Search results for "online"
showing 10 items of 4526 documents
Magnetic field driven micro-convection in the Hele-Shaw cell
2013
AbstractMicro-convection caused by ponderomotive forces of the self-magnetic field of a magnetic fluid in the Hele-Shaw cell under the action of a vertical homogeneous magnetic field is studied both experimentally and numerically. It is shown that a non-potential magnetic force at magnetic Rayleigh numbers greater than the critical value causes fingering at the interface between the miscible magnetic and non-magnetic fluids. The threshold value of the magnetic Rayleigh number depends on the smearing of the interface between fluids. Fingering with its subsequent decay due to diffusion of particles significantly increases the mixing at the interface. Velocity and vorticity fields at fingering…
Constrained control of a nonlinear two point boundary value problem, I
1994
In this paper we consider an optimal control problem for a nonlinear second order ordinary differential equation with integral constraints. A necessary optimality condition in form of the Pontryagin minimum principle is derived. The proof is based on McShane-variations of the optimal control, a thorough study of their behaviour in dependence of some denning parameters, a generalized Green formula for second order ordinary differential equations with measurable coefficients and certain tools of convex analysis.
Nonsmooth Mechanics. Convex and Nonconvex Problems
1999
Nonlinear, multivalued and possibly nonmonotone relations arise in several areas of mechanics. A multivalued or complete relation is a relation with complete vertical branches. Boundary laws of this kind connect boundary (or interface) quantities. A contact relation or a locking mechanism between boundary displacements and boundary tractions in elasticity is a representative example. Material constitutive relations with complete branches connect stress and strain tensors, or, in simplified theories, equivalent stress and strain quantities. A locking material or a perfectly plastic one is represented by such a relation. The question of nonmonotonicity is more complicated. One aspect concerns…
Monotonicity and enclosure methods for the p-Laplace equation
2018
We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the $p$-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs, one of which is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.
Robust l2-gain control for 2D nonlinear stochastic systems with time-varying delays and actuator saturation
2013
Abstract This paper is concerned with the problems of stability analysis and l2-gain control for a class of two-dimensional (2D) nonlinear stochastic systems with time-varying delays and actuator saturation. Firstly, a convex hull representation is used to describe the saturation behavior, and a sufficient condition for the existence of mean-square exponential stability of the considered system is derived. Then, a state feedback controller which guarantees the resulting closed-loop system to be mean-square exponentially stable with l2-gain performance is proposed, and an optimization procedure to maximize the estimation of domain of attraction is also given. All the obtained results are for…
A constructive theory of shape
2021
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of qualitatively similar shapes are constructed giving as input a finite ordered set of characteristic points (landmarks) and the value of a continuous parameter $\kappa \in (0,\infty)$. We prove that all shapes belonging to the same family are located within the convex hull of the landmarks. The theory is constructive in the sense that it provides a systematic means to build a mathematical model for any shape taken from the physical world. We illustrate this with a va…
Enclosure method for the p-Laplace equation
2014
We study the enclosure method for the p-Calder\'on problem, which is a nonlinear generalization of the inverse conductivity problem due to Calder\'on that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, where the inclusion is modelled as a jump in the conductivity. The result is based on a monotonicity inequality and the properties of the Wolff solutions.
Learning Groups in MOOCs : Lessons for Online Learning in Higher Education
2017
when there is interaction within online learning groups, meaningful learning is achieved. Motivating and sustaining effective student interactions requires planning, coordination and implementation of curriculum, pedagogy and technology. For our aim to understand online learning group processes to identify effective online learning group mechanisms, comparative analysis was used on a massive open online course (MOOC) run in 2015 and 2016. Qualitative (interaction on the platform) and quantitative (survey) methods were used. The findings revealed several possible ways to improve online learning group processes. This paper concludes that course organization helped in increasing individual par…
Working on understanding during collaborative online reading
2012
This study examines how students in Finland (16-18 years of age) constructed meaning and knowledge in a collaborative online reading situation. Student pairs ( n = 19) were asked to write a joint essay on a controversial issue. First, the pairs discussed the topic freely to activate their prior knowledge. Next, they gathered source material on the Internet. Finally, they composed a joint essay. The data were collected using an interaction approach to verbal protocol data, along with video screen captures. In the analysis, three units were employed: episodes ( n = 562) for describing online reading practices; utterances ( n = 944) for identifying collaborative reading strategies; and collab…
Affordances of telecollaboration tools for English for Specific Purposes online learning
2016
This paper explores students' perceptions of the affordances of different telecollaboration tools used in an innovation project for English for Specific Purposes online learning carried out between the University of Valencia (Spain) and Wofford College (South Carolina, United States) during the school year 2015-2016. Different tools for synchronous and asynchronous communication were used. The asynchronous tools included a discussion forum, a wiki, social networking websites and Google forms; while the tools used for synchronous communication were text, voice and video chat, videoconferencing tools and Google Drive. All the tools were accessible through the online platform used in the proje…