 PORTALE DELLA DIDATTICA Statistical physics and biophysics

02NQFPF

A.A. 2019/20

2019/20

Statistical physics and biophysics (Biophysics)

In this course the knowledge of statistical physics is developed, with a particular attention to modern aspects involving interacting systems and critical phenomena, and applications to the physics of biological systems, in particular biopolymers, are discussed. To this end, a few basic elements of fluid dynamics and molecular biology are also introduced.

Statistical physics and biophysics (Statistical physics)

In this course the knowledge of statistical physics is developed, with a particular attention to modern aspects involving interacting systems and critical phenomena, and applications to the physics of biological systems, in particular biopolymers, are discussed. To this end, a few basic elements of fluid dynamics and molecular biology are also introduced.

Statistical physics and biophysics (Biophysics)

This module discusses applications of statistical physics to biological systems, in particular biopolymers. To this end, basic elements of kinetics of phase transitions and molecular biology are also introduced.

Statistical physics and biophysics (Statistical physics)

In this module the knowledge of statistical physics is developed, with a particular attention to modern aspects involving interacting systems and critical phenomena.

Statistical physics and biophysics (Biophysics)

The student must acquire a deep knowledge of statistical physics, of its methodologies and its relationships with information theory. The student must also acquire some basic elements of fluid dynamics and molecular biology and must learn to apply the techniques of statistical physics to some problems from the physics of biological systems, mainly in the field of biopolymers.

Statistical physics and biophysics (Statistical physics)

The student must acquire a deep knowledge of statistical physics, of its methodologies and its relationships with information theory. The student must also acquire some basic elements of fluid dynamics and molecular biology and must learn to apply the techniques of statistical physics to some problems from the physics of biological systems, mainly in the field of biopolymers.

Statistical physics and biophysics (Biophysics)

The student must acquire some basic elements of molecular biology and must learn to apply the techniques of statistical physics to some problems from the equilibrium and nonequilibrium physics of biological systems, mainly in the field of biopolymers.

Statistical physics and biophysics (Statistical physics)

The student must acquire a deep knowledge and understanding of the statistical physics of interacting systems and of its methodologies, and must become able to solve models in this domain, using exact or approximate analytical approaches.

Statistical physics and biophysics (Biophysics)

Mathematical analysis, general physics, quantum mechanics, probability theory.

Statistical physics and biophysics (Statistical physics)

Mathematical analysis, general physics, quantum mechanics, probability theory.

Statistical physics and biophysics (Biophysics)

Mathematical analysis, general physics, quantum mechanics, probability theory.

Statistical physics and biophysics (Statistical physics)

Mathematical analysis, general physics, quantum mechanics, probability theory.

Statistical physics and biophysics (Biophysics)

1. Statistical physics (6 credits) Partition function, free energy, entropy. Ideal systems. Interacting systems: Ising model and phase transition. Approximate methods for interacting systems: mean field and generalizations, Bethe-Peierls and belief propagation. Low and high temperature expansions, duality. Free energy of the two-dimensional Ising model. The XY model in 2 dimensions. Introduction to the position space renormalization group. 2. Introduction to continuum and fluid mechanics (1.5 credits) Kinematics of a continuum body (Lagrangian and Eulerian descriptions, rigid motion, Reynolds' transport theorem), dynamics of a continuum body (principle of mass conservation, principle of conservation of linear and angular momentum, Cauchy's stress theorem and stress tensors), fluid mechanics (constitutive assumptions of ideal and viscous fluids, Reynolds' number, solutions of Navier-Stokes equations in simple situations). 3. Introduction to molecular biology (0.5 credits) The cell; small molecules; proteins and nucleic acids. 4. Statistical physics of biopolymers (4 credits) Stretching a single DNA molecule: experiments, the Freely Jointed Chain, the one-dimensional cooperative chain, the worm-like chain. DNA melting: experiments, zipper model, Poland-Scheraga model. The helix-coil transition. Polymer collapse: Flory's theory. Collapse of semiflexible polymers: lattice models and the tube model. The self-avoiding walk and the O(n) model. An introduction to protein folding and design. RNA folding and secondary structure. Protein and RNA mechanical unfolding. Molecular motors.

