Self-focusing and filamentation of optical vortex beams: Spatiotemporal analysis

We report numerical simulations supported by experimental observations of self-focusing, fillamentation, and supercontinuum generation by an optical vortex beam in a Kerr nonlinear medium in the regime of dominating nonlinearity. Despite the strong self-focusing resulting in multiple filaments ordered along the vortex ring the optical vortex remains well preserved at the exit of the nonlinear medium and in the far-field. The presented quasi-(3+1)- dimensional numerical simulations under azimuthal initial vortex ring perturbations confirm qualitatively the experimentally observed survival of the optical vortex in the course of the white light generation

Probing Exciton Localization in Single-Walled Carbon Nanotubes Using High-Resolution Near-Field Microscopy

We observe localization of excitons in semiconducting single-walled carbon nanotubes at room temperature using high-resolution near-field photoluminescence (PL) microscopy. Localization is the result of spatially confined exciton energy minima with depths of more than 15 meV connected to lateral energy gradients exceeding 2 meV/nm as evidenced by energy-resolved PL imaging. Simulations of exciton diffusion in the presence of energy variations support this interpretation predicting strongly enhanced PL at local energy minima

On Soliton Interactions for the Hierarchy of a Generalised Heisenberg Ferromagnetic Model on Symmetric Space

We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator L. The Lax representation is ℤ2× ℤ2reduced and can be naturally associated with the symmetric space SU(3)/S(U(1) × U(2)). The simplest nontrivial equation in the hierarchy is a generalization of Heisenberg ferromagnetic model. We construct the N-soliton solutions for an arbitrary member of the hierarchy by using the Zakharov-Shabat dressing method with an appropriately chosen dressing factor. Two types of soliton solutions: quadruplet and doublet solitons are found. The one-soliton solutions of NLEEs with even and odd dispersion laws have different properties. In particular, the one-soliton solutions for NLEEs with even dispersion laws are not traveling waves while their velocities and amplitudes are time dependent. Calculating the asymptotics of the N-soliton solutions for t → ± ∞ we analyze the interactions of quadruplet solitons

Partially-supervised protein subclass discovery with simultaneous annotation of functional residues

<p>Abstract</p> <p>Background</p> <p>The study of functional subfamilies of protein domain families and the identification of the residues which determine substrate specificity is an important question in the analysis of protein domains. One way to address this question is the use of clustering methods for protein sequence data and approaches to predict functional residues based on such clusterings. The locations of putative functional residues in known protein structures provide insights into how different substrate specificities are reflected on the protein structure level.</p> <p>Results</p> <p>We have developed an extension of the <it>context-specific independence </it>mixture model clustering framework which allows for the integration of experimental data. As these are usually known only for a few proteins, our algorithm implements a partially-supervised learning approach. We discover domain subfamilies and predict functional residues for four protein domain families: phosphatases, pyridoxal dependent decarboxylases, WW and SH3 domains to demonstrate the usefulness of our approach.</p> <p>Conclusion</p> <p>The partially-supervised clustering revealed biologically meaningful subfamilies even for highly heterogeneous domains and the predicted functional residues provide insights into the basis of the different substrate specificities.</p

Enhancing and redirecting carbon nanotube photoluminescence by an optical antenna

We observe the angular radiation pattern of single carbon nanotubes' photoluminescence in the back focal plane of a microscope objective and show that the emitting nanotube can be described by a single in-plane point dipole. The near-field interaction between a nanotube and an optical antenna modifies the radiation pattern that is now dominated by the antenna characteristics. We quantify the antenna induced excitation and radiation enhancement and show that the radiative rate enhancement is connected to a directional redistribution of the emission

Exciton Energy Transfer in Pairs of Single-Walled Carbon Nanotubes

We studied the exciton energy transfer in pairs of semiconducting nanotubes using high-resolution optical microscopy and spectroscopy on the nanoscale. Photoluminescence from large band gap nanotubes within bundles is observed with spatially varying intensities due to distance-dependent internanotube transfer. The range of efficient energy transfer is found to be limited to a few nanometers because of competing fast nonradiative relaxation responsible for low photoluminescence quantum yield

Gravity-Yang-Mills-Higgs unification by enlarging the gauge group

We revisit an old idea that gravity can be unified with Yang-Mills theory by enlarging the gauge group of gravity formulated as gauge theory. Our starting point is an action that describes a generally covariant gauge theory for a group G. The Minkowski background breaks the gauge group by selecting in it a preferred gravitational SU(2) subgroup. We expand the action around this background and find the spectrum of linearized theory to consist of the usual gravitons plus Yang-Mills fields charged under the centralizer of the SU(2) in G. In addition, there is a set of Higgs fields that are charged both under the gravitational and Yang-Mills subgroups. These fields are generically massive and interact with both gravity and Yang-Mills sector in the standard way. The arising interaction of the Yang-Mills sector with gravity is also standard. Parameters such as the Yang-Mills coupling constant and Higgs mass arise from the potential function defining the theory. Both are realistic in the sense explained in the paper.Comment: 61 pages, no figures (v2) some typos correcte

On Soliton Interactions for a Hierarchy of Generalized Heisenberg Ferromagnetic Models on SU(3)/S(U(1) ×\times U(2)) Symmetric Space

We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator L. The Lax representation is Z2 \times Z2 reduced and is naturally associated with the symmetric space SU(3)/S(U(1) \times U(2)). The simplest nontrivial equation in the hierarchy is a generalization of Heisenberg ferromagnetic model. We construct the N-soliton solutions for an arbitrary member of the hierarchy by using the Zakharov-Shabat dressing method with an appropriately chosen dressing factor. Two types of soliton solutions: quadruplet and doublet solitons are found. The one-soliton solutions of NLEEs with even and odd dispersion laws have different properties. In particular, the one-soliton solutions for NLEEs with even dispersion laws are not traveling waves; their velocities and their amplitudes are time dependent. Calculating the asymptotics of the N-soliton solutions for t \rightarrow \pm \infty we analyze the interactions of quadruplet solitons

Rational Bundles and Recursion Operators for Integrable Equations on A.III-type Symmetric Spaces

We analyze and compare the methods of construction of the recursion operators for a special class of integrable nonlinear differential equations related to A.III-type symmetric spaces in Cartan’s classification and having additional reductions