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Some mathematical aspects of the micro-phase separation in diblock copolymers
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Stability of singularly perturbed solutions to systems of reaction-diffusion equations
Stability theorem is presented for large amplitude singularly perturbed solutions (SPS) of reactiondiffusion systems on a finite interval. Spectral analysis shows that there exists a unique real…
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A skeleton structure of self-replicating dynamics
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Double Gyroid Morphology in a Gradient System with Nonlocal Effects
The richness of spatial structures of the diblock copolymer melts is demonstrated by the minimization of a free-energy functional of nonlocal type. The total chain length and the interface thickness…
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Minimum-risk path finding by an adaptive amoebal network.
TLDR
A model for an adaptive-tube network is presented that is in good agreement with the experimental observations and the minimum-risk path is exhibited by the organism, determined by integrating along the path.
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Spatio-temporal chaos for the Gray—Scott model
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Reliability, validity, and responsiveness of the Japanese version of the patient-rated elbow evaluation
TLDR
The cross-culturally adaptable PREE into Japanese (PREE-J) represents a reliable, valid, and responsive instrument and has evaluation capacities equivalent to those of the original PREE.
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Global Structure of Bifurcating Solutions of Some Reaction-Diffusion Systems
We study the global structure of the set of bifurcating solutions of a class of coupled nonlinear reaction-diffusion systems. Our main result is that when one of the diffusion coefficients is…
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Frustrated phases under three-dimensional confinement simulated by a set of coupled Cahn-Hilliard equations.
TLDR
A set of coupled Cahn-Hilliard equations is numerically studied as a means to find morphologies of diblock copolymers in three-dimensional spherical confinement to find a variety of energy minimizers including rings, tennis balls, Janus balls and multipods.
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Smooth unique solutions for a modified Mullins-Sekerka model arising in diblock copolymer melts
Of concern is a modified Mullins-Sekerka model arising in diblock copolymer melts. As the new feature of this system a nonlocal inhomogeneous term is introduced. It is shown that the corresponding…
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