2,124 research outputs found
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
A Model of Collaboration Network Formation with Heterogenous Skills
Collaboration networks provide a method for examining the highly
heterogeneous structure of collaborative communities. However, we still have
limited theoretical understanding of how individual heterogeneity relates to
network heterogeneity. The model presented here provides a framework linking an
individual's skill set to her position in the collaboration network, and the
distribution of skills in the population to the structure of the collaboration
network as a whole. This model suggests that there is a non-trivial
relationship between skills and network position: individuals with a useful
combination of skills will have a disproportionate number of links in the
network. Indeed, in some cases, an individual's degree is non-monotonic in the
number of skills she has--an individual with very few skills may outperform an
individual with many. Special cases of the model suggest that the degree
distribution of the network will be skewed, even when the distribution of
skills is uniform in the population. The degree distribution becomes more
skewed as problems become more difficult, leading to a community dominated by a
few high-degree superstars. This has striking implications for labor market
outcomes in industries where production is largely the result of collaborative
effort
Spatial networks in multi-region computable general equilibrium models:
The spatial dimension of economic policy is often important. However, as opposed to partial-equilibrium multi-region programming models, existing multi-region Computable General Equilibrium (CGE) models have rarely explicitly treated geographical space. This paper develops a spatial-network, mixed-complementarity CGE model that combines the strengths of CGE and partial-equilibrium programming models. We implement the model with a prototype data set for a stylized, poor, developing country with rural regions linked to an urban region that provides the gateway to international markets. We demonstrate that the model provides a good framework for analyzing the impact of higher world prices and reduced domestic transportation costs.Equilibrium (Economics), Economic policy., Spatial analysis (Statistics), Computable general equilibrium (CGE).,
Solving variational inequalities and cone complementarity problems in nonsmooth dynamics using the alternating direction method of multipliers
This work presents a numerical method for the solution of variational inequalities arising in nonsmooth flexible multibody problems that involve set-valued forces. For the special case of hard frictional contacts, the method solves a second order cone complementarity problem. We ground our algorithm on the Alternating Direction Method of Multipliers (ADMM), an efficient and robust optimization method that draws on few computational primitives. In order to improve computational performance, we reformulated the original ADMM scheme in order to exploit the sparsity of constraint jacobians and we added optimizations such as warm starting and adaptive step scaling. The proposed method can be used in scenarios that pose major difficulties to other methods available in literature for complementarity in contact dynamics, namely when using very stiff finite elements and when simulating articulated mechanisms with odd mass ratios. The method can have applications in the fields of robotics, vehicle dynamics, virtual reality, and multiphysics simulation in general
- …