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This work analyzes the dynamics of two-dimensionalspatialsolitons in dissipative media. Stable solitons are formed in a two-dimensional medium with constant dissipation due to the balancing between dissipation and the instabilities due to nonlinearity. The dynamics have also been studied for linear, quadratic and exponential loss profiles. When a beam propagates in media with dissipation, where dissipation is a function of distance, it becomes compressed. A linear loss profile results in higher compression, while compression is minimal for an exponential profile.

We introduce a dynamical model of a Bose-Einstein condensate based on the two-dimensional Gross-Pitaevskii equation, in which the nonlinear coefficient is a function of radius. The model describes a situation with spatial modulation of the negative atomic scattering length, via the Feshbach resonance controlled by a properly shaped magnetic of optical field. We focus on the configuration with the nonlinear coefficient different from zero in a circle or annulus, including the case of a narrow ring. Two-dimensional axisymmetric solitons are found in a numerical form, and also by means of a variational approximation; for an infinitely narrow ring, the soliton is found in an exact form (in the latter case, exact solitons are also found in a two-component model). A stability region for the solitons is identified by means of numerical and analytical methods. In particular, if the nonlinearity is supported on the annulus, the upper stability border is determined by azimuthal perturbations; the stability region disappears if the ratio of the inner and outer radii of the annulus exceeds a critical value . The model gives rise to bistability, as the stationary solitons coexist with stable axisymmetric breathers, whose stability region extends to higher values of the norm than that of the static solitons. The collapse threshold strongly increases with the radius of the inner hole of the annulus. Vortex solitons are found too, but they are unstable. PMID:16605465

The partition function of two-dimensionalsolitons in a heat bath of mesons is worked out to one-loop. For temperatures large compared to the meson mass, the free energy is dominated by the meson-soliton bound states and the zero modes, a consequence of Levinson's theorem. Using the Bethe-Uhlenbeck formula we compare the soliton energy-shift to the shift expected in the pole

The two-dimensional nonlinear interaction of two planar ion-acoustic solitons has been studied experimentally. When the angle between the wave vectors of the two interacting solitons is small and the soliton amplitudes approach a critical value, a resonant three-soliton interaction occurs.

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrödinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies

Fatkhulla Kh. Abdullaev; Bakhtiyor B. Baizakov; Mario Salerno

Twodimensional generalizations of the Korteweg-de Vries equation appropriate to the propagation of nonlinear ion-acoustic waves are obtained. Soliton solutions are found to exist and they are shown to be stable to twodimensional perturbations.

We study the mobility of small-amplitude solitons attached to moving defects which drag the solitons across a two-dimensional (2D) discrete nonlinear Schrödinger lattice. Findings are compared to the situation when a free small-amplitude 2D discrete soliton is kicked in a uniform lattice. In agreement with previously known results, after a period of transient motion the free soliton transforms into a

We report on the two-dimensional gap-soliton nature of exciton-polariton macroscopic coherent phases (PMCP) in a square lattice with a tunable amplitude. The resonantly excited PMCP forms close to the negative mass M point of the lattice band structure with energy within the lattice band gap and its wave function localized within a few lattice periods. The PMCPs are well described as gap solitons resulting from the interplay between repulsive polariton-polariton interactions and effective attractive forces due to the negative mass. The solitonic nature accounts for the reduction of the PMCP coherence length and optical excitation threshold with increasing lattice amplitude. PMID:24138259

Cerda-Méndez, E A; Sarkar, D; Krizhanovskii, D N; Gavrilov, S S; Biermann, K; Skolnick, M S; Santos, P V

The two-dimensional dynamics of solitons appearing during relativistic laser-plasma interaction is investigated. The analysis starts from known soliton models in one space-dimension (1D). Some of the soliton solutions are already unstable in 1D, and all suffer from transverse instability in two dimensions (2D). The most unstable modes are calculated. They give a hint to the 2D structures which appear because of transversal effects. The linear stability considerations are supplemented by full 2D nonlinear simulations.

Lehmann, G.; Laedke, E. W.; Spatschek, K. H. [Institut fuer Theoretische Physik, Heinrich-Heine-Universitaet Duesseldorf, D-40225 Duesseldorf (Germany)

Formation, evolution and interaction of two-dimensionalsolitons and wave packets in weakly dispersive and dissipative media is studied numerically. The master equation is a hybrid of the Zabolotskaya-Khokhlov and Kadomtsev-Petviashvili equations with a Kawahara term.

We study the mobility of small-amplitude solitons attached to moving defects which drag the solitons across a two-dimensional (2D) discrete nonlinear Schrödinger lattice. Findings are compared to the situation when a free small-amplitude 2D discrete soliton is kicked in a uniform lattice. In agreement with previously known results, after a period of transient motion the free soliton transforms into a localized mode pinned by the Peierls-Nabarro potential, irrespective of the initial velocity. However, the soliton attached to the moving defect can be dragged over an indefinitely long distance (including routes with abrupt turns and circular trajectories) virtually without losses, provided that the dragging velocity is smaller than a certain critical value. Collisions between solitons dragged by two defects in opposite directions are studied too. If the velocity is small enough, the collision leads to a spontaneous symmetry breaking, featuring fusion of two solitons into a single one, which remains attached to either of the two defects.

We study the mobility of small-amplitude solitons attached to moving defects which drag the solitons across a two-dimensional (2D) discrete nonlinear Schroedinger lattice. Findings are compared to the situation when a free small-amplitude 2D discrete soliton is kicked in a uniform lattice. In agreement with previously known results, after a period of transient motion the free soliton transforms into a localized mode pinned by the Peierls-Nabarro potential, irrespective of the initial velocity. However, the soliton attached to the moving defect can be dragged over an indefinitely long distance (including routes with abrupt turns and circular trajectories) virtually without losses, provided that the dragging velocity is smaller than a certain critical value. Collisions between solitons dragged by two defects in opposite directions are studied too. If the velocity is small enough, the collision leads to a spontaneous symmetry breaking, featuring fusion of two solitons into a single one, which remains attached to either of the two defects.

