Free Energy and Self-Interacting Particles

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This book examines a nonlinear system of parabolic partial differential equations (PDEs) arising in mathematical biology and statistical mechanics. In the context of biology, the system typically describes the chemotactic feature of cellular slime molds. One way of deriving these equations is via the random motion of a particle in a cellular automaton. In statistical mechanics, on the other hand, the system is associated with the motion of the mean field of self-interacting particles under gravitational force. Physically, such a system is related to Langevin, Fokkera "Planck, Liouville and gradient flow equations, which involve the issues of free energy and the second law of thermodynamics. Mathematically, the mechanism can be referred to as a quantized blowup. Actually, it is regarded as a nonlinear theory of quantum mechanics, and it comes from the mass and location quantization of the singular limit for the associated nonlinear eigenvalue problems. This book describes the whole picture, i.e., the mathematical and physical principles: derivation of a series of equations, biological modeling based on biased random walks, the study of equilibrium states via the variational structure derived from the free energy, and the quantized blowup mechanism based on several PDE techniques.

Free Energy and Self-Interacting Particles is suitable for researchers and graduate students of mathematics and applied mathematics who are interested in nonlinear PDEs in stochastic processes, cellular automatons, variational methods, and their applications to natural sciences. It is also suitable for researchers in other fields such as physics, chemistry, biology, and engineering.

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توهین به اقیلیتهای مذهبی
اهانت به مقامات سیاسی و مذهبی
اشاعه ی کودک آزاری
سایر موارد

بستن

فرمت کتاب

ebook

زبان

english

تاریخ انتشار

2005

نویسنده

Takashi Suzuki

ناشر

Birkhauser

شابک

9780817643027

20,000 تومان

خرید کتاب مطالعه نمونه درخواست ترجمه کتاب

خرید کتاب Free Energy and Self-Interacting Particles

Free Energy and Self-Interacting Particles

گزارش تخلف

فرمت کتاب

ebook

زبان

english

تاریخ انتشار

2005

نویسنده

ناشر

شابک

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