Plougkristiansen2655

Moreover, the set of bounded solutions is divided into countless subsets throughout all length scales in the complex plane. Each individual subset contains only one state of synchronization and is enclosed within fractal boundaries by c values leading to divergence.The essence of logical stochastic resonance is the dynamic manipulation of potential wells. The effect of time delay on the depth of potential wells and the width of a bistable region can be inferred by logic operations in the bistable system with time delay. In a time-delayed synthetic gene network, time delay in the synthesis process can increase the depth of the potential wells, while that in the degradation process, it can reduce the depth of the potential wells, which will result in a decrease in the width of the bistable region (the reason for time delay to induce logic operations without external driving force) and the instability of the system (oscillation). These two opposite effects imply stretching and folding, leading to complex dynamical behaviors of the system, including period, chaos, bubble, chaotic bubble, forward and reverse period doubling bifurcation, intermittency, and coexisting attractors.An understanding of the underlying mechanism of side-branching is paramount in controlling and/or therapeutically treating mammalian organs, such as lungs, kidneys, and glands. Motivated by an activator-inhibitor-substrate approach that is conjectured to dominate the initiation of side-branching in a pulmonary vascular pattern, I demonstrate a distinct transverse front instability in which new fingers grow out of an oscillatory breakup dynamics at the front line without any typical length scale. These two features are attributed to unstable peak solutions in 1D that subcritically emanate from Turing bifurcation and that exhibit repulsive interactions. The results are based on a bifurcation analysis and numerical simulations and provide a potential strategy toward also developing a framework of side-branching for other biological systems, such as plant roots and cellular protrusions.Network performance of neurons plays a vital role in determining the behavior of many physiological systems. In this paper, we discuss the wave propagation phenomenon in a network of neurons considering obstacles in the network. Numerous studies have shown the disastrous effects caused by the heterogeneity induced by the obstacles, but these studies have been mainly discussing the orientation effects. Hence, we are interested in investigating the effects of both the size and orientation of the obstacles in the wave re-entry and spiral wave formation in the network. For this analysis, we have considered two types of neuron models and a pancreatic beta cell model. In the first neuron model, we use the well-known differential equation-based neuron models, and in the second type, we used the hybrid neuron models with the resetting phenomenon. We have shown that the size of the obstacle decides the spiral wave formation in the network and horizontally placed obstacles will have a lesser impact on the wave re-entry than the vertically placed obstacles.The averaging principle for Caputo fractional stochastic differential equations has recently attracted much attention. In this paper, we investigate the averaging principle for a type of Caputo fractional stochastic differential equation. Comparing with the existing literature, we shall use different estimate methods to investigate the averaging principle, which will enrich the development of theory for Caputo fractional stochastic differential equations.Interactions in enzymes between catalytic and neighboring amino acids and how these interactions facilitate catalysis are examined. selleck products In examples from both natural and designed enzymes, it is shown that increases in catalytic rates may be achieved through elongation of the buffer range of the catalytic residues; such perturbations in the protonation equilibria are, in turn, achieved through enhanced coupling of the protonation equilibria of the active ionizable residues with those of other ionizable residues. The strongest coupling between protonation states for a pair of residues that deprotonate to form an anion (or a pair that accept a proton to form a cation) is achieved when the difference in the intrinsic pKas of the two residues is approximately within 1 pH unit. Thus, catalytic aspartates and glutamates are often coupled to nearby acidic residues. For an anion-forming residue coupled to a cation-forming residue, the elongated buffer range is achieved when the intrinsic pKa of the anion-forming residue is higher than the intrinsic pKa of the (conjugate acid of the) cation-forming residue. Therefore, the high pKa, anion-forming residues tyrosine and cysteine make good coupling partners for catalytic lysine residues. For the anion-cation pairs, the optimum difference in intrinsic pKas is a function of the energy of interaction between the residues. For the energy of interaction ε expressed in units of (ln 10)RT, the optimum difference in intrinsic pKas is within ∼1 pH unit of ε.In this work, a series of analyses are performed on ab initio molecular dynamics simulations of a hydrated excess proton in water to quantify the relative occurrence of concerted hopping events and "rattling" events and thus to further elucidate the hopping mechanism of proton transport in water. Contrary to results reported in certain earlier papers, the new analysis finds that concerted hopping events do occur in all simulations but that the majority of events are the product of proton rattling, where the excess proton will rattle between two or more waters. The results are consistent with the