Brazhnyi, Valeriy A.; Malomed, Boris A. [Centro de Fisica do Porto, Faculdade de Ciencias, Universidade do Porto, Rua Campo Alegre 687, Porto P-4169-007 (Portugal); Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel) and ICFO-Institut de Ciencies Fotoniques and Universitat Politecnica de Catalunya, Mediterranean Technology Park, E-08860 Castelldefels, Barcelona (Spain)

Existence, stability, and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel two-dimensional (2D) lattices, are investigated. The system with the onsite cubic self-focusing nonlinearity is modeled by the pair of discrete nonlinear Schrödinger equations linearly coupled at the single site. Symmetric, antisymmetric, and asymmetric complexes are constructed by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric soliton complexes exist in the entire parameter space, while the symmetric and asymmetric modes can be found below a critical value of the coupling parameter. Numerical results confirm these predictions. The symmetric complexes are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric modes. The antisymmetric complexes are subject to oscillatory and exponentially instabilities in narrow parametric regions. In bistability areas, stable antisymmetric solitons coexist with either symmetric or asymmetric ones. PMID:21929123

Petrovi?, M D; Gligori?, G; Maluckov, A; Hadžievski, Lj; Malomed, B A

We introduce a two-dimensional discrete nonlinear Schrödinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong optical lattice, or light propagation in a twisted bundle of nonlinear fibers. Two types of localized states are constructed: off-axis fundamental solitons (FSs), placed at distance R from the rotation pivot, and on-axis (R=0) vortex solitons (VSs), with vorticities S=1 and 2 . At a fixed value of rotation frequency Omega , a stability interval for the FSs is found in terms of the lattice coupling constant C , 0solitons are considered too, their stability regions being weakly affected by Omega not equal 0 . PMID:17995128

We introduce a model of a two-dimensional (2D) self-attractive medium embedded into a quasi-1D symmetric double-well potential (DWP), whose depth is subject to periodic modulations (management). The model applies to matter waves in Bose-Einstein condensates (BECs), as well as to the nonlinear transmission of light (in spatial and temporal domains alike). It is known that, in the absence of the management, the DWP induces the spontaneous symmetry breaking (SSB) of 2D solitons, when their norm exceeds a critical value. Above the SSB point, symmetric solitons are unstable, while the system supports stable asymmetric ones. The DWP also admits Josephson oscillations of solitons between the two wells. We study effects of periodic modulations of the DWP's depth on the stability of symmetric, asymmetric, and oscillating solitons. Stability areas for the solitons of these three types are produced in the plane of the modulation frequency and amplitude. The shape of the stability borders is strongly affected by the proximity of the modulation frequency to the frequency of free oscillations of the soliton in the static DWP structure, the solitons being destroyed by the modulations with an arbitrarily small amplitude at the point of the exact resonance. Similar results are obtained for an extended 2D model, which combines the transverse DWP and a longitudinal periodic potential (optical lattice, in terms of BEC). The findings are compared with those reported in other recently studied management models for 1D and 2D solitons, which makes it possible to draw general conclusions about the stability limits of solitons under the resonant management.

Sudheesh, C.; Bar-Gill, Nir; Malomed, Boris A.; Kurizki, Gershon

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensionalsolitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

da Luz, H. L. F.; Abdullaev, F. Kh.; Gammal, A.; Salerno, M.; Tomio, Lauro

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensionalsolitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Luz, H. L. F. da; Gammal, A. [Instituto de Fisica, Universidade de Sao Paulo, 05508-090 Sao Paulo, Sao Paulo (Brazil); Abdullaev, F. Kh. [CFTC, Complexo Interdisciplinar, Universidade Lisboa, Avenida Professor Gama Pinto, 2, P-1649-003 Lisboa (Portugal); Salerno, M. [Dipartimento di Fisica 'E.R. Caianiello', CNISM and INFN-Gruppo Collegato di Salerno, Universita di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); Tomio, Lauro [Instituto de Fisica, Universidade Federal Fluminense, 24210-346 Niteroi, Rio de Janeiro (Brazil); Instituto de Fisica Teorica, Universidade Estadual Paulista (UNESP), 01140-070 Sao Paulo, Sao Paulo (Brazil)

Dark solitons have provoked much interest since they were first shown to be particular solutions of the two-dimensional (1+1)-D nonlinear Schrodinger equation (NSE) with a negative (self-defocusing type) nonlinear coefficient n2. So far, only (1+1)-D temp...

Abstract The parametrically driven damped,nonlinear Schr¨odinger equation serves as an amplitude equation for a variety of resonantly forced oscillatory systems on the plane. In this note, we consider its nodal soliton solutions. We show that although the nodal solitons are stable against radially-symmetric perturbations for sufficiently large damping,coefficients, they are always unstable to azimuthal perturbations. The corresponding break-up scenarios are

We investigate a two-dimensional extended system showing chaotic and localized structures. We demonstrate the robust and stable existence of two types of exploding dissipative solitons. We show that the center of mass of asymmetric dissipative solitons undergoes a random walk despite the deterministic character of the underlying model. Since dissipative solitons are stable in two-dimensional systems we conjecture that our predictions can be tested in systems as diverse as nonlinear optics, parametric excitation of granular media and clay suspensions, and sheared electroconvection. PMID:23215228

Cartes, Carlos; Cisternas, Jaime; Descalzi, Orazio; Brand, Helmut R

\\u000a We discuss solitons in nonlinear resonators. In particular we discuss the cases of “laser” resonator, laser resonator containing\\u000a a nonlinear absorber, parametric mixing and semiconductor microresonator. In these resonators the following localized structures\\u000a (or spatialsolitons) exist: vortices, bright solitons, phase solitons, and bright and dark solitons, respectively. We discuss\\u000a the types of equations to which these systems correspond and

C. O. Weiss; V. B. Taranenko; M. Vaupel; K. Staliunas; G. Slekys; M. F. H. Tarroja

We report an observation of a stable solitonlike structure on the surface of a ferrofluid, generated by a local perturbation in the hysteretic regime of the Rosensweig instability. Unlike other pattern-forming systems with localized 2D structures, magnetic fluids are characterized by energy conservation; hence their mechanism of soliton stabilization is different from the previously discussed gain-loss balance mechanism. The radioscopic

We study the soliton type solutions arising in two-dimensional quantum chromodynamics (QCD$_{2}$). The so-called generalized sine-Gordon model (GSG) arises as the low-energy effective action of bosonized QCD$_{2}$ for unequal quark mass parameters, and it has been shown that the relevant solitons describe the normal and exotic baryonic spectrum of QCD$_{2}$ [JHEP(03)(2007)(055)]. In the first part of this chapter we classify

Using computational methods, it is found that the two-dimensional nonlinear Schrödinger (NLS) equation with a quasicrystal lattice potential admits multiple dipole and vortex solitons. The linear and the nonlinear stability of these solitons is investigated using direct simulations of the NLS equation and its linearized equation. It is shown that certain multiple vortex structures on quasicrystal lattices can be linearly unstable but nonlinearly stable. These results have application to investigations of localized structures in nonlinear optics and Bose-Einstein condensates.

