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Furthermore, the sound velocity of the ground-state and superfluidity state can be controlled effectively by tuning the periodic driving strength. Our results indicate that the periodic driving of Raman coupling provides a powerful tool to manipulate the ground-state phase transition and dynamical instability of spin-orbit-coupled BECs.We analyze collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when the active work is biased towards larger values, and is associated with alignment of particles’ orientations. A finite biasing field is needed to induce spontaneous symmetry breaking, even in large systems. Particle alignment is computed exactly for a system of two particles. For many-particle systems, we analyze the symmetry breaking by an optimal-control representation of the biased dynamics, and we propose a fluctuating hydrodynamic theory that captures the emergence of polar order in the biased state.The combined effects of external electric, magnetic, and Aharonov-Bohm (AB) flux fields on the two-dimensional hydrogen atom embedded in both Debye and quantum plasmas modeled by the more general exponential cosine Coulomb (MGECSC) potential are investigated using the general analytic approach, namely the homotopy analysis method (HAM). The analytical convergent solutions are obtained for the ground state as well as excited states at both weak and strong intensity of the external fields. The influence of the screening parameters on the quantum levels are exhaustively explored in the presence of three external fields. It is worth emphasizing that our analytical HAM results have 4-10 digits of accuracy in comparison with the numerical results. In the framework of the HAM method, there is no any small parameter different from the perturbation. Owing to this advantage, the convergent accurate solutions always can be obtained by the HAM approach even for the strong external fields. There is no limit to the value of the parameters or the strength of the external fields. It is also observed that the combined effects of the external fields play an important role on the interaction potential profile and the applied external magnetic field is the most dominant in the hydrogen atomic system. Also note that the combined effect of the fields is stronger than individual effects in both Debye and quantum plasmas. The findings obtained by the HAM-based approach in this study shed substantial light on the more complicated problems in plasmas for the atomic systems or molecular physics.The spreading dynamics of infectious diseases is determined by the interplay between geography and population mixing. There is homogeneous mixing at the local level and human mobility between distant populations. Here I model spatial location as a type and the population mixing by intra- and intertype mixing patterns. Using the theory of multitype branching process, I calculate the expected number of new infections as a function of time. In one dimension the analysis is reduced to the eigenvalue problem of a tridiagonal Teoplitz matrix. In d dimensions I take advantage of the graph cartesian product to construct the eigenvalues and eigenvectors from the eigenvalue problem in 1 one dimension. Using numerical simulations I uncover a transition from linear to multitype mixing exponential growth with increasing the population size. Given that most countries are characterized by a network of cities with more than 100 000 habitants, I conclude that the multitype mixing approximation should be the prevailing scenario.We present a model of contact process on Domany-Kinzel cellular automata with a geometrical disorder. In the 1D model, each site is connected to two nearest neighbors which are either on the left or the right. The system is always attracted to an absorbing state with algebraic decay of average density with a continuously varying complex exponent. The log-periodic oscillations are imposed over and above the usual power law and are clearly evident as p→1. This effect is purely due to an underlying topology because all sites have the same infection probability p and there is no disorder in the infection rate. An extension of this model to two and three dimensions leads to similar results. This may be a common feature in systems where quenched disorder leads to effective fragmentation of the lattice.The transport properties of the weakly nonlinear (WNL) two-dimensional (2D) quasilongitudinal dust lattice mode is studied in an experimentally realized highly viscous, strongly coupled, weakly ionized plasma [V. E. Fortov et al., Phys. ZSH-2208 solubility dmso Rev. Lett. 109, 055002 (2012)10.1103/PhysRevLett.109.055002]. The WNL dynamics is found to be described by a 2D dissipative-dispersive nonlinear partial differential equation. The analytical and computational (for gas discharge plasma parameters) results predict strong viscosity induced Shilnikov homoclinic chaos, which, in turn, can cause a phase transition.In this paper we have investigated through the numerical solution of the basic equation as well as through the dynamic model the influence of higher-order correction terms to the nonlinear amplification (absorption) and to the nonlinear refractive index on the self-frequency shift of Raman dissipative solitons. We have found a nonlinear dependence of the self-frequency shift of Raman dissipative solitons on the parameter describing intrapulse Raman scattering in the presence of the saturation of the nonlinear gain. With the increase of the absolute value of the saturation of the nonlinear gain, the maximum absolute value of the frequency shift decreases and its position moves to larger values of the parameter describing intrapulse Raman scattering. The increase in the value of the nonlinear gain leads to an increase in the maximum absolute value of the frequency shift, without changing its position. We have also observed the nonlinear dependence of the absolute value of the frequency shift on the parameter describing intrapulse Raman scattering in the presence of higher-order correction term to the nonlinear refractive index. The discovered nonlinear dependence of the self-frequency shift on the value of the saturation of the nonlinear gain as well as on the higher-order correction term to the nonlinear refractive index can be used for the better understanding and control of the spectral characteristics of Raman dissipative solitons. The dynamic model correctly describes all the features of the observed phenomena.