Showing papers in "European Physical Journal-special Topics in 2011"

Creep, relaxation and viscosity properties for basic fractional models in rheology

Abstract: The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep, relaxation and viscosity properties are considered. The basic models are those that generalize via derivatives of fractional order the classical mechanical models characterized by two, three and four parameters, that we refer to as Kelvin–Voigt, Maxwell, Zener, anti–Zener and Burgers. For each fractional model we provide plots of the creep compliance, relaxation modulus and effective viscosity in non dimensional form in terms of a suitable time scale for different values of the order of fractional derivative. We also discuss the role of the order of fractional derivative in modifying the properties of the classical models.

A survey on the stability of fractional differential equations - Dedicated to Prof. Y.S. Chen on the Occasion of his 80th Birthday

Abstract: Recently, fractional calculus has attracted much attention since it plays an important role in many fields of science and engineering. Especially, the study on stability of fractional differential equations appears to be very important. In this paper, a brief overview on the recent stability results of fractional differential equations and the analytical methods used are provided. These equations include linear fractional differential equations, nonlinear fractional differential equations, fractional differential equations with time-delay. Some conclusions for stability are similar to that of classical integer-order differential equations. However, not all of the stability conditions are parallel to the corresponding classical integer-order differential equations because of non-locality and weak singularities of fractional calculus. Some results and remarks are also included.

A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems

Abstract: How to characterize the memory property of systems is a challenging issue in the modeling and analysis of complex systems. This study makes a comparative investigation of integer-order derivative, constant-order fractional derivative and two types of variable-order fractional derivatives in characterizing the memory property of systems. The advantages and potential applications of two variable-order derivative definitions are highlighted through a comparative analysis of anomalous relaxation process.

Practitioner’s guide to laser pulse propagation models and simulation - Numerical implementation and practical usage of modern pulse propagation models

Abstract: The purpose of this article is to provide practical introduction into numerical modeling of ultrashort optical pulses in extreme nonlinear regimes The theoretic background section covers derivation of modern pulse propagation models starting from Maxwell’s equations, and includes both envelope-based models and carrier-resolving propagation equations We then continue with a detailed description of implementation in software of Nonlinear Envelope Equations as an example of a mixed approach which combines finite-difference and spectral techniques Fully spectral numerical solution methods for the Unidirectional Pulse Propagation Equation are discussed next The modeling part of this guide concludes with a brief introduction into efficient implementations of nonlinear medium responses Finally, we include several worked-out simulation examples These are mini-projects designed to highlight numerical and modeling issues, and to teach numerical-experiment practices They are also meant to illustrate, first and foremost for a non-specialist, how tools discussed in this guide can be applied in practical numerical modeling

Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics

Abstract: We revisit the Mittag-Leffler functions of a real variable t, with one, two and three order-parameters {α,β,γ}, as far as their Laplace transform pairs and complete monotonicity properties are concerned. These functions, subjected to the requirement to be completely monotone for t > 0, are shown to be suitable models for non–Debye relaxation phenomena in dielectrics including as particular cases the classical models referred to as Cole–Cole, Davidson–Cole and Havriliak–Negami. We show 3D plots of the relaxations functions and of the corresponding spectral distributions, keeping fixed one of the three order-parameters.

A fractional calculus approach to nonlocal elasticity

Abstract: If the attenuation function of strain is expressed as a power law, the formalism of fractional calculus may be used to handle Eringen nonlocal elastic model. Aim of the present paper is to provide a mechanical interpretation to this nonlocal fractional elastic model by showing that it is equivalent to a discrete, point-spring model. A one-dimensional geometry is considered; the static, kinematic and constitutive equations are presented and the governing fractional differential equation highlighted. Two numerical procedures to solve the fractional equation are finally implemented and applied to study the strain field in a finite bar under given edge displacements.