Ablowitz, Mark J.; Antar, Nalan; Bak?rta?, ?lkay; Ilan, Boaz

A brief overview of recent theoretical results concerning the existence and stability of three-dimensional solitons in self-focusing media with imprinted two-dimensional harmonic or radially symmetric Bessel optical lattices is given. It is concluded that such photonic lattices support one-parameter families of three-dimensional solitons, which are stable within one interval of the values of their energy (for harmonic lattices) or even within two intervals of the values of their energy (for Bessel lattices), provided that the lattice strength exceeds a threshold value. The Hamiltonian versus soliton norm has two or even three cuspidal points (a "swalowtail"-like bifurcation pattern, which rarely occurs in physical models). The results suggest new approaches of making stable spatiotemporal optical solitons ("light bullets") and three-dimensional solitons in attractive Bose-Einstein condensates.

We explore families of spatiotemporal dissipative solitons in a model of three-dimensional (3D) laser cavities including a combination of gain, saturable absorption, and transverse grating. The model is based on the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity and a two-dimensional (2D) periodic potential representing the grating. Fundamental and vortical solitons are found in a numerical form as attractors in this model and their stability against strong random perturbations is tested by direct simulations. The fundamental solitons are completely stable while the vortices, built as rhombus-shaped complexes of four fundamental solitons, may be split by perturbations into their constituents separating in the temporal direction. Nevertheless, a sufficiently strong grating makes the vortices practically stable objects.

Mihalache, D.; Mazilu, D. [Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest, R-077125 (Romania); Lederer, F. [Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller Universitaet Jena, Max-Wien-Platz 1, D-077743 Jena (Germany); Leblond, H. [Laboratoire POMA, CNRS FRE 2988, Universite d'Angers, 2 Bd Lavoisier, F-49045 Angers Cedex 01 (France); Malomed, B. A. [Department of Physical Electronics, Faculty of Engineering, Tel Aviv University, Tel Aviv Il-69978 (Israel)

We report on the experimental observation of two-dimensional surface solitons residing at the interface between a homogeneous square lattice and a superlattice that consists of alternating “deep” and “shallow” waveguides. By exciting single waveguides in the first row of the superlattice, we show that solitons centered on deep sites require much lower powers for their excitation than their respective counterparts centered on shallow sites. Despite the fact that the average refractive index of the superlattice waveguides is equal to the refractive index of the homogeneous lattice, the interface results in clearly asymmetric output patterns.

Heinrich, M.; Kartashov, Y. V.; Ramirez, L. P. R.; Szameit, A.; Dreisow, F.; Keil, R.; Nolte, S.; Tünnermann, A.; Vysloukh, V. A.; Torner, L.

The solitons and kinks of the SU(3) generalized sine-Gordon model (GSG) are shown to describe the baryonic spectrum of two-dimensional quantum chromodynamics (QCD2). The GSG model arises in the low-energy effective action of bosonized QCD2 with unequal quark mass parameters. The GSG potential for Nf = 3 flavors resembles the potential of the effective chiral lagrangian proposed by Witten to

We study soliton-like excitations and their time and space evolution in several two-dimensional anharmonic lattices with Morse interactions: square lattices including ones with externally fixed square lattice frame (cuprate model), and triangular lattices. We analyze the dispersion equations and lump solutions of the Kadomtsev-Petviashvili equation. Adding electrons to the lattice we find solectron bound states and offer computational evidence of how electrons can be controlled and transported by such acoustic waves and how electron-surfing occurs at the nanoscale. We also offer computational evidence of the possibility of long lasting, fast lattice soliton and corresponding supersonic, almost loss-free transfer or transport of electrons bound to such lattice solitons along crystallographic axes.

We show that defocusing Kerr media with parity-time-symmetric potentials can support one- and two-dimensional bright spatialsolitons. These solitons are found to be stable over the wide range where they exist. More importantly, we discover an exact one-dimensional solution and a closed two-dimensional solution in the structure.

Shi, Zhiwei; Jiang, Xiujuan [School of Information Engineering, Guangdong University of Technology, Guangzhou 510006 (China); Zhu, Xing [State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-Sen University, Guangzhou 510275 (China); Li, Huagang [Department of Physics, Guangdong Institute of Education, Guangzhou 510303 (China)

We consider basic types of two-dimensional (2D) vortex solitons in a three-wave model combining quadratic ?(2) and self-defocusing cubic ?-(3) nonlinearities. The system involves two fundamental-frequency (FF) waves with orthogonal polarizations and a single second-harmonic (SH) one. The model makes it possible to introduce a 2D soliton, with hidden vorticity (HV). Its vorticities in the two FF components are S1,2=±1 , whereas the SH carries no vorticity, S3=0 . We also consider an ordinary compound vortex, with 2S1=2S2=S3=2 . Without the ?-(3) terms, the HV soliton and the ordinary vortex are moderately unstable. Within the propagation distance z?15 diffraction lengths, Zdiffr , the former one turns itself into a usual zero-vorticity (ZV) soliton, while the latter splits into three ZV solitons (the splinters form a necklace pattern, with its own intrinsic dynamics). To gain analytical insight into the azimuthal instability of the HV solitons, we also consider its one-dimensional counterpart, viz., the modulational instability (MI) of a one-dimensional CW (continuous-wave) state with “hidden momentum,” i.e., opposite wave numbers in its two components, concluding that such wave numbers may partly suppress the MI. As concerns analytical results, we also find exact solutions for spreading localized vortices in the 2D linear model; in terms of quantum mechanics, these are coherent states with angular momentum (we need these solutions to accurately define the diffraction length of the true solitons). The addition of the ?-(3) interaction strongly stabilizes both the HV solitons and the ordinary vortices, helping them to persist over z up to 50Zdiffr . In terms of the possible experiment, they are completely stable objects. After very long propagation, the HV soliton splits into two ZV solitons, while the vortex with S3=2S1,2=2 splits into a set of three or four ZV solitons.

