High-order harmonic generation from diatomic molecules with large internuclear distance: The effect of two-center interference

In the present paper, we investigate the high-order harmonic generation (HHG) from diatomic molecules with large internuclear distance using a strong field approximation (SFA) model. We find that the hump and dip structure emerges in the plateau region of the harmonic spectrum, and the location of this striking structure is sensitive to the laser intensity. Our model analysis reveals that two-center interference as well as the interference between different recombination electron trajectories are responsible for the unusual enhanced or suppressed harmonic yield at a certain order, and these interference effects are greatly influenced by the laser parameters such as intensity.Comment: 5 pages,4 figure

Hypothesis testing of multiple inequalities: the method of constraint chaining

Econometric inequality hypotheses arise in diverse ways. Examples include concavity restrictions on technological and behavioural functions, monotonicity and dominance relations, one-sided constraints on conditional moments in GMM estimation, bounds on parameters which are only partially identified, and orderings of predictive performance measures for competing models. In this paper we set forth four key properties which tests of multiple inequality constraints should ideally satisfy. These are (1) (asymptotic) exactness, (2) (asymptotic)similarity on the boundary, (3) absence of nuisance parameters from the asymptotic null distribution of the test statistic, (4) low computational complexity and boostrapping cost. We observe that the predominant tests currently used in econometrics do not appear to enjoy all these properties simultaneously. We therefore ask the question : Does there exist any nontrivial test which, as a mathematical fact, satisfies the first three properties and, by any reasonable measure, satisfies the fourth ? Remarkably the answer is affirmative. The paper demonstrates this constructively. We introduce a method of test construction called chaining which begins by writing multiple inequalities as a single equality using zero-one indicator functions. We then smooth the indicator functions. The approximate equality thus obtained is the basis of a well-behaved test. This test may be considered as the baseline of a wider class of tests. A full asymptotic theory is provided for the baseline. Simulation results show that the finite-sample performance of the test matches the theory quite well

Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions

Strong short ranged positional correlations involving counterions can induce a net attractive force between negatively charged strands of DNA, and lead to the formation of ion pairs in dilute ionic solutions. But the long range of the Coulomb interactions impedes the development of a simple local picture. We address this general problem by mapping the properties of a nonuniform system with Coulomb interactions onto those of a simpler system with short ranged intermolecular interactions in an effective external field that accounts for the averaged effects of appropriately chosen long ranged and slowly varying components of the Coulomb interactions. The remaining short ranged components combine with the other molecular core interactions and strongly affect pair correlations in dense or strongly coupled systems. We show that pair correlation functions in the effective short ranged system closely resemble those in the uniform primitive model of ionic solutions, and illustrate the formation of ion pairs and clusters at low densities. The theory accurately describes detailed features of the effective attraction between two equally charged walls at strong coupling and intermediate separations of the walls. New analytical results for the minimal coupling strength needed to get any attraction and for the separation where the attractive force is a maximum are presented.Comment: 8 pages, 5 figures. To be published in PNA

Evolutionary computation enabled game theory based modelling of electricity market behaviours and applications

The collapse of the Californian electricity market system in 2001 has highlighted urgency in research in intelligent electricity trading systems and strategies involving both suppliers and customs. In their trading systems, power generation companies under the new electricity trading arrangement (NETA) of the UK are now developing gaming strategies. However, modelling of such "intelligent" market behaviours is extremely challenging, because traditional mathematical and computer modelling techniques cannot cope with the involvement of game theory. In this paper, evolutionary computation enabled modelling of such system is presented. Both competitive and cooperative game theory strategies are taken into account in evolving the intelligent model. The model then leads to intelligent trading strategy development and decision support. Experimental tests, verification and validation are carried out with various strategies, using different model scales and data published by NETA. Results show that evolutionary computation enabled game theory involved modelling and decision making provides an effective tool for NETA trading analysis, prediction and support