Cortezmckee3687

We study the transport phenomena of an inertial Brownian particle in a symmetric potential with periodicity, which is driven by an external time-periodic force and an external constant bias for both cases of the deterministic dynamics and the existence of friction coefficient fluctuations. For the deterministic case, it is shown that for suitable parameters, the existence of certain appropriate friction coefficients can enhance the transport of the particle, which may be interpreted as the negative friction coefficient; additionally, there coexist absolute, differential negative, and giant positive mobilities with increasing friction coefficients in the system. We analyze physical mechanisms hinted behind these findings via basins of attraction. For the existence of friction coefficient fluctuations, it is shown that the fluctuation can enhance or weaken, even eliminate these phenomena. We present the probability distribution of the particle's velocity to interpret these mobilities and the suitable parameters' regimes of these phenomena. In order to further understand the physical mechanism, we also study diffusions corresponding to these mobilities and find that for the small fluctuation, the negative friction appears, and there coexists absolute negative mobility, superdiffusion, and ballistic diffusion, whereas all of them vanish for the large fluctuation. Our findings may extensively exist in materials, including different defects, strains, the number of interfacial hydrogen bonds, the arrangements of ions, or graphite concentrations, which hints at the existence of different friction coefficients.The phenomenon of spontaneous symmetry breaking facilitates the onset of a plethora of nontrivial dynamical states/patterns in a wide variety of dynamical systems. Spontaneous symmetry breaking results in amplitude and phase variations in a coupled identical oscillator due to the breaking of the prevailing permutational/translational symmetry of the coupled system. Nevertheless, the role and the competing interaction of the low-pass filter and the mean-field density parameter on the symmetry breaking dynamical states are unclear and yet to be explored explicitly. The effect of low pass filtering along with the mean-field parameter is explored in conjugately coupled Stuart-Landau oscillators. The dynamical transitions are examined via bifurcation analysis. We show the emergence of a spontaneous symmetry breaking (asymmetric) oscillatory state, which coexists with a nontrivial amplitude death state. DNA Damage chemical Through the basin of attraction, the multi-stable nature of the spontaneous symmetry breaking state is examined, which reveals that the asymmetric distribution of the initial state favors the spontaneous symmetry breaking dynamics, while the symmetric distribution of initial states gives rise to the nontrivial amplitude death state. In addition, the trade-off between the cut-off frequency of the low-pass filter along with the mean-field density induces and enhances the symmetry breaking dynamical states. Global dynamical transitions are discussed as a function of various system parameters. Analytical stability curves corresponding to the nontrivial amplitude death and oscillation death states are deduced.We investigate and review the formation of two-dimensional dissipative rogue waves in cavity nonlinear optics with transverse effects. Two spatially extended systems are considered for this purpose the driven Kerr optical cavities subjected to optical injection and the broad-area surface-emitting lasers with a saturable absorber. We also consider a quasi-two-dimensional system (the two dimensions being space and time) of a fiber laser describing the complex cubic-quintic Ginzburg-Landau equation. We show that rogue waves are controllable by means of time-delayed feedback and optical injection. We show that without delayed feedback, transverse structures are stationary or oscillating. However, when the strength of the delayed feedback is increased, all the systems generate giant two-dimensional pulses that appear with low probability and suddenly appear and disappear. We characterize their formation by computing the probability distribution, which shows a long tail. Besides, we have computed the significant wave height, which measures the mean wave height of the highest third of the waves. We show that for all systems, the distribution tails expand beyond two times the significant wave height. Furthermore, we also show that optical injection may suppress the rogue wave formation in a semiconductor laser with a saturable absorber.We study a new type of attractor, the so-called reversible core, which is a mathematical image of mixed dynamics, in a strongly dissipative time-irreversible system of two adaptively coupled phase oscillators. The existence of mixed dynamics in this system was proved in our previous article [A. A. Emelianova and V. I. Nekorkin, Chaos 29, 111102 (2019)]. In this paper, we attempt to identify the dynamic mechanisms underlying the existence of mixed dynamics. We give the region of the existence of mixed dynamics on the parameter plane and demonstrate in what way, when a type of attractor changes, its main characteristics, such as its fractal dimension and the sum of Lyapunov exponents, transform. We demonstrate that when mixed dynamics appear in the system, the average frequencies of the oscillations in forward and reverse time begin to almost coincide, and its spectra gradually approach each other with an increase in the parameter responsible for the presence of mixed dynamics.Manganese-catalyzed regioselective C-H alkylation of indoles and benzo[h]quinoline with a variety of unactivated alkyl iodides is reported. Unlike other Mn-catalyzed C-H functionalization, this protocol does not require a Grignard reagent base and employs a simple and inexpensive MnBr2 as a catalyst. This method tolerates diverse functionalities, including fluoro, chloro, bromo, iodo, alkenyl, alkynyl, pyrrolyl, and carbazolyl groups. The alkylation proceeds through a single-electron transfer pathway comprising reversible C-H manganesation and involving an alkyl radical intermediate.