Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

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.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

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.

A comparison of different methods to determine diffusion length in dye-sensitized solar cells

A new steady state method for determination of the electron diffusion length in dye-sensitized solar cells (DSCs) is described and illustrated with data obtained using cells containing three different types of electrolyte. The method is based on using near-IR absorbance methods to establish pairs of illumination intensity for which the total number of trapped electrons is the same at open circuit (where all electrons are lost by interfacial electron transfer) as at short circuit (where the majority of electrons are collected at the contact). Electron diffusion length values obtained by this method are compared with values derived by intensity modulated methods and by impedance measurements under illumination. The results indicate that the values of electron diffusion length derived from the steady state measurements are consistently lower than the values obtained by the non steady-state methods. For all three electrolytes used in the study, the electron diffusion length was sufficiently high to guarantee electron collection efficiencies greater than 90%. Measurement of the trap distributions by near-IR absorption confirmed earlier observations of much higher electron trap densities for electrolytes containing Li+ ions. It is suggested that the electron trap distributions may not be intrinsic properties of the TiO2 nanoparticles, but may be associated with electron-ion interactions.

How can entrepreneurial musicians use electronic social networks to diffuse their music

Principal Topic: ''In less than ten years music labels will not exist anymore.'' Michael Smelli, former Global COO Sony/BMG MCA/QUT IMP Business Lab Digital Music Think Thanks 9 May 2009, Brisbane Big music labels such as EMI, Sony BMG and UMG have been responsible for promoting and producing a myriad of stars in the music industry over the last decades. However, the industry structure is under enormous threat with the emergence of a new innovative era of digital music. Recent years have seen a dramatic shift in industry power with the emergence of Napster and other file sharing sites, iTunes and other online stores, iPod and the MP3 revolution. Myspace.com and other social networking sites are connecting entrepreneurial artists with fans and creating online music communities independent of music labels. In 2008 the digital music business internationally grew by around 25% to 3.7 Billion US-Dollar. Digital platforms now account for around 20% of recorded music sales, up from 15 % in 2007 (IFPI Digital music report 2009). CD sales have fallen by 40% since their peak levels. Global digital music sales totalled an estimated US$ 3 Billion in 2007, an increase of 40% on 2006 figures. Digital sales account for an estimated 15% of global market, up from 11% in 2006 and zero in 2003. The music industry is more advanced in terms of digital revenues than any other creative or entertainment industry (except games). Its digital share is more than twice that of newspapers (7%), films (35) or books (2%). All these shifts present new possibilities for music entrepreneurs to act entrepreneurially and promote their music independently of the major music labels. Diffusion of innovations has a long tradition in both sociology (e.g. Rogers 1962, 2003) and marketing (Bass 1969, Mahajan et al., 1990). The context of the current project is theoretically interesting in two respects. First, the role of online social networks replaces traditional face-to-face word of mouth communications. Second, as music is a hedonistic product, this strongly influences the nature of interpersonal communications and their diffusion patterns. Both of these have received very little attention in the diffusion literature to date, and no studies have investigated the influence of both simultaneously. This research project is concerned with the role of social networks in this new music industry landscape, and how this may be leveraged by musicians willing to act entrepreneurially. Our key research question we intend to address is: How do online social network communities impact the nature, pattern and speed that music diffuses? Methodology/Key Propositions : We expect the nature/ character of diffusion of popular, generic music genres to be different from specialized, niche music. To date, only Moe & Fader (2002) and Lee et al. (2003) investigated diffusion patterns of music and these focus on forecast weekly sales of music CDs based on the advance purchase orders before the launch, rather than taking a detailed look at diffusion patterns. Consequently, our first research questions are concerned with understanding the nature of online communications within the context of diffusion of music and artists. Hence, we have the following research questions: RQ1: What is the nature of fan-to-fan ''word of mouth'' online communications for music? Do these vary by type of artist and genre of music? RQ2: What is the nature of artist-to-fan online communications for music? Do these vary by type of artist and genre of music? What types of communication are effective? Two outcomes from research social network theory are particularly relevant to understanding how music might diffuse through social networks. Weak tie theory (Granovetter, 1973), argues that casual or infrequent contacts within a social network (or weak ties) act as a link to unique information which is not normally contained within an entrepreneurs inner circle (or strong tie) social network. A related argument, structural hole theory (Burt, 1992), posits that it is the absence of direct links (or structural holes) between members of a social network which offers similar informational benefits. Although these two theories argue for the information benefits of casual linkages, and diversity within a social network, others acknowledge that a balanced network which consists of a mix of strong ties, weak ties is perhaps more important overall (Uzzi, 1996). It is anticipated that the network structure of the fan base for different types of artists and genres of music will vary considerably. This leads to our third research question: RQ3: How does the network structure of online social network communities impact the pattern and speed that music diffuses? The current paper is best described as theory elaboration. It will report the first exploratory phase designed to develop and elaborate relevant theory (the second phase will be a quantitative study of network structure and diffusion). We intend to develop specific research propositions or hypotheses from the above research questions. To do so we will conduct three focus group discussions of independent musicians and three focus group discussions of fans active in online music communication on social network sites. We will also conduct five case studies of bands that have successfully built fan bases through social networking sites (e.g. myspace.com, facebook.com). The idea is to identify which communication channels they employ and the characteristics of the fan interactions for different genres of music. We intend to conduct interviews with each of the artists and analyse their online interaction with their fans. Results and Implications : At the current stage, we have just begun to conduct focus group discussions. An analysis of the themes from these focus groups will enable us to further refine our research questions into testable hypotheses. Ultimately, our research will provide a better understanding of how social networks promote the diffusion of music, and how this varies for different genres of music. Hence, some music entrepreneurs will be able to promote their music more effectively. The results may be further generalised to other industries where online peer-to-peer communication is common, such as other forms of entertainment and consumer technologies.

