Under geometric constraints, a thin structure can respond to an external loading in an unexpected way. A paper strip that is looped and pulled can be used for simple experimentation of such a process. Here, we study this seemingly very simple phenomenon in detail by combing experiments and theory. We identify the three types of shape transitions, i.e., crease, helicoid, and pop out, from a stretched loop, and classify them in terms of parameters characterizing a ribbon geometry. We establish a transition-type diagram by compiling our extensive experimental data. Numerical simulations based on the Kirchhoff rod theory and scaling argument reveal that the pop-out transition is governed by a single characteristic length $\xi \sim b^2/h$, where $b$ and $h$ are the ribbon’s width and thickness, respectively. We also reveal the key roles of other physical effects such as the anisotropy of the bending elasticity and plastic deformations upon the shape selection mechanisms of a constraint ribbon.

Three new industrial applications of irreversible phase field models for crack growth are presented in this study. The phase field model for irreversible crack growth in an elastic material is derived as a unidirectional gradient flow of the Francfort–Marigo energy with the Ambrosio–Tortorelli regularization, which is known to be consistent with classic Griffith fracture theory. The obtained compact parabolic-elliptic system of PDEs including two regularization parameters for space and time enables us to simulate various kinds of crack behaviors with standard finite element software, without any geometric restriction on the crack path. We extend the irreversible phase field model to thermal cracking in solder and to cracking in a viscoelastic material, keeping the compact forms of the PDEs and the energy consistency. On the other hand, for hydrogen-assisted cracking in metal, we propose a compact phase field model focusing on a kinematic jamming effect of the hydrogen by a weak coupling approach. Several numerical experiments for these three models show not only their reasonableness and usefulness but also flexible extendability of the phase field approach in fracture mechanics.

We have developed a new procedure for easy and rapid identification of autonomously replicating sequences (ARSs) and have applied it to the analysis of chromosome V of Saccharomyces cerevisiae. The procedure makes use of the ordered λ phage clone bank of this chromosome that we have constructed, and includes transposition of a mini‐transposon and selection of transposon‐containing derivatives, isolation of their DNA and circularization at their cos‐ends, transformation of yeast cells with the circularized DNA, and scoring transformation frequency. The transposon used was derived from Tn5supF, contained the yeast LEU2 gene, and was placed, together with the hyperactive transposase gene, on a mini‐F plasmid for stable maintenance in Escherichia coli K‐12. Sixteen regions of chromosome V showing ARS activity were identified, of which 12 were newly found in this work. Thus, the procedure will be useful for systematic genomic scale analysis of ARSs in yeast and related organisms in which ordered clone banks have been established. The average distance between adjacent ARS‐containing regions was approximately 40 kb. Two‐dimensional gel electrophoretic analysis of chromosome replication indicated that one of the newly identified ARSs was functional as an actual in situ replication origin, at least under the conditions employed.

We formulate a phase field crack growth model for mode III fracture in a Maxwell-type viscoelastic material. To describe viscoelastic relaxation, a field variable of viscously flowed strain is employed in addition to the displacement field and damage phase field used in the original elastic model. Unlike preceding models developed in the mechanical engineering community, our model is based only on the generic procedure for deriving (uni-directional) gradient flow system from a physically natural system energy and employ no additional assumption such as the super-imposition principle for stress and strain, which is valid only for linear viscoelasticity. Numerical simulations indicate that the competition between the increase in deformation by applied loading and the viscoelastic relaxation determines whether a distinct crack propagation has occurred from an initial crack. Furthermore, we consider the numerical results from an energetic perspective.

When a gel swollen with a certain solvent is placed in the bath of another solvent, the gel swells or de-swells depending on the thermodynamic affinity to the gel. Toyotama et al. [Langmuir 22, 1952 (2006)] reported an unusual volume change of chemical gels that cannot be explained by the affinity difference: when a chemical gel saturated with water is immersed in ethylene glycol (EG), although those solvents have almost the same affinity to the polymer, the gel first shrinks and then re-swells and finally takes the same equilibrium volume as the initial. The re-entrant swelling was attributed to different diffusion rates between water and EG (dynamical asymmetry), but the detailed mechanism was not clarified. In this paper, we experimentally show that the characteristic times for the temporal shrinking and subsequent volume relaxation are proportional to the squared system size. This indicates that the phenomenon is governed by diffusive dynamics. According to this observation, we propose a coupled diffusion model explaining the physical mechanism of the re-entrant volume change.

Some types of hydro-gels have almost the same equilibrium swelling volume in water and in ethylene glycol (EG), a highly viscous liquid completely miscible with water. Experiments showed that when a gel fully swollen with EG is immersed into a large amount of water, it temporarily swells up and then relaxes to the equilibrium volume in water. The temporary swelling is explained by the friction force exerted on the gel network from the outward EG flux In this paper, we experimentally show that the temporary swelling is suppressed by adding linear PEG (polyethylene glycol) in the outer water. Although the suppression seems to be explained by the osmotic pressure (i.e., by the same mechanism as the conventional osmotic squeezing), our theoretical analysis reveals that the effect of PEG is much stronger than that expected from the equilibrium osmotic pressure, implying that the PEG chains are condensed on the gel surface.