Slow-tonic anterior latissimus dorsi (ALD) and fast-twitch posterior latissimus dorsi (PLD) muscles of 7 to 10-day-old White Leghorn chickens were crushed and allowed to be reinnervated by their own nerve, or crushed and transplanted to the other side and allowed to be reinnervated by the nerve of the side to which they were transplanted. Following transplantation, changes in the weight of the muscle, fiber-type composition and innervation pattern during regeneration were investigated. Normal growth rate of PLD was about twice that of ALD. Regenerating PLD, however, atrophied rapidly after crushing and denervation whether innervated by its own nerve or the other nerve type, whereas ALD reinnervated by its own nerve showed marked hypertrophy. PLD fibers transformed rapidly to fast-twitch alpha or slow-tonic (ST) fibers when they were reinnervated by PLD or ALD nerve, respectively. When ALD fibers were reinnervated by their own nerve, they differentiated into ST fibers that were surrounded by smaller immature fibers. ALD fibers were, however, resistant to complete control by fast-twitch PLD nerve and contained a large number of slow fibers (ST and beta) long after transplantation. Slow fibers in regenerates were initially multiply innervated, but later transformed into fast-twitch alpha fibers that were focally innervated. The mode of differentiation and innervation pattern of different muscle fiber types in regenerating muscles are discussed.

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The Harrow, Hassidim, Lloyd (HHL) algorithm, known as the pioneering algorithm for solving linear equations in quantum computers, is expected to accelerate solving large-scale linear ordinary differential equations (ODEs). To efficiently combine classical and quantum computers for high-cost chemical problems, non-linear ODEs (e.g., chemical reactions) must be linearized to the highest possible accuracy. However, the linearization approach has not been fully established yet. In this study, Carleman linearization was examined to transform nonlinear first-order ODEs of chemical reactions into linear ODEs. Although this linearization theoretically requires the generation of an infinite matrix, the original nonlinear equations can be reconstructed. For the practical use, the linearized system should be truncated with finite size and the extent of the truncation determines analysis precision. Matrix should be sufficiently large so that the precision is satisfied because quantum computers can treat such huge matrix. Our method was applied to a one-variable nonlinear $$\dot{y}=-{y}^{2}$$ y ˙ = - y 2 system to investigate the effect of truncation orders and time step sizes on the computational error. Subsequently, two zero-dimensional homogeneous ignition problems for H2–air and CH4–air gas mixtures were solved. The results revealed that the proposed method could accurately reproduce reference data. Furthermore, an increase in the truncation order improved accuracy with large time-step sizes. Thus, our approach can provide accurate numerical simulations rapidly for complex combustion systems.

The Harrow, Hassidim, Lloyd (HHL) algorithm is a quantum algorithm expected to accelerate solving large-scale linear ordinary differential equations (ODEs). To apply the HHL to non-linear problems such as chemical reactions, the system must be linearized. In this study, Carleman linearization was utilized to transform nonlinear first-order ODEs of chemical reactions into linear ODEs. Although this linearization theoretically requires the generation of an infinite matrix, the original nonlinear equations can be reconstructed. For the practical use, the linearized system should be truncated with finite size and analysis precision can be determined by the extent of the truncation. Matrix should be sufficiently large so that the precision is satisfied because quantum computers can treat. Our method was applied to a one-variable nonlinear system to investigate the effect of truncation orders in Carleman linearization and time step size on the absolute error. Subsequently, two zero-dimensional homogeneous ignition problems for H2–air and CH4–air gas mixtures were solved. The results revealed that the proposed method could accurately reproduce reference data. Furthermore, an increase in the truncation order in Carleman linearization improved accuracy even with a large time-step size. Thus, our approach can provide accurate numerical simulations rapidly for complex combustion systems.