Nonradiating anapole modes in dielectric nanoparticles

Nonradiating current configurations attract attention of physicists for many years as possible models of stable atoms. One intriguing example of such a nonradiating source is known as 'anapole'. An anapole mode can be viewed as a composition of electric and toroidal dipole moments, resulting in destructive interference of the radiation fields due to similarity of their far-field scattering patterns. Here we demonstrate experimentally that dielectric nanoparticles can exhibit a radiationless anapole mode in visible. We achieve the spectral overlap of the toroidal and electric dipole modes through a geometry tuning, and observe a highly pronounced dip in the far-field scattering accompanied by the specific near-field distribution associated with the anapole mode. The anapole physics provides a unique playground for the study of electromagnetic properties of nontrivial excitations of complex fields, reciprocity violation and Aharonov-Bohm like phenomena at optical frequencies.The work of A.E.M. was supported by the Australian Research Council via Future Fellowship program (FT110100037). The authors at DSI were supported by DSI core funds. Fabrication, Scanning Electron Microscope Imaging and NSOM works were carried out in facilities provided by SnFPC@DSI (SERC Grant 092 160 0139). Zhen Ying Pan (DSI) is acknowledged for SEM imaging. Yi Zhou (DSI) is acknowledged for silicon film growth. Leonard Gonzaga (DSI), Yeow Teck Toh (DSI) and Doris Ng (DSI) are acknowledged for development of the silicon nanofabrication procedure. B.N.C. acknowledges support from the Government of Russian Federation, Megagrant No. 14.B25.31.0019

Nonequilibrium Cooper pairing in the nonadiabatic regime

We obtain a complete solution for the mean-field dynamics of the BCS paired state with a large, but finite number of Cooper pairs in the non-adiabatic regime. We show that the problem reduces to a classical integrable Hamiltonian system and derive a complete set of its integrals of motion. The condensate exhibits irregular multi-frequency oscillations ergodically exploring the part of the phase-space allowed by the conservation laws. In the thermodynamic limit however the system can asymptotically reach a steady state.Comment: 4 pages, no figure

Discrete embedded solitons

We address the existence and properties of discrete embedded solitons (ESs), i.e., localized waves existing inside the phonon band in a nonlinear dynamical-lattice model. The model describes a one-dimensional array of optical waveguides with both the quadratic (second-harmonic generation) and cubic nonlinearities. A rich family of ESs was previously known in the continuum limit of the model. First, a simple motivating problem is considered, in which the cubic nonlinearity acts in a single waveguide. An explicit solution is constructed asymptotically in the large-wavenumber limit. The general problem is then shown to be equivalent to the existence of a homoclinic orbit in a four-dimensional reversible map. From properties of such maps, it is shown that (unlike ordinary gap solitons), discrete ESs have the same codimension as their continuum counterparts. A specific numerical method is developed to compute homoclinic solutions of the map, that are symmetric under a specific reversing transformation. Existence is then studied in the full parameter space of the problem. Numerical results agree with the asymptotic results in the appropriate limit and suggest that the discrete ESs may be semi-stable as in the continuous case.Comment: A revtex4 text file and 51 eps figure files. To appear in Nonlinearit

Sequencing the Potato Genome: Outline and First Results to Come from the Elucidation of the Sequence of the World’s Third Most Important Food Crop

Potato is a member of the Solanaceae, a plant family that includes several other economically important species, such as tomato, eggplant, petunia, tobacco and pepper. The Potato Genome Sequencing Consortium (PGSC) aims to elucidate the complete genome sequence of potato, the third most important food crop in the world. The PGSC is a collaboration between 13 research groups from China, India, Poland, Russia, the Netherlands, Ireland, Argentina, Brazil, Chile, Peru, USA, New Zealand and the UK. The potato genome consists of 12 chromosomes and has a (haploid) length of approximately 840 million base pairs, making it a medium-sized plant genome. The sequencing project builds on a diploid potato genomic bacterial artificial chromosome (BAC) clone library of 78000 clones, which has been fingerprinted and aligned into ~7000 physical map contigs. In addition, the BAC-ends have been sequenced and are publicly available. Approximately 30000 BACs are anchored to the Ultra High Density genetic map of potato, composed of 10000 unique AFLPTM markers. From this integrated genetic-physical map, between 50 to 150 seed BACs have currently been identified for every chromosome. Fluorescent in situ hybridization experiments on selected BAC clones confirm these anchor points. The seed clones provide the starting point for a BAC-by-BAC sequencing strategy. This strategy is being complemented by whole genome shotgun sequencing approaches using both 454 GS FLX and Illumina GA2 instruments. Assembly and annotation of the sequence data will be performed using publicly available and tailor-made tools. The availability of the annotated data will help to characterize germplasm collections based on allelic variance and to assist potato breeders to more fully exploit the genetic potential of potat

Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity

We consider solutions to the second-harmonic generation equations in two-and three-dimensional dispersive media in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. The general solution is obtained in an approximate analytical form by means of a variational approach, which also allows the stability of the solutions to be predicted. Then, we directly simulate the two-dimensional case, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that spatiotemporal solitons indeed exist and are stable. Furthermore, they are not, in the general case, equivalent to the previously known cylindrical spatial solitons. Direct simulations generate solitons with some internal oscillations. However, these oscillations neither grow nor do they exhibit any significant radiative damping. Numerical solutions of the stationary version of the equations produce the same solitons in their unperturbed form, i.e., without internal oscillations. Strictly stable solitons exist only if the system has anomalous dispersion at both the fundamental harmonic and second harmonic (SH), including the case of zero dispersion at SH. Quasistationary solitons, decaying extremely slowly into radiation, are found in the presence of weak normal dispersion at the second-harmonic frequency

Ion Channel Density Regulates Switches between Regular and Fast Spiking in Soma but Not in Axons

The threshold firing frequency of a neuron is a characterizing feature of its dynamical behaviour, in turn determining its role in the oscillatory activity of the brain. Two main types of dynamics have been identified in brain neurons. Type 1 dynamics (regular spiking) shows a continuous relationship between frequency and stimulation current (f-Istim) and, thus, an arbitrarily low frequency at threshold current; Type 2 (fast spiking) shows a discontinuous f-Istim relationship and a minimum threshold frequency. In a previous study of a hippocampal neuron model, we demonstrated that its dynamics could be of both Type 1 and Type 2, depending on ion channel density. In the present study we analyse the effect of varying channel density on threshold firing frequency on two well-studied axon membranes, namely the frog myelinated axon and the squid giant axon. Moreover, we analyse the hippocampal neuron model in more detail. The models are all based on voltage-clamp studies, thus comprising experimentally measurable parameters. The choice of analysing effects of channel density modifications is due to their physiological and pharmacological relevance. We show, using bifurcation analysis, that both axon models display exclusively Type 2 dynamics, independently of ion channel density. Nevertheless, both models have a region in the channel-density plane characterized by an N-shaped steady-state current-voltage relationship (a prerequisite for Type 1 dynamics and associated with this type of dynamics in the hippocampal model). In summary, our results suggest that the hippocampal soma and the two axon membranes represent two distinct kinds of membranes; membranes with a channel-density dependent switching between Type 1 and 2 dynamics, and membranes with a channel-density independent dynamics. The difference between the two membrane types suggests functional differences, compatible with a more flexible role of the soma membrane than that of the axon membrane