A Physical experimental study of variable-order fractional integrator and differentiator

Abstract: Recent research results have shown that many complex physical phenomena can be better described using variable-order fractional differential equations. To understand the physical meaning of variable-order fractional calculus, and better know the application potentials of variable-order fractional operators in physical processes, an experimental study of temperature-dependent variable-order fractional integrator and differentiator is presented in this paper. The detailed introduction of analogue realization of variable-order fractional operator, and the influence of temperature to the order of fractional operator are presented in particular. Furthermore, the potential applications of variable-order fractional operators in PIλ(t)Dμ(t) controller and dynamic-order fractional systems are suggested.

Electromagnetic excitation of nucleon resonances

Abstract: Recent progress on the extraction of electromagnetic properties of nucleon resonance excitation through pion photo- and electroproduction is reviewed. Cross section data measured at MAMI, ELSA, and CEBAF are analyzed and compared to the analysis of other groups. On this basis, we derive longitudinal and transverse transition form factors for most of the four-star nucleon resonances. Furthermore, we discuss how the transition form factors can be used to obtain empirical transverse charge densities. Contour plots of the thus derived densities are shown for the Delta, Roper, S 11, and D 13 nucleon resonances.

Star-drops formed by periodic excitation and on an air cushion – A short review

Abstract: When simply put on a solid, a liquid drop usually adopts the shape of a spherical cap or a puddle depending on its volume and on the wetting conditions. However, when the drop is subjected to a periodic field, a parametric excitation can induce a transition of shape and can break the drop’s initial axial symmetry, provided that the pinning forces at the contact-line are weak enough. Therefore, a standing wave appears at the drop interface and induces a periodic motion, with a frequency that equals half the excitation frequency. In the first part, we review the different situations where star drops can be generated from various types of periodic excitations. In the second part, we show that similar star drops can occur in a much less intuitive fashion when the drop is put on an air cushion, where no periodic motion is imposed a priori. Preliminary experiments as well as theoretical clues for a hydrodynamic interpretation, suggest that the periodic vibration is due to an inertial instability in the air layer below the drop

From social data mining to forecasting socio-economic crises

Abstract: The purpose of this White Paper of the EU Support Action “Visioneer”(see www.visioneer.ethz.ch) is to address the following goals: 1. Develop strategies to quickly increase the objective knowledge about social and economic systems. 2. Describe requirements for efficient large-scale scientific data mining of anonymized social and economic data. 3. Formulate strategies how to collect stylized facts extracted from large data set. 4. Sketch ways how to successfully build up centers for computational social science. 5. Propose plans how to create centers for risk analysis and crisis forecasting. 6. Elaborate ethical standards regarding the storage, processing, evaluation, and publication of social and economic data.

Approximate solutions to fractional subdiffusion equations

Abstract: The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown coefficients and the concept of penetration (boundary layer). The prescribed profile satisfies the boundary conditions imposed by the boundary layer that allows its coefficients to be expressed through its depth as unique parameter. The integral approach to the fractional subdiffusion equation suggests a replacement of the real distribution function by the approximate profile. The solution was performed with Riemann-Liouville time-fractional derivative since the integral approach avoids the definition of the initial value of the time-derivative required by the Laplace transformed equations and leading to a transition to Caputo derivatives. The method is demonstrated by solutions to two simple fractional subdiffusion equations (Dirichlet problems): 1) Time-Fractional Diffusion Equation, and 2) Time-Fractional Drift Equation, both of them having fundamental solutions expressed through the M-Wright function. The solutions demonstrate some basic issues of the suggested integral approach, among them: a) Choice of the profile, b) Integration problem emerging when the distribution (profile) is replaced by a prescribed one with unknown coefficients; c) Optimization of the profile in view to minimize the average error of approximations; d) Numerical results allowing comparisons to the known solutions expressed to the M-Wright function and error estimations.

Can diffuse-interface models quantitatively describe moving contact lines?

