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.

Highly sensitive refractive index sensor based on cascaded microfiber knots with Vernier effect

We propose and experimentally demonstrate a refractive index (RI) sensor based on cascaded microfiber knot resonators (CMKRs) with Vernier effect. Deriving from high proportional evanescent field of microfiber and spectrum magnification function of Vernier effect, the RI sensor shows high sensitivity as well as high detection resolution. By using the method named "Drawing-Knotting-Assembling (DKA)", a compact CMKRs is fabricated for experimental demonstration. With the assistance of Lorentz fitting algorithm on the transmission spectrum, sensitivity of 6523nm/RIU and detection resolution up to 1.533 x 10-7 RIU are obtained in the experiment which show good agreement with the numerical simulation. The proposed all-fiber RI sensor with high sensitivity, compact size and low cost can be widely used for chemical and biological detection, as well as the electronic/magnetic field measurement

Interaction dynamics in small networks of nonlinear elements

We study a small circuit of coupled nonlinear elements to investigate general features of signal transmission through networks. The small circuit itself is perceived as building block for larger networks. Individual dynamics and coupling are motivated by neuronal systems: We consider two types of dynamical modes for an individual element, regular spiking and chattering and each individual element can receive excitatory and/or inhibitory inputs and is subjected to different feedback types (excitatory and inhibitory; forward and recurrent). Both, deterministic and stochastic simulations are carried out to study the input-output relationships of these networks. Major results for regular spiking elements include frequency locking, spike rate amplification for strong synaptic coupling, and inhibition-induced spike rate control which can be interpreted as a output frequency rectification. For chattering elements, spike rate amplification for low frequencies and silencing for large frequencies is characteristic

Towards a practical implementation of coherent WDM:analytical, numerical, and experimental studies

Future optical networks will require the implementation of very high capacity (and therefore spectral efficient) technologies. Multi-carrier systems, such as Orthogonal Frequency Division Multiplexing (OFDM) and Coherent WDM (CoWDM), are promising candidates. In this paper, we present analytical, numerical, and experimental investigations of the impact of the relative phases between optical subcarriers of CoWDM systems, as well as the effect that the number of independently modulated subcarriers can have on the performance. We numerically demonstrate a five-subcarrier and three-subcarrier 10-GBd CoWDM system with direct detected amplitude shift keying (ASK) and differentially/coherently detected (D) phase shift keying (PSK). The simulation results are compared with experimental measurements of a 32-Gbit/s DPSK CoWDM system in two configurations. The first configuration was a practical 3-modulator array where all three subcarriers were independently modulated, the second configuration being a traditional 2-modulator odd/even configuration, where only odd and even subcarriers were independently modulated. Simulation and experimental results both indicate that the independent modulation implementation has a greater dependency on the relative phases between subcarriers, with a stronger penalty for the center subcarrier than the odd/even modulation scheme.

On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach

We investigate the problem of determining the stationary temperature field on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the temperature (or the heat flux) is known, and, additionally, on a portion of this exterior boundary the heat flux (or temperature) is also given. We propose a direct boundary integral approach in combination with Tikhonov regularization for the stable determination of the temperature and flux on the inclusion. To determine these quantities on the inclusion, boundary integral equations are derived using Green’s functions, and properties of these equations are shown in an L2-setting. An effective way of discretizing these boundary integral equations based on the Nystr¨om method and trigonometric approximations, is outlined. Numerical examples are included, both with exact and noisy data, showing that accurate approximations can be obtained with small computational effort, and the accuracy is increasing with the length of the portion of the boundary where the additionally data is given.