The lecture covers the theoretical foundations, essential concepts, and algorithms for the simulation of classical (non-quantum) many-particle systems in materials and molecular physics. In the exercises, you will implement these algorithms for simple systems (e.g., polymer chains, monatomic liquids, Ising  models) and gain hands-on experience with molecular simulations in order to generate suitable data and calculate physical observables.

Course contents:

• Molecular dynamics simulations and Metropolis Monte Carlo methods,
• Calculation of time-dependent observables and stationary expected values,
• Construction and parameterisation of force fields,
• Symplectic integrators and discretisation errors,
• Langevin integrators for stochastic dynamics,
• Simulation of thermodynamic ensembles,
• Methods for short- and long-range interactions.

It is recommended to get access to or a hard copy of at least one of the following books:

• Allen & Tildesley: Computer simulation of liquids, 2nd ed. (Oxford Univ. Press, 2017)
• Frenkel & Smit: Understanding molecular simulation, 2nd ed. (Acad. Press, London, 2002)
• Tuckerman: Statistical Mechanics: Theory and Molecular Simulation (Oxford Univ. Press, 2010)
• Rapaport: The art of molecular dynamics simulations, 2nd ed. (Cambridge Univ. Press, 2004)

Voraussetzungen: Grundkenntnisse in klassischer Mechanik (Hamilton-Gleichungen, Liouville-Gleichung) und statistischer Mechanik (Ensemble-Theorie, z. B. kanonisches Ensemble).

Erwartete Programmierkenntnisse: Für die Übungen können Sie eine Programmiersprache Ihrer Wahl verwenden. Es wird ein Code-Skelett in C++ bereitgestellt, Sie können aber auch Python, Fortran, Julia usw. verwenden.

Stochastic analysis is the study of stochastic processes that evolve in continuous time. We will treat the following subjects, among others:

Brownian motion, construction and properties; continuous time martingales and optional stopping; continuous semimartingales; quadratic variation; stochastic integration; Itô’s formula; random time change; martingale representation; stochastic differential equations and diffusion processes, connections with partial differential equations.

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet freitags 11:30 - 13:00 im Raum 126, Arnimallee 6 statt.

Contents:

• Basics: conditional expectation, characteristic function, convergence types, uniform integrability;
• Construction of stochastic processes and examples: Gaussian processes, Lévy processes, Brownian motion;
• martingales in discrete time: convergence, stopping theorems, inequalities;
• Markov chains in discrete and continuous time: recurrence and transience, invariant measures.

• Klenke: Wahrscheinlichkeitstheorie
• Durrett: Probability. Theory and Examples.

Weitere Literatur wird im Lauf der Vorlesung bekannt gegeben.
Further literature will be given during the lecture.

Voraussetzung: Stochastik I  und  Analysis I — III.

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet freitags 11:30 - 13:00 im Raum 126, Arnimallee 6 statt.

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet freitags 11:30 - 13:00 im Raum 126, Arnimallee 6 statt.

The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond standard Brownian motion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

The course is at the interface of probability theory and statistical mechanics. Noting that fluids constitute high-dimensional stochastic processes, I will give an introduction to the principles of liquid state theory, and we will derive the mathematical structure of the relevant correlation functions. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

Keywords:

• Brownian motion, diffusion, and stochastic processes in fluids
• harmonic analysis of correlation functions
• Zwanzig-Mori projection operator formalism
• mode-coupling approximations, long-time tails
• critical dynamics and transport anomalies

• Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
• Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

Further literature will be given during the course.

Target audience: M.Sc. Mathematik/Physik/Computational Sciences

Requirements: either Stochastics III (Stochastic differential equations) or Advanced Statistical Physics

This course teaches molecular simulation algorithms and techniques, in particular:

• Molecular dynamics algorithm and integrators
• Monte Carlo sampling
• Thermostats and barostats
• Electrostatic treatment
• Implicit vs. explicit solvent methods

It is recommended to get access to or a hard copy of at least one of the following books:

• Allen & Tildesley: Computer simulation of liquids, 2nd ed. (Oxford Univ. Press, 2017)
• Frenkel & Smit: Understanding molecular simulation, 2nd ed. (Acad. Press, London, 2002)
• Tuckerman: Statistical Mechanics: Theory and Molecular Simulation (Oxford Univ. Press, 2010)
• Rapaport: The art of molecular dynamics simulations, 2nd ed. (Cambridge Univ. Press, 2004)

Exercises will be computer based

Subject matter:
Sets, real and complex numbers, proof methods, matrices and linear systems of equations, basics of vector spaces, linear maps, representations and base transformations, determinants, inner product, orthogonal and self-adjusted operators, eigenvalues and eigenvectors, diagonalization of normal matrices.

Target group:
Students of physics, geophysics and meteorology

Requirements:
School mathematics

https://lms.fu-berlin.de/

G. Fischer, Lineare Algebra (Springer Spektrum, 2013).
K. Jänich, Lineare Algebra (Springer, 2008).
A. Beutelspacher, Lineare Algebra (Springer Spektrum, 2014).

Diese Vorlesung entspricht weitgehend der Mathematik II aus der alten Sudienordnung. Übungsbetrieb wird über FU Blackboard verwaltet

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet freitags 11:30 - 13:00 im Raum 126, Arnimallee 6 statt.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Die Veranstaltung findet freitags, 10:30 - 12:00 Uhr, im Raum 126, Arnimallee 6 statt.

Stochastic analysis is the study of stochastic processes that evolve in continuous time. We will treat the following subjects, among others:

Markov jump processes; Brownian motion; sampling theorems in continuous time; stochastic integral; Itō formula; continuous semimartingales; quadratic variation; martingale representation; stochastic differential equations and diffusion processes, connections with partial differential equations.

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet freitags 11:30 - 13:00 im Raum 126, Arnimallee 6 statt.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

Contents:

• Construction of stochastic processes;
• conditional expectation;
• martingales and Markov chains in discrete time;
• weak convergence;
• first time-continuous processes (in particular Brownian motion)

Voraussetzung: Stochastik I  und  Analysis I — III.

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet freitags 11:30 - 13:00 im Raum 126, Arnimallee 6 statt.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

This course teaches molecular simulation algorithms and techniques, in particular:

• Molecular dynamics algorithm and integrators
• Monte Carlo sampling
• Thermostats and barostats
• Electrostatic treatment
• Implicit vs. explicit solvent methods

It is recommended to get access to or a hard copy of at least one of the following books:

• Allen & Tildesley: Computer simulation of liquids, 2nd ed. (Oxford Univ. Press, 2017)
• Frenkel & Smit: Understanding molecular simulation, 2nd ed. (Acad. Press, London, 2002)
• Tuckerman: Statistical Mechanics: Theory and Molecular Simulation (Oxford Univ. Press, 2010)
• Rapaport: The art of molecular dynamics simulations, 2nd ed. (Cambridge Univ. Press, 2004)

Exercises will be computer based

Subject matter:
Sets, real and complex numbers, complete induction, matrices and linear systems of equations, basic determinants of vector space, linear images, representations and base transformations, eigenvalues and eigenvectors, diagonalization of matrices, scalar product, orthogonal and self-adjusted operators, Hermite operators.

Target group:
Students of physics, geophysics and meteorology

Requirements:
School mathematics

https://lms.fu-berlin.de/

Wird in der Vorlesung bekannt gegeben.

Diese Vorlesung entspricht weitgehend der Mathematik II aus der alten Sudienordnung. Übungsbetrieb wird über FU Blackboard verwaltet

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet freitags 11:30 - 13:00 im Raum 126, Arnimallee 6 statt.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet freitags 11:30 - 13:00 im Raum 126, Arnimallee 6 statt.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

This course teaches molecular simulation algorithms and techniques, in particular:

• Molecular dynamics algorithm and integrators
• Monte Carlo sampling
• Thermostats and barostats
• Electrostatic treatment
• Implicit vs. explicit solvent methods

It is recommended to get access to or a hard copy of at least one of the following books:

• Allen & Tildesley: Computer simulation of liquids, 2nd ed. (Oxford Univ. Press, 2017)
• Frenkel & Smit: Understanding molecular simulation, 2nd ed. (Acad. Press, London, 2002)
• Tuckerman: Statistical Mechanics: Theory and Molecular Simulation (Oxford Univ. Press, 2010)
• Rapaport: The art of molecular dynamics simulations, 2nd ed. (Cambridge Univ. Press, 2004)

Exercises will be computer based

Stochastic analysis is the study of stochastic processes that evolve in continuous time. We will treat the following subjects, among others:

Gaussian processes; Brownian motion, construction and properties; filtrations and stopping times; continuous time martingales; continuous semimartingales; quadratic variation; stochastic integration; Itô’s formula; Girsanov’s theorem and change of measure; time change; martingale representation; stochastic differential equations and diffusion processes, connections with partial differential equations.

