ICTS

We present the elements of linear response theory for driven systems, and some applications.

We present the elements of linear response theory for driven systems, and some applications.

Equilibrium statistical mechanics is built on thermal fluctuations and energy conservation. Many systems of current interest, however, including granular materials, dense suspensions, and amorphous solids, are essentially athermal, with dynamics governed instead by mechanical constraints, external driving, and dissipation.
This course provides an introduction to the statistical physics of athermal matter, focusing on how microscopic constraints give rise to macroscopic mechanical behavior. We begin with the jamming transition, isostaticity, and marginal stability, before discussing the vibrational spectrum of amorphous solids, soft modes, and the emergence of anomalous elasticity. We then examine the scaling of elastic moduli, long-range stress correlations, and continuum descriptions of disordered solids. Finally, we turn to dynamics, including yielding, plasticity, dense suspension rheology, and hydrodynamic descriptions of flowing athermal systems, highlighting some of the central open problems in the field.

We present the elements of linear response theory for driven systems, and some applications.

This set of lectures will introduce concepts in nonlinear dynamics and chaos, illustrated by interdisciplinary examples, ranging from mechanical vibrations to biological rhythms. The topics will include differential equations, bifurcations, phase plane analysis of flows on lines and circles, introduction to characteristics of chaos, iterated maps, routes to chaos, and introductory concepts in renormalization, fractals, multifractals and strange attractors.

This set of lectures will introduce concepts in nonlinear dynamics and chaos, illustrated by interdisciplinary examples, ranging from mechanical vibrations to biological rhythms. The topics will include differential equations, bifurcations, phase plane analysis of flows on lines and circles, introduction to characteristics of chaos, iterated maps, routes to chaos, and introductory concepts in renormalization, fractals, multifractals and strange attractors.

Equilibrium statistical mechanics is built on thermal fluctuations and energy conservation. Many systems of current interest, however, including granular materials, dense suspensions, and amorphous solids, are essentially athermal, with dynamics governed instead by mechanical constraints, external driving, and dissipation.
This course provides an introduction to the statistical physics of athermal matter, focusing on how microscopic constraints give rise to macroscopic mechanical behavior. We begin with the jamming transition, isostaticity, and marginal stability, before discussing the vibrational spectrum of amorphous solids, soft modes, and the emergence of anomalous elasticity. We then examine the scaling of elastic moduli, long-range stress correlations, and continuum descriptions of disordered solids. Finally, we turn to dynamics, including yielding, plasticity, dense suspension rheology, and hydrodynamic descriptions of flowing athermal systems, highlighting some of the central open problems in the field.

This set of lectures will introduce concepts in nonlinear dynamics and chaos, illustrated by interdisciplinary examples, ranging from mechanical vibrations to biological rhythms. The topics will include differential equations, bifurcations, phase plane analysis of flows on lines and circles, introduction to characteristics of chaos, iterated maps, routes to chaos, and introductory concepts in renormalization, fractals, multifractals and strange attractors.

Equilibrium statistical mechanics is built on thermal fluctuations and energy conservation. Many systems of current interest, however, including granular materials, dense suspensions, and amorphous solids, are essentially athermal, with dynamics governed instead by mechanical constraints, external driving, and dissipation.
This course provides an introduction to the statistical physics of athermal matter, focusing on how microscopic constraints give rise to macroscopic mechanical behavior. We begin with the jamming transition, isostaticity, and marginal stability, before discussing the vibrational spectrum of amorphous solids, soft modes, and the emergence of anomalous elasticity. We then examine the scaling of elastic moduli, long-range stress correlations, and continuum descriptions of disordered solids. Finally, we turn to dynamics, including yielding, plasticity, dense suspension rheology, and hydrodynamic descriptions of flowing athermal systems, highlighting some of the central open problems in the field.