The structural physical approximation conjecture

2016 ◽  
Vol 57 (1) ◽  
pp. 015218 ◽  
Author(s):  
Fred Shultz
Keyword(s):  
Physical Approximation

scholarly journals Understanding What Numbers Mean

2011 ◽  
Author(s):  
Ron Britton
Keyword(s):  
Undergraduate Education ◽  
Functional Characteristics ◽  
Physical Sense ◽  
Physical Approximation ◽  
Do So

As instructors we expect our students to understand what the numbers they generate “mean”. We expect them to be able to visualize, in real or virtual terms, some physical approximation of the “things” they are working with. This visualization provides the basis for a “logic check” on their calculations.Our profession is founded on our ability to specify, within imposed constraints, the physical and functional characteristics of a system that will provide a safe, affordable solution to a problem. Students need to develop and refine this capacity during their undergraduate education. As simple as that may seem to those of us who have experienced the realities of our particular areas of expertise, it is not intuitive. Virtually all academic engineers lament the fact that students regularly submit answers that make no physical sense. The twin questions this issue raises are:1. why do so many students seem to lack an understanding of what their computer generated numbers mean?, and2. how can we help them gain the understanding we want them to have?

On Kadison-Schwarz Approximation to Positive Maps

2020 ◽  
Vol 27 (03) ◽  
pp. 2050016
Author(s):  
Dariusz Chruściński ◽  
Farrukh Mukhamedov ◽  
Mohamed Ali Hajji
Keyword(s):  
Matrix Algebras ◽  
Positive Maps ◽  
Physical Approximation

We analyze Kadison-Schwarz approximation to positive maps in matrix algebras. This is an analogue of the well known structural physical approximation to positive maps used in entanglement theory. We study several known maps both decomposable (like transposition) and non-decomposable (like Choi map and its generalizations).

Topography Optimization of Shell Structures Under Transient Loading: A Comparative Approach

2012 ◽  
Author(s):  
Juan Camilo Medina ◽  
Andrés Tovar
Keyword(s):  
Sensitivity Analysis ◽  
Stochastic Approximation ◽  
State Of The Art ◽  
Computational Effort ◽  
Shell Structures ◽  
Comparative Approach ◽  
Shell Elements ◽  
Physical Approximation ◽  
Key Issues ◽  
Topography Optimization

Topography optimization is an innovative technique that can significantly improve the response of certain type of structures. The most challenging aspect of topography optimization is the sensitivity analysis. In this manuscript two methods to approximate the sensitivities for problems in topography optimization are introduced. The gradient is supplanted with either a stochastic approximation, or a physical approximation. Initially, an overview of the state-of-the-art in topography optimization is presented, and some key issues are explored. Subsequently, the technique is outlined, and the proposed methods are introduced. Furthermore, a numerical example in which a structure composed of shell elements is subject to a blast load is provided. This example is solved employing stochastic gradient approximation, and approximate gradient. They are compared to the widely used finite differences approximation. It is possible to observe that the proposed method significantly reduces the computational effort required to solve the problem, while considerably improving the objective function.

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