Publications - Arnd Scheel

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A. Scheel
Nonlinear eigenvalue methods for linear pointwise stability of nonlinear waves (PDF)

Refereed Journals

M. Avery, A. Scheel
Universal selection of pulled fronts (PDF)
Comm. AMS, to appear.

M. Avery, A. Scheel
Sharp decay rates for localized perturbations to the critical front in the Ginzburg-Landau equation (PDF)
J. Dyn. Diff. Eqns., to appear

M. Avery, C. Dedina, A. Smith, A. Scheel
Instability in large bounded domains — branched versus unbranched resonances (PDF)
Nonlinearity 34 (2021), 7916-7937

A. Scheel, A. Stevens, C. Tenbrock
Signaling gradients in surface dynamics as basis for planarian regeneration (PDF, Supplementary movies Cutting, Oscillations, Grafting)
J. Math. Biol. 83,6 (2021)

K. Chen, Z. Deiman, R. Goh, S. Jankovic, A. Scheel
Strain and defects in oblique stripe growth (PDF)
Multiscale Model. Simul. 19 (2021), 1236-1260

G. Faye, M. Holzer, L. Siemer, A. Scheel
Invasion into remnant instability: a case study of front dynamics (PDF)
Indiana Univ. Math. J., to appear

M. Avery, A. Scheel
Asymptotic stability of critical pulled fronts via resolvent expansions near the essential spectrum (PDF)
SIAM J. Math. Anal. 53 (2021), 2206-2242.

B. Sandstede, A. Scheel
Spiral waves: linear and nonlinear theory (PDF)
Mem. Amer. Math. Soc., to appear

A. Pauthier, A. Scheel
Advection-diffusion dynamics with nonlinear boundary flux as a model for crystal growth (PDF)
Math. Nachr. 293 (2020), 1565-1590

P. Flynn, Q. Neville, A. Scheel
Self-organized clusters in run-and-tumble processes (PDF)
DCDS-S 13 (2020), 1187-1208

A. Scheel, T. Tao
Bifurcation to coherent structures in nonlocally coupled systems (PDF)
J. Dyn. Diff. Eqns. 31 (2019), 1107-1127

M. Avery, R. Goh, O. Goodloe, A. Milewski, A. Scheel
Growing stripes, with and without wrinkles (PDF) [Moduli space movie with delicate arch, Supplementary materials]
SIAM J. Appl. Dyn. Sys. 18 (2019), 1078-1117

K. Kang, A. Scheel, A. Stevens
Global phase diagrams of run-and-tumble dynamics: equidistribution, waves, and blowup (PDF)
Nonlinearity 32 (2019), 2128-2146

G. Jaramillo, A. Scheel, Q. Wu
The effect of impurities on striped phases (PDF)
Proc. Roy. Soc. Edinb. 149 (2019), 131-168

N. Ankney, M. Avery, T. Khain, A. Scheel
Pinning and Depinning: from periodic to chaotic and random media (PDF)
Chaos 29, 013127 (2019)

R. Samuelson, Z. Singer, J. Weinburd, A. Scheel
Advection and autocatalysis as organizing principles for banded vegetation patterns (PDF)
J. Nonlinear Science 29 (2019), 255-285

B. Bakker, A. Scheel
Spatial Hamiltonian identities for nonlocally coupled systems (PDF)
Forum Sigma 6 (2018), E22, 55p

P. Carter, A. Scheel
Wave train selection by invasion fronts in the FitzHugh--Nagumo equation (PDF)
Nonlinearity 31 (2018), 5536-5572

R. Goh, A. Scheel
Pattern forming fronts in a Swift-Hohenberg equation with directional quenching - parallel and oblique stripes (PDF)
J. London Math. Soc. 98 (2018), 104-128

R. Monteiro, A. Scheel
Contact angle selection for interfaces in growing domains (PDF)
Z. Angew. Math. Mech. 98 (2018), 1086-1102

