Suzuki, Takashi
Overview
Works:  10 works in 100 publications in 2 languages and 2,163 library holdings 

Genres:  Textbooks Conference papers and proceedings 
Roles:  Author, Editor, Thesis advisor, Opponent 
Classifications:  QA377, 515 
Publication Timeline
.
Most widely held works by
Takashi Suzuki
Applied analysis : mathematical methods in natural science by
Takasi Senba(
Book
)
28 editions published between 2004 and 2011 in English and Undetermined and held by 252 WorldCat member libraries worldwide
"This book provides a general introduction to applied mathematics, such as mathematical modeling of random motion of particles, chemotaxis in biology and their theoretical study. Several tools in linear and nonlinear PDE theory and spectral theory of eigenfunction expansion are described. The book also presents the fundamental ideas in theoretical and applied analysis and discusses recent developments in nonlinear science."Résumé de l'éditeur
28 editions published between 2004 and 2011 in English and Undetermined and held by 252 WorldCat member libraries worldwide
"This book provides a general introduction to applied mathematics, such as mathematical modeling of random motion of particles, chemotaxis in biology and their theoretical study. Several tools in linear and nonlinear PDE theory and spectral theory of eigenfunction expansion are described. The book also presents the fundamental ideas in theoretical and applied analysis and discusses recent developments in nonlinear science."Résumé de l'éditeur
Operator theory and numerical methods by
Hiroshi Fujita(
Book
)
18 editions published between 2001 and 2006 in English and held by 176 WorldCat member libraries worldwide
In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed. In 1991 an article on the finite element method applied to evolutionary problems was published. Following the method, basically this book studies various schemes from operator theoretical points of view. Many parts are devoted to the finite element method, but other schemes and problems (charge simulation method, domain decomposition method, nonlinear problems, and so forth) are also discussed, motivated by the observation that practically useful schemes have fine mathematical structures and the converses are also true. This book has the following chapters: 1. Boundary Value Problems and FEM. 2. Semigroup Theory and FEM. 3. Evolution Equations and FEM. 4. Other Methods in Time Discretization. 5. Other Methods in Space Discretization. 6. Nonlinear Problems. 7. Domain Decomposition Method
18 editions published between 2001 and 2006 in English and held by 176 WorldCat member libraries worldwide
In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed. In 1991 an article on the finite element method applied to evolutionary problems was published. Following the method, basically this book studies various schemes from operator theoretical points of view. Many parts are devoted to the finite element method, but other schemes and problems (charge simulation method, domain decomposition method, nonlinear problems, and so forth) are also discussed, motivated by the observation that practically useful schemes have fine mathematical structures and the converses are also true. This book has the following chapters: 1. Boundary Value Problems and FEM. 2. Semigroup Theory and FEM. 3. Evolution Equations and FEM. 4. Other Methods in Time Discretization. 5. Other Methods in Space Discretization. 6. Nonlinear Problems. 7. Domain Decomposition Method
Mean field theories and dual variation by
Takashi Suzuki(
Book
)
16 editions published between 2008 and 2009 in English and held by 61 WorldCat member libraries worldwide
A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The socalled mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of 'duality' according to the PDE weak solutions and 'hierarchy' for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multiscale mathematical explanations of the SmoluchowskiPoisson model in nonequilibrium thermodynamics, twodimensional turbulence theory, selfdual gauge theory, and so forth. This book shows how and why many different nonlinear problems are interconnected in terms of the properties of duality and scaling, and the way to analyze them mathematically
16 editions published between 2008 and 2009 in English and held by 61 WorldCat member libraries worldwide
A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The socalled mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of 'duality' according to the PDE weak solutions and 'hierarchy' for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multiscale mathematical explanations of the SmoluchowskiPoisson model in nonequilibrium thermodynamics, twodimensional turbulence theory, selfdual gauge theory, and so forth. This book shows how and why many different nonlinear problems are interconnected in terms of the properties of duality and scaling, and the way to analyze them mathematically
Free energy and selfinteracting particles by
Takashi Suzuki(
Book
)
21 editions published between 2005 and 2008 in English and held by 30 WorldCat member libraries worldwide
This book examines a system of parabolicelliptic partial differential eq tions proposed in mathematical biology, statistical mechanics, and chemical kinetics. In the context of biology, this system of equations describes the chemotactic feature of cellular slime molds and also the capillary formation of blood vessels in angiogenesis. There are several methods to derive this system. One is the biased random walk of the individual, and another is the reinforced random walk of one particle modelled on the cellular automaton. In the context of statistical mechanics or chemical kinetics, this system of equations describes the motion of a mean?eld of many particles, interacting under the gravitational inner force or the chemical reaction, and therefore this system is af?liated with a hierarchy of equations: Langevin, FokkerPlanck, LiouvilleGel'fand, and the gradient?ow. All of the equations are subject to the second law of thermodynamics  the decrease of free energy. The mat matical principle of this hierarchy, on the other hand, is referred to as the qu tized blowup mechanism; the blowup solution of our system develops delta function singularities with the quantized mass
21 editions published between 2005 and 2008 in English and held by 30 WorldCat member libraries worldwide
