Wave-Packet Surface Propagation for Light-Induced Molecular Dissociation

Recent advances in laser technology have enabled tremendous progress in photochemistry, at the heart of which is the breaking and formation of chemical bonds. Such progress has been greatly facilitated by the development of accurate quantum-mechanical simulation method, which, however, does not necessarily accompany clear dynamical scenarios and is rather often a black box, other than being computationally heavy. Here, we develop a wave-packet surface propagation (WASP) approach to describe the molecular bond-breaking dynamics from a hybrid quantum-classical perspective. Via the introduction of quantum elements including state transitions and phase accumulations to the Newtonian propagation of the nuclear wave-packet, the WASP approach naturally comes with intuitive physical scenarios and accuracies. It is carefully benchmarked with the H2+ molecule and is shown to be capable of precisely reproducing experimental observations. The WASP method is promising for the intuitive visualization of strong-field molecular dynamics and is straightforwardly extensible toward complex molecules.Comment: 24 pages, 4 figure

Numerical Analysis for a Fractional Differential Time-Delay Model of HIV Infection of CD4 +

We study a fractional differential model of HIV infection of CD4+ T-cell, in which the CD4+ T-cell proliferation plays an important role in HIV infection under antiretroviral therapy. An appropriate method is given to ensure that both the equilibria are asymptotically stable for τ≥0. We calculate the basic reproduction number R0, the IFE E0, two IPEs E1* and E2*, and so on, and judge the stability of the equilibrium. In addition, we describe the dynamic behaviors of the fractional HIV model by using the Adams-type predictor-corrector method algorithm. At last, we extend the model to incorporate the term which we consider the loss of virion and a bilinear term during attacking the target cells

Existence and Numerical Simulation of Solutions for Fractional Equations Involving Two Fractional Orders with Nonlocal Boundary Conditions

We study a boundary value problem for fractional equations involving two fractional orders. By means of a fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. In addition, we describe the dynamic behaviors of the fractional Langevin equation by using the G2 algorithm

Neuro-Adaptive Cooperative Tracking Rendezvous of Nonholonomic Mobile Robots

This brief proposes a neuro-adaptive method for the unsolved problem of cooperative tracking rendezvous of nonholonomic mobile robots (NMRs) subject to uncertain and unmodelled dynamics. A hierarchical cooperative control framework is proposed, which consists of a novel distributed estimator along with local neuro-adaptive tracking controllers. Rigorous stability analysis as well as simulation experiments illustrate the proposed method.</p