketing by mapping and confirming interrelationships between the Internet, internationalisation and growth concepts. Secondly, the study highlights the broad scope and accelerated rate of international market growth of firms. Evidence that the Internet influences the traditional and virtual networks for the pursuit of international market growth extends the current understanding. Thirdly, this study confirms that international information, knowledge, entrepreneurship and network concepts are valid in a single model. Thus, these three contributions identify constructs, measure constructs in a multi-item capacity, map interrelationships and confirm single holistic model of ‗internetalisation‘. The main practical contribution is that the findings identified information, knowledge and entrepreneurial opportunities for firms wishing to maximise international market growth. To capitalise on these opportunities suggestions are offered to assist firms to develop greater Internet intensity and internationalisation capabilities. From a policy perspective, educational institutions and government bodies need to promote more applied programs for Internet international marketing. The study provides future researchers with a platform of identified constructs and interrelationships related to internetalisation, with which to investigate. However, a single study has limitations of generalisability; thus, future research should replicate this study. Such replication or cross validation will assist in the verification of scales used in this research and enhance the validity of causal predications. Furthermore, this study was undertaken in the Australian outward-bound context. Research in other nations, as well as research into inbound internationalisation would be fruitful.

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Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart, by the sympathetic and parasympathetic branches of the autonomic nervous system. Heart rate variability analysis is an important tool to observe the heart's ability to respond to normal regulatory impulses that affect its rhythm. A computer-based intelligent system for analysis of cardiac states is very useful in diagnostics and disease management. Like many bio-signals, HRV signals are nonlinear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of nonlinear systems and provides good noise immunity. In this work, we studied the HOS of the HRV signals of normal heartbeat and seven classes of arrhythmia. We present some general characteristics for each of these classes of HRV signals in the bispectrum and bicoherence plots. We also extracted features from the HOS and performed an analysis of variance (ANOVA) test. The results are very promising for cardiac arrhythmia classification with a number of features yielding a p-value < 0.02 in the ANOVA test.

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In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

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In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

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Improved public awareness and strong sentiments towards environmental issues will continue to create increasing demand for sustainable housing (SH) in the coming years. Despite this potential, the up-take rate of sustainable housing in new build and through home renovation is not as high as expected within the housing industry. This is in contrast to the influx of emerging building technologies, new materials and innovative designs seen in exemplar homes built worldwide. How we should use the increasing awareness of SH and emerging technologies as an impetus to change the un-sustainable designs and practices of the building industry is high on the agenda of the government and majority of the stakeholders involved. This warrants the study of multifaceted strategies that meet the needs of multiple stakeholders and integrated seamlessly into housing development processes. Specifically, the different perceptions, roles and incentives of stakeholders, who inevitably need to ensure their benefits and commercial returns, should be highlighted and acted upon. ----- This paper discusses the preliminary findings of a research project that aims to promote SH implementation by identifying and materializing the mutual benefits among key stakeholders. The aim is to be achieved through questionnaire surveys, structural equation modelling, interviews and case studies with seven major stakeholders within the Australian housing industry. This research identifies the influence and relationship of relevant factors, investigates preferences, similarities and differences between stakeholders on perceived benefits and in turn explores the mutual-benefit strategy package that facilitates decision making towards sustainable housing development.