Abstract: The three-phase contact line is a long-standing problem in the physics and hydrodynamics of interfaces. The traditional sharp-interface Navier-Stokes formulation encounters a non-integrable stress singularity, which is commonly avoided by introducing slip at the contact line. In recent years, diffuse-interface models have emerged as an alternative method. They are attractive in regularizing the singularity in a more rational manner, and in the meantime supplying a means for describing the interfacial motion on the large scale. Although a number of groups have carried out diffuse-interface computations of moving contact lines, a closer inspection shows that some fundamental questions remain to be answered. For example, how can a sharp-interface limit be realized to produce a solution that is independent of the interfacial thickness? How to determine model parameters so as to match a specific experiment? Finally, is it possible to make quantitatively accurate predictions of the moving contact line using diffuse-interface models? Using the Cahn-Hilliard model as an example, we describe these issues and suggest solutions.

Droplets evaporation: Problems and solutions

Abstract: The evaporation of single droplets and sprays into gaseous atmosphere and the evaporation of sessile liquid droplets on solid substrates are here considered. We argue that if thermodynamics is augmented with Derjaguin’s (disjoining/conjoining) pressure to handle phenomena in a vicinity of the three-phase contact line, problems like the singularity of the evaporation flux and of the viscous stress at the three-phase contact line of a sessile droplet are ruled out.

Laser micro- and nanostructuring using femtosecond Bessel beams

Abstract: We report the generation of femtosecond Bessel beams of conical half-angle 26 degrees using an axicon lens and a beam reduction imaging setup. The generated Bessel beams were applied to the micromachining of nanostructures in glass of length up to 100 μm. The effect of the incident pulse energy on the characteristics of the nano- structures was studied using optical microscopy.

Receding contact lines: From sliding drops to immersion lithography

Abstract: Instabilities of receding contact lines often occur through the formation of a corner with a very sharp tip. These dewetting structures also appear in the technology of Immersion Lithography, where water is put between the lens and the silicon wafer to increase the optical resolution. In this paper we aim to compare corners appearing in Immersion Lithography to those at the tail of gravity driven-drops sliding down an incline. We use high speed recordings to measure the dynamic contact angle and the sharpness of the corner, for varying contact line velocity. It is found that these quantities behave very similarly for Immersion Lithography and drops on an incline. In addition, the results agree well with predictions by a lubrication model for cornered contact lines, hinting at a generic structure of dewetting corners.

Introduction to fractional integrability and differentiability

Abstract: In this paper, we mainly consider fractional integral and derivatives including the Riemann-Liouville derivative, Caputo derivative, Grunwald-Letnikov derivative, Marchaud derivative, Riesz derivative, local fractional derivative, Canavati derivative. Then we introduce their existence conditions. Important issues on these fractional integral and derivatives are also included.

Aerodynamic levitation and laser heating: Applications at synchrotron and neutron sources

Abstract: Aerodynamic levitation is an effective way to suspend samples which can be heated with CO2 lasers. The advantages of this containerless technique are the simplicity and compactness of the device, making it possible to integrate it easily in different kinds of experiments. In addition, all types of materials can be used, including metals and oxides. The integration of aerodynamic levitation at synchrotron and neutron sources provides powerful tools to study the structure and dynamics of molten materials. We present here an overview of the existing techniques and of the developments made at the CEMHTI in Orleans, as well as a few examples of experimental results already obtained.

SHAKE parallelization

Abstract: SHAKE is a widely used algorithm to impose general holonomic constraints during molecular simulations. By imposing constraints on stiff degrees of freedom that require integration with small time steps (without the constraints) we are able to calculate trajectories with time steps larger by approximately a factor of two. The larger time step makes it possible to run longer simulations. Another approach to extend the scope of Molecular Dynamics is parallelization. Parallelization speeds up the calculation of the forces between the atoms and makes it possible to compute longer trajectories with better statistics for thermodynamic and kinetic averages. A combination of SHAKE and parallelism is therefore highly desired. Unfortunately, the most widely used SHAKE algorithm (of bond relaxation) is inappropriate for parallelization and alternatives are needed. The alternatives must minimize communication, lead to good load balancing, and offer significantly better performance than the bond relaxation approach. The algorithm should also scale with the number of processors. We describe the theory behind different implementations of constrained dynamics on parallel systems, and their implementation on common architectures.

