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Research Output 1999 2018

2018

Derivation of a Nonautonomous Linear Boltzmann Equation from a Heterogeneous Rayleigh Gas

Matthies, K. & Stone, G. 1 Jul 2018 In : Discrete and Continuous Dynamical Systems - Series A. 38, 7, p. 3299-3355 57 p.

Research output: Contribution to journalArticle

Linear Boltzmann Equation
Boltzmann equation
Rayleigh
Tagged Particle
Collision
1 Citations

The derivation of the linear Boltzmann equation from a Rayleigh gas particle model

Matthies, K., Stone, G. R. & Theil, F. 1 Feb 2018 In : Kinetic and Related Models. 11, 1, p. 137-177 41 p., 14450

Research output: Contribution to journalArticle

Linear Boltzmann Equation
Boltzmann equation
Ludwig Boltzmann
Rayleigh
Tagged Particle

Uniqueness of solitary waves in the high-energy limit of FPU-type chains

Herrmann, M. & Matthies, K. 8 Feb 2018 Patterns of Dynamics . Gurevich, P., Hell, J., Sandstede, B. & Scheel, A. (eds.). Springer, p. 3-15 13 p. ( Springer Proceedings in Mathematics & Statistics; vol. 205)

Research output: Chapter in Book/Report/Conference proceedingChapter

Open Access
File
Solitary Waves
Traveling Wave
High Energy
Uniqueness
Delay Differential Equations
2017

Derivation of Kinetic Equations from Particle Models

Stone, G. R. Sep 2017 160 p.

Research output: ThesisDoctoral Thesis

Open Access
File
kinetic equations
derivation
collisions
histories
BBGKY hierarchy
2016

Low regularity justification results for envelope approximations of nonlinear wave packets in periodic media

Matthies, K. & Uecker, H. Aug 2016 In : Asymptotic Analysis. 99, 1-2, p. 53-65

Research output: Contribution to journalArticle

Open Access
File
Periodic Media
Wave Packet
Nonlinear Waves
Justification
Envelope
2015
2 Citations

Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains

Herrmann, M. & Matthies, K. Aug 2015 In : Nonlinearity. 28, 8, p. 2767-2789

Research output: Contribution to journalArticle

Open Access
File

On the phase transition in certain percolation models.

Daniels, C. Oct 2015 82 p.

Research output: ThesisDoctoral Thesis

Open Access
File
arrivals
boxes
invariance
color
adsorption
2014
Open Access
File
Periodic Media
Reaction-diffusion Equations
Homogenization
Traveling Wave
Nonlinearity
2013
4 Citations

Can equations of equilibrium predict all physical equilibria? A case study from Field Dislocation Mechanics

Das, A., Acharya, A., Zimmer, J. & Matthies, K. Nov 2013 In : Mathematics and Mechanics of Solids. 18, 8, p. 803-822 20 p.

Research output: Contribution to journalArticle

Dislocation
Mechanics
Ginzburg-Landau Equation
Predict
Microstructure
6 Citations

Subsonic phase transition waves in bistable lattice models with small spinodal region

Herrmann, M., Matthies, K., Schwetlick, H. & Zimmer, J. 3 Sep 2013 In : SIAM Journal on Mathematical Analysis (SIMA). 45, 5, p. 2625-2645 21 p.

Research output: Contribution to journalArticle

Open Access
File
Lattice Model
Phase Transition
Phase transitions
Perturbation
Kinetic Relation

Travelling waves in heterogeneous media

Boden, A. 2013 (Unpublished)

Research output: ThesisDoctoral Thesis

File
Heterogeneous Media
Traveling Wave
Nonlinearity
Wave Speed
Traveling Wave Solutions
2012
2 Citations

A semigroup approach to the justification of kinetic theory

Matthies, K. & Theil, F. 2012 In : SIAM Journal on Mathematical Analysis (SIMA). 44, 6, p. 4345–4379 35 p.

Research output: Contribution to journalArticle

Open Access
File
Kinetic theory
Kinetic Theory
Justification
Semigroup
Collision
2010
9 Citations

Travelling wave solutions for a quasilinear model of field dislocation mechanics

Acharya, A., Matthies, K. & Zimmer, J. Dec 2010 In : Journal of the Mechanics and Physics of Solids. 58, 12, p. 2043-2053 11 p.

Research output: Contribution to journalArticle

File
traveling waves
drag coefficients
Drag coefficient
Mechanics
scalars
4 Citations

Validity and failure of the Boltzmann approximation of kinetic annihilation

Matthies, K. & Theil, F. 1 Feb 2010 In : Journal of Nonlinear Science. 20, 1, p. 1-46 46 p.

