Balanced Truncation Model Reduction of a Nonlinear Cable-Mass PDE System with Interior Damping

We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at one boundary. The goal of the model reduction is to produce a low order model that produces an accurate approximation to the displacement and velocity of the mass in the nonlinear mass-spring system at the opposite boundary. We first prove that the linearized and nonlinear unforced systems are well-posed and exponentially stable under certain conditions on the damping parameters, and then consider a balanced truncation method to generate the reduced order model (ROM) of the nonlinear input-output system. Little is known about model reduction of nonlinear input-output systems, and so we present detailed numerical experiments concerning the performance of the nonlinear ROM. We find that the ROM is accurate for many different combinations of model parameters

“Social media makes it inevitable to feel bad about your body”: examining self-presentation and body image of young collegiate females

The current study explored how young females who compete in aesthetic sports adopt self-presentation strategies on social media. Data from semi-structured interviews with 10 collegiate female trampolinists (aged 19–24 years) were analyzed through reflective thematic analysis, and six themes were generated; self-analysis, the best you, emotional consequences, judgment, social media perceptions, and acceptance. Framed around these themes, creative nonfiction techniques were employed to present the results as an ethnodrama. Findings illustrated how participants demonstrated a high need to present their “best self”, as failure to do so results in fear of judgment, extreme self-criticism, and, subsequently, post-prevention. Moreover, participants used upward social comparisons, and when they felt they did not match the ‘thin ideal’, often made negative associations between weight gain and attractiveness. This study contributes to body image literature by demonstrating a more detailed understanding of how social media influences one’s need to alter their self-presentation to fit in with highly pressured societal ideals. In addition, the ethnodrama provides an educational tool to stimulate reflection about the extremity of this issue in today’s modern world

A Proper Orthogonal Decomposition Approach to Approximate Balanced Truncation of Infinite Dimensional Linear Systems

We extend a method for approximate balanced reduced order model derivation for finite dimensional linear systems developed by Rowley (Int. J. Bifur. Chaos Appl. Sci. Eng. 15(3) (2005), pp. 997-1013) to infinite dimensional systems. The algorithm is related to standard balanced truncation, but includes aspects of the proper orthogonal decomposition in its computational approach. The method can be also applied to nonlinear systems. Numerical results are presented for a convection diffusion system

A Comparison of Balanced Truncation Methods for Closed Loop Systems

Real-time control of a physical system necessitates controllers that are low order. In this paper, we compare two balanced truncation methods as a means of designing low order compensators for partial differential equation (PDE) systems. The first method is the application of balanced truncation to the compensator dynamics, rather than the state dynamics, as was done in cite{Skelton:1984}. The second method, LQG balanced truncation, applies the balancing technique to the Riccati operators obtained from a specific LQG design. We discuss snapshot-based algorithms for constructing the reduced order compensators and present numerical results for a two dimensional convection diffusion PDE system

Balanced POD Algorithm for Robust Control Design for Linear Distributed Parameter Systems

A mathematical model of a physical system is never perfect; therefore, robust control laws are necessary for guaranteed stabilization of the nominal model and also nearby systems, including hopefully the actual physical system. We consider the computation of a robust control law for large-scale finite dimensional linear systems and a class of linear distributed parameter systems. The controller is robust with respect to left coprime factor perturbations of the nominal system. We present an algorithm based on balanced proper orthogonal decomposition to compute the nonstandard features of this robust control law. Numerical results are presented for a convection diffusion partial differential equation

Balanced Proper Orthogonal Decomposition for Model Reduction of Infinite Dimensional Linear Systems

In this paper, we extend a method for reduced order model derivation for finite dimensional systems developed by Rowley to infinite dimensional systems. The method is related to standard balanced truncation, but includes aspects of the proper orthogonal decomposition in its computational approach. The method is also applicable to nonlinear systems. The method is applied to a convection diffusion equation

Balanced POD for Linear PDE Robust Control Computations

A mathematical model of a physical system is never perfect; therefore, robust control laws are necessary for guaranteed stabilization of the nominal model and also nearby systems, including hopefully the actual physical system. We consider the computation of a robust control law for large-scale nite dimensional linear systems and a class of linear distributed parameter systems. The controller is robust with respect to left coprime factor perturbations of the nominal system. We present an algorithm based on balanced proper orthogonal decomposition to compute the nonstandard features of this robust control law. Convergence theory is given, and numerical results are presented for two partial di erential equation systems

Doing what it says on the tin?:A psychometric evaluation of the Assessment Experience Questionnaire

The Assessment Experience Questionnaire has been widely used to measure conditions of learning from assessment. It is one of three methods used in the ‘Transforming the Experience of Students through Assessment’ research process, originally funded by the Higher Education Academy to explore programme assessment patterns, and now used extensively in universities in the United Kingdom. Given the growth of assessment and feedback research over the last decade, the Assessment Experience Questionnaire is ripe for revision. Critics have queried its theoretical and statistical robustness. This study investigated the psychometric properties of the Assessment Experience Questionnaire, as the first step in the process of strengthening the instrument. Specifically, we examined the validity of the questionnaire with a sample of final year undergraduate students from eight UK universities (n = 633). Results were mixed, confirming that the questionnaire has some value, but indicating that not all sub-scales possess adequate psychometric properties to underpin confident conclusions. As a result, we have embarked on a process of making conceptual modifications to the Assessment Experience Questionnaire, both to update the theoretical constructs, and to ensure stronger overall validity. This article indicates the direction of these modifications, which will be outlined in a second article

Twitter discourse around competitive cycling and sports-related concussion

The purpose of this study was to explore the cycling community’s online interactions with sports-related concussion within competitive cycling. Through an analysis of twitter data (n=196), this study examined the discourse related to the problem of concussion in cycling. The results indicated that overall engagement and awareness of concussion in cycling was low but has been increasing year on year from 2008 to 2019. Thematic analysis of the data found three main themes within the online cycling community on Twitter: 1) Increasing awareness of concussion as a problem for the sport 2) A narrative of apathy in policy by governing bodies and 3) The need for better education as a result of misperceptions of concussion. Overall, these findings contribute to the limited research in the field of concussion in competitive cycling and outline the utility of social media as a platform to disseminate educational resources around the safe management of concussion in the sport