How to create an innovation accelerator

Abstract: The purpose of this White Paper of the EU Support Action "Visioneer" (see www.visioneer.ethz.ch) is to address the following goals: 1. Identify new ways of publishing, evaluating, and reporting scientific progress. 2. Promote ICT solutions to increase the awareness of new emerging trends. 3. Invent tools to enhance Europe's innovation potential. 4. Develop new strategies to support a sustainable technological development. 5. Lay the foundations for new ways to reach societal benefits and respond to industrial needs using ICT.

Photoproduction of mesons off nuclei

Abstract: Recent results for the photoproduction of mesons off nuclei are reviewed. These experiments have been performed for two major lines of research related to the properties of the strong interaction. The investigation of nucleon resonances requires light nuclei as targets for the extraction of the isospin composition of the electromagnetic excitations. This is done with quasi-free meson photoproduction off the bound neutron and supplemented with the measurement of coherent photoproduction reactions, serving as spin and/or isospin filters. Furthermore, photoproduction from light and heavy nuclei is a very efficient tool for the study of the interactions of mesons with nuclear matter and the in-medium properties of hadrons. Experiments are currently rapidly developing due to the combination of high quality tagged (and polarized) photon beams with state-of-the-art 4π detectors and polarized targets.

Efficient generation of Bessel beam arrays by means of an SLM

Abstract: We use a Spatial Light Modulator (SLM) to produce arrays of Bessel beams by using multiple axicon phase-masks on the SLM. This approach utilises the whole of the SLM, rather than just a thin annular region (which is the case if the SLM is in the far-field of the generated Bessel beams). Using the whole SLM rather than just an annular region means that the required intensity on the SLM is an order of magnitude lower for a given power in the Bessel beams. Spreading the power over the whole SLM is important for high-power applications such as laser micromachining. We allow the axicons to overlap and interfere in the hologram, so the axial length of the Bessel beam core is maintained as we add more beams to the array.

Optimisation of a low cost SLM for diffraction efficiency and ghost order suppression

Abstract: Spatial Light Modulators (SLMs) are a powerful tool in many optics laboratories, but due to the technology required for their fabrication, they are usually very expensive Recently some inexpensive devices have been produced, however their phase shift range is less than 2π, leading to a loss of diffraction efficiency for the SLM We show how to improve the first order diffraction efficiency of such an SLM by adjusting the blazing function, and obtain a 15 times increase in first order diffracted power Even a perfect SLM with 2π phase throw can produce undesired effects in some situations; for example in holographic optical tweezers it is common to find unwanted “ghost spots” near to the array of first-order spots Modulating the amplitude, by spatially modulating the blazing function, allows us to suppress the ghost spots This increases the contrast between desired and unwanted spots by more than an order of magnitude

Note on thin film equations for solutions and suspensions

Abstract: This note discusses how one may further develop thin film evolution equations for solutions and suspensions. First, we review the time evolution equation of a film or drop of simple liquid under the sole influence of wettability and capillarity and its formulation as a gradient dynamics. Second, we introduce such a gradient dynamics for a film of suspension or solution and show that it is equivalent to thin film equations in the literature. Finally, the new formulation is used to discuss extensions towards solute molecules/particles with net attractive interactions, decomposing solute-solvent systems and a solute-dependent wettability.

