Equilibrium Shapes with Stress Localisation for Inextensible Elastic Mobius and Other Strips

We formulate the problem of finding equilibrium shapes of a thin inextensible elastic strip, developing further our previous work on the Möbius strip. By using the isometric nature of the deformation we reduce the variational problem to a second-order one-dimensional problem posed on the centreline of the strip. We derive Euler–Lagrange equations for this problem in Euler–Poincaré form and formulate boundary-value problems for closed symmetric one- and two-sided strips. Numerical solutions for the Möbius strip show a singular point of stress localisation on the edge of the strip, a generic response of inextensible elastic sheets under torsional strain. By cutting and pasting operations on the Möbius strip solution, followed by parameter continuation, we construct equilibrium solutions for strips with different linking numbers and with multiple points of stress localisation. Solutions reveal how strips fold into planar or self-contacting shapes as the length-to-width ratio of the strip is decreased. Our results may be relevant for curvature effects on physical properties of extremely thin two-dimensional structures as for instance produced in nanostructured origami

Characterisation of cylindrical curves

We employ moving frames along pairs of curves at constant separation to derive various conditions for a curve to belong to the surface of a circular cylinder

Equilibrium shapes with stress localisation for inextensible elastic möbius and other strips

© Springer Science+Business Media Dordrecht 2015. We formulate the problem of finding equilibrium shapes of a thin inextensible elastic strip, developing further our previous work on the Möbius strip. By using the isometric nature of the deformation we reduce the variational problem to a second-order onedimensional problem posed on the centreline of the strip. We derive Euler-Lagrange equations for this problem in Euler-Poincaré form and formulate boundary-value problems for closed symmetric one-and two-sided strips. Numerical solutions for the Möbius strip show a singular point of stress localisation on the edge of the strip, a generic response of inextensible elastic sheets under torsional strain. By cutting and pasting operations on the Möbius strip solution, followed by parameter continuation, we construct equilibrium solutions for strips with different linking numbers and with multiple points of stress localisation. Solutions reveal how strips fold into planar or self-contacting shapes as the length-to-width ratio of the strip is decreased. Our results may be relevant for curvature effects on physical properties of extremely thin two-dimensional structures as for instance produced in nanostructured origami

Forceless Sadowsky strips are spherical

© 2018 American Physical Society. We show that thin rectangular ribbons, defined as energy-minimizing configurations of the Sadowsky functional for narrow developable elastic strips, have a propensity to form spherical shapes in the sense that forceless solutions lie on a sphere. This has implications for ribbonlike objects in (bio)polymer physics and nanoscience that cannot be described by the classical wormlike chain model. A wider class of functionals with this property is identified

Generational relationships and differences in work-life balance and subjective well-being in a South African sample

This study examined the work-life balance (WLB) and subjective well-being (SWB) of Baby Boomers, Generation X and Generation Y in the current world of work. The instruments used in this study for data collection was Work-life Balance Scale, the Trait Emotional Intelligence Questionnaire, and the Work Engagement Questionnaire. The research was conducted from the perspective of a positive psychological paradigm and investigated the interrelationship dynamics between the constructs of generations and work-life balance and work-life balance and subjective well-being, as well as the differences between the levels of work-life balance and subjective well-being across generations in a South African sample. This study calculated Exploratory Factor Analyses (EFA) and Confirmatory Factor Analyses (CFA) to examine the psychometric structure of a proposed SWB construct and to test the hypothesis that SWB is a latent variable comprising of Happiness, Optimism, Self-Esteem, and Engagement. Based on the results of the two EFA and CFA models, there is enough statistical evidence to accept this hypothesis. Correlational analysis and structural equation modelling revealed the relationships between work-life balance and subjective well-being. Regression analysis and tests for significant differences identified the differences in work-life balance and subjective well-being levels across the generations. The results revealed that there were some statistically significant differences between generations. For Baby Boomers and Generation X work-life balance was influenced by SWB factors, whilst Generation Y were mostly influenced by biographical variables. The results showed that hours worked, and hours paid were predictors of work interfering with personal life (WIPL) for both Generation X and Generation Y. Self-esteem was a significant predictor for the Baby Boomers. With regards to personal life interfering with work (PLIW) hours worked and happiness were found to be predictors for Generation X, whereas hours paid was a negative predictor for Generation Y. Furthermore, hours worked, happiness and engagement were found to predict work and personal life enhancement (WPLE) for Generation X. An overall difference was noted for happiness across the generations, with Generation Y employees having significantly lower levels of happiness than Generation X, whilst no significant difference was noted between Generation X and Baby Boomers. The current study linked the emerging constructs of positive psychology in general by investigating the relationships and differences between generations, WLB and SWB. The results could be used as a framework for IOP.The research makes a contribution to the field of Industrial and Organisational Psychology on three levels, namely, on a theoretical, an empirical and a practical level.Industrial and Organisational PsychologyD. Com. (Industrial and Organisational Psychology

Forceless folding of thin annular strips

Thin strips or sheets with in-plane curvature have a natural tendency to adopt highly symmetric shapes when forced into closed structures and to spontaneously fold into compact multi-covered configurations under feed-in of more length or change of intrinsic curvature. This disposition is exploited in nature as well as in the design of everyday items such as foldable containers. We formulate boundary-value problems (for an ODE) for symmetric equilibrium solutions of unstretchable circular annular strips and present sequences of numerical solutions that mimic different folding modes. Because of the high-order symmetry, closed solutions cannot have an internal force, i.e., the strips are forceless. We consider both wide and narrow (strictly zero-width) strips. Narrow strips cannot have inflections, but wide strips can be either inflectional or non-inflectional. Inflectional solutions are found to feature stress localisations, with divergent strain energy density, on the edge of the strip at inflections of the surface. ‘Regular’ folding gives these singularities on the inside of the annulus, while ‘inverted’ folding gives them predominantly on the outside of the annulus. No new inflections are created in the folding process as more length is inserted. We end with a discussion of an intriguing apparent connection with a deep result on the topology of curves on surfaces

Use of solid-state NMR spectroscopy for investigating polysaccharide-based hydrogels:A review

Hydrogels find application in many areas of technology and research due to their ability to combine responsiveness and robustness. A detailed understanding of their molecular structure and dynamics (which ultimately underpin their functional properties) is needed for their design to be optimized and these hydrogels to be exploited effectively. In this review, we shed light on the unique capabilities of solid-state NMR spectroscopy to reveal this information in molecular detail. We review recent literature on the advancements in solid-state NMR techniques in resolving the structure, degree of grafting, molecular organization, water-biopolymer interactions and internal dynamical behavior of hydrogels. Among various solid-state NMR techniques, 13C cross polarization (CP) magic angle spinning (MAS) NMR is examined for its ability to probe the hydrogel and its trapped solvent. Although widely applicable to many types of polymeric and supramolecular hydrogels, the current review focuses on polysaccharide-based hydrogels

The effect of the protein solubility of fish meal and the roughage content of the supplemented diet on its digestion by sheep

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