Showing papers in "European Physical Journal-special Topics in 2010"

On multi-rogue wave solutions of the NLS equation and positon solutions of the KdV equation

Abstract: We discuss multi-Peregrine breather solutions to the nonlinear Schrodinger equations which are relevant in the description of rogue waves in hydrodynamics or in nonlinear optics. We also describe some basic properties of multi-positon and positon-soliton solutions to the Korteweg-de Vries equations and speculate about their possible links with freak waves.

Editorial – Introductory remarks on “Discussion & Debate: Rogue Waves – Towards a Unifying Concept?”

Abstract: This short editorial contains the introductory remarks for the special issue “discussions and debates” on the subject of “rogue waves”. This issue is the first of its kind, in the sense that the authors have the chance to discuss the basic concepts of an emerging topic in science. Based on these discussions, an attempt to give a “definition” of a rogue wave is made.

Vector rogue waves in binary mixtures of Bose-Einstein condensates

Abstract: We study numerically rogue waves in the two-component Bose-Einstein condensates which are described by the coupled set of two Gross-Pitaevskii equations with variable scattering lengths. We show that rogue wave solutions exist only for certain combinations of the nonlinear coefficients describing two-body interactions. We present the solutions for the combinations of these coefficients that admit the existence of rogue waves.

Freak waves in laboratory and space plasmas. Freak waves in plasmas

Abstract: Generation of large-amplitude short-lived wave groups from small-amplitude initial perturbations in plasmas is discussed. Two particular wave modes existing in plasmas are considered. The first one is the ion-sound wave. In a plasmas with negative ions it is described by the Gardner equation when the negative ion concentration is close to critical. The results of numerical solution of the Gardner equation with the modulationally unstable initial condition are presented. These results clearly show the possibility of generation of freak ion-acoustic waves due to the modulational instability. The second wave mode is the Alfven wave. When this wave propagates at a small angle with respect to the equilibrium magnetic field, and its wave length is comparable with the ion inertia length, it is described by the DNLS equation. Studying the evolution of an initial perturbation using the linearized DNLS equation shows that the generation of freak Alfven waves is possible due to linear dispersive focusing. The numerical solution of the DNLS equation reveals that the nonlinear dispersive focusing can also produce freak Alfven waves.

Rogue waves - towards a unifying concept?: Discussions and debates

Abstract: This paper contains the discussion inputs by the contributors of the special issue on the subject of rogue waves.

Rogue waves in superfluid helium

Abstract: Rogue waves have been observed in superfluid helium. The experimental system consists of high intensity second sound (temperature-entropy) waves within a resonant cavity. Under steady state conditions, with a constant oscillatory driving force at the resonant frequency, the waves are turbulent and there are fluxes of energy towards both high and low frequencies. Rogue waves appear under the nonequilibrium conditions that prevail shortly after the drive has been switched on, prior to establishment of the steady state. The experiment is described briefly, relevant results are presented and discussed theoretically in terms of nonlinear wave interactions, and possible connections to rogue waves on the ocean are considered.

