Preprints 
[22] 
E. Siminos, B. Svedung Wettervik, M. Grech and T. Fülöp
Kinetic and finite ion mass effects on the transition to relativistic selfinduced transparency in laserdriven ion acceleration
arXiv:1603.06436, submitted (2017)

Journal Articles 
[21] 
B. Svedung Wettervik, T.C. Dubois, E. Siminos and T. Fülöp
Relativistic VlasovMaxwell modelling using finite volumes and adaptive mesh refinement
European Physical Journal D 71, 157 (2017)
arXiv:1606.08681

[20] 
G. SánchezArriaga, E. Siminos
Relativistic quasisolitons and embedded solitons with circular polarization in cold plasmas
J. Phys. A: Math. Theor.50, 185501 (2017)
arXiv:1606.02582
+ abstract
Linearly polarized solitary waves, arising from the interaction of an intense laser pulse with a plasma, are investigated. New localized structures, in the form of exact \Changes{numerical} nonlinear solutions of the onedimensional Maxwellfluid model for a cold plasma with fixed ions are presented. Unlike stationary circularly polarized solitary waves, the linear polarization gives rise to a breatherlike behavior and a periodic exchange of electromagnetic energy and electron kinetic energy at twice the frequency of the wave. A numerical method based on a finitedifferences scheme allows to compute a branch of solutions within the frequency range $\Omega_{min}<\Omega<\omega_{pe}$, where $\omega_{pe}$ and $\Omega_{min}$ are the electron plasma frequency and the frequency value for which the plasma density vanishes locally, respectively. A detailed description of the spatiotemporal structure of the waves and their main properties as a function of $\Omega$ are presented. Small amplitude oscillations appearing in the tail of the solitary waves, a consequence of the linear polarization and harmonic excitation, are explained with the aid of the AkhiezerPolovin system. Direct numerical simulations of the Maxwellfluid model show that these solitary waves propagate without change for a long time.

[19] 
X. Ding, H. Chaté, P. Cvitanović, E. Siminos and K. A. Takeuchi
Estimating dimension of inertial manifold from unstable periodic orbits
Phys. Rev. Lett. 117, 024101 (2016)
arXiv:1604.01859
+ abstract
We provide numerical evidence that a finitedimensional inertial manifold on which the dynamics of a chaotic dissipative dynamical system lives can be constructed solely from the knowledge of a set of unstable periodic orbits. In particular, we determine the dimension of the inertial manifold for KuramotoSivashinsky system, and find it to be equal to the `physical dimension' computed previously via the hyperbolicity properties of covariant Lyapunov vectors.

[18] 
E. Siminos, S. Skupin, A. Sävert, J. M. Cole, S. P. D. Mangles and M. C. Kaluza
Modeling ultrafast shadowgraphy in laserplasma interaction experiments
Plasma Phys. Control. Fusion 58 065004 (2016)

[17] 
A. Sävert, S. P. D. Mangles, M. Schnell, E. Siminos, J. M. Cole, M. Leier, M. Reuter, M. B. Schwab,
M. Möller, K. Poder, O. Jäckel, G. G. Paulus, C. Spielmann, S. Skupin, Z. Najmudin, and M. C. Kaluza
Direct observation of the injection dynamics of a laser wakefield accelerator using fewfemtosecond shadowgraphy
Phys. Rev. Lett. 115, 055002 (2015)
reprint