This book examines a system of parabolicelliptic partial differential eq tions proposed in mathematical biology, statistical mechanics, and chemical kinetics. In the context of biology, this system of equations describes the chemotactic feature of cellular slime molds and also the capillary formation of blood vessels in angiogenesis. There are several methods to derive this system. One is the biased random walk of the individual, and another is the reinforced random walk of one particle modelled on the cellular automaton. In the context of statistical mechanics or chemical kinetics, this system of equations describes the motion of a mean?eld of many particles, interacting under the gravitational inner force or the chemical reaction, and therefore this system is af?liated with a hierarchy of equations: Langevin, FokkerPlanck, LiouvilleGel'fand, and the gradient?ow. All of the equations are subject to the second law of thermodynamics  the decrease of free energy. The mat matical principle of this hierarchy, on the other hand, is referred to as the qu tized blowup mechanism; the blowup solution of our system develops delta function singularities with the quantized mass
Mean field theories and dual variation : mathematical structures of the mesoscopic model by
Takashi Suzuki(
Book
)
9 editions published in 2015 in English and held by 10 WorldCat member libraries worldwide
Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, nonequilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of selfassembly or bottomup selforganization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics
9 editions published in 2015 in English and held by 10 WorldCat member libraries worldwide
Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, nonequilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of selfassembly or bottomup selforganization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics
Oyo suri : Kiso moderingu kaiho by
Masahito Ōta(
Book
)
1 edition published in 2015 in Japanese and held by 3 WorldCat member libraries worldwide
1 edition published in 2015 in Japanese and held by 3 WorldCat member libraries worldwide
Genri to genshō : Sūri moderingu no shoho by
Takashi Suzuki(
Book
)
2 editions published in 2010 in Japanese and held by 3 WorldCat member libraries worldwide
2 editions published in 2010 in Japanese and held by 3 WorldCat member libraries worldwide
sūri igaku nyūmon(
Book
)
2 editions published in 2015 in Japanese and held by 2 WorldCat member libraries worldwide
2 editions published in 2015 in Japanese and held by 2 WorldCat member libraries worldwide
Modélisation de processus cancéreux et méthodes superconvergentes de résolution de problèmes d'interface sur grille cartésienne by
Olivier Gallinato Contino(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
In this thesis, we present a study about phenomena of tumor invasion, at the tissues and cell scales.The first part is devoted to two continuous mathematical models. The first one is a macroscopic model for breast cancer growth, which focuses on the transition between the stage in situ and the invasive phase of growth. This model is based on advection equations for cellular species. The geometry and possible tissue damage are taken into account. Invasion occurs when the tumor cells produce proteolytic enzymes. The second model deals with the phenomenon of invadopodia, at the cell scale.This is a free boundary problem, which describes the change in morphology of premetastatic cells,enabling them to degrade the tissues and migrate into the rest of the body. Each of these models reflects the strong coupling of biological phenomena.The second part is devoted to numerical methods specifically developed to solve these problems and overcome coupling and nonlinearities. They are built on uniform Cartesian grids, thanks to the finite difference method, and a stabilized version of the Ghost fluid method. Their peculiarity is to take full advantage of superconvergence properties of the Poisson problem solution. These properties are specifically studied, leading to the first or second order numerical computation of the problems ofbreast cancer and invadopodia, depending on the desired accuracy. These methods can also be used to solve other free boundary problems
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
In this thesis, we present a study about phenomena of tumor invasion, at the tissues and cell scales.The first part is devoted to two continuous mathematical models. The first one is a macroscopic model for breast cancer growth, which focuses on the transition between the stage in situ and the invasive phase of growth. This model is based on advection equations for cellular species. The geometry and possible tissue damage are taken into account. Invasion occurs when the tumor cells produce proteolytic enzymes. The second model deals with the phenomenon of invadopodia, at the cell scale.This is a free boundary problem, which describes the change in morphology of premetastatic cells,enabling them to degrade the tissues and migrate into the rest of the body. Each of these models reflects the strong coupling of biological phenomena.The second part is devoted to numerical methods specifically developed to solve these problems and overcome coupling and nonlinearities. They are built on uniform Cartesian grids, thanks to the finite difference method, and a stabilized version of the Ghost fluid method. Their peculiarity is to take full advantage of superconvergence properties of the Poisson problem solution. These properties are specifically studied, leading to the first or second order numerical computation of the problems ofbreast cancer and invadopodia, depending on the desired accuracy. These methods can also be used to solve other free boundary problems
Recent topics in nonlinear PDE III by
K Masuda(
)
1 edition published in 1987 in English and held by 0 WorldCat member libraries worldwide
The problems treated in this volume concern nonlinear partial differential equations occurring in the areas of fluid dynamics, free boundary problems, population dynamics and mathematical physics. Presented are new results and new methods for analysis in bifurcation, singular perturbation, variational methods, stability analysis, rearrangement, energy inequalities, etc
1 edition published in 1987 in English and held by 0 WorldCat member libraries worldwide
The problems treated in this volume concern nonlinear partial differential equations occurring in the areas of fluid dynamics, free boundary problems, population dynamics and mathematical physics. Presented are new results and new methods for analysis in bifurcation, singular perturbation, variational methods, stability analysis, rearrangement, energy inequalities, etc
Audience Level
0 

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Related Identities
 Senba, Takasi Author
 Fujita, Hiroshi Author
 Saito, Norikazu
 Masuda, Kyûya
 小林, 孝行
 山岸, 弘幸
 太田, 雅人
 Atlantis Press Publisher
 Maury, Bertrand Opponent
 Colin, Thierry (1968....). Opponent
Associated Subjects
Biology Biomathematics Calculus Calculus of variations Chemical kinetics ChemistryMathematics Differential equations Differential equations, Nonlinear Differential equations, Parabolic Differential equations, Partial Engineering mathematics Geometry, Differential Lattice dynamics Mathematical analysis Mathematical physics Mathematics Mean field theory Natural historyMathematical models Numerical analysis Operator theory Statistical mechanics