Nonlinear multicore waveguiding structures with balanced gain and loss

We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multicore waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an effective PT-symmetric dimer with asymmetric coupling. In the linear case, we find that there exist two modes with real propagation constants before an onset of the PT-symmetry breaking while other modes have always the propagation constants with nonzero imaginary parts. This leads to a stable (unstable) propagation of the modes when gain is localized in the core (ring) of the waveguiding structure. In the case of nonlinear response, we show that an interplay between nonlinearity, gain, and loss induces a high degree of instability, with only small windows in the parameter space where quasistable propagation is observed. We propose a novel stabilization mechanism based on a periodic modulation of both gain and loss along the propagation direction that allows bounded light propagation in the multicore waveguiding structures.

Dynamical Systems in Description of Nonlinear Recursive Regression Transformers

The task of approximation-forecasting for a function, represented by empirical data was investigated. Certain class of the functions as forecasting tools: so called RFT-transformers, – was proposed. Least Square Method and superposition are the principal composing means for the function generating. Besides, the special classes of beam dynamics with delay were introduced and investigated to get classical results regarding gradients. These results were applied to optimize the RFT-transformers. The effectiveness of the forecast was demonstrated on the empirical data from the Forex market.

Applied Aspects of Mathematical Modeling and Optimization of Dynamics of Charged Beams

The complex of questions connected with the analysis, estimation and structural-parametrical optimization of dynamic system is considered in this article. Connection of such problems with tasks of control by beams of trajectories is emphasized. The special attention is concentrated on the review and analysis of spent scientific researches, the attention is stressed to their constructability and applied directedness. Efficiency of the developed algorithmic and software is demonstrated on the tasks of modeling and optimization of output beam characteristics in linear resonance accelerators.

Polarization dynamics of bound state solitons in a carbon nanotubes mode locked erbium doped fiber laser

Optical solitons are important in the modern photonics. Passively mode locked erbium doped fiber lasers provide a neat platform to study soliton dynamics. Soliton interaction dynamics is important for various applications and has quite different manifestations, including e.g. such as bound state solitons [1], soliton rains [2]. Soliton interactions have been observed with different mode locking approaches such as figure-of-eight [3] and nonlinear polarization rotation [4]. Carbon nanotubes (CNT) have recently been widely applied as an efficient saturable absorber for passively mode locked fiber lasers. We have recently studied the polarization dynamics in a CNT mode locked vector soliton erbium doped fiber laser [5]. So far, the polarization dynamics of bound state solitons have yet to be investigated. In this report, we present a wide range of polarization dynamics of bound state solitons generated in a CNT mode locked erbium doped fiber laser. The fiber laser consists of ∼ 2 m highly doped erbium fiber (Liekki Er80-8/125) as the gain medium, an optical isolator to ensure unidirectional oscillation anda 980 nm laser diode is used to pump the gain through the 1550/980 nm wavelength division multiplexer. A fused 10:90 coupler is used to couple 10 % of the light out of the laser cavity and two in-line polarization controllers (NewPort) are used to control the birefringence of the cavity and polarization of the pump light respectively. The total cavity length is ∼ 7.8 m indicating a 25.7 MHz fundamental repetition rate. © 2013 IEEE.

New nonlinear regimes of pulse generation in mode- locked fiber lasers

Mode-locked fiber lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes. The complex interplay among the effects of gain/loss, dispersion and nonlinearity in a fiber cavity can be used to shape the pulses and manipulate and control the light dynamics and, hence, lead to different mode-locking regimes. Major steps forward in pulse energy and peak power performance of passively mode-locked fiber lasers have been made with the recent discovery of new nonlinear regimes of pulse generation, namely, dissipative solitons in all-normal-dispersion cavities and parabolic self-similar pulses (similaritons) in passive and active fibers. Despite substantial research in this field, qualitatively new phenomena are still being discovered. In this talk, we review recent progress in the research on nonlinear mechanisms of pulse generation in passively mode-locked fiber lasers. These include similariton mode-locking, a mode-locking regime featuring pulses with a triangular distribution of the intensity, and spectral compression arising from nonlinear pulse propagation. We also report on the possibility of achieving various regimes of advanced temporal waveform generation in a mode-locked fiber laser by inclusion of a spectral filter into the laser cavity.

