Ancient multiple-layer solutions to the Allen-Cahn equation

We consider the parabolic one-dimensional Allen-Cahn equation $$u_t= u_{xx}+ u(1-u^2)\quad (x,t)\in \mathbb{R}\times (-\infty, 0].$$ The steady state $w(x) =\tanh (x/\sqrt{2})$, connects, as a "transition layer" the stable phases $-1$ and $+1$. We construct a solution $u$ with any given number $k$ of transition layers between $-1$ and $+1$. At main order they consist of $k$ time-traveling copies of $w$ with interfaces diverging one to each other as $t\to -\infty$. More precisely, we find $$u(x,t) \approx \sum_{j=1}^k (-1)^{j-1}w(x-\xi_j(t)) + \frac 12 ((-1)^{k-1}- 1)\quad \hbox{as} t\to -\infty,$$ where the functions $\xi_j(t)$ satisfy a first order Toda-type system. They are given by $$\xi_j(t)=\frac{1}{\sqrt{2}}\left(j-\frac{k+1}{2}\right)\log(-t)+\gamma_{jk},\quad j=1,...,k,$$ for certain explicit constants $\gamma_{jk}.

Ancient shrinking spherical interfaces in the Allen-Cahn flow

We consider the parabolic Allen-Cahn equation in $\mathbb{R}^n$, $n\ge 2$, $$u_t= \Delta u + (1-u^2)u \quad \hbox{ in } \mathbb{R}^n \times (-\infty, 0].$$ We construct an ancient radially symmetric solution $u(x,t)$ with any given number $k$ of transition layers between $-1$ and $+1$. At main order they consist of $k$ time-traveling copies of $w$ with spherical interfaces distant $O(\log |t| )$ one to each other as $t\to -\infty$. These interfaces are resemble at main order copies of the {\em shrinking sphere} ancient solution to mean the flow by mean curvature of surfaces: $|x| = \sqrt{- 2(n-1)t}$. More precisely, if $w(s)$ denotes the heteroclinic 1-dimensional solution of $w'' + (1-w^2)w=0$ $w(\pm \infty)= \pm 1$ given by $w(s) = \tanh \left(\frac s{\sqrt{2}} \right)$ we have $$u(x,t) \approx \sum_{j=1}^k (-1)^{j-1}w(|x|-\rho_j(t)) - \frac 12 (1+ (-1)^{k}) \quad \hbox{ as } t\to -\infty$$ where $$\rho_j(t)=\sqrt{-2(n-1)t}+\frac{1}{\sqrt{2}}\left(j-\frac{k+1}{2}\right)\log\left(\frac {|t|}{\log |t| }\right)+ O(1),\quad j=1,\ldots ,k.$

Designing a gamified social platform for people living with dementia and their live-in family caregivers

In the current paper, a social gamified platform for people living with dementia and their live-in family caregivers, integrating a broader diagnostic approach and interactive interventions is presented. The CAREGIVERSPRO-MMD (C-MMD) platform constitutes a support tool for the patient and the informal caregiver - also referred to as the dyad - that strengthens self-care, and builds community capacity and engagement at the point of care. The platform is implemented to improve social collaboration, adherence to treatment guidelines through gamification, recognition of progress indicators and measures to guide management of patients with dementia, and strategies and tools to improve treatment interventions and medication adherence. Moreover, particular attention was provided on guidelines, considerations and user requirements for the design of a User-Centered Design (UCD) platform. The design of the platform has been based on a deep understanding of users, tasks and contexts in order to improve platform usability, and provide adaptive and intuitive User Interfaces with high accessibility. In this paper, the architecture and services of the C-MMD platform are presented, and specifically the gamification aspects. © 2018 Association for Computing Machinery.Peer ReviewedPostprint (author's final draft

MULTI AGENT-BASED ENVIRONMENTAL LANDSCAPE (MABEL) - AN ARTIFICIAL INTELLIGENCE SIMULATION MODEL: SOME EARLY ASSESSMENTS

The Multi Agent-Based Environmental Landscape model (MABEL) introduces a Distributed Artificial Intelligence (DAI) systemic methodology, to simulate land use and transformation changes over time and space. Computational agents represent abstract relations among geographic, environmental, human and socio-economic variables, with respect to land transformation pattern changes. A multi-agent environment is developed providing task-nonspecific problem-solving abilities, flexibility on achieving goals and representing existing relations observed in real-world scenarios, and goal-based efficiency. Intelligent MABEL agents acquire spatial expressions and perform specific tasks demonstrating autonomy, environmental interactions, communication and cooperation, reactivity and proactivity, reasoning and learning capabilities. Their decisions maximize both task-specific marginal utility for their actions and joint, weighted marginal utility for their time-stepping. Agent behavior is achieved by personalizing a dynamic utility-based knowledge base through sequential GIS filtering, probability-distributed weighting, joint probability Bayesian correlational weighting, and goal-based distributional properties, applied to socio-economic and behavioral criteria. First-order logics, heuristics and appropriation of time-step sequences employed, provide a simulation-able environment, capable of re-generating space-time evolution of the agents.Environmental Economics and Policy,

Artificial Intelligence Helps Primary School Teachers to Plan and Execute Physics Classroom Experiments

The research claims that artificial intelligence technologies can help and direct primary school teachers in organising classroom experiments for physics instruction. Educators now have the potential to construct experimental projects that are entertaining and efficient, all while catering to their students’ many learning styles and capabilities. This is made possible by the availability of artificial intelligence technologies. The incorporation of artificial intelligence into educational settings may result in an improvement in the overall quality of teaching as well as an improvement in the scientific performance of students. The chance to improve the learning experience for both students and teachers is available to educators who do an in-depth study on artificial intelligence-driven teaching solutions. The research highlights how artificial intelligence can transform teaching approaches in elementary school, notably in the field of physics education within the context of primary school settings

Protostar Formation in Magnetic Molecular Clouds beyond Ion Detachment: I. Formulation of the Problem and Method of Solution

We formulate the problem of the formation of magnetically supercritical cores in magnetically subcritical parent molecular clouds, and the subsequent collapse of the cores to high densities, past the detachment of ions from magnetic field lines and into the opaque regime. We employ the six-fluid MHD equations, accounting for the effects of grains (negative, positive and neutral) including their inelastic collisions with other species. We do not assume that the magnetic flux is frozen in any of the charged species. We derive a generalized Ohm's law that explicitly distinguishes between flux advection (and the associated process of ambipolar diffusion) and Ohmic dissipation, in order to assess the contribution of each mechanism to the increase of the mass-to-flux ratio of the central parts of a collapsing core and possibly to the resolution of the magnetic flux problem of star formation. We show how our formulation is related to and can be transformed into the traditional, directional formulation of the generalized Ohm's law, and we derive formulae for the perpendicular, parallel and Hall conductivities entering the latter, which include, for the first time, the effect of inelastic collisions between grains. In addition, we present a general (valid in any geometry) solution for the velocities of charged species as functions of the velocity of the neutrals and of the effective flux velocity (which can in turn be calculated from the dynamics of the system and Faraday's law). The last two sets of formulae can be adapted for use in any general non-ideal MHD code to study phenomena beyond star formation in magnetic clouds. The results, including a detailed parameter study, are presented in two accompanying papers.Comment: 17 pages, emulateapj; accepted for publication in the Astrophysical Journa

Limits to ion energy control in high density glow discharges: Measurement of absolute metastable ion concentrations

Unprecedented demands for uniformity, throughput, anisotropy, and damage control in submicron pattern transfer are spurring development of new, low pressure, high charge density plasma reactors. Wafer biasing, independent of plasma production in these new systems is intended to provide improved ion flux and energy control so that selectivity can be optimized and damage can be minimized. However, as we show here, an inherent property of such discharges is the generation of significant densities of excited, metastable ionic states that can bombard workpiece surfaces with higher translational and internal energy. Absolute metastable ion densities are measured using the technique of self-absorption, while the corresponding velocity distributions and density scaling with pressure and electron density are measured using laser-induced fluorescence. For a low pressure, helicon-wave excited plasma, the metastable ion flux is at least 24% of the total ion flux to device surfaces. Because the metastable ion density scales roughly as the reciprocal of the pressure and as the square of the electron density, the metastable flux is largest in low pressure, high charge density plasmas. This metastable ion energy flux effectively limits ion energy and flux control in these plasma reactors, but the consequences for etching and deposition of thin films depend on the material system and remain an open question

Optimising superoscillatory spots for far-field super-resolution imaging

Optical superoscillatory imaging, allowing unlabelled far-field super-resolution, has in recent years become reality. Instruments have been built and their super-resolution imaging capabilities demonstrated. The question is no longer whether this can be done, but how well: what resolution is practically achievable? Numerous works have optimised various particular features of superoscillatory spots, but in order to probe the limits of superoscillatory imaging we need to simultaneously optimise all the important spot features: those that define the resolution of the system. We simultaneously optimise spot size and its intensity relative to the sidebands for various fields of view, giving a set of best compromises for use in different imaging scenarios. Our technique uses the circular prolate spheroidal wave functions as a basis set on the field of view, and the optimal combination of these, representing the optimal spot, is found using a multi-objective genetic algorithm. We then introduce a less computationally demanding approach suitable for real-time use in the laboratory which, crucially, allows independent control of spot size and field of view. Imaging simulations demonstrate the resolution achievable with these spots. We show a three-order-of-magnitude improvement in the efficiency of focusing to achieve the same resolution as previously reported results, or a 26 % increase in resolution for the same efficiency of focusing