Inhomogeneous Field Theory Research Articles

Supersymmetric backgrounds in (1 + 1) dimensions and inhomogeneous field theory

We find a (1 + 1)-dimensional metric solution for a background hosting various supersymmetric field theories with a single non-chiral real supercharge. This supersymmetric background is globally hyperbolic even though it contains a naked null singularity. In this regard, we show that scalar wave propagation on the background is well-defined and so the curvature singularity is a mild one. Taking inspiration from our previous work, we relate the field theory on this curved background to some classes of (1 + 1)-dimensional inhomogeneous field theory in the supersymmetric setup. Utilizing our supersymmetric background, we elucidate the limitations of canonical quantization and highlight the conceptual advantages of the algebraic approach to quantization.

Toward quantization of inhomogeneous field theory

We explore the quantization of a $$(1+1)$$ -dimensional inhomogeneous scalar field theory in which Poincaré symmetry is explicitly broken. We show the ‘classical equivalence’ between a scalar field theory on curved spacetime background and its corresponding inhomogeneous scalar field theory. This implies that a hidden connection may exist among some inhomogeneous field theories, which corresponds to general covariance in field theory on curved spacetime. Based on the classical equivalence, we propose how to quantize a specific field theory with broken Poincaré symmetry inspired by standard field theoretic approaches, canonical and algebraic methods, on curved spacetime. Consequently, we show that the Unruh effect can be realized in inhomogeneous field theory and propose that it may be tested by a condensed matter experiment. We suggest that an algebraic approach is appropriate for the quantization of a generic inhomogeneous field theory.

Bifurcation and deformation during the evolution of periodic patterns on a gel film bonded to a soft substrate

In this study, we investigate the bifurcation and deformation during the evolution of periodic patterns on a gel film bonded to a soft substrate. 3D finite element analysis is performed using an inhomogeneous field theory for polymeric gels. Step-by-step eigenvalue buckling analysis is conducted to explore not only the first bifurcation, but also sequential bifurcations on bifurcated paths. When the hexagonal dimple mode occurs as the first bifurcation, the second bifurcation consists of rectangular checkerboard modes in three symmetric directions. The resulting deformation patterns are in good agreement with experiments and, surprisingly, are analogous to the in-plane buckling behavior of hexagonal honeycombs. Uniaxial, biaxial, and equibiaxial (flower-like) patterns are produced by the periodic arrangements of distorted dimples. The third and fourth bifurcations cause the coalescence of the selected dimples. This reveals the occurrence of the rectangular checkerboard modes at the second bifurcation to be the missing link in the pattern evolution from hexagonal dimples to herringbone and labyrinth patterns.

Holographic duals of inhomogeneous systems: the rainbow chain and the sine-square deformation model

A holographic dual description of inhomogeneous systems is discussed. Notably, finite temperature results for the entanglement entropy in both the rainbow chain and the sine-square deformation model are obtained holographically by choosing appropriate foliations of the Bañados– Teitelboim–Zanelli spacetime. Other inhomogeneous theories are also discussed. The entanglement entropy results are verified numerically, indicating that a wide variety of inhomogeneous field theory phenomenology can be seen in different slicings of asymptotically AdS3 spacetimes.

ポーラスゲル膜の膨潤誘起座屈に対する座屈固有値解析の適用

In this study, we perform eigenvalue buckling analysis for swelling-induced buckling of porous gel membranes. Swelling process is analyzed by increasing the chemical potential of external solvent in an inhomogeneous field theory. To investigate the point of buckling and the buckling mode, eigenvalue buckling prediction is conducted using a quasi incremental loading pattern instead of using the chemical potential, because the chemical potential is not available in eigenvalue buckling analysis. This approach is verified by analyzing pattern transformation in gel membranes with a square lattice of holes. It is found that diamond plate patterns are successfully predicted.

