Performance of a worm algorithm in ϕ4\phi^4 theory at finite quartic coupling

Worm algorithms have been very successful with the simulation of sigma models with fixed length spins which result from scalar field theories in the limit of infinite quartic coupling lambda. Here we investigate closer their algorithmic efficiency at finite and even vanishing lambda for the one component model in dimensions D = 2, 3, 4.Comment: 10 pages, 2 Fig

Strategic Uncertainty in Markets for Nonrenewable Resources: A Level- k

Existing models of nonrenewable resources assume that sophisticated agents compete with other sophisticated agents. This study instead uses a level-k approach to examine cases where the focal agent is uncertain about the strategy of his opponent or predicts that the opponent will act in a nonsophisticated manner. Level-0 players are randomized uniformly across all possible actions, and level-k players best respond to the action of player k-1. We study a dynamic nonrenewable resource game with a large number of actions. We are able to solve for the level-1 strategy by reducing the averaging problem to an optimization problem against a single action. We show that lower levels of strategic reasoning are close to the Walras and collusive benchmark, whereas higher level strategies converge to the Nash-Hotelling equilibrium. These results are then fitted to experimental data, suggesting that the level of sophistication of participants increased over the course of the experiment

Reducing global CO2 emissions with the technologies we have

The energy intensities of the various industrial sectors differ considerably across countries. This suggests a potential for emissions reductions through improved accessibility to efficient technologies. This paper estimates an upper-bound CO2 emission mitigation potential that could theoretically be achieved by improved access to efficient technologies in industrial sectors. We develop a linear optimization framework that facilitates the exchange of sectoral production technologies based on the World Input-Output Database (WIOD), assuming perfect substitutability of technologies and homogeneity within economic sectors, while ignoring barriers to technological adoption and price driven adjustments. We consider the full global supply chain network and multiple upstream production inputs in addition to energy demand. In contrast to existing literature our framework allows to consider supply chain effects of technology replacements. We use our model to calculate emission reduction potentials for varying levels of access to technology. If best practice technologies were made available globally, CO2 emissions could theoretically be reduced by more than 10 gigatons (Gt). In fact, even second-tier production technologies would create significant global reduction potentials. We decompose sectoral emission reductions to identify contributions by changes in energy intensity, supply chain effects and changes in carbon intensities. Excluding the latter, we find that considering supply chain effects increases total mitigation potentials by 14%. The largest CO2 emission reduction potentials are found for a small set of developing countries.DFG, SFB 1026, Sustainable Manufacturing - Globale Wertschöpfung nachhaltig gestalte

Modern Nonlinear Optimization Techniques for an Optimal Control of System Dynamics Models.

We study System Dynamics models with several free parameters that can be altered by the user. We assume that the user's goal is to achieve a certain dynamic behavior of the model by varying these parameters. In order to find best possible combination of parameter settings, several automatic parameter tuning methods are described in the literature and readily available within existing System Dynamic software packages. We give a survey on the available techniques in the market and describe their theoretical background. Some of these methods are already six decades old, and meanwhile newer and more powerful optimization methods have emerged in the mathematical literature. One major obstacle for their direct use are tabled data in System Dynamics models, which are usually interpreted as piecewise linear functions. However, modern optimization methods usually require smooth functions which are twice continuously differentiable. We overcome this problem by a smooth spline interpolation of the tabled data. We use a test set of three complex System Dynamic models from the literature, describe their individual transition into optimization problems, and demonstrate the applicability of modern optimization algorithms to these System Dynamics Optimization problems

Simulation of phi 4 theory in the strong coupling expansion beyond the Ising Limit