The course is organised via Blackboard: https://lms.fu-berlin.de

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet freitags 11:30 - 13:00 im Raum 126, Arnimallee 6 statt.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

Contents:

• Construction of stochastic processes;
• conditional expectation;
• martingales and Markov chains in discrete time;
• weak convergence;
• first time-continuous processes (in particular Brownian motion)

Voraussetzung: Stochastik I  und  Analysis I — III.

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet freitags 11:30 - 13:00 im Raum 126, Arnimallee 6 statt.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

This course teaches molecular simulation algorithms and techniques, in particular:

• Molecular dynamics algorithm and integrators
• Monte Carlo sampling
• Thermostats and barostats
• Electrostatic treatment
• Implicit vs. explicit solvent methods

It is recommended to get access to or a hard copy of at least one of the following books:

• Allen & Tildesley: Computer simulation of liquids, 2nd ed. (Oxford Univ. Press, 2017)
• Frenkel & Smit: Understanding molecular simulation, 2nd ed. (Acad. Press, London, 2002)
• Tuckerman: Statistical Mechanics: Theory and Molecular Simulation (Oxford Univ. Press, 2010)
• Rapaport: The art of molecular dynamics simulations, 2nd ed. (Cambridge Univ. Press, 2004)

Exercises will be computer based

Subject matter:
Sets, real and complex numbers, complete induction, matrices and linear systems of equations, basic determinants of vector space, linear images, representations and base transformations, eigenvalues and eigenvectors, diagonalization of matrices, scalar product, orthogonal and self-adjusted operators, Hermite operators.

Target group:
Students of physics, geophysics and meteorology

Requirements:
School mathematics

https://lms.fu-berlin.de/

Wird in der Vorlesung bekannt gegeben.

Diese Vorlesung entspricht weitgehend der Mathematik II aus der alten Sudienordnung.
Übungsbetrieb wird über FU Blackboard verwaltet

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet dienstags 12-13:30 in Raum 126, Arnimallee 6 statt.

The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond standard Brownian motion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

The course is at the interface of stochastic dynamical systems and statistical mechanics. Noting that fluids constitute high-dimensional stochastic processes in space in time, I will give an introduction to the principles of liquid state theory, and we will derive the mathematical structure of the relevant correlation functions. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

Keywords:

• Brownian motion, diffusion, and stochastic processes in fluids
• harmonic analysis of correlation functions
• Zwanzig-Mori projection operator formalism
• mode-coupling approximations, long-time tails
• critical dynamics and transport anomalies

• Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
• Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

Further literature will be given during the course.

Target audience: M.Sc. Mathematik/Physik/Computational Sciences

Requirements: either Stochastics III (Stochastic differential equations) or Advanced Statistical Physics

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

In this module, the students work on application-oriented problems supported by scientific computing methods.

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet dienstags 12-13:30 in Raum 126, Arnimallee 6 statt.

In this module, the students work on application-oriented problems supported by scientific computing methods.

This course teaches molecular simulation algorithms and techniques, in particular:

• Molecular dynamics algorithm and integrators
• Monte Carlo sampling
• Thermostats and barostats
• Electrostatic treatment
• Implicit vs. explicit solvent methods

Description:
Exercises will be computer based

Informationen zu dieser Online-Veranstaltung finden Sie im zugehörigen Kurs [auf/in] Blackboard:

https://lms.fu-berlin.de/webapps/blackboard/execute/announcement?method=search&course_id=_143588_1

Subject matter:
Sets, real and complex numbers, complete induction, matrices and linear systems of equations, basic determinants of vector space, linear images, representations and base transformations, eigenvalues and eigenvectors, diagonalization of matrices, scalar product, orthogonal and self-adjusted operators, Hermite operators.

Target group:
Students of physics, geophysics and meteorology

Requirements:
School mathematics

https://lms.fu-berlin.de/

Wird in der Vorlesung bekannt gegeben.

Diese Vorlesung entspricht weitgehend der Mathematik II aus der alten Sudienordnung.
Übungsbetrieb wird über FU Blackboard verwaltet

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet dienstags 12-13:30 in Raum 126, Arnimallee 6 statt.

Subject matter:
Sets, real and complex numbers, complete induction, matrices and linear systems of equations, basic determinants of vector space, linear images, representations and base transformations, eigenvalues and eigenvectors, diagonalization of matrices, scalar product, orthogonal and self-adjusted operators, Hermite operators.

Target group:
Students of physics, geophysics and meteorology

Requirements:
School mathematics

https://lms.fu-berlin.de/

Wird in der Vorlesung bekannt gegeben.

