Search Results

You are looking at 1 - 5 of 5 items for :

• Author or Editor: T
• Mathematics & Computer Sciences

Closed Newton-Cotes Trigonometrically-Fitted Formulae for Numerical Integration of the Schrödinger Equation

In this paper we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted differential methods, symplectic integrators and efficient solution of the Schr¨odinger equation. Several one step symplectic integrators have been produced based on symplectic geometry, as one can see from the literature. However, the study of multistep symplectic integrators is very poor. Zhu et. al. [1] has studied the symplectic integrators and the well known open Newton-Cotes differential methods and as a result has presented the open Newton-Cotes differential methods as multilayer symplectic integrators. The construction of multistep symplectic integrators based on the open Newton-Cotes integration methods was investigated by Chiou and Wu [2]. In this paper we investigate the closed Newton-Cotes formulae and we write them as symplectic multilayer structures. We also develop trigonometrically-fitted symplectic methods which are based on the closed Newton-Cotes formulae. We apply the symplectic schemes to the well known one-dimensional Schr¨odinger equation in order to investigate the efficiency of the proposed method to these type of problems.

P-stable Four-Step Exponentially-Fitted Method for the Numerical Integration of the Schr¨odinger Equation

In this paper we present a P-stable exponentially-fitted four-step method for the numerical solution of the radial Schr¨odinger equation. More specifically we present a method than satisfies the property of P-stability and in the same time integrates exactly any linear combination of the functions {1, x, x2, x3, exp ± w x , x exp ± w x}. We tested the efficiency of our newly obtained scheme against well known methods, with excellent results. The numerical experimentation showed that our method is considerably more efficient compared to well known methods used for the numerical solution of resonance problem of the radial Schr¨odinger equation.

CBSP: A Predictor of Sequences of Correlated Branches

A Way to Reduce Aliasing in Branch Prediction Tables

All current processors are using branch prediction in order to better exploit the pipeline. Branch prediction is based on limited size tables and thus several branches are sharing the same entry which is made of a simple 2-bit counter. This is called aliasing. Aliased branch predictors are subject to destructive interferences and removing them by the addition of a tag identifying precisely a branch to a 2-bit counter is prohibitive. An entry of our prediction table is made of several counters which predict a sequence of consecutive correlated branches and not only one. Thus, a tag can be added to an entry at a lower cost since the tag is shared by several branches. Each time a sequence is retrieved in the prediction table, it provides several predictions. An annex tagless predictor is solicited when a sequence is not found in the sequence table. Collisions are avoided in the sequence table but, to achieve a misprediction rate as low as the one of the current uptodate predictors, several tables should be used, each table being indexed through a different branch history length. Among the predictions provided by the sequences, a priority mechanism selects the most accurate i.e. the one provided by the table with the longest history. Finally, having tagged entries allows us to implement an intelligent system that dynamically adapts the branch history lengths according to the applications.

INVITED PAPER

Quantum Chemical DFT and Spectroscopic UV-Vis-NIR Analysis of a Series of Push-Pull Oligothiophenes End-Capped by Amino/Cyanovinyl Groups

series of push-pull chromophores built around thiophene-based . π-conjugating spacers and bearing various types of amino-donors and cyanovinyl-acceptors have been analyzed by means of UV-Vis- NIR spectroscopic measurements. Density functional theory (DFT) calculations have also been performed to help the assignment of the most relevant electronic features and to derive useful information about the molecular structure of these NLO-phores. The effects of the donor/acceptor substitution in the electronic and molecular properties of the .π -conjugated spacer have been addressed. The effectiveness of the intramolecular charge transfer (ICT) has also been tested as a function of the nature of the end groups (i.e., electron-donating or electron-withdrawing capabilities).