The Discrete Nonlinear Schrödinger Equation is used to study the formation of stationary localized states due to a single nonlinear impurity in a Caley tree and a dimeric nonlinear impurity in the one dimensional system. The rotational nonlinear impurity and the impurity of the form −χ | C | σ where σ is arbitrary and χ is the nonlinearity parameter are considered. Furthermore, | C | represents the absolute value of the amplitude. Altogether four cases are studies. The usual Greens function approach and the ansatz approach are coherently blended to obtain phase diagrams showing regions of different number of states in the parameter space. Equations of critical lines separating various regions in phase diagrams are derived analytically. For the dimeric problem with the impurity −χ | C | σ , three values of | χ cr |, namely, | χ cr |= 2, at σ = 0 and | χ cr |= 1 and 8 3 for σ = 2 are obtained. Last two values are lower than the existing values. Energy of the states as a function of parameters is also obtained. A model derivation for the impurities is presented. The implication of our results in relation to disordered systems comprising of nonlinear impurities and perfect sites is discussed. PACS numbers : 71.55.-i, 72.10.Fk Typeset using REVT E X

Renewed focus on the P-Si system due to its potential application in quantum computing and self-directed growth of molecular wires, has led us to study structural changes induced by P upon placement on Si(001)-p(2 × 1). Using first-principles density functional theory (DFT) based pseudopotential method, we have performed calculations for P-Si(001) system, starting from an isolated P atom on the surface, and systematically increasing the coverage up to a full monolayer. An isolated P atom can favorably be placed on an M site between two atoms of adjacent Si dimers belonging to the same Si dimer row. But being incorporated in the surface is even more energetically beneficial due to the participation of the M site as a receptor for the ejected Si. Our calculations show that up to 1 8 monolayer coverage, hetero-dimer structure resulting from replacement of surface Si atoms with P is energetically favorable. Recently observed zig-zag features in STM are found to be consistent with this replacement process. As coverage increases, the hetero-dimers give way to P-P ortho-dimers on the Si dimer rows. This behavior is similar to that of Si-Si d-dimers but are to be contrasted with the Al-Al dimers, which are found between adjacent Si dimers rows and in a paradimer arrangement. Unlike Al-Si system P-Si does not show any para to ortho transition. For both systems, the surface reconstruction is lifted at about one monolayer coverage. These calculations help us in understanding the experimental data obtained using scanning tunneling microscope.

Motivated by a recent experiment on acoustic lenses, we perform numerical calculations based on a multiple scattering technique to investigate the focusing of acoustic waves with sonic crystals formed by rigid cylinders in air. The focusing effects for crystals of various shapes are examined. The dependence of the focusing length on the filling factor is also studied. It is observed that both the shape and filling factor play a crucial role in controlling the focusing. Furthermore, the robustness of the focusing against disorders is studied. The results show that the sensitivity of the focusing behavior depends on the strength of positional disorders. The theoretical results compare favorably with the experimental observations, reported by Cervera, et al. [Phys. Rev. Lett. 88, 023902 (2002)].

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In this erratum we point out that the band structure shown in Fig. 1 in our original article is in error. The correct version is shown here in Fig. 1. The band structure in Ref. 1 is only a part of the new result. The remaining results regarding the acoustic focusing remain unaffected. The mistake is due to the inappropriate construction of the first Brillouin zone. ACKNOWLEDGMENTSThe mistake was pointed out and corrected by Mr. Chao-Hsien Kuo. We are grateful to Mr. Kuo for his kind help. We thank Dr. P.-G. Luan for helpful discussions.

2-Octyl cyanoacrylate is well tolerated in the orbit, inducing minimal inflammation. It effectively attaches muscles to porous implants without hindering permanent integration or vascularization. The exposure rate for unwrapped hydroxyapatite spheres was not caused by the adhesive, as evidenced by the lack of exposures in the porous polyethylene implant group. 2-Octyl cyanoacrylate may be effective in reducing the cost and time for enucleation surgeries when porous motility implants are used.

The formation of stationary localized states due to a power law nonlinear dimeric impurity embedded in a perfect one-dimensional chain is studied here using the appropriate discrete nonlinear Schrödinger equation. A proper ansatz is introduced in the appropriate Hamiltonian to obtain the reduced effective Hamiltonian. The Hamiltonian contains a parameter, ␤ϭ 1 / 0 , which is the ratio of stationary amplitudes at impurity sites. Relevant equations for localized states are obtained from the fixed point of the reduced dynamical system. The complete phase diagram in the (,) plane for all permissible values of ͉␤͉р1 is obtained. Furthermore, the maximum number of localized states is found to be 6. ͓S0163-1829͑97͒11417-5͔The discrete nonlinear Schrödinger equation ͑DNLSE͒ is a set of n coupled differential equationswhere V m,mϩ1 ϭV mϩ1,m à and mϭ1,2,3, . . . ,n.

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