Leblond, Hervé; Malomed, Boris A.; Mihalache, Dumitru

Using a three-dimensional mean-field model we study one-dimensional dipolar Bose-Einstein condensate (BEC) solitons on a weak two-dimensional (2D) square and triangular optical lattice (OL) potentials placed perpendicular to the polarization direction. The stabilization against collapse and expansion of these solitons for a fixed dipolar interaction and a fixed number of atoms is possible for short-range atomic interaction lying between two critical limits. The solitons collapse below the lower limit and escapes to infinity above the upper limit. One can also stabilize identical tiny BEC solitons arranged on the 2D square OL sites forming a stable 2D array of interacting droplets when the OL sites are filled with a filling factor of 1/2 or less. Such an array is unstable when the filling factor is made more than 1/2 by occupying two adjacent sites of OL. These stable 2D arrays of dipolar superfluid BEC solitons are quite similar to the recently studied dipolar Mott insulator states on 2D lattice in the Bose-Hubbard model by Capogrosso-Sansone et al. [B. Capogrosso-Sansone, C. Trefzger, M. Lewenstein, P. Zoller, G. Pupillo, Phys. Rev. Lett. 104 (2010) 125301].

We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schroedinger equation, including a local linear or nonlinear defect. Discrete solitons pinned to the defects are investigated by means of the numerical continuation from the anticontinuum limit and also using the variational approximation, which features a good agreement for strongly localized modes. The models with the time-modulated strengths of the linear or nonlinear defect are considered too. In that case, one can temporarily shift the critical norm, below which localized 2D modes cannot exist, to a level above the norm of the given soliton, which triggers the irreversible delocalization transition.

Brazhnyi, Valeriy A. [Centro de Fisica do Porto, Faculdade de Ciencias, Universidade do Porto, R. Campo Alegre 687, P-4169-007 Porto (Portugal); Malomed, Boris A. [Department of Physical Electronics, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

In this paper we address several aspects of flat Bogomolnyi-Prasad-Sommerfeld (BPS) domain walls together with their Lorentz invariant vacua of four-dimensional N=1 supergravity coupled to a chiral multiplet. The scalar field spans a one-parameter family of two-dimensional Kaehler manifolds satisfying a Kaehler-Ricci flow equation. We find that BPS equations and the scalar potential deform with respect to the real parameter related to the Kaehler-Ricci soliton. In addition, the analysis using gradient and renormalization group flows is carried out to ensure the existence of Lorentz invariant vacua related to anti-de Sitter/conformal field theory correspondence.

Gunara, Bobby Eka; Zen, Freddy Permana [Indonesia Center for Theoretical and Mathematical Physics (ICTMP) and Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132 (Indonesia)

We derive from first principles the existence of deep level localized electronic gap states, induced by hedgehog solitons, in the two-dimensional Hubbard model. These arise naturally as excitations in a new topological magnetic condensate of the many-electron system associated with ?1(SO(3)). The condenstate exhibits local spin 1/2 magnetic moments as well as topological ``spin flux.'' This flux emerges microscopically from a homotopically nontrivial phase rotation of the electron spinor field and leads to an intriguing relativistic structure for the Mott-Hubbard gap.

In this program, we have studied, experimentally and theoretically, the fundamental properties of photorefractive spatialsolitons and the features of the interactions between and among them. We brought the topic of photorefractive solitons to the very fr...

We use the cubic complex Ginzburg-Landau equation linearly coupled to a dissipative linear equation as a model for lasers with an external frequency-selective feedback. This system may also serve as a general pattern-formation model in media driven by an intrinsic gain and selective feedback. While, strictly speaking, the approximation of the laser nonlinearity by a cubic term is only valid for small field intensities, it qualitatively reproduces results for dissipative solitons obtained in models with a more complex nonlinearity in the whole parameter region where the solitons exist. The analysis is focused on two-dimensional stripe-shaped and vortex solitons. An analytical expression for the stripe solitons is obtained from the known one-dimensional soliton solution, and its relation with vortex solitons is highlighted. The radius of the vortices increases linearly with their topological charge m, therefore the stripe-shaped soliton may be interpreted as the vortex with m=?, and, conversely, vortex solitons can be realized as unstable stripes bent into stable rings. The results for the vortices are applicable for a broad class of physical systems. PMID:22060481

Paulau, P V; Gomila, D; Colet, P; Malomed, B A; Firth, W J

It is suggested that an interacting many-electron system in a two-dimensional lattice may condense into a topological magnetic state distinct from any discussed previously. This condensate exhibits local spin-1/2 magnetic moments on the lattice sites but is composed of a Slater determinant of single-electron wave functions which exist in an orthogonal sector of the electronic Hilbert space from the sector describing traditional spin-density-wave or spiral magnetic states. These one-electron spinor wave functions have the distinguishing property that they are antiperiodic along a closed path encircling any elementary plaquette of the lattice. This corresponds to a 2? rotation of the internal coordinate frame of the electron as it encircles the plaquette. The possibility of spinor wave functions with spatial antiperiodicity is a direct consequence of the two-valuedness of the internal electronic wave function defined on the space of Euler angles describing its spin. This internal space is the topologically, doubly-connected, group manifold of SO(3). Formally, these antiperiodic wave functions may be described by passing a flux which couples to spin (rather than charge) through each of the elementary plaquettes of the lattice. When applied to the two-dimensional Hubbard model with one electron per site, this new topological magnetic state exhibits a relativistic spectrum for charged, quasiparticle excitations with a suppressed one-electron density of states at the Fermi level. For a topological antiferromagnet on a square lattice, with the standard Hartree-Fock, spin-density-wave decoupling of the on-site Hubbard interaction, there is an exact mapping of the low-energy one-electron excitation spectrum to a relativistic Dirac continuum field theory. In this field theory, the Dirac mass gap is precisely the Mott-Hubbard charge gap and the continuum field variable is an eight-component Dirac spinor describing the components of physical electron-spin amplitude on each of the four sites of the elementary plaquette in the original Hubbard model. Within this continuum model we derive explicitly the existence of hedgehog Skyrmion textures as local minima of the classical magnetic energy. These magnetic solitons carry a topological winding number ? associated with the vortex rotation of the background magnetic moment field by a phase angle 2?? along a path encircling the soliton. Such solitons also carry a spin flux of ?? through the plaquette on which they are centered. The ?=1 hedgehog Skyrmion describes a local transition from the topological (antiperiodic) sector of the one-electron Hilbert space to the nontopological sector. We derive from first principles the existence of deep level localized electronic states within the Mott-Hubbard charge gap for the ?=1 and 2 solitons. The spectrum of localized states is symmetric about E=0 and each subgap electronic level can be occupied by a pair of electrons in which one electron resides primarily on one sublattice and the second electron on the other sublattice. It is suggested that flux-carrying solitons and the subgap electronic structure which they induce are important in understanding the physical behavior of doped Mott insulators.