[16] 
G. SánchezArriaga, E. Siminos, V. Saxena and I. Kourakis,
Relativistic breathertype solitary waves with linear polarization in cold plasmas
Phys. Rev. E 91, 033102 (2015)
+ abstract
Linearly polarized solitary waves, arising from the interaction of an intense laser pulse with a plasma, are investigated. New localized structures, in the form of exact \Changes{numerical} nonlinear solutions of the onedimensional Maxwellfluid model for a cold plasma with fixed ions are presented. Unlike stationary circularly polarized solitary waves, the linear polarization gives rise to a breatherlike behavior and a periodic exchange of electromagnetic energy and electron kinetic energy at twice the frequency of the wave. A numerical method based on a finitedifferences scheme allows to compute a branch of solutions within the frequency range $\Omega_{min}<\Omega<\omega_{pe}$, where $\omega_{pe}$ and $\Omega_{min}$ are the electron plasma frequency and the frequency value for which the plasma density vanishes locally, respectively. A detailed description of the spatiotemporal structure of the waves and their main properties as a function of $\Omega$ are presented. Small amplitude oscillations appearing in the tail of the solitary waves, a consequence of the linear polarization and harmonic excitation, are explained with the aid of the AkhiezerPolovin system. Direct numerical simulations of the Maxwellfluid model show that these solitary waves propagate without change for a long time.

[15] 
N. B. Budanur, P. Cvitanović, R.L. Davidchack, and E. Siminos
Reduction of SO(2) symmetry for spatially extended dynamical systems
Phys. Rev. Lett. 114, 084102 (2015)
+ abstract
Spatially extended systems, such as channel or pipe flows, are often equivariant under continuous symmetry transformations, with each state of the flow having an infinite number of equivalent solutions obtained from it by a translation or a rotation. This multitude of equivalent solutions tends to obscure the dynamics of turbulence. Here we describe the `{\fFslice}', a very simple, easy to implement reduction of SO(2) symmetry. While the method exhibits rapid variations in phase velocity whenever the magnitude of the first Fourier mode is nearly vanishing, these near singularities can be regularized by a timescaling transformation. We show that after application of the method, hitherto unseen global structures, for example KuramotoSivashinsky relative periodic orbits and unstable manifolds of travelling waves, are uncovered.

[14] 
E. Siminos, G. SanchezArriaga, V. Saxena and I. Kourakis,
Modelling relativistic solitary wave interactions in overdense plasmas: a perturbed nonlinear Schrödinger equation framework
Phys. Rev. E 90, 063104 (2014)
+ abstract
We investigate the dynamics of localized solutions of the relativistic coldfluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear SchrÃ¶dinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a selfconsistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full coldfluid model. To lowest order, a cubic nonlinear SchrÃ¶dinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifthorder terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude.

[13] 
A. Friou, D. Bénisti, L. Gremillet, E. Lefebvre, O. Morice, E. Siminos, and D.J. Strozzi
Saturation mechanisms of backward stimulated Raman scattering in a onedimensional geometry
Phys. Plasmas 20, 103103 (2013)
+ abstract
In this paper, we investigate the saturation mechanisms of backward stimulated Raman scattering (BSRS) induced by nonlinear kinetic effects. In particular, we stress the importance of accounting for both the nonlinear frequency shift of the electron plasma wave and the growth of sidebands, in order to understand what stops the coherent growth of Raman scattering. Using a Bernstein GreeneKruskal approach, we provide an estimate for the maximum amplitude reached by a BSRSdriven plasma wave after the phase of monotonic growth. This estimate is in very good agreement with the results from kinetic simulations of stimulated Raman scattering using both a Vlasov and a Particle in Cell code. Our analysis, which may be generalized to a multidimensional geometry, should provide a means to estimate the limits of backward Raman amplification or the effectiveness of strategies that aim at strongly reducing Raman reflectivity in a fusion plasma.

[12] 
F. Maucher, E. Siminos, W. Krolikowski, S. Skupin
Quasiperiodic oscillations and homoclinic orbits in the nonlinear
nonlocal Schrödinger equation
New J. Phys. 15, 083055(2013)
reprint
+ abstract
Quasiperiodic oscillations and shapetransformations of higherorder bright solitons in nonlinear nonlocal media have been frequently observed in recent years, however, the origin of these phenomena was never completely elucidated. In this paper, we perform a linear stability analysis of these higherorder solitons by solving the Bogoliubovde Gennes equations. This enables us to understand the emergence of a new oscillatory state as a growing unstable mode of a higherorder soliton. Using dynamically important states as a basis, we provide lowdimensional visualizations of the dynamics and identify quasiperiodic and homoclinic orbits, linking the latter to shapetransformations.

