Modeling of CW Yb-doped fiber lasers with highly nonlinear cavity dynamics

We develop a theoretical framework for modeling of continuous wave Yb-doped fiber lasers with highly nonlinear cavity dynamics. The developed approach has shown good agreement between theoretical predictions and experimental results for particular scheme of Yb-doped laser with large spectral broadening during single round trip. The model is capable to accurately describe main features of the experimentally measured laser outputs such as power efficiency slope, power leakage through fibre Bragg gratings, spectral broadening and spectral shape of generated radiation. © 2011 Optical Society of America.

Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

Perception of global image contrast is predicted by the same spatial integration model of gain control as detection and discrimination

How are the image statistics of global image contrast computed? We answered this by using a contrast-matching task for checkerboard configurations of ‘battenberg’ micro-patterns where the contrasts and spatial spreads of interdigitated pairs of micro-patterns were adjusted independently. Test stimuli were 20 × 20 arrays with various sized cluster widths, matched to standard patterns of uniform contrast. When one of the test patterns contained a pattern with much higher contrast than the other, that determined global pattern contrast, as in a max() operation. Crucially, however, the full matching functions had a curious intermediate region where low contrast additions for one pattern to intermediate contrasts of the other caused a paradoxical reduction in perceived global contrast. None of the following models predicted this: RMS, energy, linear sum, max, Legge and Foley. However, a gain control model incorporating wide-field integration and suppression of nonlinear contrast responses predicted the results with no free parameters. This model was derived from experiments on summation of contrast at threshold, and masking and summation effects in dipper functions. Those experiments were also inconsistent with the failed models above. Thus, we conclude that our contrast gain control model (Meese & Summers, 2007) describes a fundamental operation in human contrast vision.

Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder. © 2014 American Physical Society.

Kelvin-wave cascade in the vortex filament model

The small-scale energy-transfer mechanism in zero-temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves (KWs) transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting KWs to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with the nonlocal six-wave KW interactions as proposed by L'vov and Nazarenko.

A Harrod modell strukturális stabilitása (Structural stability of the Harrod model)

In this study it is shown that the nontrivial hyperbolic fixed point of a nonlinear dynamical system, which is formulated by means of the adaptive expectations, corresponds to the unstable equilibrium of Harrod. We prove that this nonlinear dynamical (in the sense of Harrod) model is structurally stable under suitable economic conditions. In the case of structural stability, small changes of the functions (C1-perturbations of the vector field) describing the expected and the true time variation of the capital coefficients do not influence the qualitative properties of the endogenous variables, that is, although the trajectories may slightly change, their structure is the same as that of the unperturbed one, and therefore these models are suitable for long-time predictions. In this situation the critique of Lucas or Engel is not valid. There is no topological conjugacy between the perturbed and unperturbed models; the change of the growth rate between two levels may require different times for the perturbed and unperturbed models.

Nemlineáris dinamika klasszikus növekedési modellekben (Nonlinear dynamics in classical economic growth models)

Ebben a tanulmányban a klasszikus Harrod növekedési modellt nemlineáris kiterjesztéssel, keynesi és schumpeteri tradíciók bevezetésével reprezentatív ügynök modellbe alakítjuk. A híres Lucas kritika igazolásaként megmutatjuk, hogy az intrinsic gazdasági növekedési ütemek trajektóriái vagy egy turbulens káoszba szóródnak szét, vagy egy nagyméretű rendhez vezetnek, ami elsődlegesen a megfelelő fogyasztási függvény típusától függ, s bizonyos paraméterek piaci értékei, pedig csak másodlagos szerepet játszanak. A másik meglepő eredmény empirikus, ami szerint külkereskedelmi többlet, a hazai valuta bizonyos devizapiaci értékei mellett, különös attraktorokat generálhat. _____ In this paper the classical Harrodian growth model is transformed into a representative agent model by its nonlinear extensions and the Keynesian and Schumpeterian traditions. For the proof of the celebrated Lucas critique it is shown that the trajectories of intrinsic economic growth rates either are scattered into a turbulent chaos or lead to a large scale order. It depends on the type of the appropriate consumption function, and the market values of some parameters are playing only secondary role.Another surprising result is empirical: the international trade su±cit may generate strange attractors under some exchange rate values.