Mobile data technologies and SME adoption and diffusion : an empirical study on barriers and facilitators

The technological environment in which Australian SMEs operate can be best described as dynamic and vital. The rate of technological change provides the SME owner/manager a complex and challenging operational context. Wireless applications are being developed that provide mobile devices with Internet content and e-business services. In Australia the adoption of e-commerce by large organisations has been relatively high, however the same cannot be said for SMEs where adoption has been slower than other developed countries. In contrast however mobile telephone adoption and diffusion is relatively high by SMEs. This exploratory study identifies attitudes, perceptions and issues for mobile data technologies by regional SME owner/managers across a range of industry sectors. The major issues include the sector the firm belongs to, the current adoption status of the firm, the level of mistrust of the IT industry, the cost of the technologies and the applications and attributes of the technologies.

Confusion with diffusion? Unravelling is diffusion and innovation literature with a focus on SMEs

The aim of this paper is to contribute to the understanding of various models used in research for the adoption and diffusion of information technology in small and medium-sized enterprises (SMEs). Starting with Rogers' diffusion theory and behavioural models, technology adoption models used in IS research are discussed. Empirical research has shown that the reasons why firms choose to adopt or not adopt technology is dependent on a number of factors. These factors can be categorised as owner/manager characteristics, firm characteristics and other characteristics. The existing models explaining IS diffusion and adoption by SMEs overlap and complement each other. This paper reviews the existing literature and proposes a comprehensive model which includes the whole array of variables from earlier models.

Mobile data technologies and small business adoption and diffusion : an empirical study of barriers and facilitators

The technological environment in which contemporary small- and medium-sized enterprises (SMEs) operate can only be described as dynamic. The exponential rate of technological change, characterised by perceived increases in the benefits associated with various technologies, shortening product life cycles and changing standards, provides for the SME a complex and challenging operational context. The primary aim of this research was to identify the needs of SMEs in regional areas for mobile data technologies (MDT). In this study a distinction was drawn between those respondents who were full-adopters of technology, those who were partial-adopters, and those who were non-adopters and these three segments articulated different needs and requirements for MDT. Overall, the needs of regional SMEs for MDT can be conceptualised into three areas where the technology will assist business practices; communication, e-commerce and security

Comprehensive evaluation of driver gaze pattern using fuzzy rules for driver training