[11] 
V. Saxena, I. Kourakis, G. SánchezArriaga, and E. Siminos
Interaction of spatially overlapping standing electromagnetic solitons in plasmas
Phys. Lett. A 377, 473477 (2013)
+ abstract
Numerical investigations on mutual interactions between two spatially overlapping standing electromagnetic solitons in a cold unmagnetized plasma are reported. It is found that an initial state comprising of two overlapping standing solitons evolves into different end states, depending on the amplitudes of the two solitons and the phase difference between them. For small amplitude solitons with zero phase difference, we observe the formation of an oscillating bound state whose period depends on their initial separation. These results suggest the existence of a bound state made of two solitons in the relativistic cold plasma fluid model.

[10] 
P. Cvitanović, D. BorreroEcheverry, K. M. Carroll, B. Robbins, and E. Siminos
Cartography of highdimensional flows: A visual guide to sections and slices
Chaos 22, 047506 (2012)
preprint
+ abstract
Symmetry reduction by the method of slices quotients the continuous symmetries of chaotic flows by replacing the original state space by a set of charts, each covering a neighborhood of a dynamically important class of solutions, qualitatively captured by a `template'. Together these charts provide an atlas of the symmetryreduced `slice' of state space, charting the regions of the manifold explored by the trajectories of interest. Within the slice, relative equilibria reduce to equilibria and relative periodic orbits reduce to periodic orbits. Visualizations of these solutions and their unstable manifolds reveal their interrelations and the role they play in organizing turbulence/chaos.

[9] 
E. Siminos, M. Grech, S. Skupin, T. Schlegel, and V. T. Tikhonchuk
Effect of electron heating on selfinduced transparency in relativistic intensity laserplasma interaction
Phys. Rev. E 86, 056404 (2012)
reprint
+ abstract
The effective increase of the critical density associated with the interaction of relativistically intense laser pulses with overcritical plasmas, known as selfinduced transparency, is revisited for the case of circular polarization. A comparison of particleincell simulations to the predictions of a relativistic coldfluid model for the transparency threshold demonstrates that kinetic effects, such as electron heating, can lead to a substantial increase of the effective critical density compared to coldfluid theory. These results are interpreted by a study of separatrices in the singleelectron phase space corresponding to dynamics in the stationary fields predicted by the coldfluid model. It is shown that perturbations due to electron heating exceeding a certain finite threshold can force electrons to escape into the vacuum, leading to laser pulse propagation. The modification of the transparency threshold is linked to the temporal pulse profile, through its effect on electron heating.

[8] 
G. SánchezArriaga, E. Siminos, and E. Lefebvre
Relativistic solitary waves with phase modulation embedded in long laser pulses in plasmas
Phys. Plasmas 18, 082304 (2011)
preprint
+ abstract
We investigate the existence of nonlinear phasemodulated relativistic solitary waves embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. These states are exact nonlinear solutions of the 1dimensional Maxwellfluid model for a cold plasma composed of electrons and ions. The solitary wave, which consists of an electromagnetic wave trapped in a selfgenerated Langmuir wave, presents a phase modulation when the group velocity $V$ and the phase velocity $V_{ph}$ of the long circularly polarized electromagnetic wave do not match the condition $VV_{ph}=c^2$. The main properties of the waves as a function of their group velocities, wavevectors and frequencies are studied, as well as bifurcations of the dynamical system that describes the waves when the parameter controlling the phase modulation changes from zero to a finite value. Such a transition is illustrated in the limit of small amplitude waves where an analytical solution for a grey solitary wave exists. The solutions are interpreted as the stationary state after the collision of a long laser pulse with an isolated solitary wave.

[7] 
E. Siminos, D. Bénisti, and L. Gremillet
Stability of nonlinear VlasovPoisson equilibria through spectral deformation and FourierHermite expansion
Phys. Rev. E 83, 056402 (2011)
reprint
+ abstract
We study the stability of spatially periodic, nonlinear VlasovPoisson equilibria as an eigenproblem in a FourierHermite basis (in the space and velocity variables, respectively) of finite dimension, $N$. When the advection term in Vlasov equation is dominant, the convergence with $N$ of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic BernsteinGreeneKruskal mode with multiple phase space vortices, compare our results with numerical simulations of the VlasovPoisson system and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed.

[6] 
G. SánchezArriaga, E. Siminos, and E. Lefebvre
Relativistic solitary waves modulating long laser pulses in plasmas
Plasma Phys. Contr. Fusion 53, 045011 (2011)
preprint
+ abstract
This article discusses the existence of solitary electromagnetic waves trapped in a selfgenerated Langmuir wave and embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. From the mathematical point of view they are exact solutions of the 1dimensional relativistic cold fluid plasma model with nonvanishing boundary conditions. Under the assumption of traveling wave solutions with velocity $V$ and vector potential frequency $\omega$, the fluid model is reduced to a Hamiltonian system. The solitary waves are homoclinic (grey solitons) or heteroclinic (dark solitons) orbits to fixed points. By using a dynamical systems description of the Hamiltonian system and a spectral method, we identify a great variety of solitary waves, including asymmetric ones, discuss their disappearance for certain parameter values, and classify them according to: (i) grey or dark character, (ii) the number of humps of the vector potential envelope and (iii) their symmetries. The solutions come in continuous families in the parametric $V\omega$ plane and extend up to velocities that approach the speed of light. The stability of certain types of grey solitary waves is investigated with the aid of particleincell simulations that demonstrate their propagation for a few tens of the inverse of the plasma frequency.

[5] 
E. Siminos and P. Cvitanović
Continuous symmetry reduction and return maps for highdimensional flows
Physica D 240, 187198 (2011)
preprint
+ abstract
We present two continuous symmetry reduction methods for reducing highdimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant dynamics is rewritten in terms of invariant coordinates. In the method of moving frames (or method of slices) the state space is sliced locally in such a way that each group orbit of symmetryequivalent points is represented by a single point. In either approach, numerical computations can be performed in the original statespace representation, and the solutions are then projected onto the symmetryreduced state space. The two methods are illustrated by reduction of the complex Lorenz system, a 5dimensional dissipative flow with rotational symmetry. While the Hilbert polynomial basis approach appears unfeasible for highdimensional flows, symmetry reduction by the method of moving frames offers hope.

[4] 
D. Bénisti, O. Morice, L. Gremillet, E. Siminos, and D.J. Strozzi
Selforganization and threshold of stimulated Raman scattering
Phys. Rev. Lett. 105, 015001 (2010)
reprint
+ abstract
We derive, both theoretically and using an envelope code, threshold intensities for stimulated Raman scattering which compare well with results from Vlasov simulations. To do so, we account for the nonlinear decrease of Landau damping and for the detuning induced by, both, the nonlinear wave number shift δk and frequency shift δω of the plasma wave. In particular, we show that the effect of δk may cancel out that of δω, but only in that plasma region where the laser intensity decreases along the direction of propagation of the scattered wave. Elsewhere, δk enhances the detuning effect of δω.

[3] 
D. Bénisti, O. Morice, L. Gremillet, E. Siminos, and D.J. Strozzi
Nonlinear group velocity of an electron plasma wave
Phys. Plasmas 17, 082301 (2010)
+ abstract
The nonlinear group velocity of an electron plasma wave is investigated numerically using a Vlasov code, and is found to assume values which agree very well with those predicted by a recently published theory [Phys. Rev. Lett., 103, 155002, (2009)], which we further detail here. In particular we show that, once Landau damping has been substantially reduced due to trapping, the group velocity of an electron plasma wave is not the derivative of its frequency with respect to its wave number. This result is moreover discussed physically, together with its implications in the saturation of stimulated Raman scattering.