Thermalized polarization dynamics of a discrete optical-waveguide system with four-wave mixing

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line T=∞ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained, which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.

Real-time intensity domain characterization of fibre lasers using spatio-temporal dynamics

Fibre lasers are light sources that are synonymous with stability. They can give rise to highly coherent continuous-wave radiation, or a stable train of mode locked pulses with well-defined characteristics. However, they can also exhibit an exceedingly diverse range of nonlinear operational regimes spanning a multi-dimensional parameter space. The complex nature of the dynamics poses significant challenges in the theoretical and experimental studies of such systems. Here, we demonstrate how the real-time experimental methodology of spatio-temporal dynamics can be used to unambiguously identify and discern between such highly complex lasing regimes. This two-dimensional representation of laser intensity allows the identification and tracking of individual features embedded in the radiation as they make round-trip circulations inside the cavity. The salient features of this methodology are highlighted by its application to the case of Raman fibre lasers and a partially mode locked ring fibre laser operating in the normal dispersion regime.

Control of the in-cavity dynamics in mode-locked fibre lasers

At the level of fundamental research, fibre lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes, while at the applied research level, pulses with different and optimised features – e.g., in terms of pulse duration, temporal and/or spectral intensity profile, energy, repetition rate and emission bandwidth – are sought with the general constraint of developing efficient cavity architectures. In this talk, we review our recent progress on the realisation of different regimes of pulse generation in passively mode-locked fibre lasers through control of the in-cavity propagation dynamics. We report on the possibility to achieve both parabolic self-similar and triangular pulse shaping in a mode-locked fibre laser via adjustment of the net normal dispersion and integrated gain of the cavity [1]. We also show that careful control of the gain/loss parameters of a net-normal dispersion laser cavity provides the means of achieving switching among Gaussian pulse, dissipative soliton and similariton pulse solutions in the cavity [2,3]. Furthermore, we report on our recent theoretical and experimental studies of pulse shaping by inclusion of an amplitude and phase spectral filter into the cavity of a laser. We numerically demonstrate that a mode-locked fibre laser can operate in dif- ferent pulse-generation regimes, including parabolic, flattop and triangular waveform generations, depending on the amplitude profile of the in-cavity spectral filter [4]. An application of technique using a flat-top spectral filter is demonstrated to achieve the direct generation of sinc-shaped optical Nyquist pulses of high quality and of a widely tuneable bandwidth from the laser [5]. We also report on a recently-developed versa- tile erbium-doped fibre laser, in which conventional soliton, dispersion-managed soli- ton (stretched-pulse) and dissipative soliton mode-locking regimes can be selectively and reliably targeted by programming different group-velocity dispersion profiles and bandwidths on an in-cavity programmable filter [6]. References: 1. S. Boscolo and S. K. Turitsyn, Phys. Rev. A 85, 043811 (2012). 2. J. Peng et al., Phys. Rev. A 86, 033808 (2012). 3. J. Peng, Opt. Express 24, 3046-3054 (2016). 4. S. Boscolo, C. Finot, H. Karakuzu, and P. Petropoulos, Opt. Lett. 39, 438-441 (2014). 5. S. Boscolo, C. Finot, and S. K. Turitsyn, IEEE Photon. J. 7, 7802008 (2015). 6. J. Peng and S. Boscolo, Sci. Rep. 6, 25995 (2016).

Seismic performance of hybrid fiber reinforced polymer-concrete pier frame systems