Research output: Contribution to journalArticle

Open Access
File
Boltzmann equation
Annihilation
Ludwig Boltzmann
Kinetics
Approximation
2009
1 Citations

Small planar travelling waves in two-dimensional networks of coupled oscillators

Pfrang, C. & Matthies, K. 2009 In : Dynamical Systems: An International Journal. 24, 2, p. 157-170 14 p.

Research output: Contribution to journalArticle

Open Access
File
Coupled Oscillators
Traveling Wave
Delay Equations
Reformulation
Nearest Neighbor
2008
1 Citations

Exponential averaging under rapid quasiperiodic forcing

Matthies, K. 2008 In : Advances in Differential Equations. 13, 5-6, p. 427-456 30 p.

Research output: Contribution to journalArticle

Ordinary differential equations
Forcing
Averaging
Dynamical systems
Initial conditions
3 Citations

Validity and and non-validity of propagation of chaos

Matthies, K. & Theil, F. Sep 2008 Analysis and Stochastics of Growth Processes and Interface Models. Mörter, P., Moser, R., Penrose, M., Schwetlick, H. & Zimmer, J. (eds.). Oxford, p. 101-119 19 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

chaos
propagation
approximation
ballistics
breakdown
2007
2 Citations

Exponential averaging for traveling wave solutions in rapidly varying periodic media

Matthies, K., Schneider, G. & Uecker, H. 2007 In : Mathematische Nachrichten. 280, 4, p. 408-422 15 p.

Research output: Contribution to journalArticle

5 Citations

Exponential homogenization of linear second order elliptic PDEs with periodic coefficients

Kamotski, V., Matthies, K. & Smyshlyaev, V. P. 12 Jan 2007 In : SIAM Journal on Mathematical Analysis (SIMA). 38, 5, p. 1565-1587 23 p.

Research output: Contribution to journalArticle

Open Access
File
Exponential Bound
Oscillating Coefficients
Elliptic PDE
Periodic Coefficients
Linear Order
2006

Exponential estimates in averaging and homogenisation

Matthies, K. 2006 Analysis, modeling and simulation of multiscale problems. Berlin: Springer, p. 1--19 19 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Citations

Wave pinning in strips

Matthies, K. & Wayne, C. E. Oct 2006 In : Proceedings of the Royal Society of Edinburgh Section A - Mathematics. 136, 5, p. 971-995 25 p.

Research output: Contribution to journalArticle

Open Access
File
2005
6 Citations

Homogenisation of exponential order for elliptic systems in infinite cylinders

Matthies, K. 2005 In : Asymptotic Analysis. 43, 3, p. 205-232

Research output: Contribution to journalArticle

Open Access
File
Elliptic Systems
Inhomogeneity
Homogenization
Gevrey Classes
Equilibrium Solution
2003
3 Citations
Open Access
File
Backward Error Analysis
Nonautonomous Equation
Discretization Scheme
Regularity Properties
Homoclinic Orbit
13 Citations

Exponential averaging for Hamiltonian evolution equations

Matthies, K. & Scheel, A. 2003 In : Transactions of the American Mathematical Society. 355, 2, p. 747-773

Research output: Contribution to journalArticle

Hamiltonians
Ordinary differential equations
Partial differential equations
Evolution Equation
Averaging
4 Citations
Open Access
File
23 Citations

Geometric solitary waves in a 2D mass-spring lattice

Friesecke, G. & Matthies, K. Feb 2003 In : Discrete and Continuous Dynamical Systems - Series B. 3, 1, p. 105-144

Research output: Contribution to journalArticle

Open Access
File
Solitary Waves
Solitons
Hamiltonians
Hamiltonian Dynamics
Nonexistence
2002
33 Citations

Atomic-scale localization of high-energy solitary waves on lattices

Friesecke, G. & Matthies, K. Nov 2002 In : Physica D: Nonlinear Phenomena. 171, 4, p. 211-220 10 p.

Research output: Contribution to journalArticle

Open Access
File
2001
22 Citations
File
1999

A Subshift of Finite Type in the Takens-Bogdanov Bifurcation with D 3 Symmetry

Matthies, K. 1999 In : Documenta Mathematica. 4, p. 463-485 23 p.

Research output: Contribution to journalArticle

Bogdanov-Takens Bifurcation
Subshift
Finite Type
Homoclinic Orbit
Symmetry