Diese Vorlesung entspricht weitgehend der Mathematik II aus der alten Sudienordnung.
Übungsbetrieb wird über FU Blackboard verwaltet

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet dienstags 12-13:30 in Raum 126, Arnimallee 6 statt.

This module teaches the theoretical basics and simulation techniques for simple stochastic systems (e.g. molecular models, ising models, diffusion in model potentials). Physical principles for stochastic trajectories and ensembles are combined with simulation techniques that are able to generate appropriate data.
In more detail, we will cover:

• Statistical mechanics: basis and derivations to the most important physical ensembles. Boltzmann distribution, Partition function, Expectations
• Monte-Carlo simulation: Theory, construction, convergence and implementation of Monte Carlo methods for the computation of stationary expectation values
• Kinetics: Rate theories, time correlations and other time-dependent expectations
• Molecular dynamics simulation: Theory, construction, convergence and implementation of MD simulations for the computation of dynamical expectation values

The course gives an introduction to stochastic processes and their applications in natural sciences. We start with the development of a probabilistic description of stochastic processes, which allows us then to introduce Gaussian processes and Markov chains. The "microscopic" counterpart to this description are stochastic differential equations, which provide us with representations of the random paths of many continuous processes. An important class are diffusion processes with their numerous applications.

• Meintrup und Schäffler: Stochastik (Springer, 2005)
• Klenke: Wahrscheinlichkeitstheorie (Springer, 2013)
• Øksendal: Stochastic Differential Equations (Springer, 2010)
• Gardiner: Handbook of Stochastic Methods (Springer, 2004)
• van Kampen: Stochastic Processes in Physics and Chemistry (Elsevier, 2007)

weiterführende Literatur:

• Dynkin: Markov processes (Springer, 1965)
• Feller: Probability Theory and Its Applications, Bd. 1 und 2 (Wiley, 1968-1971)
• Kallenberg: Foundations of modern probability (Springer, 2002)

This Forschungsseminar is a weekly meeting of the Compuational Statistical & Biological Physics group. It serves as a discussion platform featuring status report, paper presentations, and guest talks.

Veranstaltung findet dienstags 12-13:30 in Raum 126, Arnimallee 6 statt.

The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond simple diffusion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

The course is at the interface of stochastic dynamical systems and statistical mechanics. Starting from probability theory, I will give an introduction to the principles of liquid-state theory with a focus on dynamic aspects. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

Keywords:

• Brownian motion, diffusion, and other transport processes in fluids
• harmonic analysis of correlation functions
• linear response theory, Zwanzig-Mori projection formalism
• mode-coupling theories, long-time tails
• critical dynamics and transport anomalies

• Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
• Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

Further literature will be given during the course.

Zielgruppe: M.Sc. Informatik/Mathematik/Physik

Voraussetzungen: einige fortgeschrittene Kurse über statistische Physik oder stochastische Prozesse

Inhalt
Mengen, reelle und komplexe Zahlen, vollständige Induktion,Matrizen und lineare Gleichungssysteme, Determinanten  Grundbegriffe des Vektorraums, lineare Abbildungen, Darstellungen und Basistransformationen,  Eigenwerteund Eigenvektoren, Diagonalisierung von Matrizen, Skalarprodukt, orthogonale und selbstadjungierte Operatoren, hermitesche Operatoren.  

Zielgruppe 

Studentinnen und Studenten der Physik, Geophysik und Meteorologie  

Voraussetzungen 

Schulmathematik  

Literatur 

wird in der Vorlesung bekannt gegeben.

Diese Vorlesung entspricht weitgehend der Mathematik II aus der alten Sudienordnung

Veranstaltung findet dienstags 12-13:30 in Raum 126, Arnimallee 6 statt.

This course presents methods to compute thermodynamic and kinetic properties from molecular simulation data. Methods to generate such data are discussed, complementing the courses "Methods of molecular simulations" and "Molecular simulation II", respectively.

Topics:

• brief repetition of statistical mechanics: ensembles, phase space, equilibrium distribution;
• Metropolis and Markov chain Monte-Carlo; Molecular dynamics;
• Hybrid Monte-Carlo;
• Transition matrix;
• Langevin dynamics, Correlation functions and other data analysis methods

This lecture primarily adresses BS. and MSc Mathematics students but is also suitable as an elective for physics students.
Exercises are mandatory as they complement the lecture. Lecture will be held in either German or English. Scripts are in English. 

