To apply methods and tools of mathematical physics to some classes of models of dynamical systems and statistical mechanics, through both theoretical lectures and numerous practical exercises carried out in the computer lab.
Curriculum
teacher profile teaching materials
Statistical Mechanics models - Stochastic dynamics and applications
Mathematical model of different problems are presented as spread of epidemics,
sample problems, optimisation problems, physical problems, with numerical simulations.
Laboratory exercises are an essential part of the course.
Statistical Mechanics models, as the Ising model, and probability tools, as Markov Chain,
are applied, with references to relative theory.
A concrete mathematical introduction. In rete
O.H¨aggstr¨om: Finite Markov Chain and Algorithmic Applications,
London Mathematical Society-Student Texts 52
Mutuazione: 20410470 FM510 - APPLICAZIONI DELLA FISICA MATEMATICA in Scienze Computazionali LM-40 SCOPPOLA ELISABETTA, TERESI LUCIANO, D'AUTILIA ROBERTO
Programme
Part II-Statistical Mechanics models - Stochastic dynamics and applications
Mathematical model of different problems are presented as spread of epidemics,
sample problems, optimisation problems, physical problems, with numerical simulations.
Laboratory exercises are an essential part of the course.
Statistical Mechanics models, as the Ising model, and probability tools, as Markov Chain,
are applied, with references to relative theory.
Core Documentation
S.Freidli and Y.Velenik : Statistical Mechanics of Lattice Systems -A concrete mathematical introduction. In rete
O.H¨aggstr¨om: Finite Markov Chain and Algorithmic Applications,
London Mathematical Society-Student Texts 52
Type of delivery of the course
Theoretical lessons and exercises with scientific software.Type of evaluation
Presentation of a problem and discussion of its numerical simulation teacher profile teaching materials
Module Geometry and Mechanics.
The goal of this module is to show the relations between physical modeling and differential geometry, by discussing the fundamentals of continuum mechanics, and showing how each physical notion has its mathematical counterpart, aimed at representing the physical phenomenon under investigation. During the module, we shall consider various applications where theory is followed by numerical experiments; suggested applications are:
• Modeling of Active Soft Matter;
• Modeling of Liquid Crystals;
• Modeling for Fluid Dynamics.
Module Statistical Mechanics for Comlex System.
In this module a selection of statistical-mechanics models and probabilistics techniques will be applied to the study of complex system. In particular, the following models will be both studied from the theoretical point of view and solved with computer simulations:
• Ising model and gas on a lattice, including phase transitions and metastbility.
• Curie-Weiss modeling;
• Random Cluster Model and Potts model;
• Markov Chain, including Monte-Carlo Chain; Gibbs sampler and Metropolis algorithm, including convergence and mixing time;
• Propp-Wilson Algorithm, “perfect simulation” and “sandwiching”.
Students will be able to select other applications among the following list:
• Optimizzation (example max clique)
• Q-coloring, hard-core, random walk on iper-cube
• Diffusion models: epidemics; sentiment (contact process)
• Spinglass
• Neuronal Networks
Mutuazione: 20410470 FM510 - APPLICAZIONI DELLA FISICA MATEMATICA in Scienze Computazionali LM-40 SCOPPOLA ELISABETTA, TERESI LUCIANO, D'AUTILIA ROBERTO
Programme
The course FM510 – Applicazioni della Fisica Matematica (Application of Mathematics to Problems in Physics), is split into two modules, each with a specific focus; both modules comprehend a theoretical part and numerical simulations.Module Geometry and Mechanics.
The goal of this module is to show the relations between physical modeling and differential geometry, by discussing the fundamentals of continuum mechanics, and showing how each physical notion has its mathematical counterpart, aimed at representing the physical phenomenon under investigation. During the module, we shall consider various applications where theory is followed by numerical experiments; suggested applications are:
• Modeling of Active Soft Matter;
• Modeling of Liquid Crystals;
• Modeling for Fluid Dynamics.
Module Statistical Mechanics for Comlex System.
In this module a selection of statistical-mechanics models and probabilistics techniques will be applied to the study of complex system. In particular, the following models will be both studied from the theoretical point of view and solved with computer simulations:
• Ising model and gas on a lattice, including phase transitions and metastbility.
• Curie-Weiss modeling;
• Random Cluster Model and Potts model;
• Markov Chain, including Monte-Carlo Chain; Gibbs sampler and Metropolis algorithm, including convergence and mixing time;
• Propp-Wilson Algorithm, “perfect simulation” and “sandwiching”.
