Search

We consider the problem of reconstruction of the overall magnetisation vector (net moment) of a sample from partial data of the magnetic field. Namely, motivated by a concrete experimental setup , we deal with a situation when the magnetic field is measured on a portion of the plane in vicinity of the sample and only one (normal to the plane) component of the field is available. We assume the measurement area to be a sufficiently large disk (lying in a horizontal plane above the sample) and we obtain a set of estimates for the components of the net moment vector with the accuracy asymptotically improving with the increase of the radius of the measurement disk. Compared to our previous preliminary results, the asymptotic estimates are now rigorously justified and higher-order estimates are given. The presented approach also elucidates the derivation of asymptotic estimates of an arbitrary order. The obtained results are illustrated numerically and their robustness with respect to noise is discussed.

We investigate the turn-on process in a laser cavity where the roundtrip time is several orders of magnitude greater than the active medium timescales. In this long delay limit the electromagnetic field build-up can be mapped experimentally roundtrip after roundtrip. We show how coherence settles down starting from a stochastic initial condition. In the early stages of the turn-on, we show that power drop-outs emerge, persist for several round-trips and seed dark solitons. These latter structures exhibit a chaotic dynamics and emit radiation that can lead to an overall turbulent dynamics depending on the cavity dispersion., 6 pages, 8 figures

Using an asymptotic technique we develop a generalized version of class-B Haus partial differential equation mode-locking model that accounts for both the slow gain response to the averaged value of the field intensity and the fast gain dynamics on the scale comparable to the pulse duration. We show that unlike the conventional class-B Haus mode-locked model, our model is able to describe not only Q-switched instability of the fundamental mode-locked regime, but also the leading edge instability leading to harmonic mode-locked regimes with the increase of the pump power., 14 pages, 5 figures

Using a simple delay differential equation model we study theoretically the dynamics of a unidirectional class-A ring laser with a nonlinear amplifying loop mirror. We perform analytical linear stability analysis of the CW regimes in the large delay limit and demonstrate that these regimes can be destabilized via modulational and Turing-type instabilities, as well as by a bifurcation leading to the appearance of square-waves. We investigate the formation of square-waves and mode-locked pulses in the system. We show that mode-locked pulses are very asymmetric with exponential decay of the trailing and superexponential growth of the leading edge. We discuss asymmetric interaction of these pulses leading to a formation of harmonic mode-locked regimes.

This paper is concerned with a phase field system of Cahn-Hilliard type that is related to a tumor growth model and consists of three equations in terms of the variables order parameter, chemical potential and nutrient concentration. This system has been investigated in the recent contributions arXiv:1401.5943 [math.AP] and arXiv:1501.07057 [math.AP] from the viewpoint of well-posedness, long time behavior and asymptotic convergence as two positive viscosity coefficients tend to zero at the same time. Here, we continue the analysis performed in arXiv:1501.07057 [math.AP] by showing two independent sets of results as just one of the coefficients tends to zero, the other remaining fixed. We prove convergence results, uniqueness of solutions to the two resulting limit problems, and suitable error estimates., Comment: Key words: tumor growth, Cahn-Hilliard system, reaction-diffusion equation, asymptotic analysis, error estimates. arXiv admin note: text overlap with arXiv:1501.07057

Using a delay differential equation model with two time delays, we investigate the dynamics of a semiconductor laser with an active cavity coupled to an external passive cavity. Our numerical simulations indicate that when the coupling between the two cavities is strong enough and the round-trip time of the active cavity is an integer multiple of the round-trip time of the external passive cavity, a harmonic mode-locking regime can develop in the laser with the pulse repetition period close to the passive cavity round trip time. We also demonstrate that the output field intensity sensitively depends on the relative phase between the electric fields in the two cavities giving rise to a resonant behavior. The period and width of the resonances depend on the ratio of the round-trip times and the coupling between the two cavities. We show that the coupled cavity system under consideration can demonstrate a bistability between different regimes of generation.

Hybrid mode-locking in a two section edge-emitting semiconductor laser is studied numerically and analytically using a set of three delay differential equations. In this set the external RF signal applied to the saturable absorber section is modeled by modulation of the carrier relaxation rate in this section. Estimation of the locking range where the pulse repetition frequency is synchronized with the frequency of the external modulation is performed numerically and the effect of the modulation shape and amplitude on this range is investigated. Asymptotic analysis of the dependence of the locking range width on the laser parameters is carried out in the limit of small signal modulation. Our numerical simulations indicate that hybrid mode-locking can be also achieved in the cases when the frequency of the external modulation is approximately twice larger and twice smaller than the pulse repetition frequency of the free running passively mode-locked laser fP . Finally, we provide an experimental demonstration of hybrid mode-locking in a 20 GHz quantum-dot laser with the modulation frequency of the reverse bias applied to the absorber section close to fP =2.

In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary measurements is considered. An algorithm is given by using the fundamental solution., Comment: 10 pages

We investigate Fano-type anomalous transmission of energy of plane waves across lossless slab scatterers with periodic structure in the presence of non-robust guided modes. Our approach is based on rigorous analytic perturbation of the scattering problem near a guided mode and applies to very general structures, continuous and discrete.