不均質場理論を用いたポーラスゲル膜の座屈モード解析

不均質場理論を用いたポーラスゲル膜の座屈モード解析

Effect of prestrains on swelling-induced buckling patterns in gel films with a square lattice of holes

We investigate the effect of prestrains on swelling-induced buckling patterns in polymeric films with a square lattice of holes. To reproduce experiments conducted by Zhang et al. (2008), poly(dimethylsiloxane) (PDMS) films are pre-strained in in-plane uniaxial tension in a lattice direction, and subsequently swelled by toluene. Finite element analysis is performed using an inhomogeneous field theory of polymeric gels in equilibrium, and with the aid of artificial damping. Periodic units consisting of 2×2 and 10×10 unit cells are analyzed under a generalized plane strain assumption. Analysis of the 10×10 unit cell shows that the resulting buckling pattern depends on the increase in prestrain of ε=0, 0.2, 0.4 and 0.6, evolving as a diamond plate pattern (ε=0), a slightly distorted diamond plate pattern (ε=0.2), a binary pattern of circles and lines (ε=0.4), and a monotonous pattern of ellipses (ε=0.6). These predictions are in very good agreement with experiments. The 2×2 unit cell reveals that these different patterns appear continuously as transitional states during transformation into diamond plate patterns; prestrains in uniaxial tension delay the onset of the pattern transformation and equilibrium swelling interrupts the progress of the transformation. Parametric studies demonstrate that the pattern dependence on prestrains originates from intrinsic swelling features, and is a consequence of a particular combination of the selected polymer and solvent.

Mimicking the pattern formation of fruits and leaves using gel materials

Gel materials have recently gained more attention due to its unique capability of large and reversible volumetric changes. This study explores the possibility of mimicking the pattern formation of certain natural fruits during their growing process and leaves during drying processes through the swelling and de-swelling of gel materials. This will hopefully provide certain technical explanations on the morphology of fruits and plants. We adopt the inhomogeneous field gel theory to predict the deformation configurations of gel structures to describe the morphology of natural fruits and plants. The growing processes of apple and capsicum are simulated by imposing appropriate boundary conditions and field loading via varying the chemical potential from their immature to mature stages. The drying processes of three types of leaves with different vein structures are also investigated. The simulations lead to promising results and demonstrate that pattern formation of fruits and plants may be described from mechanical perspective by the behavior of gel materials based on the inhomogeneous field theory.

OS0513 円孔を有するゲル膜の膨潤誘起座屈パターンに及ぼす予ひずみの影響

In this study, we investigate the effect of prestrains on swelling-induced buckling patterns in polymeric films with a square lattice of holes. To reproduce experiments by Zhang et al. (2008), finite element analysis is performed using an inhomogeneous field theory of polymeric gels in equilibrium, amd prestrains prior to swelling are given as uniaxial tension along a lattice direction. A periodic unit consisting of 10×10 unit cells is analyzed under a generalized plane strain assumption. The 10×10 unit cell shows that different buckling patterns appear depending on prestrains of ε=0, 20, 40 and 60%: a diamond plate pattern (ε=0%), a slightly distorted diamond plate pattern (ε=20%), a binary pattern of circles and lines (ε=40%), and a monotonous pattern of ellipses (ε=60%). These predictions are in very good agreement with experiments.

Effect of geometrical imperfections on swelling-induced buckling patterns in gel films with a square lattice of holes

In this study, we investigate the effect of geometrical imperfections on swelling-induced buckling patterns in gel films with a square lattice of holes. Finite element analysis is performed using the inhomogeneous field theory of polymeric gels in equilibrium proposed by Hong et al. (2009). Periodic units consisting of 2×2 and 10×10 unit cells are analyzed under a generalized plane strain assumption. Geometrical imperfections are introduced using randomly oriented elliptical holes. The 2×2 unit cells show that the resulting buckling patterns are sensitive to imperfections; three different buckling patterns are obtained, and the most dominant one is the diamond plate pattern observed in experiments, which cannot be described using the model without imperfections. The 10×10 unit cells reveal that random imperfections are responsible for inducing homogeneous transformation into the diamond plate pattern. Furthermore, domain wall formation is simulated using a 10×10 unit cell model containing two elliptic holes.