MATS and LaSpec: High-precision experiments using ion traps and lasers at FAIR

Abstract: Nuclear ground state properties including mass, charge radii, spins and moments can be determined by applying atomic physics techniques such as Penning-trap based mass spectrometry and laser spectroscopy. The MATS and LaSpec setups at the low-energy beamline at FAIR will allow us to extend the knowledge of these properties further into the region far from stability. The mass and its inherent connection with the nuclear binding energy is a fundamental property of a nuclide, a unique “fingerprint”. Thus, precise mass values are important for a variety of applications, ranging from nuclear-structure studies like the investigation of shell closures and the onset of deformation, tests of nuclear mass models and mass formulas, to tests of the weak interaction and of the Standard Model. The required relative accuracy ranges from 10−5 to below 10−8 for radionuclides, which most often have half-lives well below 1 s. Substantial progress in Penning trap mass spectrometry has made this method a prime choice for precision measurements on rare isotopes. The technique has the potential to provide high accuracy and sensitivity even for very short-lived nuclides. Furthermore, ion traps can be used for precision decay studies and offer advantages over existing methods. With MATS (Precision Measurements of very short-lived nuclei using an A_dvanced Trapping System for highly-charged ions) at FAIR we aim to apply several techniques to very short-lived radionuclides: High-accuracy mass measurements, in-trap conversion electron and alpha spectroscopy, and trap-assisted spectroscopy. The experimental setup of MATS is a unique combination of an electron beam ion trap for charge breeding, ion traps for beam preparation, and a high-precision Penning trap system for mass measurements and decay studies. For the mass measurements, MATS offers both a high accuracy and a high sensitivity. A relative mass uncertainty of 10−9 can be reached by employing highly-charged ions and a non-destructive Fourier-Transform Ion-Cyclotron-Resonance (FT-ICR) detection technique on single stored ions. This accuracy limit is important for fundamental interaction tests, but also allows for the study of the fine structure of the nuclear mass surface with unprecedented accuracy, whenever required. The use of the FT-ICR technique provides true single ion sensitivity. This is essential to access isotopes that are produced with minimum rates which are very often the most interesting ones. Instead of pushing for highest accuracy, the high charge state of the ions can also be used to reduce the storage time of the ions, hence making measurements on even shorter-lived isotopes possible. Decay studies in ion traps will become possible with MATS. Novel spectroscopic tools for in-trap high-resolution conversion-electron and charged-particle spectroscopy from carrier-free sources will be developed, aiming e.g. at the measurements of quadrupole moments and E0 strengths. With the possibility of both high-accuracy mass measurements of the shortest-lived isotopes and decay studies, the high sensitivity and accuracy potential of MATS is ideally suited for the study of very exotic nuclides that will only be produced at the FAIR facility.Laser spectroscopy of radioactive isotopes and isomers is an efficient and model-independent approach for the determination of nuclear ground and isomeric state properties. Hyperfine structures and isotope shifts in electronic transitions exhibit readily accessible information on the nuclear spin, magnetic dipole and electric quadrupole moments as well as root-mean-square charge radii. The dependencies of the hyperfine splitting and isotope shift on the nuclear moments and mean square nuclear charge radii are well known and the theoretical framework for the extraction of nuclear parameters is well established. These extracted parameters provide fundamental information on the structure of nuclei at the limits of stability. Vital information on both bulk and valence nuclear properties are derived and an exceptional sensitivity to changes in nuclear deformation is achieved. Laser spectroscopy provides the only mechanism for such studies in exotic systems and uniquely facilitates these studies in a model-independent manner.The accuracy of laser-spectroscopic-determined nuclear properties is very high. Requirements concerning production rates are moderate; collinear spectroscopy has been performed with production rates as few as 100 ions per second and laser-desorption resonance ionization mass spectroscopy (combined with β-delayed neutron detection) has been achieved with rates of only a few atoms per second.This Technical Design Report describes a new Penning trap mass spectrometry setup as well as a number of complementary experimental devices for laser spectroscopy, which will provide a complete system with respect to the physics and isotopes that can be studied. Since MATS and LaSpec require high-quality low-energy beams, the two collaborations have a common beamline to stop the radioactive beam of in-flight produced isotopes and prepare them in a suitable way for transfer to the MATS and LaSpec setups, respectively.

Optics of surface disordered systems. A random walk through rough surface scattering phenomena

Abstract: No surface is perfectly flat at every length scale. However, all natural and man-made surfaces show some degree of roughness. Therefore, it is imperative to know how surface disorder may affect physical process at, or in the immediate vicinity, of the surface. In this review, we focus on the long-standing problem of electromagnetic wave scattering from randomly rough surfaces. This topic has implications and practical applications in fields of science and engineering ranging from observational astronomy to the electronic and medical industry. How randomly rough surfaces can be described statistically is outlined, and we introduce the theoretical and computational methods most frequently used in the study of light scattering from randomly rough metal or dielectric surfaces. A large part of the review is devoted to the description and the discussion of the physical origin behind various multiple scattering phenomena that can exist when light interacts with a random surface. Some of the addressed phenomena are; the enhanced backscattering and satellite peak phenomena; forward scattering (specular peak) enhancement; coherent effects in the angular intensity correlation functions and the second harmonic generated light (nonlinear effect).

