On the global existence and wave-breaking criteria for the two-component Camassa–Holm system

AbstractConsidered herein is a two-component Camassa–Holm system modeling shallow water waves moving over a linear shear flow. A wave-breaking criterion for strong solutions is determined in the lowest Sobolev space Hs, s>32 by using the localization analysis in the transport equation theory. Moreover, an improved result of global solutions with only a nonzero initial profile of the free surface component of the system is established in this Sobolev space Hs

Positive Solutions for a Class of Fourth-Order Boundary Value Problems in Banach Spaces

Using a specially constructed cone and the fixed point index theory, this work shows existence and nonexistence results of positive solutions for fourth-order boundary value problem with two different parameters in Banach spaces

Airworthiness Compliance Verification Method Based on Simulation of Complex System

AbstractA study is conducted on a new airworthiness compliance verification method based on pilot-aircraft-environment complex system simulation. Verification scenarios are established by “block diagram” method based on airworthiness criteria. A pilot-aircraft-environment complex model is set up and a virtual flight testing method based on connection of MATLAB/Simulink and Flightgear is proposed. Special researches are conducted on the modeling of pilot manipulation stochastic parameters and manipulation in critical situation. Unfavorable flight factors of certain scenario are analyzed, and reliability modeling of important system is researched. A distribution function of small probability event and the theory on risk probability measurement are studied. Nonlinear function is used to depict the relationship between the cumulative probability and the extremum of the critical parameter. A synthetic evaluation model is set up, modified genetic algorithm (MGA) is applied to ascertaining the distribution parameter in the model, and a more reasonable result is obtained. A clause about vehicle control functions (VCFs) verification in MIL-HDBK-516B is selected as an example to validate the practicability of the method

(5-Bromo-2-chloro­phen­yl)(4-ethoxy­phen­yl)methanone

In the title mol­ecule, C15H12BrClO2, the two benzene rings form a dihedral angle of 69.30 (3)°. In the crystal structure, weak inter­molecular C—H⋯O hydrogen bonds link mol­ecules into chains propagating along the b axis

Anisotropic vortex quantum droplets in dipolar Bose-Einstein condensates

Creation of stable intrinsically anisotropic self-bound states with embedded vorticity is a challenging issue. Previously, no such states in Bose-Einstein condensates (BECs) or other physical settings were known. Dipolar BEC suggests a unique possibility to predict stable anisotropic vortex quantum droplets (AVQDs). We demonstrate that they can be created with the vortex' axis oriented \emph{perpendicular} to the polarization of dipoles. The stability area and characteristics of the AVQDs in the parameter space are revealed by means of analytical and numerical methods. Further, the rotation of the polarizing magnetic field is considered, and the largest angular velocities, up to which spinning AVQDs can follow the rotation in clockwise and anti-clockwise directions, are found. Collisions between moving AVQDs are studied too, demonstrating formation of bound states with a vortex-antivortex-vortex structure. A stability domain for such stationary bound states is identified. Unstable dipolar states, that can be readily implemented by means of phase imprinting, quickly transform into robust AVQDs, which suggests a straightforward possibility for the creation of these states in the experiment.Comment: 6 pages, 6 figures, and 48 reference

Strongly anisotropic vortices in dipolar quantum droplets

We construct strongly anisotropic quantum droplets with embedded vorticity in the 3D space, with mutually perpendicular vortex axis and polarization of the atomic magnetic moments. Stability of these anisotropic vortex quantum droplets (AVQDs) is verified by means of systematic simulations. Their stability area is identified in the parametric plane of the total atom number and scattering length of contact interactions. The application of torque perpendicular to the vorticity axis gives rise to robust intrinsic oscillations or rotation of the AVQDs. Collisions between slowly and fast moving AVQDs give rise, respectively, to the elastic outcome or merger. Finally, we construct stable vortex-antivortex-vortex bound states and find their stability regions in the parameter space.Comment: 6 pages, 6 figures, and 66 Reference