At the transition point, the event-size distribution of the avalanches is found to be a power law w_τ(Δn)∼Δn^-τ, with the drop-off exponent τ=(sqrt[17]+1)/2≃2.56. This value is an exact result of the self-consistent model. The edge behavior bears signatures enabling to associate it with the dynamics of a self-organized critical (SOC) state. At the same time the critical exponents, pertaining to this state, are found to be inconsistent with classic models of avalanche transport based on sand piles and their generalizations, suggesting that the coupled avalanche-jet zonal flow system operates on different organizing principles. The results obtained have been validated in a numerical simulation of the plasma staircase using flux-driven gyrokinetic code for L-mode Tore-Supra plasma.We implement parallel versions of the generalized atmospheric Rosenbluth methods and Wang-Landau algorithms for stars and for acyclic uniform branched networks in the square lattice. These are models of monodispersed branched polymers, and we estimate the star vertex exponents σ_f for f stars, and the entropic exponent γ_G for networks with comb and brush connectivity in two dimensions. Our results verify the predicted (but not rigorously proven) exact values of the vertex exponents and we test the scaling relation [B.  https://www.selleckchem.com/products/alkbh5-inhibitor-2.html  Duplantier, J. Stat. Phys. 54, 581 (1989)JSTPBS0022-471510.1007/BF01019770]γ_G-1=[under ∑]f≥1m_fσ_ffor several acyclic branched networks in two dimensions.This paper presents a detailed description of a molecular velocity distribution-based mesoscopic kinetic approach that enables a better understanding of various nonequilibrium hydrodynamic and thermodynamic effects in shock waves, contact discontinuities, and rarefaction waves. This builds on the mesoscopic kinetic approach in a previous investigation into regular reflection shocks by further addressing the mesoscopic physical meaning of kinetic moments from the view of kinetics and the implications of the magnitude and sign of nonequilibrium kinetic moments. To deepen understanding of nonequilibrium effects, this work focuses on the one-dimensional unsteady shock tube problem, which contains the typical and essential features of the discontinuous flows, and has no interference of two-dimensional flow direction. The approach uses a lattice Boltzmann method to solve the flow field, and describes nonequilibrium effects through the nonequilibrium kinetic moments of molecular velocity distribution functions. The mechanism of nonequilibrium effect in discontinuous flows is further probed. This work develops the mesoscopic kinetic approach and clarifies the mesoscopic physics of shock waves, contact discontinuities, and rarefaction waves.Increasingly important photomechanical materials produce stress and mechanical work when illuminated. We propose experimentally accessible performance metrics for photostress and photowork, enabling comparison of materials performance. We relate these metrics to material properties, providing a framework for the design and optimization of photomechanical materials.Destruction of the quantum mechanical features of matter by decoherence restricts the applicability of quantum technologies. The limited information of the quantum features (such as coherence) in the basis-dependent observations urges the use of a basis-independent quantity for a better understanding. In this context, the state purity of a quantum system (composed of quantized pigments immersed in a noisy protein environment) is studied with a numerically exact hierarchical equations of motion approach over the wide range of the parameter domain (with the main focus on the nonzero-energy gradient). It is noted that the state purity does not necessarily reflect any significant information about the persistence of quantum features (in the dissipative environment), even when the quantum coherence survives at the steady state in both the localized and the eigenstate basis.We measure the reflection and transmission of shear waves by slabs of random dispersions of hard, dense spheres in a viscoelastic matrix. By modeling the slab as a Fabry-Pérot interferometer, we determine the effective wave number of coherent shear waves in this scattering medium and its effective mass density. We evidence the effect of the resonant rigid-body translation and rotation of the spheres on the propagation. We validate a vectorial model of multiple scattering for volume fractions of spheres up to 10%, revealing the signature of two modes of propagation.A consistent evaporation model is developed for the conservative Allen-Cahn-based phase-field lattice Boltzmann method that uses an appropriate source term to recover the advection-diffusion equation for the specific humidity. To evaluate the accuracy of the proposed scheme, simulations are conducted of a steady-state one-dimensional Stefan flow for a flat interface and a three-dimensional evaporating sessile droplet on a flat substrate for a curved interface. It is confirmed that the results for the evaporative mass flux of the Stefan flow agree well with those obtained from the analytical solution within a specific humidity range of 0.8 or less at the liquid-gas interface. For the sessile droplet case, the results for the dependence of the contact angle on the evaporative mass flux and its profile show good agreement with those obtained from the model of Hu and Larson [J. Phys. Chem. B 106, 1334 (2002)JPCBFK1520-610610.1021/jp0118322].Many biological processes including important intracellular processes are governed by biochemical reaction networks. Usually, these reaction systems operate far from thermodynamic equilibrium, implying free-energy dissipation. On the other hand, single reaction events happen often in a memory manner, leading to non-Markovian kinetics. A question then arises how do we calculate free-energy dissipation (defined as the entropy production rate) in this physically real case? We derive an analytical formula for calculating the energy consumption of a general reaction system with molecular memory characterized by nonexponential waiting-time distributions. It shows that this dissipation is composed of two parts one from broken detailed balance of an equivalent Markovian system with the same topology and substrates, and the other from the direction-time dependence of waiting-time distributions. But, if the system is in a detailed balance and the waiting-time distribution is direction-time independent, there is no energy dissipation even in the non-Markovian case.