Extracting macroscopic dynamics: model problems and algorithms
In many applications, the primary objective of numerical simulation of time-evolving systems
is the prediction of coarse-grained, or macroscopic, quantities. The purpose of this review is …
is the prediction of coarse-grained, or macroscopic, quantities. The purpose of this review is …
Theoretical tools for understanding the climate crisis from Hasselmann's programme and beyond
Klaus Hasselmann's revolutionary intuition in climate science was to use the stochasticity
associated with fast weather processes to probe the slow dynamics of the climate system …
associated with fast weather processes to probe the slow dynamics of the climate system …
Stochastic processes and applications
GA Pavliotis - Texts in applied mathematics, 2014 - Springer
The purpose of this book is to present various results and techniques from the theory of
stochastic processes and in particular diffusion processes that are useful in the study of …
stochastic processes and in particular diffusion processes that are useful in the study of …
Molecular dynamics
For a number of years, we have been exploring the underpinnings of algorithms for
simulating molecular dynamics from a mathematics perspective, ie as outsiders. We have …
simulating molecular dynamics from a mathematics perspective, ie as outsiders. We have …
Generalized Langevin Equation with Fractional Gaussian Noise:<? format?> Subdiffusion within a Single Protein Molecule
By introducing fractional Gaussian noise into the generalized Langevin equation, the
subdiffusion of a particle can be described as a stationary Gaussian process with analytical …
subdiffusion of a particle can be described as a stationary Gaussian process with analytical …
Ergodic properties of fractional Brownian-Langevin motion
We investigate the time average mean-square displacement δ 2¯(x (t))=∫ 0 t− Δ [x (t′+ Δ)−
x (t′)] 2 dt′∕(t− Δ) for fractional Brownian-Langevin motion where x (t) is the stochastic …
x (t′)] 2 dt′∕(t− Δ) for fractional Brownian-Langevin motion where x (t) is the stochastic …
Observation of a Power-Law Memory Kernel for Fluctuations<? format?> within a Single Protein Molecule
The fluctuation of the distance between a fluorescein-tyrosine pair within a single protein
complex was directly monitored in real time by photoinduced electron transfer and found to …
complex was directly monitored in real time by photoinduced electron transfer and found to …
Position-dependent memory kernel in generalized Langevin equations: Theory and numerical estimation
Generalized Langevin equations with non-linear forces and position-dependent linear
friction memory kernels, such as commonly used to describe the effective dynamics of …
friction memory kernels, such as commonly used to describe the effective dynamics of …
Viscoelastic subdiffusion: generalized Langevin equation approach
I Goychuk - Advances in Chemical Physics, 2012 - Wiley Online Library
Viscoelastic subdiffusion: generalized Langevin equation approach Page 195 VISCOELASTIC
SUBDIFFUSION: GENERALIZED LANGEVIN EQUATION APPROACH IGOR GOYCHUK …
SUBDIFFUSION: GENERALIZED LANGEVIN EQUATION APPROACH IGOR GOYCHUK …
Aging renewal theory and application to random walks
We discuss a renewal process in which successive events are separated by scale-free
waiting time periods. Among other ubiquitous long-time properties, this process exhibits …
waiting time periods. Among other ubiquitous long-time properties, this process exhibits …