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Research Output 1999 2019

  • 26 Article
  • 2 Chapter
  • 1 Conference contribution
  • 1 Conference article
2019
24 Downloads (Pure)

Rescaled Objective Solutions of Fokker-Planck and Boltzmann equations

Matthies, K. & Theil, F., 18 Apr 2019, In : SIAM Journal on Mathematical Analysis (SIMA). 51, 2, p. 1321–1348 28 p.

Research output: Contribution to journalArticle

Open Access
File
Fokker-Planck equation
shear flow
energy
symmetry

Solitary waves in atomic chains and peridynamical media

Herrmann, M. & Matthies, K., 7 Mar 2019, In : Mathematics in Engineering. 1, 2, p. 281-308 28 p.

Research output: Contribution to journalArticle

Open Access
norms
traveling waves
differential equations
solitary waves
potential energy
22 Downloads (Pure)

Stability of high-energy solitary waves in Fermi-Pasta-Ulam-Tsingou chains

Herrmann, M. & Matthies, K., 1 Sep 2019, In : Transactions of the American Mathematical Society. 372, 5, p. 3425–3486 62 p.

Research output: Contribution to journalArticle

Open Access
File
Solitary Waves
Solitons
High Energy
Unstable
Eigenvalues and eigenfunctions
2018

Asymptotic properties of high-speed waves in atomic chains

Herrmann, M. & Matthies, K., 17 Dec 2018, In : PAMM - Proceedings in Applied Mathematics and Mechanics. 18, 1, 2 p., e201800305.

Research output: Contribution to journalConference article

Asymptotic Properties
High Speed
7 Downloads (Pure)

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

Open Access
File
Linear Boltzmann Equation
Boltzmann equation
Rayleigh
Tagged Particle
Collision
2 Citations (Scopus)
60 Downloads (Pure)

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

Open Access
File
Linear Boltzmann Equation
Boltzmann equation
Ludwig Boltzmann
Rayleigh
Tagged Particle
18 Downloads (Pure)

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, Vol. 205. p. 3-15 13 p. ( Springer Proceedings in Mathematics & Statistics; vol. 205).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Open Access
File
Solitary Waves
Traveling Wave
High Energy
Uniqueness
Delay Differential Equations
2016
61 Downloads (Pure)

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

Matthies, K. & Uecker, H., 10 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 (Scopus)
61 Downloads (Pure)

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
2014
1 Citation (Scopus)
66 Downloads (Pure)
Open Access
File
Periodic Media
Reaction-diffusion Equations
Homogenization
Traveling Wave
Nonlinearity
2013
4 Citations (Scopus)

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 (Scopus)
70 Downloads (Pure)

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
2012
3 Citations (Scopus)
57 Downloads (Pure)

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
10 Citations (Scopus)
64 Downloads (Pure)

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 (Scopus)
51 Downloads (Pure)

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 Citation (Scopus)
59 Downloads (Pure)

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 Citation (Scopus)

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 (Scopus)

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
4 Citations (Scopus)

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

6 Citations (Scopus)
51 Downloads (Pure)

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

6 Citations (Scopus)
56 Downloads (Pure)

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 (Scopus)
16 Downloads (Pure)

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 (Scopus)
47 Downloads (Pure)
Open Access
File
Backward Error Analysis
Nonautonomous Equation
Discretization Scheme
Regularity Properties
Homoclinic Orbit
16 Citations (Scopus)

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 (Scopus)
57 Downloads (Pure)
Open Access
File
24 Citations (Scopus)
55 Downloads (Pure)

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
34 Citations (Scopus)
57 Downloads (Pure)

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
25 Citations (Scopus)
59 Downloads (Pure)
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