Full three-dimensional isotropic carpet cloak designed by quasi-conformal transformation optics.

A fully three-dimensional carpet cloak presenting invisibility in all viewing angles is theoretically demonstrated. The design is developed using transformation optics and three-dimensional quasi-conformal mapping. Parametrization strategy and numerical optimization of the coordinate transformation deploying a quasi-Newton method is applied. A discussion about the minimum achievable anisotropy in the 3D transformation optics is presented. The method allows to reduce the anisotropy in the cloak and an isotropic medium could be considered. Numerical simulations confirm the strategy employed enabling the design of an isotropic reflectionless broadband carpet cloak independently of the incident light direction and polarization.

Therapist interventions and client ambivalence in two cases of narrative therapy for depression.

AIM: We understand ambivalence as a cycle of opposing expressions by two internal voices. The emergence of a suppressed voice produces an innovative moment (IM), challenging the dominant voice, which represents the client's problematic self-narrative. The emergence of the IM is opposed by the dominant voice, leading to a return to the problematic self-narrative. This study analyzed therapist and client responses to each other in episodes of ambivalence. METHOD: The therapeutic collaboration coding system (TCCS) assesses whether and how the therapeutic dyad is working within the therapeutic zone of proximal development (TZPD) by examining client responses to therapist interventions. We applied the TCCS to episodes in which a good- and a poor-outcome client in narrative therapy expressed ambivalence. RESULTS: In both the good- and poor-outcome cases, the therapist responded to the emergence of ambivalence similarly, balancing challenging and supporting. The good-outcome case responded at the developmental level proposed by the therapist when challenged, while the poor-outcome case lagged behind the level proposed. DISCUSSION: This supports the theoretical explanation that the therapist did not match client's developmental level in the poor-outcome case, working beyond the client's current TZPD and contributing to the maintenance of ambivalence.