Directed Spiral Site Percolation on the Square Lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold $p_c\approx 0.655$ is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension $d_f\approx 1.733$. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as $p\to p_c$ with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution $P_s(p)$ show power law behavior with $|p-p_c|$ in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of $P_s(p)$. The results obtained are in good agreement with other model calculations.Comment: 22 pages, 7 figures, 1 tabl

Time-dependent configuration-interaction-singles calculation of the 5p5p-subshell two-photon ionization cross section in xenon

The $5p$ two-photon ionization cross section of xenon in the photon-energy range below the one-photon ionization threshold is calculated within the time-dependent configuration-interaction-singles (TDCIS) method. The TDCIS calculations are compared to random-phase-approximation (RPA) calculations [Wendin \textit{et al.}, J. Opt. Soc. Am. B \textbf{4}, 833 (1987)] and are found to reproduce the energy positions of the intermediate Rydberg states reasonably well. The effect of interchannel coupling is also investigated and found to change the cross section of the $5p$ shell only slightly compared to the intrachannel case.Comment: 11 pages, 3 figure

Kinetic proofreading at single molecular level: Aminoacylation of tRNA^{Ile} and the role of water as an editor

Proofreading/editing in protein synthesis is essential for accurate translation of information from the genetic code. In this article we present a theoretical investigation of efficiency of a kinetic proofreading mechanism that employs hydrolysis of the wrong substrate as the discriminatory step in enzyme catalytic reactions. We consider aminoacylation of tRNA^{Ile} which is a crucial step in protein synthesis and for which experimental results are now available. We present an augmented kinetic scheme and then employ methods of stochastic simulation algorithm to obtain time dependent concentrations of different substances involved in the reaction and their rates of formation. We obtain the rates of product formation and ATP hydrolysis for both correct and wrong substrates (isoleucine and valine in our case), in single molecular enzyme as well as ensemble enzyme kinetics. The present theoretical scheme correctly reproduces (i) the amplitude of the discrimination factor in the overall rates between isoleucine and valine which is obtained as (1.8 \times 10^2).(4.33 \times 10^2) = 7.8 \times 10^4, (ii) the rates of ATP hydrolysis for both Ile and Val at different substrate concentrations in the aminoacylation of tRNA^{Ile}. The present study shows a non-michaelis type dependence of rate of reaction on tRNA^{Ile} concentration in case of valine. The editing in steady state is found to be independent of amino acid concentration. Interestingly, the computed ATP hydrolysis rate for valine at high substrate concentration is same as the rate of formation of Ile-tRNA^{Ile} whereas at intermediate substrate concentration the ATP hydrolysis rate is relatively low

Strong-Field Many-Body Physics and the Giant Enhancement in the High-Harmonic Spectrum of Xenon

We resolve an open question about the origin of the giant enhancement in the high-harmonic generation (HHG) spectrum of atomic xenon around 100 eV. By solving the many-body time-dependent Schr\"odinger equation with all orbitals in the 4d, 5s, and 5p shells active, we demonstrate the enhancement results truly from collective many-body excitation induced by the returning photoelectron via two-body interchannel interactions. Without the many-body interactions, which promote a 4d electron into the 5p vacancy created by strong-field ionization, no collective excitation and no enhancement in the HHG spectrum exist.Comment: 5 pages, 4 figure