G. Faye, A. Scheel
Center manifolds without a phase space (PDF)
Trans. Amer. Math. Soc. 370 (2018), 5843-5885

A. Scheel, J. Weinburd
Wavenumber selection via spatial parameter jump (PDF)
Philos. Trans. Royal Soc. A, 376 (2017), 20170191

A. Scheel, A. Stevens
Wavenumber selection in coupled transport equations (PDF)
J. Math. Biol. 75 (2017), 1047-1073

R. Monteiro, A. Scheel
Phase separation patterns from directional quenching (PDF)
J. Nonlinear Science 27 (2017), 1339-1378 .

G. Faye, M. Holzer, A. Scheel
Linear spreading speeds from nonlinear resonant interaction (PDF)
Nonlinearity 30 (2017), 2403-2442

A. Pogan, A. Scheel
Traveling fronts bifurcating from stable layers in the presence of conservation laws (PDF)
Discr. Cont. Dyn. Sys. A 37 (2017), 2619-2651

D. Lloyd, A. Scheel
Continuation and bifurcation of grain boundaries in the Swift-Hohenberg equation (PDF)
SIAM J. Appl. Dyn. Sys. 16 (2017), 252-293

Z. Wang, R. Goh, K. Bazargan, A. Scheel, N. Saraf
Stochastic implementation and analysis of dynamical system similar to the logistic map
IEEE Trans. VLSI Sys. 25 (2017), 747-759

A. Scheel
Spinodal decomposition and coarsening fronts in the Cahn-Hilliard equation (PDF)
J. Dyn. Diff. Eqns. 29 (2017), 431-464

R. Goh, R. Beekie, D. Matthias, J. Nunley, A.Scheel
Universal wavenumber selection laws in apical growth (PDF)
Phys. Rev. E 94 (2016), 022219

R. Goh, A. Scheel
Pattern formation in the wake of triggered pushed fronts (PDF)
Nonlinearity 29 (2016), 2196-2237

T. Anderson, G. Faye, A. Scheel, D. Stauffer
Pinning and unpinning in nonlocal systems (PDF)
J. Dyn. Diff. Eqns.28 (2016), 897-923

G. Jaramillo, A. Scheel
Pacemakers in large arrays of oscillators with nonlocal coupling (PDF)
J. Diff. Eqns. 260 (2016), 2060-2090

E. Ben-Naim, A. Scheel
Pattern selection and super-patterns in the bounded confidence model (PDF)
Europhys. Lett. 112 (2015) 18002

D. Morrissey, A. Scheel
Characterizing the effect of boundary conditions on striped phases (PDF)
SIAM J. Appl. Dyn. Sys. 14 (2015), 1387-1417

R. Goh, A. Scheel
Hopf bifurcation from fronts in the Cahn-Hilliard equation (PDF)
Arch. Rational Mech. Anal. 217 (2015), 1219-1263

G. Jaramillo, A. Scheel
Deformation of striped patterns by inhomogeneities (PDF)
Math. Meth. Appl. Sci. 38 (2015), 51-65

A. Scheel, Q. Wu
Diffusive stability of Turing patterns via normal forms (PDF)
J. Dyn. Diff. Eqns. 27 (2015), 1027-1076

C. Browne, A. Dickerson. Mentors: G. Faye, A. Scheel.
Coherent structures in scalar feed-forward chains (PDF)
SIURO 7 (2014), 306-329

G. Faye, A. Scheel
Existence of pulses in excitable media with nonlocal coupling (PDF)
Adv. Math. 270 (2014), 400-456

M. Holzer, A. Scheel
Criteria for pointwise growth and their role in invasion processes (PDF)
J. Nonlinear Science 24 (2014), 661-709

M. Holzer, A. Scheel
Accelerated fronts in a two stage invasion process (PDF)
SIAM J. Math. Anal. 46 (2014), 397-427

G. Faye, A. Scheel
Fredholm properties of nonlocal differential operators via spectral flow (PDF)
Indiana Univ. Math. J. 63 (2014), 1311-1348