Nonlinear Schroedinger (NLS) equation with external potentials (lattices) possessing crystal and quasicrystal structures are studied. The fundamental solitons and band gaps are computed using a spectral fixed-point numerical scheme. Nonlinear and linear stability properties of the fundamental solitons are investigated by direct simulations and the linear stability properties of the fundamental solitons are confirmed by analysis the linearized eigenvalue problem.

Ablowitz, Mark J.; Antar, Nalan; Bakirtas, Ilkay; Ilan, Boaz [Department of Applied Mathematics, University of Colorado, Colorado 80309-0526 (United States); Istanbul Technical University, Maslak 34469, Istanbul (Turkey); School of Natural Sciences, University of California at Merced, Merced, California 95344 (United States)

We prove that line solitons of the two-dimensional hyperbolic nonlinear Schrödinger equation are unstable under transverse perturbations of arbitrarily small periods, i.e., short waves. The analysis is based on the construction of Jost functions for the continuous spectrum of Schrödinger operators, the Sommerfeld radiation conditions, and the Lyapunov-Schmidt decomposition. We derive precise asymptotic expressions for the instability growth rate in the limit of short periods.

Pelinovsky, D. E.; Rouvinskaya, E. A.; Kurkina, O. E.; Deconinck, B.

Quadratic spatialsolitons have been generated during second-harmonic generation under easy-to-achieve conditions and should be pervasive in other second-order nonlinear interactions. One of the more interesting cases is the downconversion process, which is the essence of parametric generators and oscillators. In this investigation, we report on the generation of two-dimensional quadratic spatialsolitons (QSS) in a KTP crystal near the

M. T. G. Canva; R. A. Fuerst; D. Baboiu; G. I. Stegeman; G. Assanto

We uncover that, in contrast to the common belief, stable dissipative solitons exist in media with uniform gain in the presence of nonuniform cubic losses, whose local strength grows with coordinate ? (in one dimension) faster than |?|. The spatially-inhomogeneous absorption also supports new types of solitons, that do not exist in uniform dissipative media. In particular, single-well absorption profiles give rise to spontaneous symmetry breaking of fundamental solitons in the presence of uniform focusing nonlinearity, while stable dipoles are supported by double-well absorption landscapes. Dipole solitons also feature symmetry breaking, but under defocusing nonlinearity. PMID:22330503

Borovkova, Olga V; Kartashov, Yaroslav V; Vysloukh, Victor A; Lobanov, Valery E; Malomed, Boris A; Torner, Lluis

We study theoretically the nonlinear propagation of a narrow optical wave packet through a cholesteric liquid crystal. We derive the equations governing the weakly nonlinear dynamics of an optical field by taking into account the coupling with the liquid crystal. We constructed the solution as the superposition of four narrow wave packets centered around the linear eigenmodes of the helical structure whose corresponding envelopes A are slowly varying functions of their arguments. We found a system of four coupled equations to describe the resulting vector wave packet which has some integration constants and that under special conditions reduces to the nonlinear Schrödinger equation with space-dependent coefficients. We solved this equation both, using a variational approach and performing numerical calculations. We calculated analytically the solitonspatial scales, the transported power, the nonlinear refraction index, and its wavelength dependence, showing that this has its maxima at the edges of the reflection band. We also exhibit the existence of some other exact but non-self-focused solutions.

A two-dimensional biochemical sensor has been developed for spatially resolved imaging and sensing with 0.2?M glutamate sensitivity and fast response. The glutamate sensor was made by covalently immobilizing glutamate dehydrogenase onto flat silica plates. The two-dimensional sensor has the advantage of capturing simultaneous measurements at multiple points and may thus allow better understanding of many biological and chemical processes through

The dynamics of two-dimensional s-polarized solitary waves is investigated with the aid of particle-in-cell (PIC) simulations. Instead of the usual excitation of the waves with a laser pulse, the PIC code was directly initialized with the numerical solutions from the fluid plasma model. This technique allows the analysis of different scenarios including the theoretical problems of the solitary wave stability and their collision as well as features already measured during laser-plasma experiments such as the emission of electromagnetic bursts when the waves reach the plasma-vacuum interface, or their expansion on the ion time scale, usually named post-soliton evolution. Waves with a single density depression are stable whereas multihump solutions decay to several waves. Contrary to solitons, two waves always interact through a force that depends on their relative phases, their amplitudes, and the distance between them. On the other hand, the radiation pattern at the plasma-vacuum interface was characterized, and the evolution of the diameter of different waves was computed and compared with the ''snow plow'' model.

Sanchez-Arriaga, G.; Lefebvre, E. [CEA, DAM, DIF, F-91297 Arpajon (France)

A two-dimensional (2-D) signal with a variable spatial frequency is proposed as a watermark in the spatial domain. This watermark is characterized by a linear frequency change. It can be efficiently detected by using 2-D space\\/spatial-frequency distributions. The projections of the 2-D Wigner distribution-the 2-D Radon-Wigner distribution, are used in order to emphasize the watermark detection process. The watermark robustness

We address the problem of directional mobility of discrete solitons in two-dimensional rectangular lattices, in the framework of a discrete nonlinear Schrödinger model with saturable on-site nonlinearity. A numerical constrained Newton-Raphson method is used to calculate two-dimensional Peierls-Nabarro energy surfaces, which describe a pseudopotential landscape for the slow mobility of coherent localized excitations, corresponding to continuous phase-space trajectories passing close to stationary modes. Investigating the two-parameter space of the model through independent variations of the nonlinearity constant and the power, we show how parameter regimes and directions of good mobility are connected to the existence of smooth surfaces connecting the stationary states. In particular, directions where solutions can move with minimum radiation can be predicted from flatter parts of the surfaces. For such mobile solutions, slight perturbations in the transverse direction yield additional transverse oscillations with frequencies determined by the curvature of the energy surfaces, and with amplitudes that for certain velocities may grow rapidly. We also describe how the mobility properties and surface topologies are affected by inclusion of weak lattice anisotropy.