As an alternative to transverse spiral or hoop steel reinforcement, fiber reinforced polymers (FRPs) were introduced to the construction industry in the 1980’s. The concept of concrete-filled FRP tube (CFFT) has raised great interest amongst researchers in the last decade. FRP tube can act as a pour form, protective jacket, and shear and flexural reinforcement for concrete. However, seismic performance of CFFT bridge substructure has not yet been fully investigated. Experimental work in this study included four two-column bent tests, several component tests and coupon tests. Four 1/6-scale bridge pier frames, consisting of a control reinforced concrete frame (RCF), glass FRP-concrete frame (GFF), carbon FRP-concrete frame (CFF), and hybrid glass/carbon FRP-concrete frame (HFF) were tested under reverse cyclic lateral loading with constant axial loads. Specimen GFF did not show any sign of cracking at a drift ratio as high as 15% with considerable loading capacity, whereas Specimen CFF showed that lowest ductility with similar load capacity as in Specimen GFF. FRP-concrete columns and pier cap beams were then cut from the pier frame specimens, and were tested again in three point flexure under monotonic loading with no axial load. The tests indicated that bonding between FRP and concrete and yielding of steel both affect the flexural strength and ductility of the components. The coupon tests were carried out to establish the tensile strength and elastic modulus of each FRP tube and the FRP mold for the pier cap beam in the two principle directions of loading. A nonlinear analytical model was developed to predict the load-deflection responses of the pier frames. The model was validated against test results. Subsequently, a parametric study was conducted with variables such as frame height to span ratio, steel reinforcement ratio, FRP tube thickness, axial force, and compressive strength of concrete. A typical bridge was also simulated under three different ground acceleration records and damping ratios. Based on the analytical damage index, the RCF bridge was most severely damaged, whereas the GFF bridge only suffered minor repairable damages. Damping ratio was shown to have a pronounced effect on FRP-concrete bridges, just the same as in conventional bridges. This research was part of a multi-university project, which is founded by the National Science Foundation (NSF) - Network for Earthquake Engineering Simulation Research (NEESR) program.

Análise do uso do Portal de Periódicos da CAPES na perspectiva de mestres e doutores formados pelo Programa de Pós-graduação em Administração da UFRN

The Brazilian CAPES Journal Portal aims to provide Information in Science and Technology (IST) for academic users. Thus, it is considered a relevant instrument for post-graduation dynamics and the country´s Science and Technology (S&T) development. Despite its importance, there are still few studies that focus on the policy analysis and efficiency of these resources. This research aims to fill in this gap once it proposes an analysis of the use of the CAPES Journal Portal done on behalf of the master´s and doctoral alumni of the Post Graduate Program in Management (PPGA) at the Federal University of Rio Grande do Norte (UFRN). The operationalization of the research´s main objective was possible through the specific objectives: characterize graduate profile as CAPES Journal Portal users b) identify motivation for the use of CAPES Journal Portal c) detect graduate satisfaction degree in information seeking done at CAPES Journal Portal d) verify graduate satisfaction regarding the use of the CAPES Journal Portal e) verify the use of the information that is obtained by graduates in the development of their academic activities. The research is of descriptive nature employing a mixed methodological strategy in which quantitative approach predominates. Data collection was done through a web survey questionnaire. Quantitative data analysis was made possible through the use of a statistical method. As for qualitative analysis, there was use of the Brenda Dervin´s sense-making approach as well as content analysis in open ended questions. The research samples were composed by 90 graduate students who had defended their dissertation/thesis in the PPGA program at UFRN in the time span of 2010-2013. This represented by 88% of this population. As for user profile, the analysis has made evident that there are no quantitative differences related to gender. There is predominance of male graduates that were aged 26 to 30 years old. As for female graduates, the great majority were 31 o 35 years old. Most graduates had Master´s degree scholarship in order to support their study. It was also seen that the great majority claim to use the Portal during their post graduation studies. The main reasons responsible for non use was: preference for the use of other data bases and lack of knowledge regarding the Portal. It was observed that the most used information resources were theses and dissertations. Data also indicate preference for complete text. Those who have used the Portal also claimed to have used other electronic information fonts in order to fulfill their information needs. The information fonts that were researched outside in the Portal were monographs, dissertations and thesis. Scielo was the most used information font. Results reveal that access and use of the Portal has been done in a regular manner during post graduation studies. But on the other hand, graduates also make use of other electronic information fonts in order to meet their information needs. The study also confirmed the important mission performed by the Portal regarding Brazilian scientific communication production. This was seen even though users have reported the need for improvement in some aspects such as: periodic training in order to promote, encourage and teach more effective use of the portal; investment aiming the expansion of Social Sciences Collection in the Portal as well as the need to implement continuous evaluation process related to user satisfaction in regarding the services provided.