proposed "special-pair dance" model of the hydrated excess proton wherein the acceptor water molecule for the proton transfer will quickly change (resonate between three equivalent special pairs) until a decisive proton hop occurs. To remove the misleading effect of simple rattling, a filter was applied to the trajectory such that hopping events that were followed by back hops to the original water are not counted. A steep reduction in the number of multiple hopping events is found when the filter is applied, suggesting that many multiple hopping events that occur in the unfiltered trajectory are largely the product of rattling, contrary to prior suggestions. Comparing the continuous correlation function of the filtered and unfiltered trajectories, we find agreement with experimental values for the proton hopping time and Eigen-Zundel interconversion time, respectively.The non-uniform growth of microstructures in dendritic form inside the battery during prolonged charge-discharge cycles causes short-circuit as well as capacity fade. We develop a feedback control framework for the real-time minimization of such microstructures. Due to the accelerating nature of the branched evolution, we focus on the early stages of growth, identify the critical ramified peaks, and compute the effective time for the dissipation of ions from the vicinity of those branching fingers. The control parameter is a function of the maximum interface curvature (i.e., minimum radius) where the rate of runaway is the highest. The minimization of the total charging time is performed for generating the most packed microstructures, which correlate closely with those of considerably higher charging periods, consisting of constant and uniform square waves. The developed framework could be utilized as a smart charging protocol for safe and sustainable operation of rechargeable batteries, where the branching of the microstructures could be correlated with the sudden variation in the current/voltage.This article presents the application of the reactive step molecular dynamics simulation method [M. Biedermann, D. Diddens, and A. Heuer, J. Chem. Theory Comput. 17, 1074 (2021)] toward two different atomistic, chemically reactive systems. During reactive steps, transitions from reactant to product molecules are modeled according to physically correct transition probabilities based on quantum chemical information about the reactions such as molecular reaction rates via instant exchange of the employed force field and a subsequent, short relaxation of the structure. In the first application, we study the follow-up reactions of singly reduced ethylene carbonate (EC) radicals in EC solution, first, via extensive ab initio molecular dynamics simulations and, second, with the reactive step algorithm. A direct comparison of both simulation methods shows excellent agreement. Then, we employ the reactive step algorithm to simulate the enolate formation of 2-methylcyclopropanone with the base lithium diisopropylamine. Thereby, we can demonstrate that the reactive step algorithm is also capable of capturing effects from kinetic vs thermodynamic control of chemical reactions during simulation.The vibrational subsystem analysis is a useful approach that allows for evaluating the spectrum of modes of a given system by integrating out the degrees of freedom accessible to the environment. The approach could be utilized for exploring the collective dynamics of a membrane protein (system) coupled to the lipid bilayer (environment). However, the application to membrane proteins is limited due to high computational costs of modeling a sufficiently large membrane environment unbiased by end effects, which drastically increases the size of the investigated system. We derived a recursive formula for calculating the reduced Hessian of a membrane protein embedded in a lipid bilayer by decomposing the membrane into concentric cylindrical domains with the protein located at the center. The approach allows for the design of a time- and memory-efficient algorithm and a mathematical understanding of the convergence of the reduced Hessian with respect to increasing membrane sizes. The application to the archaeal aspartate transporter GltPh illustrates its utility and efficiency in capturing the transporter's elevator-like movement during its transition between outward-facing and inward-facing states.In multi-configurational time-dependent Hartree (MCTDH) approaches, different multi-layered wavefunction representations can be used to represent the same physical wavefunction. Transformations between different equivalent representations of a physical wavefunction that alter the tree structure used in the multi-layer MCTDH wavefunction representation interchange the role of single-particle functions (SPFs) and single-hole functions (SHFs) in the MCTDH formalism. While the physical wavefunction is invariant under these transformations, this invariance does not hold for the standard multi-layer MCTDH equations of motion. Introducing transformed SPFs, which obey normalization conditions typically associated with SHFs, revised equations of motion are derived. These equations do not show the singularities resulting from the inverse single-particle density matrix and are invariant under tree transformations. Based on the revised equations of motion, a new integration scheme is introduced. The scheme combines the advantages of the constant mean-field approach of Beck and Meyer [Z. Phys. D 42, 113 (1997)] and the singularity-free integrator suggested by Lubich [Appl. Math. Res. Express 2015, 311]. Numerical calculations studying the spin boson model in high dimensionality confirm the favorable properties of the new integration scheme.