Literatur:

Øksendal: Stochastic Differential Equations (Springer, 2010)
Klenke: Wahrscheinlichkeitstheorie (Springer, 2013)
Meintrup und Schäffler: Stochastik (Springer, 2005)
Gardiner: Handbook of Stochastic Methods (Springer, 2004)
van Kampen: Stochastic Processes in Physics and Chemistry (Elsevier, 2007)

weiterführende Literatur:
Dynkin: Markov processes (Springer, 1965)
Feller: Probability Theory and Its Applications, Bd. 1 und 2 (Wiley, 1968-1971)
Kallenberg: Foundations of modern probability (Springer, 2002)

Veranstaltung findet dienstags 12-13:30 in Raum 126, Arnimallee 6 statt.

The liquid state comprises a large class of materials ranging from simple
fluids (argon) and molecular fluids (water) to soft matter systems such as
polymer solutions (ketchup), colloidal suspensions (wall paint), and
heterogeneous media (cell cytoplasm). The basic transport mode in liquids is
that of diffusion due to thermal fluctuations, but already the simplest liquids
exhibit a non-trivial dynamic response well beyond simple diffusion. From the
early days of the field, computer simulations have played a central role in
identifying complex dynamics and testing the approximations of their
theoretical descriptions. On the other hand, theory imposes constraints on the
analysis of experimental or simulation data.

The course will give an introduction to the principles of liquid-state theory
with a focus on dynamic aspects. The second part makes contact to recent
research and gives an overview on selected topics. The exercises are split into
a theoretical part, discussed in biweekly lessons, and a practical part in form
of a small simulation project conducted during a block session (2 days) after
the lecture phase.

Keywords:

- Brownian motion, diffusion, and other transport processes in fluids
- linear response theory
- Zwanzig-Mori formalism
- mode-coupling theories, long-time tails
- critical dynamics in mixtures
- anomalous transport on percolation clusters (Lorentz model)

Literature:

- Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).

- Höfling and Franosch, Anomalous transport in the crowded world of biological
  cells, Rep. Prog. Phys. 76, 046602 (2013).

Further literature will be given during the course.

- Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).

- Höfling and Franosch, Anomalous transport in the crowded world of biological
  cells, Rep. Prog. Phys. 76, 046602 (2013).

Further literature will be given during the course.

Target audience: M.Sc. Physik/Computational Sciences/Mathematik

Requirements: Some knowledge in either statistical physics or stochastic
processes will be of advantage.

Inhalt

Mengen, reelle und komplexe Zahlen, vollständige Induktion, Begriff des Vektorraums, lineare Abbildungen, Darstellungen und Basistransformationen, Matrizen und lineare Gleichungssysteme, Determinanten, Eigenwerte und Eigenvektoren, Diagonalisierung von Matrizen, Skalarprodukt, orthogonale und hermitesche Operatoren.

Zielgruppe

Studentinnen und Studenten der Physik, Geophysik und Meteorologie  

Voraussetzungen

Schulmathematik

Übungsbetrieb

Der Übungsbetrieb erfolgt über FU e-Learning.

Nach Anmeldung im Campus Management sollte der Kurs unter "Mein Campus" auftauchen.

• G. Fischer: Lineare Algebra (Springer Spektrum, 2013).
• K. Jänich: Lineare Algebra (Springer, 2013).
• A. Beutelspacher: Lineare Algebra (Springer Spektrum, 2014).

Selected topics on stochastic processes with applications in natural sciences and finance.

Possible subjects for seminar talks are:

• Lévy processes
• Linear filtering problem
• Feynman-Kac formula
• Random time change
• Girsanov theorem
•  
• Bayesian inference
• Stochastic enzyme kinetics
• Random resistor networks
• Boltzmann's H-theorem
• Zwanzig-Mori projection formalism
• Fluctuation theorems
•  
• Geometric Brownian motion
• Stochastic control
• Optimal stopping
• Black-Scholes formula

Literaturliste wird zu Beginn der Veranstaltung bekanntgegeben.

Erstes Treffen Mittwoch, 19.10. 14:00, R. 108/109, 1. OG, Arnimallee 6. Weitere Termine nach Absprache.

Voraussetzungen: Stochastik I, Analysis I-II

Up to 10 master students of physics, mathematics, and computer science will collaborate on a software development project from the realm of computational physics and scientific computing. We will specify the desired features and behaviour of the software to be developed, depending on the size and composition of the group – a typical project will include generation and analysis of numerical/simulation data as well as data management and storage. To meet the different backgrounds of physicists, mathematicians, and computer scientists, the project will include aspects of theoretical physics (understanding theory and physical models), numerics (such as simulation aspects) as well as pure informatics (such as data processing, database design and development, software architecture design). We will meet once a week to discuss progress and problems. Students will self-organize (with our assistance) in terms of dividing work and presenting results.