NMR studies on simple liquids in confinement

Abstract: NMR studies on liquids in various types of confinements are reviewed. The discussion includes results for the size, the morphology, and the filling of pores. Moreover, it deals with the phase behaviors, the local structures, and in particular, the local dynamics of confined liquids. Findings for soft and hard confinements of various sizes are considered. The main focus is on the time scales of and the mechanisms for dynamics of simple liquids in simple confinements. From the methodical point of view, the review is restricted to NMR work in homogeneous magnetic fields, i.e, field-gradient approaches are not included.

Cluster dynamics and cluster size distributions in systems of self-propelled particles

Abstract: Systems of self-propelled particles (SPP) interacting by a velocity alignment mechanism in the presence of noise exhibit rich clustering dynamics. Often, clusters are responsible for the distribution of (local) information in these systems. Here, we investigate the properties of individual clusters in SPP systems, in particular the asymmetric spreading behavior of clusters with respect to their direction of motion. In addition, we formulate a Smoluchowski-type kinetic model to describe the evolution of the cluster size distribution (CSD). This model predicts the emergence of steady-state CSDs in SPP systems. We test our theoretical predictions in simulations of SPP with nematic interactions and find that our simple kinetic model reproduces qualitatively the transition to aggregation observed in simulations.

Freak waves in crossing seas

Abstract: We consider the modulational instability in crossing seas as a potential mechanism for the formation of freak waves. The problem is discussed in terms of a system of two coupled Nonlinear Schroedinger equations. The asymptotic validity of such system is discussed. For some specific angles between the two wave trains, the equations reduce to an integrable system. A stability analysis of these equations is discussed. Furthermore, we present an analytical study of the maximum amplification factor for an unstable plane wave solution. Results indicate that angles between 10∘ and 30∘ are the most probable for establishing a freak wave sea. We show that the theoretical expectations are consistent with numerical simulations of the Euler equations.

On the statistical interpretation of optical rogue waves

Abstract: Numerical simulations are used to discuss various aspects of “optical rogue wave” statistics observed in noise-driven fiber supercontinuum generation associated with highly incoherent spectra. In particular, we consider how long wavelength spectral filtering influences the characteristics of the statistical distribution of peak power, and we contrast the statistics of the spectrally filtered SC with the statistics of both the peak power of the most red-shifted soliton in the SC and the maximum peak power across the full temporal field with no spectral selection. For the latter case, we show that the unfiltered statistical distribution can still exhibit a long-tail, but the extreme-events in this case correspond to collisions between solitons of different frequencies. These results confirm the importance of collision dynamics in supercontinuum generation. We also show that the collision-induced events satisfy an extended hydrodynamic definition of “rogue wave” characteristics.

The localization transition of the two-dimensional Lorentz model

Abstract: We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over many decades in time, which is rationalized in terms of an underlying percolation transition of the void space. In the vicinity of this critical density the dynamics follows the anomalous one up to a crossover time scale where the motion becomes either diffusive or localized. We analyze the scaling behavior of the time-dependent diffusion coefficient D(t) including corrections to scaling. Away from the critical density, D(t) exhibits universal hydrodynamic long-time tails both in the diffusive as well as in the localized phase.

Rogue internal waves in the ocean: Long wave model

Abstract: Rogue waves can be categorized as unexpectedly large waves, which are temporally and spatially localized. They have recently received much attention in the water wave context, and also been found in nonlinear optical fibers. In this paper, we examine the issue of whether rogue internal waves can be found in the ocean. Because large-amplitude internal waves are commonly observed in the coastal ocean, and are often modeled by weakly nonlinear long wave equations of the Korteweg-de Vries type, we focus our attention on this shallow-water context. Specifically, we examine the occurrence of rogue waves in the Gardner equation, which is an extended version of the Korteweg-de Vries equation with quadratic and cubic nonlinearity, and is commonly used for the modelling of internal solitary waves in the ocean. Importantly, we choose that version of the Gardner equation for which the coefficient of the cubic nonlinear term and the coefficient of the linear dispersive term have the same sign, as this allows for modulational instability. From numerical simulations of the evolution of a modulated narrow-band initial wave field, we identify several scenarios where rogue waves occur.

