Short-time maximum entropy method analysis of molecular dynamics simulation: Unimolecular decomposition of formic acid

We performed spectral analysis by using the maximum entropy method instead of the traditional Fourier transform technique to investigate the short-time behavior in molecular systems, such as the energy transfer between vibrational modes and chemical reactions. This procedure was applied to direct ab initio molecular dynamics calculations for the decomposition of formic acid. More reactive trajectories of dehydrolation than those of decarboxylation were obtained for Z-formic acid, which was consistent with the prediction of previous theoretical and experimental studies. Short-time maximum entropy method analyses were performed for typical reactive and non-reactive trajectories. Spectrograms of a reactive trajectory were obtained; these clearly showed the reactant, transient, and product regions, especially for the dehydrolation path.     

Lagrangian motion of fluid particles in gravity–capillary standing waves

A third-order analytical solution for the gravity–capillary standing wave is derived in Lagrangian coordinates through the Lindstedt–Poincare perturbation method. By numerical computation, the dynamical properties of nonlinear standing waves with surface tension in finite water depth, including particle trajectory and surface profile are investigated. We find that the presence of surface tension leads to a change of the crest form. Moreover, we also find that the particle trajectories near the surface oscillate back and forth along the arcs which will change from concave to convex as the inverse Bond number increases. There is no mass transport of the particles in a wave period.     

Stereodynamics of the reactions Ne+H2+/Ne+D2+/Ne+T2

The vector correlations between products and reagents for the reactions Ne+H + 2 , Ne+D + 2 , and Ne+T + 2 are calculated by means of the quasi-classical trajectory method on a new potential energy surface constructed by Lü et al. [J. Chem. Phys. 2010 132, 014303]. The polarization-dependent differential cross-sections (2π/σ)(dσ 00 /dω t ), (2π/σ)(dσ 20 /dω t ), (2π/σ)(dσ 22+ /dω t ), and (2π/σ)(dσ 21 /dω t ), and the distributions of P (θ r ), P (φ r ), and P (θ r ,φ r ) are calculated. The isotopic effect, which is associated with the difference in mass factor among the three reactions, is revealed.     

Stereodynamics of the reactions Ne+H₂⁺/Ne+D₂⁺/Ne+T₂

The vector correlations between products and reagents for the reactions Ne+H + 2 , Ne+D + 2 , and Ne+T + 2 are calculated by means of the quasi-classical trajectory method on a new potential energy surface constructed by Lü et al. [J. Chem. Phys. 2010 132, 014303]. The polarization-dependent differential cross-sections (2π/σ)(dσ 00 /dω t ), (2π/σ)(dσ 20 /dω t ), (2π/σ)(dσ 22+ /dω t ), and (2π/σ)(dσ 21 /dω t ), and the distributions of P (θ r ), P (φ r ), and P (θ r ,φ r ) are calculated. The isotopic effect, which is associated with the difference in mass factor among the three reactions, is revealed.     

Collision energy effect on the H′ + BrH (ν = 0, j = 0) → H′Br + H reaction: A quasi-classical trajectory study

Theoretical studies on the dynamics of the exchange reaction H′ + BrH (ν = 0, j = 0) → H′Br + H are performed on potential energy surface (PES) (Kurosaki et al., private communication) for the ground state using the quasi-classical trajectory method. The cross sections, computed at the collision energies (E_c) of 0.5-2.0 eV, are in good agreement with the earlier quantum wave packet results. The rotational, vibrational, and translational fractions in the total energy and the vibrational distribution for the product molecule are calculated at the same collision-energy range. The results support the repulsive character of the PES. In the considered E_c range, it has little chance to occur in an indirect reaction. The alignment and orientation of the product H′Br are investigated in detail with stereodynamics. The results show that E_c can effect on both the alignment and the orientation of product.     