R. Goh, A. Scheel
Triggered fronts in the complex Ginzburg-Landau equation (PDF)
J. Nonlinear Science 24 (2014), 117-144

A. Scheel, Q. Wu
Small-amplitude grain boundaries of arbitrary angle in the Swift-Hohenberg equation (PDF)
Z. Angew. Math. Mech. 94 (2014), 203-232

K. Bose, T. Cox, S. Silvestri, P. Varin. Mentors: M. Holzer, A. Scheel.
Invasion fronts and pattern formation in a model of chemotaxis in one and two dimensions. (PDF)
SIURO 6 (2013), 228-245

A. Pogan, A. Scheel, K. Zumbrun
Quasi-gradient systems, modulational dichotomies, and stability of spatially periodic patterns
Diff. Int. Eqns. 26 (2013), 383-432

M. Holzer, A. Scheel
A slow pushed front in a Lotka-Volterra competition model (PDF)
Nonlinearity 25 (2012), 2151-2179

M. Haragus, A. Scheel
Dislocations in an anisotropic Swift-Hohenberg equation (PDF)
Comm. Math. Phys. 315 (2012), 311-335

M. Haragus, A. Scheel
Grain boundaries in the Swift-Hohenberg equation (PDF)
European J. Appl. Math. 23 (2012), 737-759

A. Pogan, A. Scheel
Layers in the presence of conservation laws (PDF)
J. Dyn. Diff. Eqns. 24 (2012), 249-287

B. Sandstede, A. Scheel, G. Schneider, H. Uecker
Diffusive mixing of periodic wave trains in reaction-diffusion systems (PDF)
J. Differential Eqns. 252 (2012), 3541-3574

A. Pogan, A. Scheel
Fredholm properties of radially symmetric, second order differential operators (PDF)
Int. J. Dyn. Sys. Diff. Eqns. 3 (2011), 289-327

T. Gallay, A. Scheel
Diffusive stability of oscillations in reaction-diffusion systems (PDF)
Trans. Amer. Math. Soc. 363 (2011), 2571-2598

R. Goh, S. Mesuro, A. Scheel
Spatial wavenumber selection in recurrent precipitation (PDF)
SIAM J. Appl. Dyn. Sys. 10 (2011), 360-402

J. Bellay, A. Scheel
Coherent structures near the boundary between excitable and oscillatory media (PDF)
Dyn. Syst. 25 (2010), 111-132

A. Pogan, A. Scheel
Instability of spikes in the presence of conservation laws (PDF)
Z. Angew. Math. Phys. 61 (2010), 979-998

A. Scheel, E. van Vleck
Lattice differential equations embedded into reaction-diffusion systems (PDF)
Proc. Royal Soc. Edinburgh A, 139A (2009), 193-207

A. Doelman, B. Sandstede, A. Scheel, G. Schneider
The dynamics of modulated wave trains (PDF)
Mem. Amer. Math. Soc. 199 (2009)

A. Scheel
Robustness of Liesegang patterns (PDF)
Nonlinearity 22 (2009), 457-483

A. Scheel, J.D. Wright
Colliding dissipative pulses - the shooting manifold (PDF)
J. Differential Eqns. 245 (2008), 59-79

B. Sandstede, A. Scheel
Hopf bifurcation from viscous shock waves (PDF)
SIAM J. Math. Anal. 39 (2008), 2033-2052

B. Sandstede, A. Scheel
Relative Morse indices, Fredholm indices, and group velocities (PDF)
Discr. Cont. Dyn. Sys. A 20 (2008), 139-158

M. Haragus, A. Scheel
Interfaces between rolls in the Swift-Hohenberg equation (PDF)
Int. J. Dyn. Sys. Diff. Eqns. 1 (2007), 89-97