Theoretical methods for the calculation of Bragg curves and 3D distributions of proton beams

Abstract: The well-known Bragg-Kleeman rule R CSDA = A ⋅ E has become a pioneer work in radiation physics of charged particles and is still a useful tool to estimate the range R CSDA of approximately monoenergetic protons with initial energy E 0 in a homogeneous medium The rule is based on the continuous-slowing-down-approximation (CSDA) It results from a generalized (nonrelativistic) Langevin equation and a modification of the phenomenological friction term The complete integration of this equation provides information about the residual energy E(z) and dE(z)/dz at each position z(0 ≦ z ≦ R CSDA) A relativistic extension of the generalized Langevin equation yields the formula R CSDA = A ⋅ (E 0 + E/2M ⋅ c 2)p The initial energy of therapeutic protons satisfies E 0 ≪ 2M ⋅ c 2(M ⋅ c 2 = 938276 MeV), which enables us to consider the relativistic contributions as correction terms Besides this phenomenological starting-point, a complete integration of the Bethe-Bloch equation (BBE) is developed, which also provides the determination of R CSDA, E(z) and dE(z)/dz and uses only those parameters given by the BBE itself (ie, without further empirical parameters like modification of friction) The results obtained in the context of the aforementioned methods are compared with Monte-Carlo calculations (GEANT4); this Monte-Carlo code is also used with regard to further topics such as lateral scatter, nuclear interactions, and buildup effects In the framework of the CSDA, the energy transfer from protons to environmental atomic electrons does not account for local fluctuations Based on statistical quantum mechanics, an analysis of the Gaussian convolution and the Landau-Vavilov distribution function is carried out to describe these fluctuations The Landau tail is derived as Hermite polynomial corrections of a Gaussian convolution It is experimentally confirmed that proton Bragg curves with E 0 ≧ 120 MeV show a buildup, which increases with the proton energy This buildup is explained by a theoretical analysis of impinging proton beamlets In order to obtain a complete dose calculation model for proton treatment planning, some further aspects have to be accounted for: the decrease of the fluence of the primary protons due to nuclear interactions, the transport of released secondary protons, the dose contribution of heavy recoil nuclei, the inclusion of lateral scatter of the primary and secondary protons based on Moliere’s multiple-scatter theory, and the scatter contributions of collimators This study also presents some results which go beyond proton dose calculation models; namely, the application of the relativistic generalization of the Bragg-Kleeman rule to electrons and, in an appendix, a method to determine inelastic cross-sections of therapeutic protons in media of therapeutic interest

Review and update of lens and grid schlieren and motion camera schlieren

Abstract: Optical density variation in fluids and transparent solids can often be studied by examining the effect of refraction of light passing through the medium. The schlieren technique has proven to be particularly well suited for these applications, and has been widely used for wind-tunnel studies. Newer variations of this technique have extended it to a wide range of applications. The lens and grid schlieren systems have been used to examine aerodynamic flow fields that were previously difficult to study with conventional schlieren systems. Motion camera schlieren was developed to obtain the flow field around aircraft in flight and rocket sleds. This paper gives an up to date review of the background and development of the lens and grid schlieren and motion camera schlieren techniques and includes examples of many of the flows studied using the techniques, including some previously unpublished ones. In addition, some preliminary results from new versions of both types of systems are described.