Students will be able to select other applications among the following list:
• Optimizzation (example max clique)
• Q-coloring, hard-core, random walk on iper-cube
• Diffusion models: epidemics; sentiment (contact process)
• Spinglass
• Neuronal Networks
Core Documentation
Lecture notes; scientific software.Type of delivery of the course
Theory and practicals with computers; practicals have a noteworthy role in these lectures.Type of evaluation
The students are required to produce a written report containing the description of a select problem and a discussion about the numerical experiments.Mutuazione: 20410470 FM510 - APPLICAZIONI DELLA FISICA MATEMATICA in Scienze Computazionali LM-40 SCOPPOLA ELISABETTA, TERESI LUCIANO, D'AUTILIA ROBERTO
teacher profile teaching materials
Statistical Mechanics models - Stochastic dynamics and applications
Mathematical model of different problems are presented as spread of epidemics,
sample problems, optimisation problems, physical problems, with numerical simulations.
Laboratory exercises are an essential part of the course.
Statistical Mechanics models, as the Ising model, and probability tools, as Markov Chain,
are applied, with references to relative theory.
A concrete mathematical introduction. In rete
O.H¨aggstr¨om: Finite Markov Chain and Algorithmic Applications,
London Mathematical Society-Student Texts 52
Mutuazione: 20410470 FM510 - APPLICAZIONI DELLA FISICA MATEMATICA in Scienze Computazionali LM-40 SCOPPOLA ELISABETTA, TERESI LUCIANO, D'AUTILIA ROBERTO
Programme
Part II-Statistical Mechanics models - Stochastic dynamics and applications
Mathematical model of different problems are presented as spread of epidemics,
sample problems, optimisation problems, physical problems, with numerical simulations.
Laboratory exercises are an essential part of the course.
Statistical Mechanics models, as the Ising model, and probability tools, as Markov Chain,
are applied, with references to relative theory.
Core Documentation
S.Freidli and Y.Velenik : Statistical Mechanics of Lattice Systems -A concrete mathematical introduction. In rete
O.H¨aggstr¨om: Finite Markov Chain and Algorithmic Applications,
London Mathematical Society-Student Texts 52
Type of delivery of the course
Theoretical lessons and exercises with scientific software.Type of evaluation
Presentation of a problem and discussion of its numerical simulation teacher profile teaching materials
Module Geometry and Mechanics.
The goal of this module is to show the relations between physical modeling and differential geometry, by discussing the fundamentals of continuum mechanics, and showing how each physical notion has its mathematical counterpart, aimed at representing the physical phenomenon under investigation. During the module, we shall consider various applications where theory is followed by numerical experiments; suggested applications are:
• Modeling of Active Soft Matter;
• Modeling of Liquid Crystals;
• Modeling for Fluid Dynamics.
Module Statistical Mechanics for Comlex System.
In this module a selection of statistical-mechanics models and probabilistics techniques will be applied to the study of complex system. In particular, the following models will be both studied from the theoretical point of view and solved with computer simulations:
• Ising model and gas on a lattice, including phase transitions and metastbility.
• Curie-Weiss modeling;
• Random Cluster Model and Potts model;
• Markov Chain, including Monte-Carlo Chain; Gibbs sampler and Metropolis algorithm, including convergence and mixing time;
• Propp-Wilson Algorithm, “perfect simulation” and “sandwiching”.
Students will be able to select other applications among the following list:
• Optimizzation (example max clique)
• Q-coloring, hard-core, random walk on iper-cube
• Diffusion models: epidemics; sentiment (contact process)
• Spinglass
• Neuronal Networks
Mutuazione: 20410470 FM510 - APPLICAZIONI DELLA FISICA MATEMATICA in Scienze Computazionali LM-40 SCOPPOLA ELISABETTA, TERESI LUCIANO, D'AUTILIA ROBERTO
Programme
The course FM510 – Applicazioni della Fisica Matematica (Application of Mathematics to Problems in Physics), is split into two modules, each with a specific focus; both modules comprehend a theoretical part and numerical simulations.Module Geometry and Mechanics.
The goal of this module is to show the relations between physical modeling and differential geometry, by discussing the fundamentals of continuum mechanics, and showing how each physical notion has its mathematical counterpart, aimed at representing the physical phenomenon under investigation. During the module, we shall consider various applications where theory is followed by numerical experiments; suggested applications are:
• Modeling of Active Soft Matter;
• Modeling of Liquid Crystals;
• Modeling for Fluid Dynamics.
Module Statistical Mechanics for Comlex System.
In this module a selection of statistical-mechanics models and probabilistics techniques will be applied to the study of complex system. In particular, the following models will be both studied from the theoretical point of view and solved with computer simulations:
• Ising model and gas on a lattice, including phase transitions and metastbility.
• Curie-Weiss modeling;
• Random Cluster Model and Potts model;
• Markov Chain, including Monte-Carlo Chain; Gibbs sampler and Metropolis algorithm, including convergence and mixing time;
• Propp-Wilson Algorithm, “perfect simulation” and “sandwiching”.
