Optical vortices in the Ginzburg–Landau equation with cubic–quintic nonlinearity

In a dissipative system with cubic–quintic nonlinearity, the curious evolution of optical vortex beams characterized by different topological charges (TCs) is simulated numerically and presented their evolution profiles. We find that new vortices will be induced during propagation, and the behavior of vortices, as affected by the TC and the number of beads of the incident beam, as well as its size, is also discussed. Common rules associated with the initial conditions coming from various incident beams are developed to determine the number of induced vortices and the corresponding rotation direction. Attributed to the nonlinearity, during propagation we see the beams slowly expand to induce new vortices, which commonly appear in oppositely charged pairs, while the net topological charge of the vortex is conserved. Our results not only deepen the understanding of optical vortices, but also widen their potential applications.     

Optimal input design for hydrodynamic derivatives estimation of nonlinear dynamic model of AUV

Input design has a dominant role in developing the dynamic model of an autonomous underwater vehicle (AUV) through system identification. Optimal input design is the process of generating informative inputs that can be used to provide a good-quality dynamic model of AUV. In this paper, amplitude-modulated pseudo-random binary signal (APRBS) inputs are optimally designed in order to estimate the hydrodynamic derivatives of an AUV’s nonlinear dynamic model. The input controls are designed so as to minimize uncertainty in estimating hydrodynamic derivatives. The employed approach can design multiple inputs and apply constraints on an AUV system’s inputs and outputs. The genetic algorithm is utilized to solve the constraint optimization problem. The presented algorithm is used for designing the input signals of Hydrolab300 AUV, and the estimation obtained by these inputs is compared with that of zigzag maneuver. According to the results, the designed APRBS inputs improve the uncertainties that exist in estimating hydrodynamic derivatives better than zigzag inputs.     

Modeling of the mode dynamics generated by Madison Symmetric Torus machine utilizing a modified sine-Gordon equation

In this paper, a new dynamic model is presented for the experimental data generated by the Madison Symmetric Torus (MST) machine. The model is based on a modified sine-Gordon (SG) dynamic equation. The modified sine-Gordon equation model effectively captures the behavior of the slinky mode in reversed-field pinch experiments. In addition, this paper demonstrates how the derived model accurately describes the behavior of the localized magnetohydrodynamic mode (slinky mode) that appears in reversed-field pinch toroidal magnetic confinement systems. The modified SG equation model is solved analytically by using the perturbation method. The resulting model is fit to match a variety of experimental results in the MST reversed-field pinch experiment. The efficacy of the newly developed model in effectively representing the slinky mode is verified by comparing obtained analytical solution to experimentally measured data.     

Effects of multiple delays on dynamics of a five-neuron network model

A five-neuron network model with multiple delays is proposed. This paper presents the combined effect of different delays on the dynamics of the proposed network. Pitchfork bifurcation is discussed in detail with the variation of the value of coupled weight or attenuation rate of internal neurons. By analyzing the corresponding characteristic equation, some stable criteria on delay-dependence and delay-independence are derived including multiple delays and coupled weights and the periodic oscillation arises bifurcated from the trivial equilibrium after the network loses its stability. Stable regions on delay-dependence are displayed in the two delayed parameter plane. It is shown that multiple delays can produce stability switching between resting state and periodic activity. Finally, theoretical results are justified by providing two illustrative examples.     

Modules over cluster-tilted algebras that do not lie on local slices

We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number of (isoclasses of) these modules.     

Efficient synthesis of 3,4-dihydropyrano[3,2-c]chromenes catalyzed by Ni(II)-functionalized Li<Superscript>+</Superscript>-Montmorillonite in a one-pot fashion under solvent-free conditions

A family of 3,4-dihydropyrano[3,2-c]chromenes were synthesized from 4-hydroxycoumarin and malononitrile via a one-pot reaction under solvent-free conditions at 100 °C catalyzed by Ni@Imine-Li⁺-MMT. This methodology tolerates most of the substrates and has the merits of lower loading of the catalyst, absence of solvents, excellent yields and reusability of the catalyst. A reasonable mechanism is also proposed. This catalytic system can be reused for at least five times with a negligible loss of activity. The prepared catalyst was characterized by using FTIR, TGA, SEM, TEM, uv-DRS, EDX and XRD.     

Evolving groups

The class of evolving groups is defined and investigated, as well as their connections to examples in the field of Galois cohomology. Evolving groups are proved to be Sylow Tower groups in a rather strong sense. In addition, evolving groups are characterized as semidirect products of two nilpotent groups of coprime orders where the action of one on the other is via automorphisms that map each subgroup to a conjugate.     

Rapid Learning-Based and Geologically Consistent History Matching

Various types of data become available at different stages of a reservoir’s life. The production data are integrated into the flow simulation models through a process referred to as history matching. The history-matching process is iterative, and it usually involves a large number of simulation runs. Hence, this process requires significant computational time. In most history-matching methods, the initial geological assumptions in the reservoir model are destroyed or significantly altered in the process. Furthermore, they do not account for the information obtained during the previous trials, and lack learning from the previous failures. In this paper, we introduce a new methodology that maintains the geological realism. The candidate realizations are selected through a learning-based history-matching (LHM) algorithm by which all the previously successful patterns are preserved and used to assist the construction of the next realizations. The various pieces of matching regions are assembled together to make a pool of the successful candidates. Such regions are then utilized for making an auxiliary dataset in a multiscale framework by which the next model is generated. To prevent from trapping in local minima, ideas from the genetic algorithm is adapted. The LHM algorithm can be applied to both categorical and continuous distributions. The LHM provides a conditional map by which the new production data are immediately incorporated into the existing reservoir models. We apply the LHM algorithm to various 2D and 3D examples with very complex binary and continuous properties. The algorithm is shown to produce history-matched models with significantly smaller CPU times.     

Infinitely many reducts of homogeneous structures

It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts.