Lev Haim

Followers

Following

Co-authors

Public Views

Lev Haim

Ehud Meron

Ben Gurion University of the Negev

Arik Yochelis

Ben Gurion University of the Negev

Tel Aviv University

Interests

Uploads

Papers by Lev Haim

Fronts and patterns in a spatially forced CDIMA reaction

Physical chemistry chemical physics : PCCP, Jan 21, 2014

We use the CDIMA chemical reaction and the Lengyel-Epstein model of this reaction to study resona... more We use the CDIMA chemical reaction and the Lengyel-Epstein model of this reaction to study resonant responses of a pattern-forming system to time-independent spatial periodic forcing. We focus on the 2 : 1 resonance, where the wavenumber of a one-dimensional periodic forcing is about twice the wavenumber of the natural stripe pattern that the unforced system tends to form. Within this resonance, we study transverse fronts that shift the phase of resonant stripe patterns by π. We identify phase fronts that shift the phase discontinuously, and pairs of phase fronts that shift the phase continuously, clockwise and anti-clockwise. We further identify a front bifurcation that destabilizes the discontinuous front and leads to a pair of continuous fronts. This bifurcation is the spatial counterpart of the nonequilibrium Ising-Bloch (NIB) bifurcation in temporally forced oscillatory systems. The spatial NIB bifurcation that we find occurs as the forcing strength is increased, unlike earlier...

Download

Competing resonances in spatially forced pattern-forming systems

Physical Review E, 2013

Spatial periodic forcing can entrain a pattern-forming system in the same way as temporal periodi... more Spatial periodic forcing can entrain a pattern-forming system in the same way as temporal periodic forcing can entrain an oscillator. The forcing can lock the pattern's wave number to a fraction of the forcing wave number within tonguelike domains in the forcing parameter plane, it can increase the pattern's amplitude, and it can also create patterns below their onset. We derive these results using a multiple-scale analysis of a spatially forced Swift-Hohenberg equation in one spatial dimension. In two spatial dimensions the one-dimensional forcing can induce a symmetry-breaking instability that leads to two-dimensional (2D) patterns, rectangular or oblique. These patterns resonate with the forcing by locking their wave-vector component in the forcing direction to half the forcing wave number. The range of this type of 2:1 resonance overlaps with the 1:1 resonance tongue of stripe patterns. Using a multiple-scale analysis in the overlap region we show that the 2D patterns can destabilize the 1:1 resonant stripes even at exact resonance. This result sheds new light on the use of spatial periodic forcing for controlling patterns.

Download

Nonlinear waves and shocks in relativistic two-fluid hydrodynamics

Journal of Plasma Physics, 2012

Relativistic shocks are present in a number of objects where violent processes are accompanied by... more Relativistic shocks are present in a number of objects where violent processes are accompanied by relativistic outflows of plasma. The magnetization parameter σ = B2/4πnmc2 of the ambient medium varies in wide range. Shocks with low σ are expected to substantially enhance the magnetic fields in the shock front. In non-relativistic shocks the magnetic compression is limited by nonlinear effects related to the deceleration of flow. Two-fluid analysis of perpendicular relativistic shocks shows that the nonlinearities are suppressed for σ≪1 and the magnetic field reaches nearly equipartition values when the magnetic energy density is of the order of the ion energy density, Beq2 ~ 4πnmic2γ. A large cross-shock potential eφ/mic2γ0 ~ B2/Beq2 develops across the electron–ion shock front. This potential is responsible for electron energization.

Download

Spatial forcing of pattern-forming systems that lack inversion symmetry

by Ehud Meron and Lev Haim

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

The entrainment of periodic patterns to spatially periodic parametric forcing is studied. Using a... more The entrainment of periodic patterns to spatially periodic parametric forcing is studied. Using a weak nonlinear analysis of a simple pattern formation model we study the resonant responses of one-dimensional systems that lack inversion symmetry. Focusing on the first three n:1 resonances, in which the system adjusts its wavenumber to one nth of the forcing wavenumber, we delineate commonalities and differences among the resonances. Surprisingly, we find that all resonances show multiplicity of stable phase states, including the 1:1 resonance. The phase states in the 2:1 and 3:1 resonances, however, differ from those in the 1:1 resonance in remaining symmetric even when the inversion symmetry is broken. This is because of the existence of a discrete translation symmetry in the forced system. As a consequence, the 2:1 and 3:1 resonances show stationary phase fronts and patterns, whereas phase fronts within the 1:1 resonance are propagating and phase patterns are transients. In additi...

Reversing desertification as a spatial resonance problem

by Ehud Meron and Lev Haim

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

An important environmental application of pattern control by periodic spatial forcing is the rest... more An important environmental application of pattern control by periodic spatial forcing is the restoration of vegetation patterns in water-limited ecosystems that went through desertification. Vegetation restoration is often based on periodic landscape modulations that intercept overland water flow and form favorable conditions for vegetation growth. Viewing this method as a spatial resonance problem, we show that plain realizations of this method, assuming a complete vegetation response to the imposed modulation pattern, suffer from poor resilience to rainfall variability. By contrast, less intuitive realizations, based on the inherent spatial modes of vegetation growth and involving partial vegetation implantation, can be highly resilient and equally productive. We derive these results using two complementary models, a realistic vegetation model, and a simple pattern formation model that lends itself to mathematical analysis and highlights the universal aspects of the behaviors foun...

Download

Non-monotonic resonance in a spatially forced Lengyel-Epstein model

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015

We study resonant spatially periodic solutions of the Lengyel-Epstein model modified to describe ... more We study resonant spatially periodic solutions of the Lengyel-Epstein model modified to describe the chlorine dioxide-iodine-malonic acid reaction under spatially periodic illumination. Using multiple-scale analysis and numerical simulations, we obtain the stability ranges of 2:1 resonant solutions, i.e., solutions with wavenumbers that are exactly half of the forcing wavenumber. We show that the width of resonant wavenumber response is a non-monotonic function of the forcing strength, and diminishes to zero at sufficiently strong forcing. We further show that strong forcing may result in a π/2 phase shift of the resonant solutions, and argue that the nonequilibrium Ising-Bloch front bifurcation can be reversed. We attribute these behaviors to an inherent property of forcing by periodic illumination, namely, the increase of the mean spatial illumination as the forcing amplitude is increased.

Reversing desertification as a spatial resonance problem

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

Spatial forcing of pattern-forming systems that lack inversion symmetry

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

Competing resonances in spatially forced pattern-forming systems

by Ehud Meron and Lev Haim

Physical Review E, 2013

Spatial periodic forcing can entrain a pattern-forming system in the same way as temporal periodi... more Spatial periodic forcing can entrain a pattern-forming system in the same way as temporal periodic forcing can entrain an oscillator. The forcing can lock the pattern&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s wave number to a fraction of the forcing wave number within tonguelike domains in the forcing parameter plane, it can increase the pattern&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s amplitude, and it can also create patterns below their onset. We derive these results using a multiple-scale analysis of a spatially forced Swift-Hohenberg equation in one spatial dimension. In two spatial dimensions the one-dimensional forcing can induce a symmetry-breaking instability that leads to two-dimensional (2D) patterns, rectangular or oblique. These patterns resonate with the forcing by locking their wave-vector component in the forcing direction to half the forcing wave number. The range of this type of 2:1 resonance overlaps with the 1:1 resonance tongue of stripe patterns. Using a multiple-scale analysis in the overlap region we show that the 2D patterns can destabilize the 1:1 resonant stripes even at exact resonance. This result sheds new light on the use of spatial periodic forcing for controlling patterns.

Fronts and patterns in a spatially forced CDIMA reaction

by Milos Dolnik, Raphael Nagao, Lev Haim, and Ehud Meron

Physical chemistry chemical physics : PCCP, Jan 21, 2014

Download

Fronts and patterns in a spatially forced CDIMA reaction

Physical chemistry chemical physics : PCCP, Jan 21, 2014

Download

Competing resonances in spatially forced pattern-forming systems

Physical Review E, 2013

Download

Nonlinear waves and shocks in relativistic two-fluid hydrodynamics

Journal of Plasma Physics, 2012

Download

Spatial forcing of pattern-forming systems that lack inversion symmetry

by Ehud Meron and Lev Haim

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

Reversing desertification as a spatial resonance problem

by Ehud Meron and Lev Haim

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

Download

Non-monotonic resonance in a spatially forced Lengyel-Epstein model

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015

Reversing desertification as a spatial resonance problem

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

Spatial forcing of pattern-forming systems that lack inversion symmetry

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

Competing resonances in spatially forced pattern-forming systems

by Ehud Meron and Lev Haim

Physical Review E, 2013

Spatial periodic forcing can entrain a pattern-forming system in the same way as temporal periodi... more Spatial periodic forcing can entrain a pattern-forming system in the same way as temporal periodic forcing can entrain an oscillator. The forcing can lock the pattern&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s wave number to a fraction of the forcing wave number within tonguelike domains in the forcing parameter plane, it can increase the pattern&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s amplitude, and it can also create patterns below their onset. We derive these results using a multiple-scale analysis of a spatially forced Swift-Hohenberg equation in one spatial dimension. In two spatial dimensions the one-dimensional forcing can induce a symmetry-breaking instability that leads to two-dimensional (2D) patterns, rectangular or oblique. These patterns resonate with the forcing by locking their wave-vector component in the forcing direction to half the forcing wave number. The range of this type of 2:1 resonance overlaps with the 1:1 resonance tongue of stripe patterns. Using a multiple-scale analysis in the overlap region we show that the 2D patterns can destabilize the 1:1 resonant stripes even at exact resonance. This result sheds new light on the use of spatial periodic forcing for controlling patterns.

Fronts and patterns in a spatially forced CDIMA reaction

by Milos Dolnik, Raphael Nagao, Lev Haim, and Ehud Meron

Physical chemistry chemical physics : PCCP, Jan 21, 2014

Download

Lev Haim

Uploads

Papers by Lev Haim

Log In