The over representation of novice drivers in crashes is alarming. Research indicates that one in five drivers’ crashes within their first year of driving. Driver training is one of the interventions aimed at decreasing the number of crashes that involve young drivers. Currently, there is a need to develop comprehensive driver evaluation system that benefits from the advances in Driver Assistance Systems. Since driving is dependent on fuzzy inputs from the driver (i.e. approximate distance calculation from the other vehicles, approximate assumption of the other vehicle speed), it is necessary that the evaluation system is based on criteria and rules that handles uncertain and fuzzy characteristics of the drive. This paper presents a system that evaluates the data stream acquired from multiple in-vehicle sensors (acquired from Driver Vehicle Environment-DVE) using fuzzy rules and classifies the driving manoeuvres (i.e. overtake, lane change and turn) as low risk or high risk. The fuzzy rules use parameters such as following distance, frequency of mirror checks, gaze depth and scan area, distance with respect to lanes and excessive acceleration or braking during the manoeuvre to assess risk. The fuzzy rules to estimate risk are designed after analysing the selected driving manoeuvres performed by driver trainers. This paper focuses mainly on the difference in gaze pattern for experienced and novice drivers during the selected manoeuvres. Using this system, trainers of novice drivers would be able to empirically evaluate and give feedback to the novice drivers regarding their driving behaviour.

Analysis of linear relationships in block ciphers

This thesis is devoted to the study of linear relationships in symmetric block ciphers. A block cipher is designed so that the ciphertext is produced as a nonlinear function of the plaintext and secret master key. However, linear relationships within the cipher can still exist if the texts and components of the cipher are manipulated in a number of ways, as shown in this thesis. There are four main contributions of this thesis. The first contribution is the extension of the applicability of integral attacks from word-based to bitbased block ciphers. Integral attacks exploit the linear relationship between texts at intermediate stages of encryption. This relationship can be used to recover subkey bits in a key recovery attack. In principle, integral attacks can be applied to bit-based block ciphers. However, specific tools to define the attack on these ciphers are not available. This problem is addressed in this thesis by introducing a refined set of notations to describe the attack. The bit patternbased integral attack is successfully demonstrated on reduced-round variants of the block ciphers Noekeon, Present and Serpent. The second contribution is the discovery of a very small system of equations that describe the LEX-AES stream cipher. LEX-AES is based heavily on the 128-bit-key (16-byte) Advanced Encryption Standard (AES) block cipher. In one instance, the system contains 21 equations and 17 unknown bytes. This is very close to the upper limit for an exhaustive key search, which is 16 bytes. One only needs to acquire 36 bytes of keystream to generate the equations. Therefore, the security of this cipher depends on the difficulty of solving this small system of equations. The third contribution is the proposal of an alternative method to measure diffusion in the linear transformation of Substitution-Permutation-Network (SPN) block ciphers. Currently, the branch number is widely used for this purpose. It is useful for estimating the possible success of differential and linear attacks on a particular SPN cipher. However, the measure does not give information on the number of input bits that are left unchanged by the transformation when producing the output bits. The new measure introduced in this thesis is intended to complement the current branch number technique. The measure is based on fixed points and simple linear relationships between the input and output words of the linear transformation. The measure represents the average fraction of input words to a linear diffusion transformation that are not effectively changed by the transformation. This measure is applied to the block ciphers AES, ARIA, Serpent and Present. It is shown that except for Serpent, the linear transformations used in the block ciphers examined do not behave as expected for a random linear transformation. The fourth contribution is the identification of linear paths in the nonlinear round function of the SMS4 block cipher. The SMS4 block cipher is used as a standard in the Chinese Wireless LAN Wired Authentication and Privacy Infrastructure (WAPI) and hence, the round function should exhibit a high level of nonlinearity. However, the findings in this thesis on the existence of linear relationships show that this is not the case. It is shown that in some exceptional cases, the first four rounds of SMS4 are effectively linear. In these cases, the effective number of rounds for SMS4 is reduced by four, from 32 to 28. The findings raise questions about the security provided by SMS4, and might provide clues on the existence of a flaw in the design of the cipher.