Statistical physics and biophysics (Statistical physics)

1. Statistical physics (6 credits) Partition function, free energy, entropy. Ideal systems. Interacting systems: Ising model and phase transition. Approximate methods for interacting systems: mean field and generalizations, Bethe-Peierls and belief propagation. Low and high temperature expansions, duality. Free energy of the two-dimensional Ising model. The XY model in 2 dimensions. Introduction to the position space renormalization group. 2. Introduction to continuum and fluid mechanics (1.5 credits) Kinematics of a continuum body (Lagrangian and Eulerian descriptions, rigid motion, Reynolds' transport theorem), dynamics of a continuum body (principle of mass conservation, principle of conservation of linear and angular momentum, Cauchy's stress theorem and stress tensors), fluid mechanics (constitutive assumptions of ideal and viscous fluids, Reynolds' number, solutions of Navier-Stokes equations in simple situations). 3. Introduction to molecular biology (0.5 credits) The cell; small molecules; proteins and nucleic acids. 4. Statistical physics of biopolymers (4 credits) Stretching a single DNA molecule: experiments, the Freely Jointed Chain, the one-dimensional cooperative chain, the worm-like chain. DNA melting: experiments, zipper model, Poland-Scheraga model. The helix-coil transition. Polymer collapse: Flory's theory. Collapse of semiflexible polymers: lattice models and the tube model. The self-avoiding walk and the O(n) model. An introduction to protein folding and design. RNA folding and secondary structure. Protein and RNA mechanical unfolding. Molecular motors.

Statistical physics and biophysics (Biophysics)

Kinetics of phase transitions: thermodynamics of interfaces, metastability and classical nucleation theory, domain coarsening, phase ordering with or without conservation laws (12 hours). Introduction to molecular biology: the cell; small molecules; proteins and nucleic acids. (4 hours). Stretching a single DNA molecule: experiments, the Freely Jointed Chain, the one-dimensional cooperative chain, the worm-like chain (10 hours). DNA melting: experiments, zipper model, Poland-Scheraga model (7 hours). The helix-coil transition. Polymer collapse: Flory's theory. Collapse of semiflexible polymers: lattice models and the tube model. The self-avoiding walk and the O(n) model. (6 hours). An introduction to protein folding and design. RNA folding and secondary structure. Protein and RNA mechanical unfolding (15 hours). Molecular motors (6 hours).

Statistical physics and biophysics (Statistical physics)

1. Statistical physics Review: canonical and grand-canonical ensembles, non-interacting systems (10 hours). The Ising model: introduction and exact solutions in one dimension and on the fully connected graph (10 hours). Mean-field approximation (10 hours). Beyond mean-field approximation: Bethe-Peierls and belief propagation (5 hours). The two-dimensional Ising model: Peierls argument, low- and high-temperature expansions, free energy in zero field on a square lattice. The two-dimensional XY model at low temperatures (15 hours). An introduction to the real-space renormalization group (10 hours).

Statistical physics and biophysics (Biophysics)

Statistical physics and biophysics (Statistical physics)

Statistical physics and biophysics (Biophysics)

Statistical physics and biophysics (Statistical physics)

Statistical physics and biophysics (Biophysics)

Frontal lectures, using mainly blackboard in blocks 1. Statistical physics and 2. Introduction to continuum and fluid mechanics, mainly slides in block 3. Introduction to molecular biology, and a mixture of both in block 4. Statistical physics of biopolymers. Problems are proposed after completing each topic and then solved after a few lectures, so that students have time to try and find their own solutions.

Statistical physics and biophysics (Statistical physics)

Frontal lectures, using mainly blackboard in blocks 1. Statistical physics and 2. Introduction to continuum and fluid mechanics, mainly slides in block 3. Introduction to molecular biology, and a mixture of both in block 4. Statistical physics of biopolymers. Problems are proposed after completing each topic and then solved after a few lectures, so that students have time to try and find their own solutions.