Naether, Uta; Vicencio, Rodrigo A.; Johansson, Magnus

We use Hamiltonian ray tracing and phase-space representation to describe the propagation of a single spatialsoliton and soliton collisions in a Kerr nonlinear medium. Hamiltonian ray tracing is applied using the iterative nonlinear beam propagation method, which allows taking both wave effects and Kerr nonlinearity into consideration. Energy evolution within a single spatialsoliton and the exchange of energy when two solitons collide are interpreted intuitively by ray trajectories and geometrical shearing of the Wigner distribution functions.

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatialsolitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatialsolitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatialsolitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatialsolitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatialsolitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatialsolitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatialsolitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatialsolitons in systems with parity-time symmetry will also be discussed briefly.

Chen, Zhigang; Segev, Mordechai; Christodoulides, Demetrios N.

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatialsolitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatialsolitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatialsolitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatialsolitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatialsolitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatialsolitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatialsolitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatialsolitons in systems with parity-time symmetry will also be discussed briefly. PMID:22836010

Chen, Zhigang; Segev, Mordechai; Christodoulides, Demetrios N

Two-dimensional Fourier spatial power spectra of equivalent magnetization values are presented for a region that includes a large portion of the western United States. The magnetization values were determined by inversion of POGO satellite data, assuming a magnetic crust 40 km thick, and were located on an 11 x 10 array with 300 km grid spacing. The spectra appear to

Two-dimensional Fourier spatial power spectra of equivalent magnetization values are presented for a region that includes a large portion of the western United States. The magnetization values were determined by inversion of POGO satellite data, assuming a magnetic crust 40 km thick, and were located on an 11 x 10 array with 300 km grid spacing. The spectra appear to be in good agreement with values of the crustal geomagnetic field spatial power spectra given by McLeod and Coleman (1980) and with the crustal field model given by Serson and Hannaford (1957). The spectra show evidence of noise at low frequencies in the direction along the satellite orbital track (N-S). indicating that for this particular data set additional filtering would probably be desirable. These findings illustrate the value of two-dimensionalspatial power spectra both for describing the geomagnetic field statistically and as a guide for diagnosing possible noise sources.

Two-dimensional Fourier spatial power spectra of equivalent magnetization values are presented for a region that includes a large portion of the western United States. The magnetization values were determined by inversion of POGO satellite data, assuming a magnetic crust 40 km thick, and were located on an 11 x 10 array with 300 km grid spacing. The spectra appear to be in good agreement with values of the crustal geomagnetic field spatial power spectra given by McLeod and Coleman (1980) and with the crustal field model given by Serson and Hannaford (1957). The spectra show evidence of noise at low frequencies in the direction along the satellite orbital track (N-S). indicating that for this particular data set additional filtering would probably be desirable. These findings illustrate the value of two-dimensionalspatial power spectra both for describing the geomagnetic field statistically and as a guide for diagnosing possible noise sources.

Recently, high-density surface EMG electrode grids and multi-channel amplifiers became available for non-invasive recording of human motor units (MUs). We present a way to decompose surface EMG signals into MU firing patterns, whereby we concentrate on the importance of two-dimensionalspatial differences between the MU action potentials (MUAPs). Our method is exemplified with high-density EMG data from the vastus lateralis muscle of a single subject. Bipolar and Laplacian spatial filtering was applied to the monopolar raw signals. From the single recording in this subject six different simultaneously active MUs could be distinguished using the spatial differences between MUAPs in the direction perpendicular to the muscle fiber direction. After spike-triggered averaging, 125-channel two-dimensional MUAP templates were obtained. Template-matching allowed tracking of all MU firings. The impact of spatial information was measured by using subsets of the MUAP templates, either in parallel or perpendicular to the muscle fiber direction. The use of one-dimensional spatial information perpendicular to the muscle fiber direction was superior to the use of a linear array electrode in the longitudinal direction. However, to detect the firing events of the MUs with a high accuracy, as needed for instance for estimation of firing synchrony, two-dimensional information from the complete grid electrode appears essential. PMID:16904342

Kleine, Bert U; van Dijk, Johannes P; Lapatki, Bernd G; Zwarts, Machiel J; Stegeman, Dick F

We report on what is, to our knowledge, the first experimental observation of spatialsoliton interaction with charged conductive microelectrodes in nematic liquid crystals. We show that solitons can undergo voltage-controlled deflection and reflection with a nematicon steering larger than 100° over distances of a few micrometers. Using bias-defined perturbations, we observe reconfigurable soliton geometries with several reflections. PMID:24690868

Experimental observation of spatialsolitons in azobenzene-doped organic polymer is demonstrated in dye-doped polymer bulk material. Solitons cannot only be formed in this material with linearly polarized light, but also with circularly polarized light. An interesting phenomenon is revealed that the soliton is polarization-dependent. The solitons with the same intensity but with different polarizations have different widths. The experimental results are further theoretically explained with the dynamics model based on a photochemical process, namely photoisomerization.

We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose–Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of stable nonlinear single or multi-vortex excitations. The potential instability of the single vortex is also examined and is found to possess similar characteristics to those of the nodeless cloud. We also report that, contrary to what is known, e.g., for the atomic BEC case, stable stationary gray ring solitons (that can be thought of as radial forms of Nozaki–Bekki holes) can be found for polariton condensates in suitable parametric regimes. In other regimes, however, these may also suffer symmetry-breaking instabilities. The dynamical, pattern-forming implications of the above instabilities are explored through direct numerical simulations and, in turn, give rise to waveforms with triangular or quadrupolar symmetry.

Rodrigues, A. S.; Kevrekidis, P. G.; Carretero-González, R.; Cuevas-Maraver, J.; Frantzeskakis, D. J.; Palmero, F.

