Spectral Sidebands and Multi-Pulse Formation in Passively Mode Locked Lasers

Pulse formation in passively mode locked lasers is often accompanied with dispersive waves that form of spectral sidebands due to spatial inhomogoneities in the laser cavity. Here we present an explicit calculation of the amplitude, frequency, and precise shape of the sidebands accompanying a soliton-like pulse. We then extend the study to the global steady state of mode locked laser with a variable number of pulses, and present experimental results in a mode locked fiber laser that confirm the theory. The strong correlation between the temporal width of the sidebands and the measured spacing between the pulses in multipulse operation suggests that the sidebands have an important role in the inter-pulse interaction.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Mysterious frequency combs in erbium-doped fiber lasers at low temperatures

We report on the observation of puzzling nonuniform, but ordered, frequency combs in erbium-doped fiber lasers at low temperatures, between 3 K and 14 K. At ~14 K the combs disappear. The combs contain ~240 lines and have nonuniform frequency spacings that starts from ~25 GHz at ~1540.5 nm and decreases, almost monotonically, to ~100 MHz within (1.8-2) nm. We discuss possibilities that they result from enlarged regular mode-comb spacings, from prime numbers-based solitary waves free of four-wave mixing or result from gain gratings. However, we think that the combs originate from multi-lasing lines allowed in inhomogeneous gain broadening, dominant at low temperatures, together with a small power dependent homogeneous broadening part, responsible for the spacing between the lines.Comment: 12 pages, 3 figure

Parametrization of Scale-Invariant Self-Adjoint Extensions of Scale-Invariant Symmetric Operators

On a Hilbert space H, we consider a symmetric scale-invariant operator with equal defect numbers. It is assumed that the operator has at least one scale invariant self-adjoint extension in H. We prove that there is a one-to-one correspondence between (generalized) resolvents of scale-invariant extensions and solutions of some functional equation. Two examples of Dirac-type operators are considered

Thermodynamic Analysis of Benzene Alkylation with Ethylene

Thermodynamic and kinetic regularities of benzene alkylation with ethylene in the presence of aluminium chloride with the methods of quantum chemistry were defined. The method used in this study is Semi-empirical method based on Neglecting of Diatomic Overlap approximation at PM3 level. All obtained data will be used for the mathematical model development of the considered process possessing high predictive potential

Interface Friction Parameters for the Mathematical Modeling of Shell Structures with Infill

Thin metal or reinforced concrete shells with granular infill structures are considered in this article. These structures are massive and they are used as support for the construction of berthing quays, piers, artificial islands, shore protection, and other structures of coastal infrastructure. It is more convenient to use the thin shell structures during the development of the Arctic shelf, because it is possible to install them from the ice side. In addition, it is possible to enhance the technology and install thin shells with infill on deeper solid foundation layers. A mathematical model for the stresses on a compressible foundation soil in front of a thin cylindrical shell with infill due to the eccentric loading is developed. A modeling and experimental determination of the interface strength of the contact surface between the infill and the inner surface of the shell is proposed. The details of the construction stages and testing of the physical model used for the experiments are discussed. The effects of the interface friction on the shell behavior and on the foundation stresses in front of the wall are investigated. The influence of parameters affecting the interaction between the soil infill and the inner surface of the shell material is determined. It is based on a comparison of experimental results with calculations performed using the proposed mathematical model. The obtained parameters and proposed methods can be used in numerical simulations using the finite element method to analyze and design the thin shell structures with soil infill. The findings of the study and proposed methods can also be applied to the thin shell structures used in other facilities such as hydraulic, industrial, civil, and transportation

Mathematical Model of the Shell with the Infill for Retaining Structures

A description of finite element model and analysis of a shell with an infill is performed. A large diameter thin cylindrical shell structure with the edge leaning against compressible foundation soil is analyzed. Different materials are considered individually for the models of each structure shell and infill component (metal or reinforced concrete shell, and granular or elastic infill in a shell and foundation soil loaded by the structure). Contact conditions between 1) the infill and the shell’s inner surface and 2) between the foundation material and the shell edge are analyzed. An example of calculating strain conditions in the shell according to the proposed finite element model and tasks of its development process and specification are provided in this paper

Frequency-scanning considerations in axionlike dark matter spin-precession experiments

Galactic dark matter may consist of axionlike particles (ALPs) that can be described as an "ultralight bosonic field" oscillating at the ALP Compton frequency. The ALP field can be searched for using nuclear magnetic resonance (NMR), where resonant precession of spins of a polarized sample can be sensitively detected. The ALP mass to which the experiment is sensitive is scanned by sweeping the bias magnetic field. The scanning either results in detection of ALP dark matter or rules out ALP dark matter with sufficiently strong couplings to nuclear spins over the range of ALP masses corresponding to the covered span of Larmor frequencies. In this work, scanning strategies are analyzed with the goal of optimizing the parameter-space coverage via a proper choice of experimental parameters (e.g., the effective transverse relaxation time)