Nonlinear Flow in Karst Formations

The variation of effective hydraulic conductivity as a function of specific discharge in several 0.2-m and 0.3-m cubes of Key Largo Limestone was investigated. The experimental results closely match the Forchheimer equation. Defining the pore-size length scale in terms of Forchheimer parameters, it is demonstrated that significant deviations from Darcian flow will occur when the Reynolds number exceeds 0.11. A particular threshold model previously proposed for use in karstic formations does not show strong agreement with the data near the onset of nonlinear flow.

The transducer model for contrast detection and discrimination: formal relations, implications, and an empirical test.

The transducer function mu for contrast perception describes the nonlinear mapping of stimulus contrast onto an internal response. Under a signal detection theory approach, the transducer model of contrast perception states that the internal response elicited by a stimulus of contrast c is a random variable with mean mu(c). Using this approach, we derive the formal relations between the transducer function, the threshold-versus-contrast (TvC) function, and the psychometric functions for contrast detection and discrimination in 2AFC tasks. We show that the mathematical form of the TvC function is determined only by mu, and that the psychometric functions for detection and discrimination have a common mathematical form with common parameters emanating from, and only from, the transducer function mu and the form of the distribution of the internal responses. We discuss the theoretical and practical implications of these relations, which have bearings on the tenability of certain mathematical forms for the psychometric function and on the suitability of empirical approaches to model validation. We also present the results of a comprehensive test of these relations using two alternative forms of the transducer model: a three-parameter version that renders logistic psychometric functions and a five-parameter version using Foley's variant of the Naka-Rushton equation as transducer function. Our results support the validity of the formal relations implied by the general transducer model, and the two versions that were contrasted account for our data equally well.

Experimental verification of the vibro-impact capsule model

Date of Acceptance: 03/09/15 Acknowledgments Dr. Yang Liu would like to acknowledge the financial support for the Small Research Grant (31841) by the Carnegie Trust for the Universities of Scotland.

Experimental verification of the vibro-impact capsule model

Date of Acceptance: 03/09/15 Acknowledgments Dr. Yang Liu would like to acknowledge the financial support for the Small Research Grant (31841) by the Carnegie Trust for the Universities of Scotland.

Capacity estimates for optical transmission based on the nonlinear Fourier transform

What is the maximum rate at which information can be transmitted error-free in fibre-optic communication systems? For linear channels, this was established in classic works of Nyquist and Shannon. However, despite the immense practical importance of fibre-optic communications providing for >99% of global data traffic, the channel capacity of optical links remains unknown due to the complexity introduced by fibre nonlinearity. Recently, there has been a flurry of studies examining an expected cap that nonlinearity puts on the information-carrying capacity of fibre-optic systems. Mastering the nonlinear channels requires paradigm shift from current modulation, coding and transmission techniques originally developed for linear communication systems. Here we demonstrate that using the integrability of the master model and the nonlinear Fourier transform, the lower bound on the capacity per symbol can be estimated as 10.7 bits per symbol with 500 GHz bandwidth over 2,000 km.

Modeling 2R regenerator based on High Nonlinear Dispersion Imbalanced Loop Mirror (HN-DILM)

The model of Reshaping and Re-amplification (2R) regenerator based on High Nonlinear Dispersion Imbalanced Loop Mirror (HN-DILM) has been designed to examine its capability to reduce the necessary of fiber loop length and input peak power by deploying High Non linear Fiber (HNLF) compared to Dispersion Shifted Fiber (DSF). The simulation results show by deployed a HNLF as a nonlinear element in Dispersion Imbalanced Loop Mirror (DILM) requires only 400mW peak powers to obtain a peak of transmission compared to DSF which requires a higher peak power at 2000mW to obtain a certain transmissivity. It also shows that HNLF required shorter fiber length to achieve the highest transmission. The 2R regenerator also increases the extinction ratio (ER) of the entire system. © 2010 IEEE.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.