We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of stable nonlinear single or multi-vortex excitations. The potential instability of the single vortex is also examined and is found to possess similar characteristics to those of the nodeless cloud. We also report that, contrary to what is known, e.g., for the atomic BEC case, stable stationary gray ring solitons (that can be thought of as radial forms of Nozaki-Bekki holes) can be found for polariton condensates in suitable parametric regimes. In other regimes, however, these may also suffer symmetry-breaking instabilities. The dynamical, pattern-forming implications of the above instabilities are explored through direct numerical simulations and, in turn, give rise to waveforms with triangular or quadrupolar symmetry. PMID:24674920

Rodrigues, A S; Kevrekidis, P G; Carretero-González, R; Cuevas-Maraver, J; Frantzeskakis, D J; Palmero, F

A computational study of spatially evolving two-dimensional free shear flows has been performed using direct numerical simulation of the Navier-Stokes equations in order to investigate the ability of these two-dimensional simulations to predict the overall flow-field quantities of the corresponding three-dimensional ``real'' turbulent flows. The effects of inflow forcing on these two-dimensional flows has also been studied. Simulations were performed of shear layers, as well as weak (large co-flow and relatively weak shear) and strong (small co-flow and relatively strong shear) jets. Several combinations of discrete forcing with and without a broadband background spectrum were used. Although spatially evolving direct simulations of shear layers have been performed in the past, no such simulations of the plane jet have been performed to the best of our knowledge. It was found that, in the two-dimensional shear layers, external forcing led to a strong increase in the initial growth of the shear-layer thickness, followed by a region of decreased growth as in physical experiments. The final downstream growth rate was essentially unaffected by forcing. The mean velocity profile and the naturally evolving growth rate of the shear layer in the case of broadband forcing compare well with experimental data. However, the total and transverse fluctuation intensities are larger in the two-dimensional simulations with respect to experimental data. In the weak-jet simulations it was found that symmetric forcing completely overwhelms the natural tendency to transition to the asymmetric jet column mode downstream. It was observed that two-dimensional simulations of ``strong'' jets with a low speed co-flow led to a fundamentally different flow with large differences even in mean velocity profiles with respect to experimental data for planar jets. This was a result of the dominance of the two-dimensional mechanism of vortex dipole ejection in the flow due to the lack of spanwise instabilities. Experimental studies of planar jets do not show vortex dipole formation and ejection. A three-dimensional ``strong''-jet simulation showed the rapid evolution of three-dimensionality effectively preventing this two-dimensional mechanism, as expected from experimental results.

Based on spatialsoliton solution of a (2+1)-dimensional inhomogeneous nonlinear Schrödinger equation in the presence of the parity-time symmetric potential, we discuss nonlinear tunnelling effect when spatialsoliton passes through the diffraction well and diffraction barrier. When the spatialsoliton passes through the diffraction well, the nonlinear tunnelling effect happens, that is, its amplitude diminishes and after the well, its amplitude then adds. When the spatialsoliton passes through the diffraction barrier, the nonlinear tunnelling effect does not happen.

The directional emission intensities emerging from a two-dimensional rectangular cavity of semi-transparent media in which is imposed a spatial variable refractive index, have been determined by a curved ray-tracing method determining the trajectories of radiation propagation and integrating the radiative transfer equation on each of these trajectories. Cases of affine refractive indexes with respect to the space variables are examined,

This paper presents a fast technique for fine estimation of two-dimensional (2-D) parameters, based on a parabolic interpolation of the same ambiguity function samples, and aimed at block-oriented estimation of the spatial shift between pairs of images in video sequences. Expressions for the bias and variance of the position error and the prediction error are derived. The method is tested

Recently, high-density surface EMG electrode grids and multi-channel amplifiers became available for non-invasive recording of human motor units (MUs). We present a way to decompose surface EMG signals into MU firing patterns, whereby we concentrate on the importance of two-dimensionalspatial differences between the MU action potentials (MUAPs). Our method is exemplified with high-density EMG data from the vastus lateralis

Bert U. Kleine; Johannes P. van Dijk; Bernd G. Lapatki; Machiel J. Zwarts; Dick F. Stegeman

It is commonly known that two-dimensional mean-field models of optical and matter waves with cubic self-attraction cannot produce stable solitons in free space because of the occurrence of collapse in the same setting. By means of numerical analysis and variational approximation, we demonstrate that the two-component model of the Bose-Einstein condensate with the spin-orbit Rashba coupling and cubic attractive interactions gives rise to solitary-vortex complexes of two types: semivortices (SVs, with a vortex in one component and a fundamental soliton in the other), and mixed modes (MMs, with topological charges 0 and ±1 mixed in both components). These two-dimensional composite modes can be created using the trapping harmonic-oscillator (HO) potential, but remain stable in free space, if the trap is gradually removed. The SVs and MMs realize the ground state of the system, provided that the self-attraction in the two components is, respectively, stronger or weaker than the cross attraction between them. The SVs and MMs which are not the ground states are subject to a drift instability. In free space (in the absence of the HO trap), modes of both types degenerate into unstable Townes solitons when their norms attain the respective critical values, while there is no lower existence threshold for the stable modes. Moving free-space stable solitons are also found in the present non-Galilean-invariant system, up to a critical velocity. Collisions between two moving solitons lead to their merger into a single one. PMID:24730926

The research about fast transient and spatially non-homogenous nuclear reactor accident analysis of two-dimensional nuclear reactor has been done. This research is about prediction of reactor behavior is during accident. In the present study, space-time diffusion equation is solved by using direct methods which consider spatial factor in detail during nuclear reactor accident simulation. Set of equations that obtained from full implicit finite-difference discretization method is solved by using iterative methods ADI (Alternating Direct Implicit). The indication of accident is decreasing macroscopic absorption cross-section that results large external reactivity. The power reactor has a peak value before reactor has new balance condition. Changing of temperature reactor produce a negative Doppler feedback reactivity. The reactivity will reduce excess positive reactivity. Temperature reactor during accident is still in below fuel melting point which is in secure condition.

Yulianti, Yanti; Su'Ud, Zaki; Waris, Abdul; Khotimah, S. N.; Shafii, M. Ali

A real-time measurement method for two-dimensional (2D) spatial distribution of the electron temperature and plasma density was developed. The method is based on the floating harmonic method and the real time measurement is achieved with little plasma perturbation. 2D arrays of the sensors on a 300 mm diameter wafer-shaped printed circuit board with a high speed multiplexer circuit were used. Experiments were performed in an inductive discharge under various external conditions, such as powers, gas pressures, and different gas mixing ratios. The results are consistent with theoretical prediction. Our method can measure the 2D spatial distribution of plasma parameters on a wafer-level in real-time. This method can be applied to plasma diagnostics to improve the plasma uniformity of plasma reactors for plasma processing.