Students will be able to select other applications among the following list:
• Optimizzation (example max clique)
• Q-coloring, hard-core, random walk on iper-cube
• Diffusion models: epidemics; sentiment (contact process)
• Spinglass
• Neuronal Networks
Core Documentation
Lecture notes; scientific software.Type of delivery of the course
Theory and practicals with computers; practicals have a noteworthy role in these lectures.Type of evaluation
The students are required to produce a written report containing the description of a select problem and a discussion about the numerical experiments.Mutuazione: 20410470 FM510 - APPLICAZIONI DELLA FISICA MATEMATICA in Scienze Computazionali LM-40 SCOPPOLA ELISABETTA, TERESI LUCIANO, D'AUTILIA ROBERTO
teacher profile teaching materials
Statistical Mechanics models - Stochastic dynamics and applications
Mathematical model of different problems are presented as spread of epidemics,
sample problems, optimisation problems, physical problems, with numerical simulations.
Laboratory exercises are an essential part of the course.
Statistical Mechanics models, as the Ising model, and probability tools, as Markov Chain,
are applied, with references to relative theory.
A concrete mathematical introduction. In rete
O.H¨aggstr¨om: Finite Markov Chain and Algorithmic Applications,
London Mathematical Society-Student Texts 52
Programme
Part II-Statistical Mechanics models - Stochastic dynamics and applications
Mathematical model of different problems are presented as spread of epidemics,
sample problems, optimisation problems, physical problems, with numerical simulations.
Laboratory exercises are an essential part of the course.
Statistical Mechanics models, as the Ising model, and probability tools, as Markov Chain,
are applied, with references to relative theory.
Core Documentation
S.Freidli and Y.Velenik : Statistical Mechanics of Lattice Systems -A concrete mathematical introduction. In rete
O.H¨aggstr¨om: Finite Markov Chain and Algorithmic Applications,
London Mathematical Society-Student Texts 52
Reference Bibliography
Dropbox on line.Type of delivery of the course
Theoretical lessons and exercises with scientific software.Type of evaluation
Presentation of a problem and discussion of its numerical simulation teacher profile teaching materials
Module Geometry and Mechanics.
The goal of this module is to show the relations between physical modeling and differential geometry, by discussing the fundamentals of continuum mechanics, and showing how each physical notion has its mathematical counterpart, aimed at representing the physical phenomenon under investigation. During the module, we shall consider various applications where theory is followed by numerical experiments; suggested applications are:
• Modeling of Active Soft Matter;
• Modeling of Liquid Crystals;
• Modeling for Fluid Dynamics.
Module Statistical Mechanics for Comlex System.
In this module a selection of statistical-mechanics models and probabilistics techniques will be applied to the study of complex system. In particular, the following models will be both studied from the theoretical point of view and solved with computer simulations:
• Ising model and gas on a lattice, including phase transitions and metastbility.
• Curie-Weiss modeling;
• Random Cluster Model and Potts model;
• Markov Chain, including Monte-Carlo Chain; Gibbs sampler and Metropolis algorithm, including convergence and mixing time;
• Propp-Wilson Algorithm, “perfect simulation” and “sandwiching”.
Students will be able to select other applications among the following list:
• Optimizzation (example max clique)
• Q-coloring, hard-core, random walk on iper-cube
• Diffusion models: epidemics; sentiment (contact process)
• Spinglass
• Neuronal Networks
Programme
The course FM510 – Applicazioni della Fisica Matematica (Application of Mathematics to Problems in Physics), is split into two modules, each with a specific focus; both modules comprehend a theoretical part and numerical simulations.Module Geometry and Mechanics.
The goal of this module is to show the relations between physical modeling and differential geometry, by discussing the fundamentals of continuum mechanics, and showing how each physical notion has its mathematical counterpart, aimed at representing the physical phenomenon under investigation. During the module, we shall consider various applications where theory is followed by numerical experiments; suggested applications are:
• Modeling of Active Soft Matter;
• Modeling of Liquid Crystals;
• Modeling for Fluid Dynamics.
Module Statistical Mechanics for Comlex System.
In this module a selection of statistical-mechanics models and probabilistics techniques will be applied to the study of complex system. In particular, the following models will be both studied from the theoretical point of view and solved with computer simulations:
• Ising model and gas on a lattice, including phase transitions and metastbility.
• Curie-Weiss modeling;
• Random Cluster Model and Potts model;
• Markov Chain, including Monte-Carlo Chain; Gibbs sampler and Metropolis algorithm, including convergence and mixing time;
• Propp-Wilson Algorithm, “perfect simulation” and “sandwiching”.
Students will be able to select other applications among the following list:
• Optimizzation (example max clique)
• Q-coloring, hard-core, random walk on iper-cube
• Diffusion models: epidemics; sentiment (contact process)
• Spinglass
• Neuronal Networks
Core Documentation
Lecture notes; scientific software.Reference Bibliography
Tonti E. The reason for analogies between physical theories. Applied Mathematical Modelling. 1976 https://en.wikipedia.org/wiki/Enzo_TontiType of delivery of the course
Theory and practicals with computers; practicals have a noteworthy role in these lectures.Type of evaluation
The students are required to produce a written report containing the description of a select problem and a discussion about the numerical experiments.