Statistical physics and biophysics (Biophysics)

Frontal lectures, using mainly slides for discussing biological facts and experimental results, mainly blackboard for discussing models and solving problems. Problems are proposed after completing each topic and then solved after a few lectures, so that students have time to try and find their own solutions.

Statistical physics and biophysics (Statistical physics)

Frontal lectures, using mainly blackboard. Problems are proposed after completing each topic and then solved after a few lectures, so that students have time to try and find their own solutions.

Statistical physics and biophysics (Biophysics)

M. Plischke and B. Bergersen, Equilibrium statistical physics, World scientific R.K. Pathria and P.D. Beale, Statistical mechanics, Academic Press L. Peliti, Statistical mechanics in a nutshell, Bollati Boringhieri J.P. Sethna, Entropy, order parameters and complexity, Clarendon K. Sneppen and G. Zocchi, Physics in molecular biology, Cambridge P. Nelson, Biological Physics, Freeman B. Alberts et al, Molecular biology of the cell, Garland Lecture notes and slides will be provided.

Statistical physics and biophysics (Statistical physics)

M. Plischke and B. Bergersen, Equilibrium statistical physics, World scientific R.K. Pathria and P.D. Beale, Statistical mechanics, Academic Press L. Peliti, Statistical mechanics in a nutshell, Bollati Boringhieri J.P. Sethna, Entropy, order parameters and complexity, Clarendon K. Sneppen and G. Zocchi, Physics in molecular biology, Cambridge P. Nelson, Biological Physics, Freeman B. Alberts et al, Molecular biology of the cell, Garland Lecture notes and slides will be provided.

Statistical physics and biophysics (Biophysics)

K. Sneppen and G. Zocchi, Physics in molecular biology, Cambridge P. Nelson, Biological Physics, Freeman B. Alberts et al, Molecular biology of the cell, Garland Lecture notes and slides will be provided.

Statistical physics and biophysics (Statistical physics)

M. Plischke and B. Bergersen, Equilibrium statistical physics, World scientific R.K. Pathria and P.D. Beale, Statistical mechanics, Academic Press L. Peliti, Statistical mechanics in a nutshell, Bollati Boringhieri J.P. Sethna, Entropy, order parameters and complexity, Clarendon Lecture notes and slides will be provided.

Statistical physics and biophysics (Biophysics)

Modalit� di esame: prova orale obbligatoria;

Statistical physics and biophysics (Statistical physics)

Modalit� di esame: prova orale obbligatoria;

Statistical physics and biophysics (Biophysics)

The exam is based on an oral tests, which can be splitted in up to three parts, one for block 1. Statistical Physics, one for block 2. Introduction to continuum and fluid mechanics and one for blocks 3. Introduction to molecular biology and 4. Statistical physics of biopolymers. In case of splitting, the final grade is the weighted average of the grades of each block. Each test typically involve questions on 2-3 topics, the first one being chosen by the student.

Statistical physics and biophysics (Statistical physics)

The exam is based on an oral tests, which can be splitted in up to three parts, one for block 1. Statistical Physics, one for block 2. Introduction to continuum and fluid mechanics and one for blocks 3. Introduction to molecular biology and 4. Statistical physics of biopolymers. In case of splitting, the final grade is the weighted average of the grades of each block. Each test typically involve questions on 2-3 topics, the first one being chosen by the student.

Statistical physics and biophysics (Biophysics)

Exam: compulsory oral exam;

Statistical physics and biophysics (Statistical physics)

Exam: compulsory oral exam;

Statistical physics and biophysics (Biophysics)

The exam is based on an oral test. The test typically involves questions on 2-3 topics, the first one being chosen by the student. The ability of the student to apply the techniques of statistical physics to problems from the physics of biological systems is tested by asking to discuss models of biopolymers and the relationship of their predictions to phenomenology.

Statistical physics and biophysics (Statistical physics)

The exam is based on an oral test. The test typically involve questions on 2-3 topics, the first one being chosen by the student. The knowledge of statistical physics and its methodologies is tested by asking the student to derive proofs of the main results. The ability to solve models is tested by asking the student to compute partition functions or thermodynamical observables for models of interacting systems.

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