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Applied Mathematics (Applied Dynamical Systems, Nonlinear Analysis, Verified Numerical Computation) Lab (Tomoyuki Miyaji)
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The lab studies the formation and breakdown of patterns using dynamical systems and numerical computation.
AboutAbout the lab
Exploring, with computation and mathematics, how patterns emerge and break down
The Miyaji Lab studies, through mathematical models, phenomena in nature and society in which patterns emerge or break down.
Mainly from the viewpoint of bifurcations in dynamical systems, it investigates them using numerical simulation and numerical bifurcation analysis.
Verified numerical computation, which uses computers to rigorously prove results, is also one of its research tools.
Key terms
- Bifurcation
- A sudden, drastic change in the behavior of solutions when a value in an equation is changed gradually
- Verified numerical computation
- A method that accounts for even a computer's rounding errors and mathematically guarantees that a computed result is correct
- Mathematical model
- A description of how a phenomenon works, expressed in mathematical formulas
ResearchResearch themes
The lab studies phenomena related to pattern formation and breakdown through mathematical models, mainly from the viewpoint of bifurcations in dynamical systems.
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MembersFaculty
- Associate ProfessorTomoyuki Miyaji
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Turing morphogen pattern resembling cheetah dappling” Philip Ball / CC BY 4.0 (cropped)
- Computing the whole picture of dynamics: “LogisticMap BifurcationDiagram” PAR / Public domain (cropped)
- Related lab (Condensed Matter Physics Lab): “FQHE Hall” Jakubtr / CC BY-SA 3.0 (cropped)
- Related lab (Applied Mathematics (Nonlinear Analysis, Topological Fluid Dynamics, Numerical Analysis, Uncertainty Quantification) Lab (Takashi Sakajo)): “VortexStreet01” Gary Koopman / Public domain (cropped)
- Related lab (Condensed Matter Theory Lab): “Ytterbium Optical Lattice Clock” KRISS, the Korean Research Institute of Standards and Science / CC BY-SA 3.0 (cropped)
- Related lab (Statistical Physics and Dynamics Lab): “Phase separation in Kupchan partitioning” Ikramul Hasan Imran / CC BY 4.0 (cropped)
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