Glass transition under confinement-what can be learned from calorimetry

Abstract: Calorimetry is an effective analytical tool to characterize the glass transition and phase transitions under confinement. Calorimetry offers a broad dynamic range regarding heating and cooling rates, including isothermal and temperature modulated operation. Today 12 orders of magnitude in scanning rate can be covered by combining different types of calorimeters. The broad dynamic range, comparable to dielectric spectroscopy, is especially of interest for the study of kinetically controlled processes like crystallization or glass transition. Accuracy of calorimetric measurements is not very high. Commonly it does not reach 0.1% and often accuracy is only a few percent. Nevertheless, calorimetry can reach high sensitivity and reproducibility. Both are of particular interest for the study of confined systems. Low addenda heat capacity chip calorimeters are capable to measure the step in heat capacity at the glass transition in nanometer thin films. The good reproducibility is used for the study of glass forming materials confined by nanometer sized structures, like porous glasses, semicrystalline structures, nanocomposites, phase separated block copolymers, etc. Calorimetry allows also for the frequency dependent measurement of complex heat capacity in a frequency range covering several orders of magnitude. Here I exclusively consider calorimetry and its application to glass transition in confined materials. In most cases calorimetry reveals only a weak dependence of the glass transition temperature on confinement as long as the confining dimensions are above 10 nm. Why these findings contradict many other studies applying other techniques to similar systems is still an unsolved problem of glass transition in confinement.

Mach reflection and KP solitons in shallow water

Abstract: Reflection of an obliquely incident solitary wave onto a vertical wall is studied analytically and experimentally. We use the Kadomtsev-Petviashivili (KP) equation to analyze the evolution and its asymptotic state. Laboratory experiments are performed using the laser induced fluorescent (LIF) technique, and detailed features and amplifications at the wall are measured. Due to the lack of physical interpretation of the theory, the numerical results were previously thought not in good agreement with the theory. With proper treatment, we demonstrate that the KP theory provides an excellent model to predict the present laboratory results as well as the previous numerical results. The KP theory also indicates that the present laboratory apparatus is too short to achieve the asymptotic state. The laboratory and numerical results suggest that the maximum of the predicted four-fold amplification would be difficult to be realized in the real-fluid environment. The reality of this amplification remains obscure.

Electron interactions and charge ordering in CuO2 compounds

Abstract: We present results of inelastic light scattering experiments on single-crystalline La2-xSrxCuO4 in the doping range 0.00 ≤ x = p ≤ 0.30 and Tl2Ba2CuO6+δ at p = 0.20 and p = 0.24. The main emphasis is placed on the response of electronic excitations in the antiferromagnetic phase, in the pseudogap range, in the superconducting state, and in the essentially normal metallic state at x ≥ 0.26, where no superconductivity could be observed. In most of the cases we compare B1g and B2g spectra which project out electronic properties close to (π, 0) and (π/2,π/2), respectively. In the channel of electron-hole excitations we find universal behavior in B2g symmetry as long as the material exhibits superconductivity at low temperature. In contrast, there is a strong doping dependence in B1g symmetry: (i) In the doping range 0.20 ≤ p ≤ 0.25 we observe rapid changes of shape and temperature dependence of the spectra. (ii) In La2-xSrxCuO4 new structures appear for x < 0.13 which are superposed on the electron-hole continuum. The temperature dependence as well as model calculations support an interpretation in terms of charge-ordering fluctuations. For x ≤ 0.05 the response from fluctuations disappears in B1g and appears in B2g symmetry in full agreement with the orientation change of stripes found by neutron scattering. While, with a grain of salt, the particle-hole continuum is universal for all cuprates the response from fluctuating charge order in the range 0.05 ≤ p < 0.16 is so far found only in La2-xSrxCuO4. We conclude that La2-xSrxCuO4 is close to static charge order and, for this reason, may have a suppressed Tc.

An ARPES view on the high-Tc problem: Phonons vs. spin-fluctuations

Abstract: We review the search for a mediator of high-T c superconductivity focusing on ARPES experiment. In case of HTSC cuprates, we summarize and discuss a consistent view of electronic interactions that provides natural explanation of both the origin of the pseudogap state and the mechanism for high temperature superconductivity. Within this scenario, the spin-fluctuations play a decisive role in formation of the fermionic excitation spectrum in the normal state and are sufficient to explain the high transition temperatures to the superconducting state while the pseudogap phenomenon is a consequence of a Peierls-type intrinsic instability of electronic system to formation of an incommensurate density wave. On the other hand, a similar analysis being applied to the iron pnictides reveals especially strong electron-phonon coupling that suggests important role of phonons for high-T c superconductivity in pnictides.

