Direct ab initio dynamics calculations of thermal rate constants for the CH4 + O2 = CH3 + HO2 reaction

Thermal rate constants of the CH₄ + O₂ = CH₃ + HO₂ reaction were calculated from first principles using both the conventional transition state theory (TST) and canonical variational TST methods with correction from the explicit hindered rotation treatment. The CCSD(T)/aug-cc-pVTZ//BH&HLYP/aug-cc-pVDZ method was used to characterize the necessary potential energy surface along the minimum energy path. We found that the correction for hindered rotation treatment, as well as the re-crossing effects noticeably affect the rate constants of the title process. The calculated rate constants for both forward and reverse directions are expressed in the modified Arrhenius form as \(k_{\text{forward}}^{\text{CVT/HR}} = 2.157 \times 10^{ - 18} \times T^{2.412} \times \,\exp \,( - \frac{25812}{T})\) and \(k_{\text{reverse}}^{\text{CVT/HR}} = 1.375 \times 10^{ - 19} \times T^{2.183} \times \,{\kern 1pt} \exp \,\,(\frac{2032}{T})\) (cm³ molecule^?1 s^?1) for the temperature range of 300–2,500 K. Being in good agreement with literature data, the results provide solid basis information for the investigation of the entire alkane + O₂ = alkyl radical + HO₂ reaction class.     

Polynomial time algorithms to determine weakly reversible realizations of chemical reaction networks

Weak reversibility is a crucial structural property of chemical reaction networks (CRNs) with mass action kinetics, because it has major implications related to the existence, uniqueness and stability of equilibrium points and to the boundedness of solutions. In this paper, we present two new algorithms to find dynamically equivalent weakly reversible realizations of a given CRN. They are based on linear programming and thus have polynomial time-complexity. Hence, these algorithms can deal with large-scale biochemical reaction networks, too. Furthermore, one of the methods is able to deal with linearly conjugate networks, too.     

Rigid impacts of three-dimensional rocking structures

Studies of rocking motion aim to explain the remarkable earthquake resistance of rocking structures. State-of-the-art assessment methods are mostly based on planar models, despite ongoing efforts to understand the significance of three-dimensionality. Impacts are essential components of rocking motion. We present experimental measurements of free-rocking blocks on a rigid surface, focusing on extreme sensitivity of impacts to geometric imperfections, unpredictability, and the emergence of three-dimensional motion via spontaneous symmetry breaking. These results inspire the development of new impact models of three-dimensional facet and edge impacts of polyhedral objects. Our model is a natural generalization of existing planar models based on the seminal work of George W. Housner. Model parameters are estimated empirically for rectangular blocks. Finally, new perspectives in earthquake assessment of rocking structures are discussed.

     

A review of predator–prey systems with dormancy of predators

The predator–prey system has received much attention in the field of ecology and evolution. The interaction and competition between populations in nature can be described by the predator–prey system. Under large-amplitude fluctuations caused by harsh environmental conditions, the dormant progeny has been found as an effective strategy to prevent extinction. In this review paper, recent developments of dormancy in predator–prey systems are reviewed. The significant impacts of dormancy on the competition and evolution in predator–prey systems are then discussed through different models. The connections between dormancy in predator–prey systems and the game-theoretic Parrondo’s paradox are also discussed: the dormitive predator with inferior traits can outcompete the perennially active predator by switching between two losing strategies. Future outlook about the dormancy research in predator–prey systems is also discussed.

     

On a problem of Bourgain concerning the $$L_p$$ norms of exponential sums

For \(n \ge 1\) let

$$\begin{aligned} {\mathcal {A}}_n := \bigg \{ P: P(z) = \sum \limits _{j=1}^n{z^{k_j}}: 0 \le k_1 < k_2 < \cdots < k_n, k_j \in {\mathbb {Z}} \bigg \}, \end{aligned}$$

that is, \({\mathcal {A}}_n\) is the collection of all sums of \(n\) distinct monomials. These polynomials are also called Newman polynomials. Let

$$\begin{aligned} M_{p}(Q) := \left( \int _{0}^{1}{\left| Q(e^{i2\pi t}) \right| ^p\,dt} \right) ^{1/p}, \qquad p > 0. \end{aligned}$$

We define

$$\begin{aligned} S_{n,p} := \sup _{Q \in {\mathcal {A}}_n}{\frac{M_p(Q)}{\sqrt{n}}} \qquad \text{ and } \qquad S_p := \liminf _{n \rightarrow \infty }{S_{n,p}} \le \Sigma _p := \limsup _{n \rightarrow \infty }{S_{n,p}}. \end{aligned}$$

We show that

$$\begin{aligned} \Sigma _p \ge \Gamma (1+p/2)^{1/p}, \qquad p \in (0,2). \end{aligned}$$

The special case \(p=1\) recaptures a recent result of Aistleitner [1], the best known lower bound for \(\Sigma _1\).

     

Transparency enhancement for an active knee orthosis by a constraint-free mechanical design and a gait phase detection based predictive control

This paper proposes a novel mechanical design of a lower limb exoskeleton device which prevents the residual stresses due to arthro-kinematics movements of synovial joints and by the way allows effective compensation for dynamic disturbances in osteo-kinematic movements of the wearer. Here, the exoskeleton is only actuated at the knee joints to provide assistive torques, which are required to assist the anatomical joint motion and to increase the transparency of the device. Dynamic simulations of a virtual human equipped with this exoskeleton are used to quantify the disturbances induced by the device during locomotion and to show the benefit of passive mechanisms introduced in the mechanical attaches as well. The authors also demonstrated how the device’s transparency can be improved by providing the motor torques in order to compensate the inertial and gravitational effects. This can be done rely on the knowledge of the locomotion movement phases. A robust gait phase detection method was implemented on the experimental device in order to identify specific gait phases in real time. This method exploits the K-nearest neighbors algorithm to identify the k-closest trained vectors, coupling with a discrete time Markov chain to determine the phases shift probability during the gait cycle. This gait detection algorithm was tested with a percentage of success of more than 95% when the subjects walked with constant and variable stride lengths.     

Subcritical Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations

We show the existence of a subcritical Hopf bifurcation in thedelay-differential equation model of the so-called regenerative machine toolvibration. The calculation is based on the reduction of the infinite-dimensional problem to a two-dimensional center manifold. Due to the specialalgebraic structure of the delayed terms in the nonlinear part of the equation,the computation results in simple analytical formulas. Numerical simulationsgave excellent agreement with the results.     

Intramolecular 1,3-dipolar cycloadditions of norbornadiene-tethered nitrile oxides.

Efficient routes to the synthesis of norbornadiene-tethered nitrile oxides have been developed, and their intramolecular 1,3-dipolar cycloadditions were studied. The cycloadditions occurred in good yields for a variety of substrates and were found to be highly regio- and stereoselective, giving single regio- and stereoisomers in most cases.