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.

Lattice approach to the dynamics of the DPSK-encoded soliton trains

We study the dynamical properties of the RZ-DPSK encoded sequences, focusing on the instabilities in the soliton train leading to the distortions of the information transmitted. The problem is reformulated within the framework of complex Toda chain model which allows one to carry out the simplified description of the optical soliton dynamics. We elucidate how the bit composition of the pattern affects the initial (linear) stage of the train dynamics and explain the general mechanisms of the appearance of unstable collective soliton modes. Then we discuss the nonlinear regime using asymptotic properties of the pulse stream at large propagation distances and analyze the dynamical behavior of the train classifying different scenarios for the pattern instabilities. Both approaches are based on the machinery of Hermitian and non-Hermitian lattice analysis. © 2010 IEEE.

The Effects of Organic Matter Amendments and Migratory Waterfowl on Greenhouse Gas and Nutrient Dynamics in Managed Coastal Plain Wetlands

Wetland ecosystems provide many valuable ecosystem services, including carbon (C) storage and improvement of water quality. Yet, restored and managed wetlands are not frequently evaluated for their capacity to function in order to deliver on these values. Specific restoration or management practices designed to meet one set of criteria may yield unrecognized biogeochemical costs or co-benefits. The goal of this dissertation is to improve scientific understanding of how wetland restoration practices and waterfowl habitat management affect critical wetland biogeochemical processes related to greenhouse gas emissions and nutrient cycling. I met this goal through field and laboratory research experiments in which I tested for relationships between management factors and the biogeochemical responses of wetland soil, water, plants and trace gas emissions. Specifically, I quantified: (1) the effect of organic matter amendments on the carbon balance of a restored wetland; (2) the effectiveness of two static chamber designs in measuring methane (CH4) emissions from wetlands; (3) the impact of waterfowl herbivory on the oxygen-sensitive processes of methane emission and coupled nitrification-denitrification; and (4) nitrogen (N) exports caused by prescribed draw down of a waterfowl impoundment.

The potency of CH4 emissions from wetlands raises the concern that widespread restoration and/or creation of freshwater wetlands may present a radiative forcing hazard. Yet data on greenhouse gas emissions from restored wetlands are sparse and there has been little investigation into the greenhouse gas effects of amending wetland soils with organic matter, a recent practice used to improve function of mitigation wetlands in the Eastern United States. I measured trace gas emissions across an organic matter gradient at a restored wetland in the coastal plain of Virginia to test the hypothesis that added C substrate would increase the emission of CH4. I found soils heavily loaded with organic matter emitted significantly more carbon dioxide than those that have received little or no organic matter. CH4 emissions from the wetland were low compared to reference wetlands and contrary to my hypothesis, showed no relationship with the loading rate of added organic matter or total soil C. The addition of moderate amounts of organic matter (< 11.2 kg m-2) to the wetland did not greatly increase greenhouse gas emissions, while the addition of high amounts produced additional carbon dioxide, but not CH4.

I found that the static chambers I used for sampling CH4 in wetlands were highly sensitive to soil disturbance. Temporary compression around chambers during sampling inflated the initial chamber CH4 headspace concentration and/or lead to generation of nonlinear, unreliable flux estimates that had to be discarded. I tested an often-used rubber-gasket sealed static chamber against a water-filled-gutter seal chamber I designed that could be set up and sampled from a distance of 2 m with a remote rod sampling system to reduce soil disturbance. Compared to the conventional design, the remotely-sampled static chambers reduced the chance of detecting inflated initial CH4 concentrations from 66 to 6%, and nearly doubled the proportion of robust linear regressions from 45 to 86%. The new system I developed allows for more accurate and reliable CH4 sampling without costly boardwalk construction.

