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Physical understanding of how the interplay between symmetries and nonlinear effects can control the scaling and multiscaling properties in a coupled driven system, such as magnetohydrodynamic turbulence or turbulent binary fluid mixtures, remains elusive. To address this generic issue, we construct a conceptual nonlinear hydrodynamic model, parametrized jointly by the nonlinear coefficients, and the spatial scaling of the variances of the advecting stochastic velocity and the stochastic additive driving force, respectively. By using a perturbative one-loop dynamic renormalization group method, we calculate the multiscaling exponents of the suitably defined equal-time structure functions of the dynamical variable. [https://www.selleckchem.com/products/ro5126766-ch5126766.html find more] We show that depending upon the control parameters the model can display a variety of universal scaling behaviors ranging from simple scaling to multiscaling.A colloidal particle is often termed "Janus" when some portion of its surface is coated by a second material which has distinct properties from the native particle. The anisotropy of Janus particles enables unique behavior at interfaces. However, rigorous methodologies to predict Janus particle dynamics at interfaces are required to implement these particles in complex fluid applications. Previous work studying Janus particle dynamics does not consider van der Waals interactions and realistic, nonuniform coating morphology. Here we develop semianalytic equations to accurately calculate the potential landscape, including van der Waals interactions, of a Janus particle with nonuniform coating thickness above a solid boundary. The effects of both nonuniform coating thickness and van der Waals interactions significantly influence the potential landscape of the particle, particularly in high ionic strength solutions, where the particle samples positions very close to the solid boundary. The equations developed herein facilitate more simple, accurate, and less computationally expensive characterization of conservative interactions experienced by a confined Janus particle than previous methods.The Kuramoto model serves as an illustrative paradigm for studying the synchronization transitions and collective behaviors in large ensembles of coupled dynamical units. In this paper, we present a general framework for analytically capturing the stability and bifurcation of the collective dynamics in oscillator populations by extending the global coupling to depend on an arbitrary function of the Kuramoto order parameter. In this generalized Kuramoto model with rotation and reflection symmetry, we show that all steady states characterizing the long-term macroscopic dynamics can be expressed in a universal profile given by the frequency-dependent version of the Ott-Antonsen reduction, and the introduced empirical stability criterion for each steady state degenerates to a remarkably simple expression described by the self-consistent equation [Iatsenko et al., Phys. Rev. Lett. 110, 064101 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.064101]. Here, we provide a detailed description of the spectrum structure in the complex plane by performing a rigorous stability analysis of various steady states in the reduced system. More importantly, we uncover that the empirical stability criterion for each steady state involved in the system is completely equivalent to its linear stability condition that is determined by the nontrivial eigenvalues (discrete spectrum) of the linearization. Our study provides a new and widely applicable approach for exploring the stability properties of collective synchronization, which we believe improves the understanding of the underlying mechanisms of phase transitions and bifurcations in coupled dynamical networks.The emergent photoactive materials obtained through photochemistry make it possible to directly convert photon energy to mechanical work. There has been much recent work in developing appropriate materials, and a promising system is semicrystalline polymers of the photoactive molecule azobenzene. We develop a phase field model with two order parameters for the crystal-melt transition and the trans-cis photoisomerization to understand such materials, and the model describes the rich phenomenology. We find that the photoreaction rate depends sensitively on temperature At temperatures below the crystal-melt transition temperature, photoreaction is collective, requires a critical light intensity, and shows an abrupt first-order phase transition manifesting nucleation and growth; at temperatures above the transition temperature, photoreaction is independent and follows first-order kinetics. Further, the phase transition depends significantly on the exact forms of spontaneous strain during the crystal-melt and trans-cis transitions. A nonmonotonic change of photopersistent cis ratio with increasing temperature is observed accompanied by a reentrant crystallization of trans below the melting temperature. A pseudo phase diagram is subsequently presented with varying temperature and light intensity along with the resulting actuation strain. These insights can assist the further development of these materials.In this work we have used lattice Monte Carlo to determine the orientational order of a system of biaxial particles confined between two walls inducing perfect order and subjected to an electric field perpendicular to the walls. The particles are set to interact with their nearest neighbors through a biaxial version of the Lebwohl-Lasher potential. A particular set of values for the molecular reduced polarizabilities defining the potential used was considered; the Metropolis sampling algorithm was used in the Monte Carlo simulations. The relevant order parameters were determined in the middle plane of the sample and for some cases across the whole thickness of the sample. We have determined the temperature-electric field phase diagram for this system and found, as expected, five different system configurations corresponding to three different mesophases. At low temperatures and low fields the system finds itself in an undistorted biaxial phase. On increasing the field at low temperatures, a Freedericksz transition takes place and the secondary directors reorient towards the field while the primary director stays undistorted and parallel to the walls.