Solving 2^{nd} order parabolic system by simulations of Markov jump processes

There are known methods of approximating the solution of parabolic 2^{nd} order systems by solving stochastic differential equations instead. The main idea is based on the fact that a stochastic differential equation defines a diffusion process, generated by an elliptic differential operator on R^{d}. We propose a difference scheme for the elliptic operator, which possesses the structure of Markov (jump) process. The existence of such a scheme is proved, the proof relying on the choice of new coordinates in which the elliptic operator is "almost\u27\u27 Laplacian, and has the properties necessary for discretization. Time discretization, which involves difference schemes for parabolic equations with known stability difficulties, can thus be replaced by space discretization and simulation of the associated Markov (jump) process

Grid edge system simulation and evaluation tool (GESSO): Development of a tool for the modelling and design of distributed cooperating microgrids

As advancements are made in the availability of small renewable generation power storage technologies, nations are starting to see a trend towards more distributed power and generation. As times change, changes must also be made to the ways in which we consume and distribute power. Distributed microgrids represent the ability for communities to cooperate in the distribution of power within neighborhoods. This thesis explores the structure of neighborhood scale distributed microgrids, defining the features and components needed to provide for accurate simulation. Techniques are developed for the integration of non-homogeneous microgrid systems to allow for smart grid-edge trading between units and microgrids. Exploration is conducted on the features required for an interactive system allowing the design and modelling of individual microgrid components and of neighborhood-scale microgrids, including the design of per-unit smart control schemes, and a proof of concept implementation is created allowing for simulation of non-homogeneous neighborhood scale fractal microgrids with arbitrary complexity. Sample cases are presented in order to demonstrate the effectiveness of the tool. The presented sample cases serve to demonstrate the effectiveness of small non-homogeneous microgrids, including those involving third party storage leasing services, and analysis is performed on the expected economic impacts of these types of systems

A framework for proof certificates in finite state exploration

Model checkers use automated state exploration in order to prove various properties such as reachability, non-reachability, and bisimulation over state transition systems. While model checkers have proved valuable for locating errors in computer models and specifications, they can also be used to prove properties that might be consumed by other computational logic systems, such as theorem provers. In such a situation, a prover must be able to trust that the model checker is correct. Instead of attempting to prove the correctness of a model checker, we ask that it outputs its "proof evidence" as a formally defined document--a proof certificate--and that this document is checked by a trusted proof checker. We describe a framework for defining and checking proof certificates for a range of model checking problems. The core of this framework is a (focused) proof system that is augmented with premises that involve "clerk and expert" predicates. This framework is designed so that soundness can be guaranteed independently of any concerns for the correctness of the clerk and expert specifications. To illustrate the flexibility of this framework, we define and formally check proof certificates for reachability and non-reachability in graphs, as well as bisimulation and non-bisimulation for labeled transition systems. Finally, we describe briefly a reference checker that we have implemented for this framework.Comment: In Proceedings PxTP 2015, arXiv:1507.0837

An Algorithm for Probabilistic Alternating Simulation

In probabilistic game structures, probabilistic alternating simulation (PA-simulation) relations preserve formulas defined in probabilistic alternating-time temporal logic with respect to the behaviour of a subset of players. We propose a partition based algorithm for computing the largest PA-simulation, which is to our knowledge the first such algorithm that works in polynomial time, by extending the generalised coarsest partition problem (GCPP) in a game-based setting with mixed strategies. The algorithm has higher complexities than those in the literature for non-probabilistic simulation and probabilistic simulation without mixed actions, but slightly improves the existing result for computing probabilistic simulation with respect to mixed actions.Comment: We've fixed a problem in the SOFSEM'12 conference versio