I explored the relationship between CH4 emissions and aquatic herbivores, which are recognized for imposing top-down control on the structure of wetland ecosystems. The biogeochemical consequences of herbivore-driven disruption of plant growth, and in turn, mediated oxygen transport into wetland sediments, were not previously known. Two growing seasons of herbivore exclusion experiments in a major waterfowl overwintering wetland in the Southeastern U.S. demonstrate that waterfowl herbivory had a strong impact on the oxygen-sensitive processes of CH4 emission and nitrification. Denudation by herbivorous birds increased cumulative CH4 flux by 233% (a mean of 63 g CH4 m-2 y-1) and inhibited coupled nitrification-denitrification, as indicated by nitrate availability and emissions of nitrous oxide. The recognition that large populations of aquatic herbivores may influence the capacity for wetlands to emit greenhouse gases and cycle nitrogen is particularly salient in the context of climate change and nutrient pollution mitigation goals. For example, our results suggest that annual emissions of 23 Gg of CH4 y-1 from ~55,000 ha of publicly owned waterfowl impoundments in the Southeastern U.S. could be tripled by overgrazing.

Hydrologically controlled moist-soil impoundment wetlands provide critical habitat for high densities of migratory bird populations, thus their potential to export nitrogen (N) to downstream waters may contribute to the eutrophication of aquatic ecosystems. To investigate the relative importance of N export from these built and managed habitats, I conducted a field study at an impoundment wetland that drains into hypereutrophic Lake Mattamuskeet. I found that prescribed hydrologic drawdowns of the impoundment exported roughly the same amount of N (14 to 22 kg ha-1) as adjacent fertilized agricultural fields (16 to 31 kg ha-1), and contributed approximately one-fifth of total N load (~45 Mg N y-1) to Lake Mattamuskeet. Ironically, the prescribed drawdown regime, designed to maximize waterfowl production in impoundments, may be exacerbating the degradation of habitat quality in the downstream lake. Few studies of wetland N dynamics have targeted impoundments managed to provide wildlife habitat, but a similar phenomenon may occur in some of the 36,000 ha of similarly-managed moist-soil impoundments on National Wildlife Refuges in the southeastern U.S. I suggest early drawdown as a potential method to mitigate impoundment N pollution and estimate it could reduce N export from our study impoundment by more than 70%.

In this dissertation research I found direct relationships between wetland restoration and impoundment management practices, and biogeochemical responses of greenhouse gas emission and nutrient cycling. Elevated soil C at a restored wetland increased CO2 losses even ten years after the organic matter was originally added and intensive herbivory impact on emergent aquatic vegetation resulted in a ~230% increase in CH4 emissions and impaired N cycling and removal. These findings have important implications for the basic understanding of the biogeochemical functioning of wetlands and practical importance for wetland restoration and impoundment management in the face of pressure to mitigate the environmental challenges of global warming and aquatic eutrophication.

Dynamics of the Disk-Pendulum Coupled System With Vertical Excitation

This paper investigates the static and dynamic characteristics of the semi-elliptical rocking disk on which a pendulum pinned. This coupled system’s response is also analyzed analytically and numerically when a vertical harmonic excitation is applied to the bottom of the rocking disk. Lagrange’s Equation is used to derive the motion equations of the disk-pendulum coupled system. The second derivative test for the system’s potential energy shows how the location of the pendulum’s pivotal point affects the number and stability of equilibria, and the change of location presents different bifurcation diagrams for different geometries of the rocking disk. For both vertically excited and unforced cases, the coupled system shows chaos easily, but the proper chosen parameters can still help the system reach and keep the steady state. For the steady state of the vertically excited rocking disk without a pendulum, the variation of the excitation’s amplitude and frequency result in the hysteresis for the amplitude of the response. When a pendulum is pinned on the rocking disk, three major categories of steady states are presently in the numerical way.

Dynamical Heterogeneity and Nonlinear Susceptibility in Short-Ranged Attractive Supercooled Liquids

Recent work has demonstrated the strong qualitative differences between the dynamics near a glass transition driven by short-ranged repulsion and one governed by short-ranged attraction. Here, we study in detail the behavior of non-linear, higher-order correlation functions that measure the growth of length scales associated with dynamical heterogeneity in both types of systems. We find that this measure is qualitatively different in the repulsive and attractive cases with regards to the wave vector dependence as well as the time dependence of the standard non-linear four-point dynamical susceptibility. We discuss the implications of these results for the general understanding of dynamical heterogeneity in glass-forming liquids.