The intrinsic frame of reference and the Dhivehi ‘FIBO’ system

While geocentric and relative frames of reference have figured prominently in the literature on spatial language and cognition, the intrinsic frame of reference has received less attention, though various subtypes of the intrinsic frame have been proposed. This paper presents a revised classification of the intrinsic frame, distinguishing between three subtypes: a ‘direct’ subtype, an ‘object-centered’ subtype and a ‘figure-anchored’ subtype, with a cross-cutting distinction between ‘function-based’ and ‘shape-based’ systems. In addition, the ‘FIBO’ (front = inner, back = outer) system in Dhivehi is analyzed as an example of a borderline case, with some important features of the intrinsic frame but also some differences, presenting a challenge for existing frame of reference classifications. The rotational properties of these various systems are also considered. The analysis underscores the considerable diversity within intrinsic systems but also points to a closer relationship between intrinsic and extrinsic frames than has previously been appreciated. This may have implications for broader theoretical issues including how frames of reference are acquired, how speech communities come to use different frames and whether patterns of frame use in discourse shape patterns of non-verbal frame use.

Two-scale shape optimisation based on numerical homogenisation techniques and variational sensitivity analysis

This contribution presents a theoretical and computational framework for two-scale shape optimisation of nonlinear elastic structures. Particularly, minimum compliance optimisation problems with composite (matrix-inclusion) microstructures subjected to static loads and volume-type design constraints are focused. A homogenisation-based FE$$^2$$ 2 scheme is extended by an enhanced formulation of variational (shape) sensitivity analysis based on Noll’s intrinsic, frame-free formulation of continuum mechanics. The obtained overall two-scale sensitivity information couples shape variations across micro- and macroscopic scales. A numerical example demonstrates the capabilities of the proposed variational sensitivity analysis and the (shape) optimisation framework. The investigations involve a mesh morphing scheme for the design parametrisation at both macro- and microscopic scales.

Review of Shape Phase Transition Studies for Bose-Fermi Systems: The Effect of the Odd-Particle on the Bosonic Core

The quantum phase transition studies we have done during the last few years for odd-even systems are reviewed. The focus is on the quantum shape phase transition in Bose-Fermi systems. They are studied within the Interacting Boson-Fermion Model (IBFM). The geometry is included in this model by using the intrinsic frame formalism based on the concept of coherent states. First, the critical point symmetries E(5/4) and E(5/12) are summarized. E(5/4) describes the case of a single j=3/2 particle coupled to a bosonic core that undergoes a transition from spherical to γ-unstable. E(5/12) is an extension of E(5/4) that describes the multi-j case (j=1/2,3/2,5/2) along the same transitional path. Both, E(5/4) and E(5/12), are formulated in a geometrical context using the Bohr Hamiltonian. Similar situations can be studied within the IBFM considering the transitional path from UBF(5) to OBF(6). Such studies are also presented. No critical points have been proposed for other paths in odd-even systems as, for instance, the transition from spherical to axially deformed shapes. However, the study of such shape phase transition can be done easily within the IBFM considering the path from UBF(5) (spherical) to SUBF(3) (axial deformed). Thus, in a second part, this study is presented for the multi-j case. Energy levels and potential energy surfaces obtained within the intrinsic frame formalism of the IBFM Hamiltonian are discussed. Finally, our recent works within the IBFM for a single-j fermion coupled to a bosonic core that performs different shape phase transitional paths are reviewed. All significant paths in the model space are studied: from spherical to γ-unstable shape, from spherical to axially deformed (prolate and oblate) shapes, and from prolate to oblate shape passing through the γ-unstable shape. The aim of these applications is to understand the effect of the coupled fermion on the core when moving along a given transitional path and how the coupled fermion modifies the bosonic core around the critical points.

Spatial Reasoning With Multiple Intrinsic Frames of Reference

Establishing and updating spatial relationships between objects in the environment is vital to maintaining situation awareness and supporting many socio-spatial tasks. In a complex environment, people often need to utilize multiple reference systems that are intrinsic to different objects (intrinsic frame of reference, IFOR), but these IFORs may conflict with each other in one or more ways. Current spatial cognition theories do not adequately address how people handle multi-IFOR reasoning problems. Two experiments manipulated relative orientations of two task-relevant objects with intrinsic axes of orientation as well as their relative task salience. Response times (RTs) decreased with increasing salience of the targeted IFOR. In addition, RTs increased as a consequence of intrinsic orientation conflict, but not by amount of orientation difference. The results suggest that people encounter difficulties when they have to process two conflicting IFOR representations, and that they seem to prioritize processing of each IFOR by salience.

GENERATOR COORDINATE METHOD AND INTRINSIC SYMMETRIES

Symmetry problems of the generator coordinate method (GCM) in intrinsic frame of a many-body system (nuclei) are considered. The appropriate generator functions and the corresponding GCM equations are derived. An important role of the symmetrization group in construction of Griffin–Hill–Wheeler (GHW) equations is emphasized.