Diese Arbeit beschäftigt sich mit der Simulation der phi**4-Theorie mit dem Wurm-Algorithmus, einer Simulationsmethode die sich als sehr effizient bei der Betrachtung kritischer Systeme gezeigt hat. Die Entwicklung der Theorie in die Strong-Coupling-Expansion wird beschrieben und zwei Varianten des Wurm-Algorithmus werden vorgestellt. Eine Implementierung des Algorithmus in C wird angefertigt und die Ergebnisse von Tests im Ising- und Gauß-Limes sowie in phi**4-Theorie mit endlicher Wechselwirkung werden präsentiert und mit einer konventionellen Metropolis-Simulation verglichen. Anschließend wird die Dynamik des Algorithmus ausführlich im freien sowie im wechselwirkenden Fall der Theorie in zwei, drei und vier Dimensionen untersucht. In der freien zweidimensionalen Theorie weist der Algorithmus ausgeprägtes Critical Slowing Down mit kritischen Exponenten von bis zu 1.6 auf. In drei Dimensionen liegen alle kritischen Exponenten unter 1.0, und in vier Dimensionen messen wir kritische Exponenten von bis zu 0.6. Wir präsentieren eine Heuristik, die dieses Verhalten auf lange Autokorrelationen in der Besetzung des Link-Feldes zurückführt. Unsere Messungen in der wechselwirkenden Theorie werden bei lambda=0.5 durchgeführt. Autokorrelationszeiten sind hier wesentlich kürzer als in der freien Theorie. Kritische Exponenten sind von Observable zu Observable sehr unterschiedlich, liegen aber in jedem Fall unter 0.55. In vielen Fällen wird auch ein ein logarithmischer Zusammenhang festgestellt. Ein Methode zur Schätzung der renormierten Kopplung mit dem Wurm-Algorithmus wird vorgestellt. Tests zeigen jedoch, dass sich dieser Ansatz nicht für kritische Systeme eignet.This thesis reports on the simulation of phi**4 theory using the worm algorithm, a recent simulation method which has been proven to eliminate critical slowing down in a number of statistical systems. The untruncated strong coupling represention of the theory is derived and two variants of the worm algorithm for phi**4 theory are presented. The algorithm is implemented in C, and we report on tests in the Ising and Gaussian limits of the theory as well as at finite coupling strengths, and compare results with a standard Metropolis simulation. The dynamical behavior of the algorithm is examined in detail in the Gaussian case and in the interacting case at lambda=0.5 in two, three and four dimensions. We find substantial critical slowing down in the two-dimensional Gaussian case and measure critical exponents of up to 1.6. This is reduced in three dimensions where we measure critical exponents below one, and further reduced in four dimensions where critical exponents are below 0.6. We present some heuristic arguments that this is due to very long autocorrelations in the population of the link field. In the interacting theory, we find short autocorrelations independent of the dimension of the theory. Different observables here show distinct dynamical behavior, but all measured critical exponents are below 0.55. In several cases we also find logarithmic behavior. An approach to the estimation of the renormalized coupling using the worm algorithm is presented, but tests show that it is ill-suited for critical systems

Trajectory optimisation for inland water vessels based on a next generation PNT‐Unit

Routing and manoeuver planning are accepted tasks of deep sea vessel navigation to increase the safety on sea and to improve the time- and resource efficient transport of goods and passengers. Trajectory optimization of inland water vessels is a similar navigational task intended to ensure a safe passing of bridges and an efficient locking of vessels. A resilient provision of position, navigation, and timing (PNT) characterising vessels’ position and movement in real time is an essential basis for a reliable description of traffic situation. At last the quality and completeness of traffic situation parameter and the applied mathematical optimisation procedure determine the effectiveness and reliability of trajectory optimization. The paper presents the general architecture of a driver assistance system and discusses an optimisation approach based on first numerical results

Using white‐box nonlinear optimization methods in system dynamics policy improvement

We present a new strategy for the direct optimization of the values of policy functions. This approach is particularly well suited to model actors with a global perspective on the system and relies heavily on modern mathematical white‐box optimization methods. We demonstrate our strategy on two classical models: market growth and World2. Each model is first transformed into an optimization problem by defining how the actor can influence the models' dynamics and by choosing objective functions to measure improvements. To improve comparability between different runs, we also introduce a comparison measure for possible interventions. We solve the optimization problems, discuss the resulting policies and compare them to the existing results from the literature. In particular, we present a run of the World2 model which significantly improves the published “towards a global equilibrium” run with equal cost of intervention