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We establish that the initial value problem for a generalised Burgers equation considered in part I of this paper, is well-posed. We also establish several qualitative properties of solutions to the initial value problem utilised in part I of the paper., Comment: 14 pages. No figures

This paper introduces the APIA architecture for policy-aware intentional agents. These agents, acting in changing environments, are driven by intentions and yet abide by domain-relevant policies. This work leverages the AIA architecture for intention-driven intelligent agents by Blount, Gelfond, and Balduccini. It expands AIA with notions of policy compliance for authorization and obligation policies specified in the language AOPL by Gelfond and Lobo. APIA introduces various agent behavior modes, corresponding to different levels of adherence to policies. APIA reasoning tasks are reduced to computing answer sets using the Clingo solver and its Python API., Comment: In Proceedings ICLP 2021, arXiv:2109.07914

Self-organization is a process where a stable pattern is formed by the cooperative behavior between parts of an initially disordered system without external control or influence. It has been introduced to multi-agent systems as an internal control process or mechanism to solve difficult problems spontaneously. However, because a self-organizing multi-agent system has autonomous agents and local interactions between them, it is difficult to predict the behavior of the system from the behavior of the local agents we design. This paper proposes a logic-based framework of self-organizing multi-agent systems, where agents interact with each other by following their prescribed local rules. The dependence relation between coalitions of agents regarding their contributions to the global behavior of the system is reasoned about from the structural and semantic perspectives. We show that the computational complexity of verifying such a self-organizing multi-agent system is in exponential time. We then combine our framework with graph theory to decompose a system into different coalitions located in different layers, which allows us to verify agents' full contributions more efficiently. The resulting information about agents' full contributions allows us to understand the complex link between local agent behavior and system level behavior in a self-organizing multi-agent system. Finally, we show how we can use our framework to model a constraint satisfaction problem.

In this paper we develop and significantly extend the thermal phase change model, introduced in [12], describing the process of paraffinic wax layer formation on the interior wall of a circular pipe transporting heated oil, when subject to external cooling. In particular we allow for the natural dependence of the solidifying paraffinic wax conductivity on local temperature. We are able to develop a complete theory, and provide efficient numerical computations, for this extended model. Comparison with recent experimental observations is made, and this, together with recent reviews of the physical mechanisms associated with wax layer formation, provide significant support for the thermal model considered here., Comment: 34 pages, 5 figures. Reference [12] is to https://doi.org/10.1093/qjmam/hbt025

We present extensions of the comparison and maximum principles available for nonlinear non-local integro-differential operators $P:\mathcal{C}^{2,1}(\Omega \times (0,T])\times L^\infty (\Omega \times (0,T])\to\mathbb{R}$, of the form $P[u] = L[u] -f(\cdot ,\cdot ,u,Ju)$ on $\Omega \times (0,T]$. Here, we consider: unbounded spatial domains $\Omega \subset \mathbb{R}^n$, with $T>0$; sufficiently regular second order linear parabolic partial differential operators $L$; sufficiently regular semi-linear terms $f:(\Omega \times (0,T]) \times \mathbb{R}^2\to\mathbb{R}$; and the non-local term $Ju= \int_{{\Omega}}\phi(x-y)u(y,t)dy$, with $\phi$ in a class of non-negative sufficiently summable kernels. We also provide examples illustrating the limitations and applicability of our results., Comment: 12 pages, 0 figures