Solitons supported by localized nonlinearities in periodic media

Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BECs) loaded into optical lattices, are often described by the nonlinear Schr\"odinger/Gross-Pitaevskii equation with a sinusoidal potential. Here, we consider a model based on such a periodic potential, with the nonlinearity (attractive or repulsive) concentrated either at a single point or at a symmetric set of two points, which are represented, respectively, by a single {\delta}-function or a combination of two {\delta}-functions. This model gives rise to ordinary solitons or gap solitons (GSs), which reside, respectively, in the semi-infinite or finite gaps of the system's linear spectrum, being pinned to the {\delta}-functions. Physical realizations of these systems are possible in optics and BEC, using diverse variants of the nonlinearity management. First, we demonstrate that the single {\delta}-function multiplying the nonlinear term supports families of stable regular solitons in the self-attractive case, while a family of solitons supported by the attractive {\delta}-function in the absence of the periodic potential is completely unstable. We also show that the {\delta}-function can support stable GSs in the first finite gap in both the self-attractive and repulsive models. The stability analysis for the GSs in the second finite gap is reported too, for both signs of the nonlinearity. Alongside the numerical analysis, analytical approximations are developed for the solitons in the semi-infinite and first two finite gaps, with the single {\delta}-function positioned at a minimum or maximum of the periodic potential. In the model with the symmetric set of two {\delta}-functions, we study the effect of the spontaneous symmetry breaking of the pinned solitons. Two configurations are considered, with the {\delta}-functions set symmetrically with respect to the minimum or maximum of the potential

A nonpolynomial Schroedinger equation for resonantly absorbing gratings

We derive a nonlinear Schroedinger equation with a radical term, in the form of the square root of (1-|V|^2), as an asymptotic model of the optical medium built as a periodic set of thin layers of two-level atoms, resonantly interacting with the electromagnetic field and inducing the Bragg reflection. A family of bright solitons is found, which splits into stable and unstable parts, exactly obeying the Vakhitov-Kolokolov criterion. The soliton with the largest amplitude, which is |V| = 1, is found in an explicit analytical form. It is a "quasi-peakon", with a discontinuity of the third derivative at the center. Families of exact cnoidal waves, built as periodic chains of quasi-peakons, are found too. The ultimate solution belonging to the family of dark solitons, with the background level |V| = 1, is a dark compacton, also obtained in an explicit analytical form. Those bright solitons which are unstable destroy themselves (if perturbed) attaining the critical amplitude, |V| = 1. The dynamics of the wave field around this critical point is studied analytically, revealing a switch of the system into an unstable phase. Collisions between bright solitons are investigated too. The collisions between fast solitons are quasi-elastic, while slowly moving ones merge into breathers, which may persist or perish (in the latter case, also by attaining |V| = 1).Comment: Physical Review A, in pres

Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors

We predict the existence of spatiotemporal solitons (``light bullets'') in two-dimensional self-induced transparency media embedded in a Bragg grating. The "bullets" are found in an approximate analytical form, their stability being confirmed by direct simulations. These findings suggest new possibilities for signal transmission control and self-trapping of light.Comment: RevTex, 3 pages, 2 figures, to be published in PR

Scattering of slow-light gap solitons with charges in a two-level medium

The Maxwell-Bloch system describes a quantum two-level medium interacting with a classical electromagnetic field by mediation of the the population density. This population density variation is a purely quantum effect which is actually at the very origin of nonlinearity. The resulting nonlinear coupling possesses particularly interesting consequences at the resonance (when the frequency of the excitation is close to the transition frequency of the two-level medium) as e.g. slow-light gap solitons that result from the nonlinear instability of the evanescent wave at the boundary. As nonlinearity couples the different polarizations of the electromagnetic field, the slow-light gap soliton is shown to experience effective scattering whith charges in the medium, allowing it for instance to be trapped or reflected. This scattering process is understood qualitatively as being governed by a nonlinear Schroedinger model in an external potential related to the charges (the electrostatic permanent background component of the field).Comment: RevTex, 14 pages with 5 figures, to appear in J. Phys. A: Math. Theo

Control of Azomethine Cycloaddition Stereochemistry by CF<inf>3</inf> Group: Structural Diversity of Fluorinated β-Proline Dimers

