Spatiotemporal optical bullets in two-dimensional fiber arrays and their stability

Long-lived light bullets fully localized in both space and time can be generated in novel photonic media such as multicore optical fiber or waveguide arrays. In this paper we present detailed theoretical analysis on the existence and stability of the discrete-continuous light bullets using a very generic model that occurs in a number of applications.

Hydrodynamic modeling of mineral wool fiber suspensions in a two-dimensional flow

A consequence of a loss of coolant accident is that the local insulation material is damaged and maybe transported to the containment sump where it can penetrate and/or block the sump strainers. An experimental and theoretical study, which examines the transport of mineral wool fibers via single and multi-effect experiments is being performed. This paper focuses on the experiments and simulations performed for validation of numerical models of sedimentation and resuspension of mineral wool fiber agglomerates in a racetrack type channel. Three velocity conditions are used to test the response of two dispersed phase fiber agglomerates to two drag correlations and to two turbulent dispersion coefficients. The Eulerian multiphase flow model is applied with either one or two dispersed phases.

Lichen competition: two-dimensional warfare in slow motion

Lichens, a symbiotic association between a filamentous fungus and an alga, are often dominant in stressful environments such as the surfaces of rock and tree bark. Under these conditions, lichens experience extremes of temperature, moisture supply, and low availability of nutrients. As a consequence, lichens sequester a high proportion of their carbon production for stress resistance rather than for growth. Hence, as a group lichens are particularly slow growing organisms with many species growing at less than 2mm per year and some at less than 0.5mm per year. Whether or not competition occurs between lichen thalli in these communities is controversial. This article discusses the evidence that competition occurs between lichens on rock and tree bark and assesses whether competitive effects are likely to be important in structuring these communities.

Hydrodynamic modeling of mineral wool fiber suspensions in a two-dimensional channel flow

A consequence of a loss of coolant accident is the damage of adjacent insulation materials (IM). IM may then be transported to the containment sump strainers where water is drawn into the ECCS (emergency core cooling system). Blockage of the strainers by IM lead to an increased pressure drop acting on the operating ECCS pumps. IM can also penetrate the strainers, enter the reactor coolant system and then accumulate in the reactor pressure vessel. An experimental and theoretical study that concentrates on mineral wool fiber transport in the containment sump and the ECCS is being performed. The study entails fiber generation and the assessment of fiber transport in single and multi-effect experiments. The experiments include measurement of the terminal settling velocity, the strainer pressure drop, fiber sedimentation and resuspension in a channel flow and jet flow in a rectangular tank. An integrated test facility is also operated to assess the compounded effects. Each experimental facility is used to provide data for the validation of equivalent computational fluid dynamic models. The channel flow facility allows the determination of the steady state distribution of the fibers at different flow velocities. The fibers are modeled in the Eulerian-Eulerian reference frame as spherical wetted agglomerates. The fiber agglomerate size, density, the relative viscosity of the fluid-fiber mixture and the turbulent dispersion of the fibers all affect the steady state accumulation of fibers at the channel base. In the current simulations, two fiber phases are separately considered. The particle size is kept constant while the density is modified, which affects both the terminal velocity and volume fraction. The relative viscosity is only significant at higher concentrations. The numerical model finds that the fibers accumulate at the channel base even at high velocities; therefore, modifications to the drag and turbulent dispersion forces can be made to reduce fiber accumulation.

Two-dimensional optical power distribution of side-out-coupled radiation from tilted FBGs in multimode fibre

Two-dimensional optical power distribution of the out-coupled radiation from UV-inscribed tilted fibre Bragg gratings (TFBGs) in multimode fibre (MMF) has been side-detected with high spatial/spectral resolution, showing a near-identical radiation mode profile to that measured from the fibre-end detection method. A comparative investigation of the radiation characteristics of TFBGs fabricated in singlemode fibre (SMF) and MMF clearly indicates that the radiation out-coupling is stronger and spatially more confined in MMF. The unique spatial-to-spectral encoding property of the coupling mechanism offers potential application in low-cost WDM devices.

A method of fundamental solutions for two-dimensional heat conduction

We investigate an application of the method of fundamental solutions (MFS) to heat conduction in two-dimensional bodies, where the thermal diffusivity is piecewise constant. We extend the MFS proposed in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction, Eng. Anal. Bound. Elem. 32 (2008), pp. 697–703] for one-dimensional heat conduction with the sources placed outside the space domain of interest, to the two-dimensional setting. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be obtained efficiently with small computational cost.

Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity

We investigate two numerical procedures for the Cauchy problem in linear elasticity, involving the relaxation of either the given boundary displacements (Dirichlet data) or the prescribed boundary tractions (Neumann data) on the over-specified boundary, in the alternating iterative algorithm of Kozlov et al. (1991). The two mixed direct (well-posed) problems associated with each iteration are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen via the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The MFS-based iterative algorithms with relaxation are tested for Cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the proposed method.