J.D.M. Rademacher, A. Scheel
Instabilities of wave trains and Turing patterns in large domains (PDF )
Int. J. Bif. Chaos 16 (2007), 2679-2691

J.D. Wright, A. Scheel
Solitary waves and their linear stability in weakly coupled KdV equations (PDF)
Z. Angew. Math. Phys. 58 (2007), 535-570

B. Sandstede, A. Scheel
Period-doubling of spiral waves and defects (PDF)
SIAM J. Appl. Dyn. Syst. 6 (2007), 494-547

M. Haragus, A. Scheel
Stable viscous shocks in elliptic conservation laws (PDF)
Indiana Univ. Math. J. 56 (2007), 1261-1278

J.D.M. Rademacher, A. Scheel
The saddle-node of nearly homogeneous wave trains in reaction-diffusion systems (PDF)
J. Dyn. Diff. Eqns. 19 (2007), 479-496

J.D.M. Rademacher, B. Sandstede, A. Scheel
Computing absolute and essential spectra using continuation (PDF)
Physica D 229 (2007), 166-183

R. Kollár, A. Scheel
Coherent structures generated by inhomogeneities in oscillatory media (PDF)
SIAM J. Appl. Dyn. Syst. 6 (2007), 236-262

M. Haragus, E. Lombardi, A. Scheel
Spectral stability of wave trains in the Kawahara equation (PDF)
J. Math. Fluid Mechanics 8 (2006), 482-509

A. Scheel
Coarsening fronts (PDF)
Arch. Rational Mech. Anal. 181 (2006), 505-534

M. Haragus, A. Scheel
Almost planar waves in anisotropic media (PDF)
Comm. Partial Differential Equations 31 (2006), 791-815

M. Haragus, A. Scheel
Corner defects in almost planar interface propagation (PDF)
Ann. Inst. H. Poincare (C) Anal. Non Lineaire 23 (2006), 283-329

B. Sandstede and A. Scheel
Curvature effects on spiral spectra: Generation of point eigenvalues near branch points (PDF)
Phys. Rev. E 73 (2006), 016217

B. Sandstede, A. Scheel
Basin boundaries and bifurcations near convective instabilities: A case study (PDF)
J. Differential Eqns. 208 (2005), 176-193

B. Sandstede, A. Scheel
Absolute instabilities of standing pulses (PDF)
Nonlinearity 18 (2005), 331-378

B. Sandstede, A. Scheel
Evans function and blow-up methods in critical eigenvalue problems (PDF)
Discr. Cont. Dyn. Sys. 10 (2004), 941-964

B. Sandstede, A. Scheel
Defects in oscillatory media: toward a classification (PDF)
SIAM J. Appl. Dyn. Syst. 3 (2004), 1-68

A. Scheel
Radially symmetric patterns of reaction-diffusion systems (PDF)
Mem. Amer. Math. Soc. 165 (2003)

D.Pelinovsky, A. Scheel
Stability analysis of stationary light transmission in nonlinear photonic structures (PDF)
J. Nonlinear Science 13 (2003), 347-396

A. Doelman, B. Sandstede, A. Scheel, and G. Schneider
Propagation of hexagonal patterns near onset (PDF)
Europ. J. Appl. Math. 14 (2003), 85-110

K. Matthies, A. Scheel
Exponential veraging for Hamiltonian evolution equations (PDF)
Trans. Amer. Math. Soc. 355 (2003), 747-773

J. Härterich, B. Sandstede, A. Scheel
Exponential dichotomies for non-autonomous functional differential equations of mixed type (PDF)
Indiana Univ. Math. J. 51 (2002), 1081-1109

M. Haragus, A. Scheel
Linear stability and instability of ion-acoustic plasma solitary waves (PDF)
Physica D 170 (2002), 13-30

M. Haragus, A. Scheel
Finite-wavelength stability of capillary-gravity solitary waves (PDF)
Commun. Math. Phys. 225 (2002), 487-521

