Continuous configuration time-dependent self-consistent field method for polyatomic quantum dynamical problems

A new continuous configuration time-dependent self-consistent field method has been developed to study polyatomic dynamical problems by using the discrete variable representation for the reaction system, and applied to a reaction system coupled to a bath. The method is very efficient because the equations involved are as simple as those in the traditional single configuration approach, and can account for the correlations between the reaction system and bath modes rather well. (C) American Institute of Physics.

Time-dependent Hyperstar algorithm for robust vehicle navigation in time-dependent stochastic road networks.

The vehicle navigation problem studied in Bell (2009) is revisited and a time-dependent reverse Hyperstar algorithm is presented. This minimises the expected time of arrival at the destination, and all intermediate nodes, where expectation is based on a pessimistic (or risk-averse) view of unknown link delays. This may also be regarded as a hyperpath version of the Chabini and Lan (2002) algorithm, which itself is a time-dependent A* algorithm. Links are assigned undelayed travel times and maximum delays, both of which are potentially functions of the time of arrival at the respective link. The driver seeks probabilities for link use that minimise his/her maximum exposure to delay on the approach to each node, leading to the determination of the pessimistic expected time of arrival. Since the context considered is vehicle navigation where the driver is not making repeated trips, the probability of link use may be interpreted as a measure of link attractiveness, so a link with a zero probability of use is unattractive while a link with a probability of use equal to one will have no attractive alternatives. A solution algorithm is presented and proven to solve the problem provided the node potentials are feasible and a FIFO condition applies for undelayed link travel times. The paper concludes with a numerical example.

Time-dependent transport through molecular junctions.

We investigate transport properties of molecular junctions under two types of bias--a short time pulse or an ac bias--by combining a solution for Green's functions in the time domain with electronic structure information coming from ab initio density functional calculations. We find that the short time response depends on lead structure, bias voltage, and barrier heights both at the molecule-lead contacts and within molecules. Under a low frequency ac bias, the electron flow either tracks or leads the bias signal (resistive or capacitive response) depending on whether the junction is perfectly conducting or not. For high frequency, the current lags the bias signal due to the kinetic inductance. The transition frequency is an intrinsic property of the junctions.

Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals.

Time-dependent density functional theory (TDDFT) has broad application in the study of electronic response, excitation and transport. To extend such application to large and complex systems, we develop a reformulation of TDDFT equations in terms of non-orthogonal localized molecular orbitals (NOLMOs). NOLMO is the most localized representation of electronic degrees of freedom and has been used in ground state calculations. In atomic orbital (AO) representation, the sparsity of NOLMO is transferred to the coefficient matrix of molecular orbitals (MOs). Its novel use in TDDFT here leads to a very simple form of time propagation equations which can be solved with linear-scaling effort. We have tested the method for several long-chain saturated and conjugated molecular systems within the self-consistent charge density-functional tight-binding method (SCC-DFTB) and demonstrated its accuracy. This opens up pathways for TDDFT applications to large bio- and nano-systems.

Vacuum arc remelting time dependent modelling

Newly developed numerical modelling tools are described, which address the 3-dimensional (3D) time-dependent magnetohydrodynamic and thermal behaviour in the liquid pool zone in the adjacent ingot, electrode and crucible. The melting electrode film flow and the droplet detachment initiation are simulated separately by an axisymmetric transient model.

Modelling of the time-dependent flow behaviour of lead-free solder pastes used for flip-chip assembly applications

The market for solder paste materials in the electronic manufacturing and assembly sector is very large and consists of material and equipment suppliers and end users. These materials are used to bond electronic components (such as flip-chip, CSP and BGA) to printed circuit boards (PCB's) across a range of dimensions where the solder interconnects can be in the order of 0.05mm to 5mm in size. The non-Newtonian flow properties exhibited by solder pastes during its manufacture and printing/deposition phases have been of practical concern to surface mount engineers and researchers for many years. The printing of paste materials through very small-sized stencil apertures is known to lead to increased stencil clogging and incomplete transfer of paste to the substrate pads. At these very narrow aperture sizes the paste rheology and particle-wall interactions become crucial for consistent paste withdrawal. These non-Newtonian effects must be understood so that the new paste formulations can be optimised for consistent printing. The focus of the study reported in this paper is the characterisation of the rheological properties of solder pastes and flux mediums, and the evaluation of the effect of these properties on the pastes' printing performance at the flip-chip assembly application level. Solder pastes are known to exhibit a thixotropic behaviour, which is recognised by the decrease in apparent viscosity of paste material with time when subjected to a constant shear rate. The proper characterisation of this time-dependent theological behaviour of solder pastes is crucial for establishing the relationships between the pastes' structure and flow behaviour; and for correlating the physical parameters with paste printing performance. In this paper, we present a number of methods which have been developed for characterising the time-dependent and non-Newtonian rheological behaviour of solder pastes and flux mediums as a function of shear rates. We also present results of the study of the rheology of the solder pastes and flux mediums using the structural kinetic modelling approach, which postulates that the network structure of solder pastes breaks down irreversibly under shear, leading to time and shear dependent changes in the flow properties. Our results show that for the solder pastes used in the study, the rate and extent of thixotropy was generally found to increase with increasing shear rate. The technique demonstrated in this study has wide utility for R&D personnel involved in new paste formulation, for implementing quality control procedures used in solder paste manufacture and packaging; and for qualifying new flip-chip assembly lines

A discrete time-dependent method for metastable atoms and molecules in intense fields

The full-dimensional time-dependent Schrodinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange mesh methods. The method is applied to calculate the quasienergies and ionization probabilities of atomic and molecular systems in intense static and dynamic electric fields. The gauge invariance and accuracy of the method is established. Applications to multiphoton ionization of positronium, the hydrogen atom and the hydrogen molecular ion are presented. At very high laser intensity, above the saturation threshold, we extend the method using a scaling technique to estimate the quasienergies of metastable states of the hydrogen molecular ion. The results are in good agreement with recent experiments. (C) 2004 American Institute of Physics.

Time-dependent tight binding

Starting from a Lagrangian mean-field theory, a set of time-dependent tight-binding equations is derived to describe dynamically and self-consistently an interacting system of quantum electrons and classical nuclei. These equations conserve norm, total energy and total momentum. A comparison with other tight-binding models is made. A previous tight-binding result for forces on atoms in the presence of electrical current flow is generalized to the time-dependent domain and is taken beyond the limit of local charge neutrality.

Molecular conduction: Do time-dependent simulations tell you more than the Landauer approach?

A dynamical method for simulating steady-state conduction in atomic and molecular wires is presented which is both computationally and conceptually simple. The method is tested by calculating the current-voltage spectrum of a simple diatomic molecular junction, for which the static Landauer approach produces multiple steady-state solutions. The dynamical method quantitatively reproduces the static results and provides information on the stability of the different solutions. (c) 2006 American Institute of Physics.

Observing time-dependent vibrational quantum dynamics in deuterium hydride molecular ions

Few-cycle laser pulses are used to "pump and probe" image the vibrational wavepacket dynamics of a HD+ molecular ion. The quantum dephasing and revival structure of the wavepacket are mapped experimentally with time-resolved photodissociation imaging. The motion of the molecule is simulated using a quantum-mechanical model predicting the observed structure. The coherence of the wavepacket is controlled by varying the duration of the intense laser pulses. By means of a Fourier transform analysis both the periodicity and relative population of the vibrational states of the excited molecular ion have been characterized.