Two-dimensional optical power distribution of side-out-coupled radiation from tilted FBGs in multimode fibre

Two-dimensional optical power distribution of the out-coupled radiation from UV-inscribed tilted fibre Bragg gratings (TFBGs) in multimode fibre (MMF) has been side-detected with high spatial/spectral resolution, showing a near-identical radiation mode profile to that measured from the fibre-end detection method. A comparative investigation of the radiation characteristics of TFBGs fabricated in singlemode fibre (SMF) and MMF clearly indicates that the radiation out-coupling is stronger and spatially more confined in MMF. The unique spatial-to-spectral encoding property of the coupling mechanism offers potential application in low-cost WDM devices.

Two-dimensional viscoelastic discrete triangular system with negative-stiffness components

Potential applications of high-damping and high-stiffness composites have motivated extensive research on the effects of negative-stiffness inclusions on the overall properties of composites. Recent theoretical advances have been based on the Hashin-Shtrikman composite models, one-dimensional discrete viscoelastic systems and a two-dimensional nested triangular viscoelastic network. In this paper, we further analyze the two-dimensional triangular structure containing pre-selected negative-stiffness components to study its underlying deformation mechanisms and stability. Major new findings are structure-deformation evolution with respect to the magnitude of negative stiffness under shear loading and the phenomena related to dissipation-induced destabilization and inertia-induced stabilization, according to Lyapunov stability analysis. The evolution shows strong correlations between stiffness anomalies and deformation modes. Our stability results reveal that stable damping peaks, i.e. stably extreme effective damping properties, are achievable under hydrostatic loading when the inertia is greater than a critical value. Moreover, destabilization induced by elemental damping is observed with the critical inertia. Regardless of elemental damping, when the inertia is less than the critical value, a weaker system instability is identified.

Two-dimensional optical power distribution of side-out-coupled radiation from tilted FBGs in multimode fibre

Two-dimensional optical power distribution of the out-coupled radiation from UV-inscribed tilted fibre Bragg gratings (TFBG) in multimode fibre (MMF) has been side-detected with high spatial spectral resolution, showing a near-identical radiation mode profile to that measured from the fibre-end detection method. A comparative investigation of the radiation characteristics of TFBGs fabricated in singlemode fibre (SMF) and MMF clearly indicates that the radiation out-coupling is stronger and spatially more confined in MMF. The unique spatial-to-spectral encoding property of the coupling mechanism offers potential application in low-cost WDM devices.

Identification and relative quantification of tyrosine nitration in a model peptide using two-dimensional infrared spectroscopy

Nitration of tyrosine in proteins and peptides is a post-translational modification that occurs under conditions of oxidative stress. It is implicated in a variety of medical conditions, including neurodegenerative and cardiovascular diseases. However, monitoring tyrosine nitration and understanding its role in modifying biological function remains a major challenge. In this work, we investigate the use of electron-vibration-vibration (EVV) two-dimensional infrared (2DIR) spectroscopy for the study of tyrosine nitration in model peptides. We demonstrate the ability of EVV 2DIR spectroscopy to differentiate between the neutral and deprotonated states of 3-nitrotyrosine, and we characterize their spectral signatures using information obtained from quantum chemistry calculations and simulated EVV 2DIR spectra. To test the sensitivity of the technique, we use mixed-peptide samples containing various levels of tyrosine nitration, and we use mass spectrometry to independently verify the level of nitration. We conclude that EVV 2DIR spectroscopy is able to provide detailed spectroscopic information on peptide side-chain modifications and to detect nitration levels down to 1%. We further propose that lower nitration levels could be detected by introducing a resonant Raman probe step to increase the detection sensitivity of EVV 2DIR spectroscopy. (Graph Presented).

Multiscale molecular dynamics/hydrodynamics implementation of two dimensional “Mercedes Benz” water model

A multiscale Molecular Dynamics/Hydrodynamics implementation of the 2D Mercedes Benz (MB or BN2D) [1] water model is developed and investigated. The concept and the governing equations of multiscale coupling together with the results of the two-way coupling implementation are reported. The sensitivity of the multiscale model for obtaining macroscopic and microscopic parameters of the system, such as macroscopic density and velocity fluctuations, radial distribution and velocity autocorrelation functions of MB particles, is evaluated. Critical issues for extending the current model to large systems are discussed.

Universal profile of the vortex condensate in two-dimensional turbulence

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate—a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.

Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.

Resonance properties of domain boundaries in quasi-two dimensional antiferromagnets

The so-called "internal modes" localized near the domain boundaries in quasi-two dimensional antiferromagnets are investigated. The possible localized states are classified and their frequency dependences on the system discreteness parameter λ=J/β, which describes the ratio of the magnitudes of the exchange interplane interaction and the magnetic anisotropy, are found. A sudden change in the spectrum of the local internal modes is observed at a critical value of this parameter, λ=λb=3/4, where the domain wall shifts from a collinear to a canted shape. When λ<λb there are one symmetric and two antisymmetric local modes, and when λ>λb the modes are two symmetric, one antisymmetric, and one shear. For discreteness parameters close to the critical value, the frequencies of some of the local modes lie deep inside the gap for the linear AFM magnon spectrum and can be observed experimentally. © 2010 American Institute of Physics.