Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems

This paper presents a Finite Element Model, which has been used for forecasting the diffusion of innovations in time and space. Unlike conventional models used in diffusion literature, the model considers the spatial heterogeneity. The implementation steps of the model are explained by applying it to the case of diffusion of photovoltaic systems in a local region in southern Germany. The applied model is based on a parabolic partial differential equation that describes the diffusion ratio of photovoltaic systems in a given region over time. The results of the application show that the Finite Element Model constitutes a powerful tool to better understand the diffusion of an innovation as a simultaneous space-time process. For future research, model limitations and possible extensions are also discussed

G-CSC Report 2010

The present report gives a short summary of the research of the Goethe Center for Scientific Computing (G-CSC) of the Goethe University Frankfurt. G-CSC aims at developing and applying methods and tools for modelling and numerical simulation of problems from empirical science and technology. In particular, fast solvers for partial differential equations (i.e. pde) such as robust, parallel, and adaptive multigrid methods and numerical methods for stochastic differential equations are developed. These methods are highly adanvced and allow to solve complex problems.. The G-CSC is organised in departments and interdisciplinary research groups. Departments are localised directly at the G-CSC, while the task of interdisciplinary research groups is to bridge disciplines and to bring scientists form different departments together. Currently, G-CSC consists of the department Simulation and Modelling and the interdisciplinary research group Computational Finance

Complex networks analysis in socioeconomic models

This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the field of complex networks, the present summary adds insights on the statistical mechanical approach, and on the most relevant computational aspects for the treatment of these systems. As the most frequently used model for interacting agent-based systems, a brief description of the statistical mechanics of the classical Ising model on regular lattices, together with recent extensions of the same model on small-world Watts-Strogatz and scale-free Albert-Barabasi complex networks is included. Other sections of the chapter are devoted to applications of complex networks to economics, finance, spreading of innovations, and regional trade and developments. The chapter also reviews results involving applications of complex networks to other relevant socioeconomic issues, including results for opinion and citation networks. Finally, some avenues for future research are introduced before summarizing the main conclusions of the chapter.Comment: 39 pages, 185 references, (not final version of) a chapter prepared for Complexity and Geographical Economics - Topics and Tools, P. Commendatore, S.S. Kayam and I. Kubin Eds. (Springer, to be published

Modelling innovation and the macroeconomics of low-carbon transitions: theory, perspectives and practical use

This is the author accepted manuscript. The final version is available from Taylor & Francis (Routledge) via the DOI in this record.Energy and climate policies may have significant economy-wide impacts, which are regularly assessed based on quantitative energy-environment-economy models. These tend to vary in their conclusions on the scale and direction of the likely macroeconomic impacts of a low-carbon transition. This paper traces the characteristic discrepancies in models’ outcomes to their origins in different macro-economic theories, most importantly their treatment of technological innovation and finance. We comprehensively analyse the relevant branches of macro-innovation theory and group them into two classes: ‘Equilibrium’ and ‘Non-equilibrium’. While both approaches are rigorous and self-consistent, they frequently yield opposite conclusions for the economic impacts of low-carbon policies. We show that model outcomes are mainly determined by their representations of monetary and finance dimensions, and their interactions with investment, innovation and technological change. Improving these in all modelling approaches is crucial for strengthening the evidence base for policy making and gaining a more consistent picture of the macroeconomic impacts of achieving emissions reductions objectives. The paper contributes towards the ongoing effort of enhancing the transparency and understanding of sophisticated model mechanisms applied to energy and climate policy analysis. It helps tackle the overall “black box” critique, much-cited in policy circles and elsewhere