Econophysics – complex correlations and trend switchings in financial time series

Abstract: This article focuses on the analysis of financial time series and their correlations. A method is used for quantifying pattern based correlations of a time series. With this methodology, evidence is found that typical behavioral patterns of financial market participants manifest over short time scales, i.e., that reactions to given price patterns are not entirely random, but that similar price patterns also cause similar reactions. Based on the investigation of the complex correlations in financial time series, the question arises, which properties change when switching from a positive trend to a negative trend. An empirical quantification by rescaling provides the result that new price extrema coincide with a significant increase in transaction volume and a significant decrease in the length of corresponding time intervals between transactions. These findings are independent of the time scale over 9 orders of magnitude, and they exhibit characteristics which one can also find in other complex systems in nature (and in physical systems in particular). These properties are independent of the markets analyzed. Trends that exist only for a few seconds show the same characteristics as trends on time scales of several months. Thus, it is possible to study financial bubbles and their collapses in more detail, because trend switching processes occur with higher frequency on small time scales. In addition, a Monte Carlo based simulation of financial markets is analyzed and extended in order to reproduce empirical features and to gain insight into their causes. These causes include both financial market microstructure and the risk aversion of market participants.

Dynamics of wetting and Kramers’ theory

Abstract: We investigate the potential link between Kramer’s treatment of rate processes and the molecular-kinetic theory of wetting. The results of recent large-scale simulations of dynamic wetting are used to illustrate and validate our analysis. We find that both theories predict that, for a given driving force, the velocity of the contact line is inversely proportional to the viscosity. They also predict that the velocity will depend with a negative exponent on the strength of solid-liquid interactions, which for simple systems can be represented to good approximation by the reversible work of adhesion Wa 0.

Subordination pathways to fractional diffusion

Abstract: The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and under power law regime is splitted into three distinct random walks: (rw 1), a random walk along the line of natural time, happening in operational time; (w 2), a random walk along the line of space, happening in operational time; (rw 3), the inversion of (rw 1), namely a random walk along the line of operational time, happening in natural time. Via the general integral equation of CTRW and appropriate rescaling, the transition to the diffusion limit is carried out for each of these three random walks. Combining the limits of (rw 1) and (rw 2) we get the method of parametric subordination for generating particle paths, whereas combination of (rw 2) and (rw 3) yields the subordination integral for the sojourn probability density in space - time fractional diffusion.

From social simulation to integrative system design

Abstract: The purpose of this White Paper of the EU Support Action “Visioneer” (see www.visioneer.ethz.ch) is to address the following goals: 1. Develop strategies to build up social simulation capacities. 2. Suggest ways to build up an “artificial societies” community that aims at simulating real and alternative societies by means of supercomputers, grid or cloud computing. 3. Derive proposals to establish centers for integrative systems design.

Non-hydrodynamic collective modes in liquid metals and alloys

Abstract: A short review of analytical and numerical results, obtained for collective dynamics in liquid metals and alloys within a theoretical approach of Generalized Collective Modes (GCM) is presented. The GCM approach permits to represent dynamic structure factors in wide ranges of wave numbers and frequencies as a sum of contributions from hydrodynamic and non-hydrodynamic processes. The origin of collective modes that make important contributions to dynamic structure factors beyond the hydrodynamic regime in liquid metals and alloys is discussed.

GPU-computing in econophysics and statistical physics

Abstract: A recent trend in computer science and related fields is general purpose computing on graphics processing units (GPUs), which can yield impressive performance. With multiple cores connected by high memory bandwidth, today’s GPUs offer resources for non-graphics parallel processing. This article provides a brief introduction into the field of GPU computing and includes examples. In particular computationally expensive analyses employed in financial market context are coded on a graphics card architecture which leads to a significant reduction of computing time. In order to demonstrate the wide range of possible applications, a standard model in statistical physics – the Ising model – is ported to a graphics card architecture as well, resulting in large speedup values.

Some dry facts about dynamic wetting

Abstract: Some aspects of research into the dynamic wetting phenomenon are discussed where multidisciplinarity of the dynamic wetting community becomes a hindrance rather than an advantage. An instance of this is when the accumulated knowledge is cast into mathematical models that mix conceptual frameworks inherent in different levels of description. An attempt is made to establish some common reference points for the modelling and outline a research programme that utilizes the already obtained results and the complementary expertise of several sectors of the research community.