Pattern formation in plants via instability theory of hydrogels

In this paper, we demonstrate how deformation patterns of leaves and fruits in growing and drying processes can be described via the inhomogeneous field theory. The distorted deformation of ribbed leaves and the ridge formation on fruit surfaces can be understood as the energy-minimizing mechanical buckling patterns. The swelling and de-swelling induced instabilities of various membrane structures or elastic sheets on elastic or gel-like substrates are simulated using the inhomogeneous field theory of a polymeric network in equilibrium with solvent and mechanical constraints. The article describes briefly the inhomogeneous field theory of hydrogel deformation and the buckling patterns of thin hydrogel films on thick substrates. The theory is then adopted to simulate the growth and drying processes of leaves and fruits through the buckling phenomena observed in the film gel of various shapes, geometric proportions, chemical potentials and mechanical constraints. The key idea is to show that the hydrogel deformation theory can capture the deformation process and various states of plant growth or drying. The study has been made in an attempt to mimic the shapes of fruits and leaves from the swelling/deswelling patterns of hydrogel films. The study provides the possibility of exploring the origin of the intriguing natural phenomena of leaves and fruits.

OS0910 円孔を有するゲル薄膜の膨潤座屈に初期不整の及ぼす影響

In this study, we investigate the influence of geometrical imperfections on swelling-induced buckling patterns in gel films with holes in a square array. Finite element analysis is performed using the inhomogeneous field theory of polymeric gels in equilibrium proposed by Hong et al. (2009). Periodic units consisting of 2×2 unit cells are analyzed under a generalized plane strain assumption. Geometrical imperfections are introduced using randomly oriented elliptical holes. Results show that the resulting buckling patterns are sensitive to imperfections; three different buckling patterns are obtained, and the most dominant one is the diamond plate pattern observed in experiments, which cannot be described using the model without imperfections.

ANALYTICAL SOLUTIONS OF POLYMERIC GEL STRUCTURES UNDER BUCKLING AND WRINKLE

One of the unique properties of polymeric gel is that the volume and shape of gel can dramatically change even at mild variation of external stimuli. Though a variety of instability patterns of slender and thin film gel structures due to swelling have been observed in various experimental studies, many are not well understood. This paper presents the analytical solutions of swelling-induced instability of various slender and thin film gel structures. We have adopted the well developed constitutive relation of inhomogeneous field theory of a polymeric network in equilibrium with a solvent and mechanical load or constraint with the incremental modulus concept for slender beam and thin film gel structures. The formulas of buckling and wrinkle conditions and critical stress values are derived for slender beam and thin film gel structures under swelling-induced instability using nonlinear buckling theories of beam and thin film structures. For slender beam structure, we construct the stability diagram with the distinct stable and unstable zones. The critical slenderness ratio and corresponding critical stresses are provided for different dimensionless material parameters. For thin film gel structures, we consider the thin film gel on an elastic foundation with different stiffness. The analytical solutions of critical stress and corresponding wrinkle wavelength, as well as buckling condition (or critical chemical potential) are given. These analytical solutions will provide a guideline for gel structure design used in polymeric gels MEMS and NEMS structures such as sensors and actuators. More importantly, the work provides a theoretical foundation of gel structure buckling and wrinkle, instability phenomena are different from normal engineering or material buckling.

Modeling and simulation of buckling of polymeric membrane thin film gel

The swelling- and deswelling-induced instabilities of various membrane structures are simulated using the inhomogeneous field theory of a polymeric network in equilibrium with a solvent and mechanical load/constraint and the Finite Element subroutine developed in ABAQUS. The simulating results of these membrane gels are compared with available experimental results, and a reliable prediction in deformation pattern and critical conditions has been achieved. The study has been made in attempt to mimic the shape of a plant leaves from the swelling/deswelling patterns of a gel. Furthermore, this study provides a possibility to explore the origin of intriguing natural phenomena of plants.