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Inhalt

• This course is the sequel of the course of Stochastics I. The main objective is to go beyond the first principles in probability theory by introducing the general language of measure theory, and the application of this framework in a wide variety of probabilistic scenarios.
  More precisely, the course will cover the following aspects of probability theory:
• Measure theory and the Lebesgue integral
• Convergence of random variables and 0-1 laws
• Generating functions: branching processes and characteristic functions
• Markov chains
• Introduction to martingales

[1] Øksendal: Stochastic Differential Equations (Springer, 2010)5
[2] Klenke: Wahrscheinlichkeitstheorie (Springer, 2013)
[3]Gardiner: Handbook of Stochastic Methods (Springer, 2004)
[4]van Kampen: Stochastic Processes in Physics and Chemistry (Elsevier, 2007)
[5] Dynkin: Markov processes (Springer, 1965)

Zielgruppe: B.Sc. Mathematik und B.Sc./M.Sc. Physik
Die Vorlesung richtet sich vorrangig an Studierende mit Ziel B.Sc. Mathematik, eignet sich aber auch als Wahlfach für Physikstudenten (ab 4. Semester). Die begleitende Übung ist verpflichtend und stellt inhaltlich eine wesentliche Ergänzung dar.

Inhalt: The course provides an introduction to stochastic processes with applications in physics and chemistry. We will develop the mathematical theory in the language of modern probability theory, mostly following the book by Øksendal. The results are then applied to diffusion problems and non-Markovian transport (as in heterogeneous fluids), with the Brownian motion of a colloidal particle serving as paradigmatic example. Further, we will discuss the modelling of chemical reactions, the derivation of stochastic equations of motion from a many-particle Liouville dynamics, and recent developments in non-equilibrium physics. The course is given in English and accompanied by a mandatory problem class.

1. Stochastic processes and correlation functions
   (elements of probability theory, expectation, stochastic processes, dynamic correlation functions)
2. Molecular transport phenomena
   (Brownian motion of a tracer, complex fluids, fluctuation–dissipation theorem, correlations in space and time)
3. Stochastic differential equations
   (Ito and Stratonovich integral, martingale processes, Ito diffusion, Dynkin's formula)
4. Markov processes
   (Markov chains, diffusion processes, Fokker–Planck equation, detailed balance, first-passage time problems)
5. Statistical mechanics
   (linear response theory, Zwanzig–Mori projection formalism, exact Langevin equations)
6. Non-equilibrium thermodynamics
   (modern fluctuation theorems, stochastic thermodynamics, balance equations, Onsager relations)

Zielgruppe: M.Sc. Mathematik, M.Sc. Physics

Voraussetzungen: Analysis I - III

Literatur (alphabetisch):

• Dynkin: Markov processes (Springer, 1965)
• Gardiner: Handbook of Stochastic Methods (Springer, 2004)
• Hansen, McDonald: Theory of Simple Liquids (Academic, 2006)
• Kubo, Toda, Hashitsume: Statistical Physics II (Springer, 1998)
• Øksendal: Stochastic Differential Equations (Springer, 2010)
• Paul, Baschnagel: Stochastic Processes (Springer, 2013)
• van Kampen: Stochastic Processes in Physics and Chemistry (Elsevier, 2007)

The seminar provides an overview of recent topics in soft matter physics with focus on theoretical results and modern simulation methods. Each student will present one topic during 45 minutes with subsequent discussions.
The seminar is limited to 14 participants.

Possible topics:

1. Molecular dynamics simulations
2. Theory of Brownian motion
3. Anomalous transport in crowded media
4. Phase transitions
5. Free energy calculations by Monte Carlo simulations
6. Polymer theory
7. Poisson-Boltzmann theory
8. Algorithms for electrostatic interactions
9. Diffusion in many-particle suspensions
10. Long-time anomalies of the diffusion in liquids
11. Hydrodynamic interactions
12. Simulation methods for coarse-grained solvents
13. Physics of the glass transition
14. GPU-accelerated molecular dynamics simulations

Voraussetzungen: good knowledge in classical and statistical mechanics, thermodynamics, electrodynamics

Zielgruppe: M.Sc. Mathematik, M.Sc. Physics