Removal of malaria-infected red blood cells using magnetic cell separators: A computational study

High gradient magnetic field separators have been widely used in a variety of biological applications. Recently, the use of magnetic separators to remove malaria-infected red blood cells (pRBCs) from blood circulation in patients with severe malaria has been proposed in a dialysis-like treatment. The capture efficiency of this process depends on many interrelated design variables and constraints such as magnetic pole array pitch, chamber height, and flow rate. In this paper, we model the malaria-infected RBCs (pRBCs) as paramagnetic particles suspended in a Newtonian fluid. Trajectories of the infected cells are numerically calculated inside a micro-channel exposed to a periodic magnetic field gradient. First-order stiff ordinary differential equations (ODEs) governing the trajectory of particles under periodic magnetic fields due to an array of wires are solved numerically using the 1st to 5th order adaptive step Runge-Kutta solver. The numerical experiments show that in order to achieve a capture efficiency of 99% for the pRBCs it is required to have a longer length than 80 mm; this implies that in principle, using optimization techniques the length could be adjusted, i.e., shortened to achieve 99% capture efficiency of the pRBCs.     

Multivalued Exponentiation Analysis

We continue with the exponentiation analysis of multivalued maps defined on Banach spaces. In Part I of this work we have explored the Maclaurin exponentiation technique which is based on the use of a suitable power series. Now we focus the attention on the so-called recursive exponentiation method. Recursive exponentials are specially useful when it comes to study the reachable set associated to a differential inclusion of the form . The definition of the recursive exponential of uses as ingredient the set of trajectories associated to the discrete time system . Although we are taking inspiration from a recent paper by Alvarez et al. [1] on the relation between continuous and discrete time evolution systems, our analysis and results go far beyond the particular context of convex processes considered by these authors.     

Study of weighted Monte Carlo algorithms with branching

Various weighted algorithms for numerical statistical simulation are formulated and studied. The trajectory of an algorithm branches when the current weighting factor exceeds unity. As a result, the weight of an individual branch does not exceed unity and the variance of the estimate for the computed functional is finite. The unbiasedness and finiteness of the variance of estimates are analyzed using the recurrence “partial“ averaging method formulated in this study. The estimation of the particle reproduction factor and solutions to the Helmholtz equation are considered as applications. The comparative complexity of the algorithms is examined using a test problem. The variances of weighted algorithms with branching as applied to integral equations with power nonlinearity are analyzed.     

Dynamic optimal strategy for monitoring disease recurrence

Surveillance to detect cancer recurrence is an important part of care for cancer survivors.In this paper we discuss the design of optimal strategies for early detection of disease recurrence based on each patient’s distinct biomarker trajectory and periodically updated risk estimated in the setting of a prospective cohort study.We adopt a latent class joint model which considers a longitudinal biomarker process and an event process jointly,to address heterogeneity of patients and disease,to discover distinct biomarker trajectory patterns,to classify patients into different risk groups,and to predict the risk of disease recurrence.The model is used to develop a monitoring strategy that dynamically modifies the monitoring intervals according to patients’ current risk derived from periodically updated biomarker measurements and other indicators of disease spread.The optimal biomarker assessment time is derived using a utility function.We develop an algorithm to apply the proposed strategy to monitoring of new patients after initial treatment.We illustrate the models and the derivation of the optimal strategy using simulated data from monitoring prostate cancer recurrence over a 5-year period.     

转动激发对O+HBr→OH+Br反应的立体动力学性质的准经典轨线理论研究

基于Peterson得到的ab initio势能面,运用准经典轨线的方法研究了转动激发对 O+HBr→OH +Br反应动力学的矢量性质的影响.讨论了当碰撞能为0.3~eV时不同转动量子数情况下的极化微分散射截面以及描述k-j′两矢量相关和k-k′-j′三矢量相关的分布函数p(θ_r)和p(φ_r). 计算结果表明: 随着转动量子数的增加,产物的转动极化减弱, 而且产物的前向散射占主导地位.