[2] 
D. Bénisti, O. Morice, L. Gremillet, E. Siminos, and D.J. Strozzi
Nonlinear kinetic description of Raman growth using an envelope code, and comparisons with Vlasov simulations
Phys. Plasmas 17, 102311 (2010)
+ abstract
In this paper, we present our nonlinear kinetic modeling of stimulated Raman scattering in a uniform and collisionless plasma using envelope equations. We recall the derivation of these equations, as well as our theoretical predictions for each of the nonlinear kinetic terms, the precision of which having been carefully checked against Vlasov simulations. We particularly focus here on the numerical resolution of these equations, which requires the additional concept of ``selfoptimization'' that we explain, and we describe the envelope code BRAMA that we used. As an application of our modeling, we present onedimensional BRAMA simulations of stimulated Raman scattering which predict threshold intensities, as well as time scales for Raman growth above threshold, in very good agreement with those inferred from Vlasov simulations. Finally, we discuss the differences between our modeling and other published ones.

[1] 
P. Cvitanović, R.L. Davidchack, and E. Siminos
On the State Space Geometry of the KuramotoSivashinsky Flow in a Periodic Domain
SIAM J. Appl. Dyn. Syst. 9, 133 (2010)
reprint
+ abstract
The continuous and discrete symmetries of the KuramotoSivashinsky system restricted to a spatially periodic domain play a prominent role in shaping the invariant sets of its chaotic dynamics. The continuous spatial translation symmetry leads to relative equilibrium (traveling wave) and relative periodic orbit (modulated traveling wave) solutions. The discrete symmetries lead to existence of equilibrium and periodic orbit solutions, induce decomposition of state space into invariant subspaces, and enforce certain structurally stable heteroclinic connections between equilibria. We show, on the example of a particular smallcell KuramotoSivashinsky system, how the geometry of its dynamical state space is organized by a rigid `cage' built by heteroclinic connections between equilibria, and demonstrate the preponderance of unstable relative periodic orbits and their likely role as the skeleton underpinning spatiotemporal turbulence in systems with continuous symmetries. We also offer novel visualizations of the highdimensional KuramotoSivashinsky state space flow through projections onto lowdimensional, PDE representation independent, dynamically invariant intrinsic coordinate frames, as well as in terms of the physical, symmetry invariant energy transfer rates.

Thesis 
[0] 
E. Siminos
Recurrent spatiotemporal structures in presence of continuous symmetries
Ph.D. Thesis, School of Physics, Georgia Institute of Technology, Atlanta, GA, May 2009
pdf
+ abstract
When statistical assumptions do not hold and coherent structures are present in spatially extended systems such as fluid flows, flame fronts and field theories, a dynamical description of turbulent phenomena becomes necessary. In the dynamical systems approach, theory of turbulence for a given system, with given boundary conditions, is given by (a) the geometry of its infinitedimensional state space and (b) the associated measure, that is, the likelihood that asymptotic dynamics visits a given state space region.
In this thesis this vision is pursued in the context of KuramotoSivashinsky system, one of the simplest physically interesting spatially extended nonlinear systems. With periodic boundary conditions, continuous translational symmetry endows state space with additional structure that often dictates the type of observed solutions. At the same time, the notion of recurrence becomes relative: asymptotic dynamics visits the neighborhood of any equivalent, translated point, infinitely often. Identification of points related by the symmetry group action, termed symmetry reduction, although conceptually simple as the group action is linear, is hard to implement in practice, yet it leads to dramatic simplification of dynamics.
Here we propose a scheme, based on the method of moving frames of Cartan, to efficiently project solutions of highdimensional truncations of partial differential equations computed in the original space to a reduced state space. The procedure simplifies the visualization of highdimensional flows and provides new insight into the role the unstable manifolds of equilibria and traveling waves play in organizing KuramotoSivashinsky flow. This in turn elucidates the mechanism that creates unstable modulated traveling waves (periodic orbits in reduced space) that provide a skeleton of the dynamics. The compact description of dynamics thus achieved sets the stage for reduction of the dynamics to mappings between a set of Poincare sections.

