Beyond an Input/Output Paradigm for Systems: Design Systems by Intrinsic Geometry

Systems

Germano Resconi²  Ignazio Licata³  Gianfranco Minati¹ 

[1] Department of Mathematics, Catholic University, via Trieste 17 Brescia, Italy; E-Mail;Department of Mathematics, Catholic University, via Trieste 17 Brescia, Italy; E-Mail:;ISEM, Institute for Scientific Methodology, 90146 Palermo, Italy

关键词: intrinsic geometry;    holonomic constraints;    nonholonomic systems;    dissipative systems;    free stress material;    Cartan moving reference;    Maxwell-like Gauge approach;    generalized Gauge as compensation;    non-conservative gravity;    gravity with torsion;    physical theory as system;    crystal defects;    memristors;   

DOI  :  10.3390/systems2040661

来源: mdpi

【 摘 要 】

Given a stress-free system as a perfect crystal with points or atoms ordered in a three dimensional lattice in the Euclidean reference space, any defect, external force or heterogeneous temperature change in the material connection that induces stress on a previously stress-free configuration changes the equilibrium configuration. A material has stress in a reference which does not agree with the intrinsic geometry of the material in the stress-free state. By stress we mean forces between parts when we separate one part from another (tailing the system), the stress collapses to zero for any part which assumes new configurations. Now the problem is that all the new configurations of the parts are incompatible with each other. This means that close loop in the earlier configuration now is not closed and that the two paths previously joining the same two points now join different points from the same initial point so the final point is path dependent. This phenomenon is formally described by the commutators of derivatives in the new connection of the stress-free parts of the system under the control of external currents. This means that we lose the integrability property of the system and the possibility to generate global coordinates. The incompatible system can be represented by many different local references or Cartan moving Euclidean reference, one for any part of the system that is stress-free. The material under stress when is free assumes an equilibrium configuration or manifold that describes the intrinsic “shape” or geometry of the natural stress—the free state of the material. Therefore, we outline a design system by geometric compensation as a prototypical constructive operation.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland.