Abstract. This paper presents the new and now open-source version 2.1 of the REgional Model of INvestments and Development (REMIND). REMIND, as an integrated assessment model (IAM), provides an integrated view of the global energy–economy–emissions system and explores self-consistent transformation pathways. It describes a broad range of possible futures and their relation to technical and socio-economic developments as well as policy choices. REMIND is a multiregional model incorporating the economy and a detailed representation of the energy sector implemented in the General Algebraic Modeling System (GAMS). It uses non-linear optimization to derive welfare-optimal regional transformation pathways of the energy-economic system subject to climate and sustainability constraints for the time horizon from 2005 to 2100. The resulting solution corresponds to the decentralized market outcome under the assumptions of perfect foresight of agents and internalization of external effects. REMIND enables the analyses of technology options and policy approaches for climate change mitigation with particular strength in representing the scale-up of new technologies, including renewables and their integration in power markets. The REMIND code is organized into modules that gather code relevant for specific topics. Interaction between different modules is made explicit via clearly defined sets of input and output variables. Each module can be represented by different realizations, enabling flexible configuration and extension. The spatial resolution of REMIND is flexible and depends on the resolution of the input data. Thus, the framework can be used for a variety of applications in a customized form, balancing requirements for detail and overall runtime and complexity.

Abstract. This paper presents the new and now open-source version 2.1 of the REgional Model of INvestments and Development (REMIND). REMIND, as an Integrated Assessment Model (IAM), provides an integrated view on the global energy-economy-emissions system and explores self-consistent transformation pathways. It describes a broad range of possible futures and their relation to technical and socio-economic developments as well as policy choices. REMIND is a multi-regional model incorporating the economy and a detailed representation of the energy sector implemented in the General Algebraic Modeling System (GAMS). It uses non-linear optimization to derive welfare-optimal regional transformation pathways of the energy-economic system subject to climate and sustainability constraints for the time horizon 2005 to 2100. The resulting solution corresponds to the decentral market outcome under the assumptions of perfect foresight of agents and internalization of external effects. REMIND enables analyses of technology options and policy approaches for climate change mitigation with particular strength in representing the scale-up of new technologies, including renewables and their integration in power markets. The REMIND code is organized into modules that gather code relevant for specific topics. Interaction between different modules is made explicit via clearly defined sets of input/output variables. Each module can be represented by different realizations enabling flexible configuration and extension. The spatial resolution of REMIND is flexible and depends on the resolution of the input data. The framework can thus be used for a variety of applications in a customized form balancing requirements for detail and overall run-time and complexity.

We consider the Kuramoto-Sakaguchi model of identical coupled phase oscillators with a common noisy forcing. While common noise always tends to synchronize the oscillators, a strong repulsive coupling prevents the fully synchronous state and leads to a nontrivial distribution of oscillator phases. In previous numerical simulations, a formation of stable multicluster states has been observed in this regime. However we argue here, that because identical phase oscillators in the Kuramoto-Sakaguchi model form a partially integrable system according to the Watanabe-Strogatz theory, the formation of clusters is impossible. Integrating with various time steps reveals that clustering is a numerical artifact, explained by the existence of higher order Fourier terms in the errors of the employed numerical integration schemes. Monitoring the induced change in certain integrals of motion we quantify these errors. We support these observations by showing, on the basis of the analysis of the corresponding Fokker-Planck equation, that two-cluster states are non-attractive. On the other hand, in ensembles of general limit cycle oscillators, such as Van der Pol oscillators, due to an anharmonic phase response function, as well as additional amplitude dynamics, multiclusters can occur naturally.a)

The Kuramoto model, despite its popularity as a mean field theory for many synchronization phenomenon of oscillatory systems, is limited to a first order harmonic coupling of phases. For higher order coupling, there only exists a low-dimensional theory in the thermodynamic limit. In this paper, we extend the formulation used by Watanabe and Strogatz to obtain a low-dimensional description of a system of arbitrary size of identical oscillators coupled all-to-all via their higher order modes. We use a non-trivial second harmonic model exhibiting asymmetrical clustering to demonstrate an application of the formulation, to explore certain features of its dynamics using analytical theory, as well as to discuss certain phenomena not observed at the level of first order harmonic coupling.