Cyclic synchronous patterns within paired discontinuous routes.

Several of these heuristics were tested in this work for a set of molecular electronic Hamiltonians. On average, grouping qubit-wise commuting terms reduced the number of operators to measure three times less compared to the total number of terms in the considered Hamiltonians.In Paper I [O. Coquand and M. Sperl, J. Chem. Phys. 152, 124112 (2020)], we derived analytical expressions for the structure factor of the square-shoulder potential in a perturbative way around the high- and low-temperature regimes. Here, various physical properties of these solutions are derived. In particular, we investigate the large wave number sector and relate it to the contact values of the pair-correlation function. Then, the thermoelastic properties of the square-shoulder fluids are discussed.Multisite phosphorylation plays an important role in regulating switch-like protein activity and has been used widely in mathematical models. Tegatrabetan supplier With the development of new experimental techniques and more molecular data, molecular phosphorylation processes emerge in many systems with increasing complexity and sizes. These developments call for simple yet valid stochastic models to describe various multisite phosphorylation processes, especially in large and complex biochemical networks. To reduce model complexity, this work aims at simplifying the multisite phosphorylation mechanism by a stochastic Hill function model. Furthermore, this work optimizes regions of parameter space to match simulation results from the stochastic Hill function with the distributive multisite phosphorylation process. While traditional parameter optimization methods have been focusing on finding the best parameter vector, in most circumstances, modelers would like to find a set of parameter vectors that generate similar system dynamics and results. This paper proposes a general α-β-γ rule to return an acceptable parameter region of the stochastic Hill function based on a quasi-Newton stochastic optimization algorithm. Different objective functions are investigated characterizing different features of the simulation-based empirical data, among which the approximate maximum log-likelihood method is recommended for general applications. Numerical results demonstrate that with an appropriate parameter vector value, the stochastic Hill function model depicts the multisite phosphorylation process well except the initial (transient) period.Many measurements have indicated that thin polymer films in their glass state exhibit a mobile interfacial layer that grows in thickness upon heating, while some measurements indicate the opposite trend. Moreover, simulations and limited measurements on glass-forming liquids at temperatures above the glass transition temperature Tg exhibit a growing interfacial mobility scale ξ upon cooling. To better understand these seemingly contradictory trends, we perform molecular dynamics simulations over a temperature regime for which our simulated polymer film enters a non-equilibrium glassy state and find that the relaxation time τα within the film interior, relative to the polymer-air interfacial layer, exhibits a maximum near the computational Tg. Correspondingly, we also observe that the interfacial mobility length scale exhibits a maximum near Tg, explaining the apparent reversal in the temperature dependence of this scale between the glass and liquid states. We show that the non-monotonic variation of ξ and the relative interfacial mobility to the film interior arise qualitatively from a non-monotonic variation of the gradient of the effective activation free energy of the film; we then obtain a quantitative description of this phenomenon by introducing a phenomenological model that describes the relaxation time layer-by-layer in the film for a temperature range both above and below Tg of the film as a whole. This analysis reveals that the non-monotonic trend in the relative interfacial mobility and ξ both arise primarily from the distinctive temperature dependence of relaxation in the interfacial layer, which apparently remains in local equilibrium over the whole temperature range investigated.The properties of molecules and materials containing light nuclei are affected by their quantum mechanical nature. Accurate modeling of these quantum nuclear effects requires computationally demanding path integral techniques. Considerable success has been achieved in reducing the cost of such simulations by using generalized Langevin dynamics to induce frequency-dependent fluctuations. Path integral generalized Langevin equation methods, however, have this far been limited to the study of static, thermodynamic properties due to the large perturbation to the system's dynamics induced by the aggressive thermostatting. Here, we introduce a post-processing scheme, based on analytical estimates of the dynamical perturbation induced by the generalized Langevin dynamics, which makes it possible to recover meaningful time correlation properties from a thermostatted trajectory. We show that this approach yields spectroscopic observables for model and realistic systems that have an accuracy comparable to much more demanding approximate quantum dynamics techniques based on full path integral simulations.In this work, we investigate the Fe3O4 (001) surface/water interface by combining several theoretical approaches, ranging from a hybrid functional method (HSE06) to density-functional tight-binding (DFTB) to molecular mechanics (MM). First, we assess the accuracy of the DFTB method to correctly reproduce HSE06 results on structural details and energetics and available experimental data for adsorption of isolated water, dimers, and trimers up to a water monolayer. Second, we build two possible configurations of a second and a third overlayer and perform molecular dynamics simulations with DFTB, monitoring the water orientation, the H-bond network, and the ordered water structure formation. To make our models more realistic, we then build a 12 nm-thick water multilayer on top of the Fe3O4 (001) surface slab model, which we investigate through MM-molecular dynamics (MD). The water layer structuring, revealed by the analysis of the atomic positions from a long MM-MD run for this large MM model, extends up to about 6-7 Å and nicely compares with that observed for a water trilayer model.Tegatrabetan supplier