© 2016 American Chemical Society.β-Proline-functionalized dimers consisting of homochiral monomeric units were synthesized by a non-peptidic coupling method for the first time. The applied synthetic methodology is based on 1,3-dipolar cycloaddition chemistry of azomethine ylides and provides absolute control over the β-proline backbone stereogenic centers. An o-(trifluoromethyl)phenyl substituent contributes to appropriate stabilization of the definite acrylamide chiral cis conformation and to achieve the dipole reactivity that is not observed for aryl groups lacking strong electronegative character

The actinobacterial transcription factor RbpA binds to the principal sigma subunit of RNA polymerase

RbpA is a small non-DNA-binding transcription factor that associates with RNA polymerase holoenzyme and stimulates transcription in actinobacteria, including Streptomyces coelicolor and Mycobacterium tuberculosis. RbpA seems to show specificity for the vegetative form of RNA polymerase as opposed to alternative forms of the enzyme. Here, we explain the basis of this specificity by showing that RbpA binds directly to the principal σ subunit in these organisms, but not to more diverged alternative σ factors. Nuclear magnetic resonance spectroscopy revealed that, although differing in their requirement for structural zinc, the RbpA orthologues from S. coelicolor and M. tuberculosis share a common structural core domain, with extensive, apparently disordered, N- and C-terminal regions. The RbpA-σ interaction is mediated by the C-terminal region of RbpA and σ domain 2, and S. coelicolor RbpA mutants that are defective in binding σ are unable to stimulate transcription in vitro and are inactive in vivo. Given that RbpA is essential in M. tuberculosis and critical for growth in S. coelicolor, these data support a model in which RbpA plays a key role in the σ cycle in actinobacteria

Solitons in one-dimensional photonic crystals

We report results of a systematic analysis of spatial solitons in the model of 1D photonic crystals, built as a periodic lattice of waveguiding channels, of width D, separated by empty channels of width L-D. The system is characterized by its structural "duty cycle", DC = D/L. In the case of the self-defocusing (SDF) intrinsic nonlinearity in the channels, one can predict new effects caused by competition between the linear trapping potential and the effective nonlinear repulsive one. Several species of solitons are found in the first two finite bandgaps of the SDF model, as well as a family of fundamental solitons in the semi-infinite gap of the system with the self-focusing nonlinearity. At moderate values of DC (such as 0.50), both fundamental and higher-order solitons populating the second bandgap of the SDF model suffer destabilization with the increase of the total power. Passing the destabilization point, the solitons assume a flat-top shape, while the shape of unstable solitons gets inverted, with local maxima appearing in empty layers. In the model with narrow channels (around DC =0.25), fundamental and higher-order solitons exist only in the first finite bandgap, where they are stable, despite the fact that they also feature the inverted shape

Adenine and guanine recognition of stop codon is mediated by different N domain conformations of translation termination factor eRF1

Positioning of release factor eRF1 toward adenines and the ribose-phosphate backbone of the UAAA stop signal in the ribosomal decoding site was studied using messenger RNA (mRNA) analogs containing stop signal UAA/UAAA and a photoactivatable cross-linker at definite locations. The human eRF1 peptides cross-linked to these analogs were identified. Cross-linkers on the adenines at the 2nd, 3rd or 4th position modified eRF1 near the conserved YxCxxxF loop (positions 125–131 in the N domain), but cross-linker at the 4th position mainly modified the tripeptide 26-AAR-28. This tripeptide cross-linked also with derivatized 3′-phosphate of UAA, while the same cross-linker at the 3′-phosphate of UAAA modified both the 26–28 and 67–73 fragments. A comparison of the results with those obtained earlier with mRNA analogs bearing a similar cross-linker at the guanines indicates that positioning of eRF1 toward adenines and guanines of stop signals in the 80S termination complex is different. Molecular modeling of eRF1 in the 80S termination complex showed that eRF1 fragments neighboring guanines and adenines of stop signals are compatible with different N domain conformations of eRF1. These conformations vary by positioning of stop signal purines toward the universally conserved dipeptide 31-GT-32, which neighbors guanines but is oriented more distantly from adenines