Wim van Saarloos - Academia.edu (original) (raw)

Papers by Wim van Saarloos

Physical review, Jun 1, 1989

Depending on the growth condition, bacterial colonies can exhibit different morphologies. As argu... more Depending on the growth condition, bacterial colonies can exhibit different morphologies. As argued by Ben-Jacob et al. there is biological and modeling evidence that a nonlinear diffusion coefficient of the type D(b)ϭD 0 b k is a basic mechanism that underlies almost all of the patterns and generates a long-wavelength instability. We study a reaction-diffusion system with a nonlinear diffusion coefficient and find that a unique planar traveling front solution exists whose velocity is uniquely determined by k and DϭD 0 /D n , where D n is the diffusion coefficient of the nutrient. Due to the fact that the bacterial diffusion coefficient vanishes when b→0, in the front solution b vanishes in a singular way. As a result the standard linear stability analysis for fronts cannot be used. We introduce an extension of the stability analysis that can be applied to singular fronts, and use the method to perform a linear stability analysis of the planar bacteriological growth front. We show that a nonlinear diffusion coefficient generates a long-wavelength instability for kϾ0 and DϽD c (k). We map out the region of stability in the D-k-plane and determine the onset of stability that is given by D c (k). Both, for D→0 and k→ϱ the dynamics of the growth zone essentially reduces to that of a sharp interface problem that is reminiscent of a so-called one-sided growth problem where the growth velocity is proportional to the gradient of a diffusion field ahead of the interface. The moving boundary approximation that we derive in these limits is quite accurate but surprisingly does not become a proper asymptotic theory in the strict mathematical sense in the limit D→0, due to lack of full separation of scales on all dynamically relevant length scales. Our linear stability analysis and sharp interface formulation will also be applicable to other examples of interface formation due to nonlinear diffusion, like in porous media or in the problem of vortex motion in superconductors.

Contemporary Physics, 2013

The title ‘Europe to the Stars’ does not give away what this book is about, but the subtitle ‘ESO... more The title ‘Europe to the Stars’ does not give away what this book is about, but the subtitle ‘ESO’s first 50 years of exploring the southern sky’ does. ESO is the ‘European Southern Observatory’ which is the short form of its full name ‘European Organisation for Astronomical Research in the Southern Hemisphere’. It was founded in 1962 by Belgium, Germany, France, The Netherlands and Sweden and today has 15 member countries which in a joined effort run several astronomical observatories on sites in Chile. While the headquarters are in Garching, Germany, observation sites are located at Paranal, La Silla, Chajnantor and (planned) Armazones in the high Chilean desert. Together, these sites host a multitude of different instruments, the most famous (and largest) of which may be the Very Large Telescope and Atacama Large Millimeter Array (ALMA). ESO hosts the largest ground-based astronomical observation projects worldwide with about 800 staff, an annual budget of around 150 million Euros, producing several hundred scientific publications per year. ESO observatories have recorded the most distant gamma-ray burst, the first image of an exoplanet, the oldest star known in the Milky Way and the richest planetary system, did a detailed study of stars orbiting the Milky Way black hole, and provided the data showing that the expansion of the Universe is accelerating (a discovery which won the two participating research teams the Nobel prize in 2011). The present book is there to illustrate the history of the ESO, its important people, the sites and instruments, but also the extreme and often beautiful landscape the observatories have been built in. The choice of the word ‘illustrate’ shall convey that this book is all about pictures both of the observatories themselves (and what is related to them) and of the observations which have been made, typically full-page colour pictures of astronomical objects such as galaxies, star clusters and nebulae which have been selected for their aesthetics and beauty. The book contains about 300 colour pictures plus a DVD with a one-hour documentary about ESO including a comprehensive bonus section. The text is written in the style of an essay and structured in 10 chapters plus appendices with a full list and details of ESO’s telescopes and the timeline of ESO. The chapters are ‘Setting the Scene’ (about the southern hemisphere), ‘The Birth of ESO’, ‘In the Saddle’, ‘Cosmic Voyage’, ‘The Paranal Miracle’, ‘The Soul of ALMA’, ‘Bridging Borders’, ‘Catching the Light’, ‘The Desert Country’ and ‘Giant Eye on the Sky’. The latter refers to the planned ‘European Extremely Large Telescope’, the E-ELT, which is a 40m class telescope currently in the design phase, and which will be the world’s largest optical and near-infrared telescope. The light-gathering power of this telescope will allow detailed studies of planets around other stars, the earliest objects in the Universe, supermassive black holes, and the nature and distribution of the dark matter and dark energy which dominate the universe. Overall, the book is well made with impressive pictures on high-quality paper and is nice to have. It is not scientific at any point, but documents the organisation’s history, places, people and instruments, largely graphically. It is certainly interesting for anyone connected to astronomy, but also for people with an interest in photography and the beauty of astronomical objects and the desert landscape.

Journal of Fluid Mechanics, 2020

We perform direct numerical simulations of spiral turbulent Taylor-Couette (TC) flow for 400 Re i... more We perform direct numerical simulations of spiral turbulent Taylor-Couette (TC) flow for 400 Re i 1200 and −2000 Re o −1000, i.e. counter-rotation. The aspect ratio Γ = height/gap width of the domain is 42 Γ 125, with periodic boundary conditions in the axial direction, and the radius ratio η = r i /r o = 0.91. We show that, with decreasing Re i or with decreasing Re o , the formation of a turbulent spiral from an initially 'featureless turbulent' flow can be described by the phenomenology of the Ginzburg-Landau equations, similar as seen in the experimental findings of Prigent et al.

The Journal of Physical Chemistry, 1989

an adequate portrait of the diffusion process. Correspondingly, it seems clear the the use of a c... more an adequate portrait of the diffusion process. Correspondingly, it seems clear the the use of a classical diffusive description of the electronic motion with a phenomenological diffusion constant is faithful down to quite small distances and time scales. A new challenge for analytical theory is thus presented. The prevalent theory of ionic dynamics in solution derives from the hydrodynamic approach due to Zwanzigzl that evaluates the additional dielectric friction term arising in a polar solvent. In its sophisticated extended formulation by Hubbard and cow o r k e r~,~~*~~ this theory is relatively successful compared to experimental data. Analytical treatments along these lines for the classical diffusion of a particle that responds instantaneously to polarization fluctuations, but lacks any classical inertial behavior, are clearly of great interest in light of the picture presented here for the electronic motion. It is an interesting question whether the deformability of the electronic distribution from a spherical shape plays any important role. Computer simulation investigations of such alternative pseudoclassical models are accessible in any case, and it appears likely that our understanding of the transport properties of electrons in complicated dense polar fluids will make further strides in the near future.

NATO ASI Series, 1991

We summarize the main results and implications of our work on the calculation of cellular shapes ... more We summarize the main results and implications of our work on the calculation of cellular shapes in directional solidification using the asymptotic matching method introduced by Dombre and Hakim. For cells with narrow grooves, the finite Pe'clet number corrections to the cellular profiles that reduce to the Saffman-Taylor solutions for Pe'clet number p-» 0, turn out to be small. We argue that there are several discrepancies between the behavior of these Saffman-Taylor like cells and those observed in experiments as well as numerical studies that suggest that this branch of solutions is not always the physically relevant one for directional solidification.

Stability and shapes of cellular profiles in directional solidification: expansion and matching m... more Stability and shapes of cellular profiles in directional solidification: expansion and matching methods

Europhysics Letters (EPL) has a new online home at www.epljournal.org Take a look for the latest ... more Europhysics Letters (EPL) has a new online home at www.epljournal.org Take a look for the latest journal news and information on: • reading the latest articles, free! • receiving free e-mail alerts • submitting your work to EPL www.epljournal.org August2008 EPL,83(2008)44001 doi:10.1209/0295-5075/83/44001 www.epljournal.org

Physical Review Letters, 1985

Physica D: Nonlinear Phenomena, 1992

An important clement in the long-time dynamics of pattern forming systems is a class of solutions... more An important clement in the long-time dynamics of pattern forming systems is a class of solutions we will call "coherent structures". These are states that are either themselves localized, or that consist of domains of regular patterns connected by localized defects or interfaces. This paper summarizes and extends recent work on such coherent structures in the one-dimensional complex Ginzburg-Landau equation and its generalizations, for which rather complete information can be obtained on the existence and competition of fronts, pulses, sources and sinks. For the special subclass of uniformly translating structures, the solutions are derived from a set of ordinary differential equations that can be interpreted as a flow in a three-dimensional phase space. Fixed points of the flow correspond to the two basic building blocks of coherent structures, uniform amplitude states and evanescent waves whose amplitude decreases smoothly to zero. A study of the stability of the fixed points under the flow leads to results on the existence and multiplicity of the different coherent structures. The dynamical analysis of the original partial differential equation focusses on the competition between pulses and fronts, and is expressed in terms of a set of conjectures for front propagation that generalize the "marginal stability" and "pinch-point" approaches of earlier authors. These rules, together with an exact front solution whose dynamics plays an important role in the selection of patterns, yield an analytic expression for the upper limit of the range of existence of pulse solutions, as well as a determination of the regions of parameter space where uniformly translating fron t solutions can exist. Extensive numerical simulations show consistency with these rules and conjectures for the existence of fronts and pulses. In the parameter ranges where no uniformly translating fronts can exist, examples are shown of irregularly spreading fronts that generate strongly chaotic regions, as well as nonuniformly translating fronts that lead to uniform amplitude states. Recent perturbative treatments based on expansions about the nonlinear Schr6dinger equation are generalized to perturbations of the cubic-quintic and derivative Schr~idinger equations, for which both pulses and fronts exist in the unperturbed system. Comparison of the results with the exact solutions shows that the perturbation theory only yields a subset of the relevant solutions. Nevertheless, those that are obtained are found to be consistent with the general conjectures, and in particular they provide an analytic demonstration of front/pulse competition. While the discussion of the competition between fronts and pulses focusses on the complex Ginzburg-Landau equation with quintic terms and a subcritical bifurcation, a number of results are also presented for the cubic equation. In particular, the existence of a family of moving source solutions derived by Bekki and Nozaki for this equation contradicts the naive counting arguments. We attribute this contradiction to a hidden symmetry of the solution but have not been able to show explicitly how this symmetry affects the phase space orbits.

Physica D: Nonlinear Phenomena, 2006

We report on the residence times of capillary waves above a given height hhh and on the typical w... more We report on the residence times of capillary waves above a given height hhh and on the typical waiting time in between such fluctuations. The measurements were made on phase separated colloid-polymer systems by laser scanning confocal microscopy. Due to the Brownian character of the process, the stochastics vary with the chosen measurement interval Deltat\Delta tDeltat. In experiments, the discrete

Physical review, Jun 1, 1989

Depending on the growth condition, bacterial colonies can exhibit different morphologies. As argu... more Depending on the growth condition, bacterial colonies can exhibit different morphologies. As argued by Ben-Jacob et al. there is biological and modeling evidence that a nonlinear diffusion coefficient of the type D(b)ϭD 0 b k is a basic mechanism that underlies almost all of the patterns and generates a long-wavelength instability. We study a reaction-diffusion system with a nonlinear diffusion coefficient and find that a unique planar traveling front solution exists whose velocity is uniquely determined by k and DϭD 0 /D n , where D n is the diffusion coefficient of the nutrient. Due to the fact that the bacterial diffusion coefficient vanishes when b→0, in the front solution b vanishes in a singular way. As a result the standard linear stability analysis for fronts cannot be used. We introduce an extension of the stability analysis that can be applied to singular fronts, and use the method to perform a linear stability analysis of the planar bacteriological growth front. We show that a nonlinear diffusion coefficient generates a long-wavelength instability for kϾ0 and DϽD c (k). We map out the region of stability in the D-k-plane and determine the onset of stability that is given by D c (k). Both, for D→0 and k→ϱ the dynamics of the growth zone essentially reduces to that of a sharp interface problem that is reminiscent of a so-called one-sided growth problem where the growth velocity is proportional to the gradient of a diffusion field ahead of the interface. The moving boundary approximation that we derive in these limits is quite accurate but surprisingly does not become a proper asymptotic theory in the strict mathematical sense in the limit D→0, due to lack of full separation of scales on all dynamically relevant length scales. Our linear stability analysis and sharp interface formulation will also be applicable to other examples of interface formation due to nonlinear diffusion, like in porous media or in the problem of vortex motion in superconductors.

Contemporary Physics, 2013

The title ‘Europe to the Stars’ does not give away what this book is about, but the subtitle ‘ESO... more The title ‘Europe to the Stars’ does not give away what this book is about, but the subtitle ‘ESO’s first 50 years of exploring the southern sky’ does. ESO is the ‘European Southern Observatory’ which is the short form of its full name ‘European Organisation for Astronomical Research in the Southern Hemisphere’. It was founded in 1962 by Belgium, Germany, France, The Netherlands and Sweden and today has 15 member countries which in a joined effort run several astronomical observatories on sites in Chile. While the headquarters are in Garching, Germany, observation sites are located at Paranal, La Silla, Chajnantor and (planned) Armazones in the high Chilean desert. Together, these sites host a multitude of different instruments, the most famous (and largest) of which may be the Very Large Telescope and Atacama Large Millimeter Array (ALMA). ESO hosts the largest ground-based astronomical observation projects worldwide with about 800 staff, an annual budget of around 150 million Euros, producing several hundred scientific publications per year. ESO observatories have recorded the most distant gamma-ray burst, the first image of an exoplanet, the oldest star known in the Milky Way and the richest planetary system, did a detailed study of stars orbiting the Milky Way black hole, and provided the data showing that the expansion of the Universe is accelerating (a discovery which won the two participating research teams the Nobel prize in 2011). The present book is there to illustrate the history of the ESO, its important people, the sites and instruments, but also the extreme and often beautiful landscape the observatories have been built in. The choice of the word ‘illustrate’ shall convey that this book is all about pictures both of the observatories themselves (and what is related to them) and of the observations which have been made, typically full-page colour pictures of astronomical objects such as galaxies, star clusters and nebulae which have been selected for their aesthetics and beauty. The book contains about 300 colour pictures plus a DVD with a one-hour documentary about ESO including a comprehensive bonus section. The text is written in the style of an essay and structured in 10 chapters plus appendices with a full list and details of ESO’s telescopes and the timeline of ESO. The chapters are ‘Setting the Scene’ (about the southern hemisphere), ‘The Birth of ESO’, ‘In the Saddle’, ‘Cosmic Voyage’, ‘The Paranal Miracle’, ‘The Soul of ALMA’, ‘Bridging Borders’, ‘Catching the Light’, ‘The Desert Country’ and ‘Giant Eye on the Sky’. The latter refers to the planned ‘European Extremely Large Telescope’, the E-ELT, which is a 40m class telescope currently in the design phase, and which will be the world’s largest optical and near-infrared telescope. The light-gathering power of this telescope will allow detailed studies of planets around other stars, the earliest objects in the Universe, supermassive black holes, and the nature and distribution of the dark matter and dark energy which dominate the universe. Overall, the book is well made with impressive pictures on high-quality paper and is nice to have. It is not scientific at any point, but documents the organisation’s history, places, people and instruments, largely graphically. It is certainly interesting for anyone connected to astronomy, but also for people with an interest in photography and the beauty of astronomical objects and the desert landscape.

Journal of Fluid Mechanics, 2020

We perform direct numerical simulations of spiral turbulent Taylor-Couette (TC) flow for 400 Re i... more We perform direct numerical simulations of spiral turbulent Taylor-Couette (TC) flow for 400 Re i 1200 and −2000 Re o −1000, i.e. counter-rotation. The aspect ratio Γ = height/gap width of the domain is 42 Γ 125, with periodic boundary conditions in the axial direction, and the radius ratio η = r i /r o = 0.91. We show that, with decreasing Re i or with decreasing Re o , the formation of a turbulent spiral from an initially 'featureless turbulent' flow can be described by the phenomenology of the Ginzburg-Landau equations, similar as seen in the experimental findings of Prigent et al.

The Journal of Physical Chemistry, 1989

an adequate portrait of the diffusion process. Correspondingly, it seems clear the the use of a c... more an adequate portrait of the diffusion process. Correspondingly, it seems clear the the use of a classical diffusive description of the electronic motion with a phenomenological diffusion constant is faithful down to quite small distances and time scales. A new challenge for analytical theory is thus presented. The prevalent theory of ionic dynamics in solution derives from the hydrodynamic approach due to Zwanzigzl that evaluates the additional dielectric friction term arising in a polar solvent. In its sophisticated extended formulation by Hubbard and cow o r k e r~,~~*~~ this theory is relatively successful compared to experimental data. Analytical treatments along these lines for the classical diffusion of a particle that responds instantaneously to polarization fluctuations, but lacks any classical inertial behavior, are clearly of great interest in light of the picture presented here for the electronic motion. It is an interesting question whether the deformability of the electronic distribution from a spherical shape plays any important role. Computer simulation investigations of such alternative pseudoclassical models are accessible in any case, and it appears likely that our understanding of the transport properties of electrons in complicated dense polar fluids will make further strides in the near future.

NATO ASI Series, 1991

We summarize the main results and implications of our work on the calculation of cellular shapes ... more We summarize the main results and implications of our work on the calculation of cellular shapes in directional solidification using the asymptotic matching method introduced by Dombre and Hakim. For cells with narrow grooves, the finite Pe'clet number corrections to the cellular profiles that reduce to the Saffman-Taylor solutions for Pe'clet number p-» 0, turn out to be small. We argue that there are several discrepancies between the behavior of these Saffman-Taylor like cells and those observed in experiments as well as numerical studies that suggest that this branch of solutions is not always the physically relevant one for directional solidification.

Stability and shapes of cellular profiles in directional solidification: expansion and matching m... more Stability and shapes of cellular profiles in directional solidification: expansion and matching methods

Europhysics Letters (EPL) has a new online home at www.epljournal.org Take a look for the latest ... more Europhysics Letters (EPL) has a new online home at www.epljournal.org Take a look for the latest journal news and information on: • reading the latest articles, free! • receiving free e-mail alerts • submitting your work to EPL www.epljournal.org August2008 EPL,83(2008)44001 doi:10.1209/0295-5075/83/44001 www.epljournal.org

Physical Review Letters, 1985

Physica D: Nonlinear Phenomena, 1992

An important clement in the long-time dynamics of pattern forming systems is a class of solutions... more An important clement in the long-time dynamics of pattern forming systems is a class of solutions we will call "coherent structures". These are states that are either themselves localized, or that consist of domains of regular patterns connected by localized defects or interfaces. This paper summarizes and extends recent work on such coherent structures in the one-dimensional complex Ginzburg-Landau equation and its generalizations, for which rather complete information can be obtained on the existence and competition of fronts, pulses, sources and sinks. For the special subclass of uniformly translating structures, the solutions are derived from a set of ordinary differential equations that can be interpreted as a flow in a three-dimensional phase space. Fixed points of the flow correspond to the two basic building blocks of coherent structures, uniform amplitude states and evanescent waves whose amplitude decreases smoothly to zero. A study of the stability of the fixed points under the flow leads to results on the existence and multiplicity of the different coherent structures. The dynamical analysis of the original partial differential equation focusses on the competition between pulses and fronts, and is expressed in terms of a set of conjectures for front propagation that generalize the "marginal stability" and "pinch-point" approaches of earlier authors. These rules, together with an exact front solution whose dynamics plays an important role in the selection of patterns, yield an analytic expression for the upper limit of the range of existence of pulse solutions, as well as a determination of the regions of parameter space where uniformly translating fron t solutions can exist. Extensive numerical simulations show consistency with these rules and conjectures for the existence of fronts and pulses. In the parameter ranges where no uniformly translating fronts can exist, examples are shown of irregularly spreading fronts that generate strongly chaotic regions, as well as nonuniformly translating fronts that lead to uniform amplitude states. Recent perturbative treatments based on expansions about the nonlinear Schr6dinger equation are generalized to perturbations of the cubic-quintic and derivative Schr~idinger equations, for which both pulses and fronts exist in the unperturbed system. Comparison of the results with the exact solutions shows that the perturbation theory only yields a subset of the relevant solutions. Nevertheless, those that are obtained are found to be consistent with the general conjectures, and in particular they provide an analytic demonstration of front/pulse competition. While the discussion of the competition between fronts and pulses focusses on the complex Ginzburg-Landau equation with quintic terms and a subcritical bifurcation, a number of results are also presented for the cubic equation. In particular, the existence of a family of moving source solutions derived by Bekki and Nozaki for this equation contradicts the naive counting arguments. We attribute this contradiction to a hidden symmetry of the solution but have not been able to show explicitly how this symmetry affects the phase space orbits.

Physica D: Nonlinear Phenomena, 2006

We report on the residence times of capillary waves above a given height hhh and on the typical w... more We report on the residence times of capillary waves above a given height hhh and on the typical waiting time in between such fluctuations. The measurements were made on phase separated colloid-polymer systems by laser scanning confocal microscopy. Due to the Brownian character of the process, the stochastics vary with the chosen measurement interval Deltat\Delta tDeltat. In experiments, the discrete