885,836 research outputs found
Fixpoint Games on Continuous Lattices
Many analysis and verifications tasks, such as static program analyses and
model-checking for temporal logics reduce to the solution of systems of
equations over suitable lattices. Inspired by recent work on lattice-theoretic
progress measures, we develop a game-theoretical approach to the solution of
systems of monotone equations over lattices, where for each single equation
either the least or greatest solution is taken. A simple parity game, referred
to as fixpoint game, is defined that provides a correct and complete
characterisation of the solution of equation systems over continuous lattices,
a quite general class of lattices widely used in semantics. For powerset
lattices the fixpoint game is intimately connected with classical parity games
for -calculus model-checking, whose solution can exploit as a key tool
Jurdzi\'nski's small progress measures. We show how the notion of progress
measure can be naturally generalised to fixpoint games over continuous lattices
and we prove the existence of small progress measures. Our results lead to a
constructive formulation of progress measures as (least) fixpoints. We refine
this characterisation by introducing the notion of selection that allows one to
constrain the plays in the parity game, enabling an effective (and possibly
efficient) solution of the game, and thus of the associated verification
problem. We also propose a logic for specifying the moves of the existential
player that can be used to systematically derive simplified equations for
efficiently computing progress measures. We discuss potential applications to
the model-checking of latticed -calculi and to the solution of fixpoint
equations systems over the reals
Synchronisation of time--delay systems
We present the linear-stability analysis of synchronised states in coupled
time-delay systems. There exists a synchronisation threshold, for which we
derive upper bounds, which does not depend on the delay time. We prove that at
least for scalar time-delay systems synchronisation is achieved by transmitting
a single scalar signal, even if the synchronised solution is given by a
high-dimensional chaotic state with a large number of positive
Lyapunov-exponents. The analytical results are compared with numerical
simulations of two coupled Mackey-Glass equations
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Significance of the microfluidic concepts for the improvement of macroscopic models of transport phenomena
This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.Complexity of transport phenomena - ranging from macroscopic motion of matter, heat transfer, over to the molecular motions determining the overall flow properties of fluids, or generally aggregation states of matter – inhibited development of a single mathematical model describing simultaneously
transport processes at all relevant scales. In classical engineering sciences at each scale level we have different equations, different fundamental variables and different methods of solution [4]. The established basis of the classical fluid dynamics - the Navier-Stokes equations [1, 3] - have apparently nothing in common with molecular physics. At the macroscopic scale of motion the molecular structure of matter
and the microscopic molecular motions are ignored (even though they determine the local macroscopic behaviour) [1, 3, 4]. To describe multiphase flows, still other methods must be used – increasing further the
number of equations, methods of solution etc. The serious disadvantage of this approach is, that equations describing macroscopic models (Navier-Stokes and there from derived equations), introduce multiple
theoretical problems: - higher order continuity requirements [3]; - numerous paradoxes in simple macroscopic flows (Bernoulli eq.); - different equations with different fundamental variables and different methods of solution, build a set of
disciplines devoted in principle to a single problem – dynamics of disperse systems
XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations
XMDS2 is a cross-platform, GPL-licensed, open source package for numerically
integrating initial value problems that range from a single ordinary
differential equation up to systems of coupled stochastic partial differential
equations. The equations are described in a high-level XML-based script, and
the package generates low-level optionally parallelised C++ code for the
efficient solution of those equations. It combines the advantages of high-level
simulations, namely fast and low-error development, with the speed, portability
and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS
package, and features support for a much wider problem space while also
producing faster code.Comment: 9 pages, 5 figure
Homogenization of weakly coupled systems of Hamilton--Jacobi equations with fast switching rates
We consider homogenization for weakly coupled systems of Hamilton--Jacobi
equations with fast switching rates. The fast switching rate terms force the
solutions converge to the same limit, which is a solution of the effective
equation. We discover the appearance of the initial layers, which appear
naturally when we consider the systems with different initial data and analyze
them rigorously. In particular, we obtain matched asymptotic solutions of the
systems and rate of convergence. We also investigate properties of the
effective Hamiltonian of weakly coupled systems and show some examples which do
not appear in the context of single equations.Comment: final version, to appear in Arch. Ration. Mech. Ana
Higher-order CFD and Interface Tracking Methods on Highly-Parallel MPI and GPU systems
A computational investigation of the effects on parallel performance of higher-order accurate schemes was carried out on two different computational systems: a traditional CPU based MPI cluster and a system of four Graphics Processing Units (GPUs) controlled by a single quad-core CPU. The investigation was based on the solution of the level set equations for interface tracking using a High-Order Upstream Central (HOUC) scheme. Different variants of the HOUC scheme were employed together with a 3rd-order TVD Runge-Kutta time integration. An increase in performance of two orders of magnitude was seen when comparing a single CPU core to a single GPU with a greater increase at higher orders of accuracy and at lower precision
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