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We show the equivalence between the Hamiltonian and non-Hamiltonian forms of a fourth-order nonlinear Schrödinger equation for a particular example of the physical system described by the nonlinear Klein-Gordon equation with cubic nonlinearity.We study the effect of a rapid quench to zero temperature in a model with competing interactions, evolving through conserved spin dynamics. In a certain regime of model parameters, we find that the model belongs to the broader class of kinetically constrained models, however, the dynamics is different from that of a glass. The system shows stretched exponential relaxation with the unusual feature that the relaxation time diverges as a power of the system size. selleck products Explicitly, we find that the spatial correlation function decays as exp(-2r/sqrt[L]) as a function of spatial separation r in a system with L sites in the steady state, while the temporal autocorrelation function follows exp[-(t/τ_L)^1/2], where t is the time and τ_L proportional to L. In the coarsening regime, after time t_w, there are two growing length scales, namely L(t_w)∼t_w^1/2 and R(t_w)∼t_w^1/4; the spatial correlation function decays as exp[-r/R(t_w)]. Interestingly, the stretched exponential form of the autocorrelation function of a single typical sample in the steady state differs markedly from that averaged over an ensemble of initial conditions resulting from different quenches; the latter shows a slow power-law decay at large times.A pore-network model is an upscaled representation of the pore space and fluid displacement, which is used to simulate two-phase flow through porous media. We use the results of pore-scale imaging experiments to calibrate and validate our simulations, and specifically to find the pore-scale distribution of wettability. We employ energy balance to estimate an average, thermodynamic, contact angle in the model, which is used as the initial estimate of contact angle. We then adjust the contact angle of each pore to match the observed fluid configurations in the experiment as a nonlinear inverse problem. The proposed algorithm is implemented on two sets of steady state micro-computed-tomography experiments for water-wet and mixed-wet Bentheimer sandstone. As a result of the optimization, the pore-by-pore error between the model and experiment is decreased to less than that observed between repeat experiments on the same rock sample. After calibration and matching, the model predictions for capillary pressure and relative permeability are in good agreement with the experiments. The proposed algorithm leads to a distribution of contact angle around the thermodynamic contact angle. We show that the contact angle is spatially correlated over around 4 pore lengths, while larger pores tend to be more oil-wet. Using randomly assigned distributions of contact angle in the model results in poor predictions of relative permeability and capillary pressure, particularly for the mixed-wet case.Modern large engineered network systems normally work in cooperation and incorporate dependencies between their components for purposes of efficiency and regulation. Such dependencies may become a major risk since they can cause small-scale failures to propagate throughout the system. Thus, the dependent nodes could be a natural target for malicious attacks that aim to exploit these vulnerabilities. Here we consider a type of targeted attack that is based on the dependencies between the networks. We study strategies of attacks that range from dependency-first to dependency-last, where a fraction 1-p of the nodes with dependency links, or nodes without dependency links, respectively, are initially attacked. We systematically analyze, both analytically and numerically, the percolation transition of partially interdependent networks, where a fraction q of the nodes in each network are dependent on nodes in the other network. We find that for a broad range of dependency strength q, the “dependency-first” attack strategy is actually less effective, in terms of lower critical percolation threshold p_c, compared with random attacks of the same size. In contrast, the “dependency-last” attack strategy is more effective, i.e., higher p_c, compared with a random attack. This effect is explained by exploring the dynamics of the cascading failures initiated by dependency-based attacks. We show that while “dependency-first” strategy increases the short-term impact of the initial attack, in the long term the cascade slows down compared with the case of random attacks and vice versa for “dependency-last.” Our results demonstrate that the effectiveness of attack strategies over a system of interdependent networks should be evaluated not only by the immediate impact but mainly by the accumulated damage during the process of cascading failures. This highlights the importance of understanding the dynamics of avalanches that may occur due to different scenarios of failures in order to design resilient critical infrastructures.We focus on the self-propelled motion of an oil droplet within an aqueous phase or an aqueous droplet within an oil phase, which originates from an interfacial chemical reaction of surfactant. The droplet motion has been explained by mathematical models, which require the assumption that the chemical reaction increases the interfacial tension. However, several experimental reports have demonstrated self-propelled motion with the chemical reaction decreasing the interfacial tension. Our motivation is to construct an improved mathematical model, which explains these experimental observations. In this process, we consider the concentrations of the reactant and product on the interface and of the reactant in the bulk. Our numerical calculations indicate that the droplet potentially moves in the cases of both an increase and a decrease in the interfacial tension. In addition, the reaction rate and size dependencies of the droplet speed observed in experiments were well reproduced using our model. These results indicate the potential of our model as a universal one for droplet motion.In chemical reaction networks, bistability can only occur far from equilibrium. It is associated with a first-order phase transition where the control parameter is the thermodynamic force. At the bistable point, the entropy production is known to be discontinuous with respect to the thermodynamic force. We show that the fluctuations of the entropy production have an exponential volume-dependence when the system is bistable. At the phase transition, the exponential prefactor is the height of the effective potential barrier between the two fixed-points. Our results obtained for Schlögl’s model can be extended to any chemical network.