B. Sandstede, A. Scheel
On the structure of spectra of modulated travelling waves (PDF)
Math. Nachr. 232 (2001), 39-93

B. Sandstede, A. Scheel
Super-spiral structures of meandering and drifting spiral waves (PDF)
Phys. Rev. Lett. 86 (2001), 171-174

B. Sandstede, A. Scheel
On the stability of periodic travelling waves with large spatial period (PDF)
J. Differential Eqns. 172 (2001), 134-188

B. Sandstede, A. Scheel
Essential instabilities of fronts: bifurcation and bifurcation failure (PDF)
Dynamical Systems 16 (2001), 1-28

B. Sandstede, A. Scheel
Absolute versus convective instability of spiral waves (PDF)
Phys. Rev. E. 62 (2000), 7708-7714

B. Sandstede, A. Scheel
Absolute and convective instabilities of waves on unbounded and large bounded domains (PDF)
Physica D 145 (2000), 233-277

B. Sandstede, A. Scheel
Gluing unstable fronts and backs together can produce stable pulses (PDF)
Nonlinearity 13 (2000), 1465-1482

B. Sandstede, A. Scheel
Spectral stability of modulated travelling waves bifurcating near essential instabilities (PDF)
Proc. Roy. Soc. Edinb. A 130 (2000), 419-448

G. J. Lord, D. Peterhof, B. Sandstede, A. Scheel
Numerical computation of solitary waves in infinite cylindrical domains (PDF)
SIAM J. Numerical Analysis 37 (2000), 1420-1454

B. Sandstede, A. Scheel
Essential instability of pulses and bifurcations to modulated travelling waves (PDF)
Proc. Roy. Soc. Edinb. A 129 (1999), 1263-1290

B. Sandstede, A. Scheel, C. Wulff
Bifurcations and dynamics of spiral waves ( PDF)
J. Nonlinear Science 9 (1999), 439-478

B. Fiedler, A. Scheel, M.I. Vishik
Large patterns of elliptic systems in infinite cylinders (PDF)
J. Math. Pures Appl. 77 (1998), 879-907

A. Scheel
Bifurcation to spiral waves in reaction-diffusion systems (PDF)
SIAM J. Math. Anal. 29 (1998), 1399-1418

A. Scheel
Subcritical bifurcation to infinitely many rotating waves (PDF)
J. Math. Anal. Appl. 215 (1997), 252-261

B. Sandstede, A. Scheel, C. Wulff
Dynamics of spiral waves on unbounded domains using center-manifold reduction (PDF)
J. Differential Eqns. 141 (1997), 122-149

D. Peterhof, B. Sandstede, A. Scheel
Exponential dichotomies for solitary wave solutions of semilinear elliptic equations on infinite cylinders (PDF)
J. Differential Eqns. 140 (1997), 266-308

B. Sandstede, A. Scheel, C. Wulff
Center manifold reduction for spiral wave dynamics (PDF)
C. R. Acad. Sci. Paris, Serie I, t.324 (1997), 153-158

P. Chossat, M. Krupa, I. Melbourne, A. Scheel
Transverse bifurcations of homoclinic cycles (PDF)
Physica D 100 (1997) 85-100

A. Scheel
Existence of fast travelling waves for some parabolic equations --- a dynamical systems approach. (PDF)
J. Dyn. Diff. Eqns. 8 (1996), 469-548

B. Fiedler, B. Sandstede, A. Scheel, C. Wulff
Bifurcation from relative equilibria of noncompact group actions: skew products, meanders, and drifts (PDF)
Documenta Mathematica 1 (1996), 479-505.

B. Sandstede, A. Scheel
Forced symmetry breaking of homoclinic cycles (PDF)
Nonlinearity 8 (1995), 333-365

A. Scheel
Fast travelling waves for convective reaction-diffusion equations
C. R. Acad. Sci. Paris, Serie I, t. 317 (1993), 347-351.

A. Scheel
Fast travelling waves for the Cahn-Hilliard equation in an infinite strip
C. R. Acad. Sci. Paris, Serie I, t. 317 (1993), 261-265.

A. Scheel, P. Chossat
Bifurcation d'orbites periodiques a partir d'un cycle homocline symetrique (PDF)
C. R. Acad. Sci. Paris, Serie I, t. 314 (1992), 49-54.

Review Articles

M. Haragus, A. Scheel
A bifurcation approach to non-planar traveling waves in reaction-diffusion systems (PDF)
GAMM-Mitt. 30, (2007), 75-95.

B. Fiedler, A. Scheel
Spatio-Temporal Dynamics of Reaction-Diffusion Patterns (PDF)
In Trends in Nonlinear Analysis, M. Kirkilionis, S. Krömker, R. Rannacher, F. Tomi (Eds.), Springer-Verlag, Berlin, 2003 (145 pages).

B. Sandstede, A. Scheel, C. Wulff
Dynamical behavior of patterns with euclidean symmetry
In ``Pattern formation in continuous and coupled systems'', M. Golubitsky, D. Luss and S. Strogatz (eds.), Springer-Verlag. IMA Volumes in Mathematics and its Applications 115 (1999), 249-264.

Proceedings and book chapters

A. Scheel and S. Tikhomirov
Depinning asymptotics in ergodic media (PDF)
In P. Gurevich, J. Hell, B. Sandstede, and A. Scheel, editors, Patterns of Dynamics, 88--108, Cham, 2017. Springer International Publishing.

K. Bazargan, N. Sarag, A. Scheel, Z. Wang.
Randomness Meets Feedback: Stochastic Implementation of Logistic Map Dynamical System
In "Design Automation Conference", 2015 52nd ACM/EDAC/IEEE.

A. Scheel.
Pattern formation.
In 'The Princeton Companion to Applied Mathematics', Princeton Univ. Press, 2015.

M. Kotzagiannidis, J. Peterson, J. Redford, A. Scheel, Q. Wu
Stable pattern selection through invasion fronts in closed two-species reaction-diffusion systems (PDF)
In RIMS Kokyuroku Bessatsu B31 (2012), Far-From-Equilibrium Dynamics, eds. T. Ogawa, K. Ueda , pp 79-93.

R. Goh, S. Mesuro, A. Scheel
Coherent structures in reaction-diffusion models for precipitation (PDF)
Special volume on "Precipitation patterns in reaction-diffusion systems", Research Signpost (2010), 73-93.

A. Pogan, A. Scheel
Instability of adially-mmetric spikes in systems with a conserved quantity (PDF)
Fields Institute Communications 64 (2013), 119-140.

B. Sandstede, A. Scheel
Absolute and convective stability in large domains
In Proceedings of Equadiff 99, B. Fiedler, K. Gröoger, and J. Sprekels (eds.), World Scientific Publishing, Singapore (2000), 797-800.

M. Efendiev, A. Scheel
Upper and lower bounds for the Hausdorff dimension of the attractor for reaction-diffusion equations in R\sup n
In Proceedings of ``Nonlinear evolution equations and application'', M.Otani (ed.), RIMS, Kyoto (1999), 81-90.

P. Chossat, M. Krupa, I. Melbourne, A. Scheel
Magnetic dynamos in rotating convection --- a dynamical systems approach
Dyn. Cont. Discrete Impulsive Syst. 5 (1999), 327-340.

A. Scheel
Meandering spirals
Z. Angew. Math. Mech. 79 (1999) 163-166.


DEA INLN, Nice 1991
Bifurcation d'orbites periodiques a partir de cycles homoclines en presence de symetrie (PDF)

PhD, FU Berlin, 1994
Existence of fast travelling waves for some parabolic equations - a dynamical systems approach

Habilitation, FU Berlin, 2001
Radially symmetric patterns of reaction-diffusion systems

Arnd Scheel's Home Page
The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota.