PT-symmetry and supersymmetry: interconnection of broken and unbroken phases

The broken and unbroken phases of P T and supersymmetry in optical systems are explored for a complex refractive index profile in the form of a Scarf potential, under the framework of supersymmetric quantum mechanics. The transition from unbroken to the broken phases of P T -symmetry, with the merger of eigenfunctions near the exceptional point is found to arise from two distinct realizations of the potential, originating from the underlying supersymmetry. Interestingly, in P T -symmetric phase, spontaneous breaking of supersymmetry occurs in a parametric domain, possessing non-trivial shape invariances, under reparametrization to yield the corresponding energy spectra. One also observes a parametric bifurcation behaviour in this domain. Unlike the real Scraf potential, in P T -symmetric phase, a connection between complex isospecrtal superpotentials and modified Korteweg-de Vries equation occurs, only with certain restrictive parametric conditions. In the broken P T -symmetry phase, supersymmetry is found to be intact in the entire parameter domain yielding the complex energy spectra, with zero-width resonance occurring at integral values of a potential parameter.

Design of a Beam-Based Variable Stiffness Actuator via Shape Optimization in a CAD/CAE Environment

Industrial robots are commonly designed to be very fast and stiff in order to achieve extremely precise position control capabilities. Nonetheless, high speeds and power do not allow for a safe physical interaction between robots and humans. With the exception of the latest generation lightweight arms, purposely design for human-robot collaborative tasks, safety devices shall be employed when workers enter the robots workspace, in order to reduce the chances of injuries. In this context, Variable Stiffness Actuators (VSA) potentially represent an effective solution for increasing robot safety. In light of this consideration, the present paper describes the design optimization of a VSA architecture previously proposed by the authors. In this novel embodiment, the VSA can achieve stiffness modulation via the use of a pair of compliant mechanisms with distributed compliance, which act as nonlinear springs with proper torque-deflection characteristic. Such elastic elements are composed of slender beams whose neutral axis is described by a spline curve with non-trivial shape. The beam geometry is determined by leveraging on a CAD/CAE framework allowing for the shape optimization of complex flexures. The design method makes use of the modeling and simulation capabilities of a parametric CAD software seamlessly connected to a FEM tool (i.e. Ansys Workbench). For validation purposes, proof-concept 3D printed prototypes of both non-linear elastic element and overall VSA are finally produced and tested. Experimental results fully confirm that the compliant mechanism behaves as expected.

Application of a Selection Theorem to Hyperspace Contractibility

For X a metric continuum, 2X denotes the hyper space of all nonempty subcompacta, with the topology induced by the Hausdorff metric H, and C(X) ⊂ 2X the hyperspace of subcontinua. These hyperspaces are continua, in fact are arcwise-connected, since there exist order arcs between each hyperspace element and the element X. They also have trivial shape, i.e., maps of the hyperspaces into ANRs are homotopic to constant maps. For a detailed discussion of these and other general hyperspace properties, we refer the reader to Nadler's monograph [4].The question of hyperspace contractibility was first considered by Wojdyslawski [8], who showed that 2X and C(X) are contractible if X is locally connected. Kelley [2] gave a more general condition (now called property K) which is sufficient, but not necessary, for hyperspace contractibility. The continuum X has property K if for every there exists δ > 0 such that, for every pair of points x, y with d(x, y) < δ and every subcontinuum M containing x, there exists a subcontinuum N containing y with .