Surface oil flow visualization

Abstract: A brief review of the use of surface oil flow visualization (SOFV) in wind tunnel testing is provided. The first part of the review discusses the concept of flow separation in three-dimensions and the resulting surface topology. This is followed by a review of the SOFV technique and its ability to reveal surface topologies in three-dimensional flow. The discussion is illustrated by examples. The application of modern digital techniques is highlighted.

Real-time measurements, rare events and photon economics

Abstract: Rogue events otherwise known as outliers and black swans are singular, rare, events that carry dramatic impact. They appear in seemingly unconnected systems in the form of oceanic rogue waves, stock market crashes, evolution, and communication systems. Attempts to understand the underlying dynamics of such complex systems that lead to spectacular and often cataclysmic outcomes have been frustrated by the scarcity of events, resulting in insufficient statistical data, and by the inability to perform experiments under controlled conditions. Extreme rare events also occur in ultrafast physical sciences where it is possible to collect large data sets, even for rare events, in a short time period. The knowledge gained from observing rare events in ultrafast systems may provide valuable insight into extreme value phenomena that occur over a much slower timescale and that have a closer connection with human experience. One solution is a real-time ultrafast instrument that is capable of capturing singular and randomly occurring non-repetitive events. The time stretch technology developed during the past 13 years is providing a powerful tool box for reaching this goal. This paper reviews this technology and discusses its use in capturing rogue events in electronic signals, spectroscopy, and imaging. We show an example in nonlinear optics where it was possible to capture rare and random solitons whose unusual statistical distribution resemble those observed in financial markets. The ability to observe the true spectrum of each event in real time has led to important insight in understanding the underlying process, which in turn has made it possible to control soliton generation leading to improvement in the coherence of supercontinuum light. We also show a new class of fast imagers which are being considered for early detection of cancer because of their potential ability to detect rare diseased cells (so called rogue cells) in a large population of healthy cells.

Delay control of coherence resonance in type-I excitable dynamics

Abstract: We consider a simple paradigmatic system of type-I excitability subject to noise and time-delayed feedback. This system is governed by a global bifurcation, namely a saddle-node bifurcation on a limit cycle. In the absence of noise, delay can induce complex dynamics including multiple stable and unstable periodic orbits. Random fluctuations result in coherence resonance in dependence on the noise strength. We show that this effect can be enhanced by delayed feedback control with suitably chosen feedback strength and time delay.

Complex dynamics in delay-differential equations with large delay

Abstract: We investigate the dynamical properties of delay differential equations with large delay. Starting from a mathematical discussion of the singular limit τ → ∞, we present a novel theoretical approach to the stability properties of stationary solutions in such systems. We introduce the notion of strong and weak instabilities and describe a method that allows us to calculate asymptotic approximations of the corresponding parts of the spectrum. The theoretical results are illustrated by several examples, including the control of unstable steady states of focus type by time delayed feedback control and the stability of external cavity modes in the Lang-Kobayashi system for semiconductor lasers with optical feedback.

Dielectric spectroscopy and dynamics in confinement

Abstract: There are numerous reasons, such as frequency range and sensitivity, to employ dielectric spectroscopy for investigating how confinement alters the dynamics of liquids, supercooled liquids, or polymers. However, care has to be taken to account for the fact that the sample is a heterogeneous dielectric, i.e. a mixture of the confining matrix material and the liquid filler whose dynamics are of interest. Since dielectric permittivity is not an additive quantity, extracting the dynamics of the filler can be complicated or even impossible, and the Maxwell-Wagner relations will not always solve the problem. Some guidelines on how to interpret dielectric data on confined systems will be presented.

Under which conditions the Benjamin-Feir instability may spawn an extreme wave event: A fully nonlinear approach

Abstract: Within the framework of the fully nonlinear water waves equations, we consider a Stokes wavetrain modulated by the Benjamin-Feir instability in the presence of both viscous dissipation and forcing due to wind. The wind model corresponds to the Miles’ theory. By introducing wind effect on the waves, the present paper extends the previous works of [6] and [7] who neglected wind input. It is also a continuation of the study developed by [9] who considered a similar problem within the framework of the NLS equation. The marginal stability curve derived from the fully nonlinear numerical simulations coincides with the curve obtained by [9] from a linear stability analysis. Furthermore, it is found that wind input goes in the subharmonic mode of the modulation whereas dissipation damps the fundamental mode of the initial Stokes wavetrain.

Perfluorinated surfactants as model charged systems for understanding the effect of confinement on proton transport and water mobility in fuel cell membranes. A study by QENS

Abstract: We have investigated the dynamical properties of water confined in mesomorphous phases of perfluorinated sulfonic surfactants. These systems mimic the physico-chemical properties of the perfluorinated Nafion membranes which are used as electrolyte in fuel cells. As the surfactants offer the advantage to self-assemble in well defined organized phases (such as hexagonal and lamellar phases), they could be used as model charged systems to understand the structure-transport relationship in complex real materials. Indeed, the geometry as well as the typical confinement size can be easily controlled and tuned through water concentration and temperature. A QENS study of hexagonal and lamellar phases has been performed on both time-of-flight and backscattering spectrometers to cover a dynamic range from picoseconds to nanoseconds. Analysis of the data with localized translational diffusion models shows the existence of a strong confinement effect that depends on the geometry. Typical confinement sizes and diffusion coefficients can be extracted from the QENS analysis and compared to the Nafion membrane.

Extreme events in optics: Challenges of the MANUREVA project

Abstract: In this contribution we describe and discuss a series of challenges and questions relating to understanding extreme wave phenomena in optics. Many aspects of these questions are being studied in the framework of the MANUREVA project: a multidisciplinary consortium aiming to carry out mathematical, numerical and experimental studies in this field. The central motivation of this work is the 2007 results from optical physics [D. Solli et al., Nature 450, 1054 (2007)] that showed how a fibre-optical system can generate large amplitude extreme wave events with similar statistical properties to the infamous hydrodynamic rogue waves on the surface of the ocean. We review our recent work in this area, and discuss how this observation may open the possibility for an optical system to be used to directly study both the dynamics and statistics of extreme-value processes, a potential advance comparable to the introduction of optical systems to study chaos in the 1970s.

A model for oscillations and pattern formation in protoplasmic droplets of Physarum polycephalum

Abstract: A mechano-chemical model for the spatiotemporal dynamics of free calcium and the thickness in protoplasmic droplets of the true slime mold Physarum polycephalum is derived starting from a physiologically detailed description of intracellular calcium oscillations proposed by Smith and Saldana (Biopys. J. 61, 368 (1992)). First, we have modified the Smith-Saldana model for the temporal calcium dynamics in order to reproduce the experimentally observed phase relation between calcium and mechanical tension oscillations. Then, we formulate a model for spatiotemporal dynamics by adding spatial coupling in the form of calcium diffusion and advection due to calcium-dependent mechanical contraction. In another step, the resulting reaction-diffusion model with mechanical coupling is simplified to a reaction-diffusion model with global coupling that approximates the mechanical part. We perform a bifurcation analysis of the local dynamics and observe a Hopf bifurcation upon increase of a biochemical activity parameter. The corresponding reaction-diffusion model with global coupling shows regular and chaotic spatiotemporal behaviour for parameters with oscillatory dynamics. In addition, we show that the global coupling leads to a long-wavelength instability even for parameters where the local dynamics possesses a stable spatially homogeneous steady state. This instability causes standing waves with a wavelength of twice the system size in one dimension. Simulations of the model in two dimensions are found to exhibit defect-mediated turbulence as well as various types of spiral wave patterns in qualitative agreement with earlier experimental observation by Takagi and Ueda (Physica D, 237, 420 (2008)).