Kim, Young-Cheol [Department of Nanoscale Semiconductor Engineering, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791 (Korea, Republic of); Jang, Sung-Ho; Oh, Se-Jin; Lee, Hyo-Chang; Chung, Chin-Wook [Department of Electrical Engineering, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791 (Korea, Republic of)

A theory is presented to show that dark and grey spatialsolitons can be formed spontaneously in azobenzene-containing polymers (ACPs) with photoisomerization nonlinearity by simultaneously considering the angle hole burning (AHB) effect and the photoinduced molecular reorientation (PMR) effect. It shows that compared to that of the AHB effect, the contribution of the PMR to the formation of solitons is evident and cannot be ignored. It is found that the dependence of the width of this kind of solitons on the intensity of the light beam is similar to that of photorefractive solitons.

Finding exact analytical soliton profile solutions is only possible for certain types of non-linear media. In most cases one must resort to numerical techniques to find the soliton profile. In this work we present numerical calculations of spatialsoliton profiles in nematic liquid crystals. The nonlinearity is governed by the optical-field-induced liquid crystal director reorientation, which is described by a system of coupled nonlinear partial differential equations. The soliton profile is found using an iterative scheme whereby the induced waveguide and mode profiles are calculated alternatively until convergence is achieved. In this way it is also possible to find higher order solitons. The results in this work can be used to accurately design all-optical interconnections with soliton beams. PMID:20389338

Beeckman, J; Neyts, K; Vanbrabant, P J M; James, R; Fernandez, F A

In the absence of detector arrays, a single pixel coupled with a spatially selective mask has been shown to be a practical solution to imaging problems in the terahertz and sub-millimeter wave domains. In this paper we demonstrate real-time two-dimensional imager for sub-millimeter waves that is based on a spatially selective image plane mask. The imager consists of a heterodyne source and receiver pair, image forming optics, a spatially selective mask, data acquisition hardware, and image reconstruction software. The optics form an image onto the spatially selective mask and linear measurements of the image are made. The mask must be designed to ensure maximum transmission, measurement linearity, and measurement to measurement independence and our design parameters are presented. Once enough linearly independent measurements are made, the image is reconstructed by solving a system of linear equations that is generated from the mask patterns and the corresponding measurements. We show that for image sizes envisioned for many current applications, this image reconstruction technique is computationally efficient and can be implemented in real time. We present images collected using this system, discuss the results, and discuss other applications for some components of the imager.

Fully-sampled two-dimensional (2D) arrays can have two-way focusing of the ultrasound beam in both lateral directions leading to high quality, real-time three-dimensional (3D) imaging. However, fully-sampled 2D arrays with very large element counts (>16,000) are difficult to manufacture due to interconnect density and large element electrical impedance. As an alternative, row-column or crossed electrode arrays have been proposed to simplify transducer fabrication and system integration. These types of arrays consist of two one-dimensional arrays oriented perpendicular to each other. Using conventional delay-and-sum beamforming, each array performs one-way focusing in perpendicular lateral directions which yield higher sidelobe and acoustic clutter levels compared to fully-sampled 2D arrays with two-way focusing. In this paper, the use of spatial matched filters to improve focusing of row-column arrays is investigated. On receive, data from each element are first spatial match filtered in the elevation direction. After summation, the data are filtered again in the azimuth direction. Beam widths comparable to one-way focusing are seen in azimuth and beam widths comparable to two-way focusing are achieved in elevation. 3D beam patterns from computer simulation results using a 7.5?MHz 128?×?128 row-column array are shown with comparison to a fully sampled 2D array. PMID:24180780

We show that excitability is generic in systems displaying dissipative solitons when spatial inhomogeneities and drift are present. Thus, dissipative solitons in systems which do not have oscillatory states, such as the prototypical Swift-Hohenberg equation, display oscillations and type I and II excitability when adding inhomogeneities and drift to the system. This rich dynamical behavior arises from the interplay between the pinning to the inhomogeneity and the pulling of the drift. The scenario presented here provides a general theoretical understanding of oscillatory regimes of dissipative solitons reported in semiconductor microresonators. Our results open also the possibility to observe this phenomenon in a wide variety of physical systems. PMID:23432247

In this work, we propose a single-atom interferometer based on a fully two-dimensionalspatial adiabatic passage process using a system of three identical harmonic traps in a triangular geometry. While the transfer of a single atom from the ground state of one trap to the ground state of the most distant one can successfully be achieved in a robust way for a broad range of parameter values, we point out the existence of a specific geometrical configuration of the traps for which a crossing of two energy eigenvalues occurs and the transfer of the atom fails. Instead, the wave function is robustly split into a coherent superposition between two of the traps. We show that this process can be used to construct a single-atom interferometer and discuss its performance in terms of the final population distribution among the asymptotic eigenstates of the individual traps. This interferometric scheme could be used to study space-dependent fields from ultrashort to relatively large distances, or the decay of the coherence of superposition states as a function of the distance.

Menchon-Enrich, R.; McEndoo, S.; Busch, Th.; Ahufinger, V.; Mompart, J.

It is suggested that an interacting many-electron system in a two-dimensional lattice may condense into a topological magnetic state distinct from any discussed previously. This condensate exhibits local spin-1\\/2 magnetic moments on the lattice sites but is composed of a Slater determinant of single-electron wave functions which exist in an orthogonal sector of the electronic Hilbert space from the sector

In this paper we answer the question: “what types of spatialsoliton can be formed based on two-photon-isomerisation (TPI)”. The conclusion that anti-dark solitons are not supported by monotonic nonlinearity should cast light on the notion of fundamental spatialsolitons. The idea to obtain a bright TPI soliton with the joining of a background light or with the coupling of a dark soliton offers new schemes of light-controlling-light.

Liang, J. C.; Cai, Z. B.; Sun, Y. Z.; Yi, L.; Wang, H. C.

We describe and evaluate a new analysis technique, spatial wavelet analysis (SWA), to automatically estimate the location, height, and crown diameter of individual trees within mixed conifer open canopy stands from light detection and ranging (lidar) data. Two-dimensional Mexican hat wavelets, over a range of likely tree crown diameters, were convolved with lidar canopy height models. Identification of local maxima

Michael J. Falkowski; Alistair M. S. Smith; Andrew T. Hudak; Paul E. Gessler; Lee A. Vierling; Nicholas L. Crookston

A method is proposed to generate and study the dynamics of spatial light solitons in a birefringent medium with quadratic nonlinearity. Although no analytical expression for propagating solitons has been obtained, our numerical simulations show the existence of stable localized spatialsolitons in the frequency forbidden band gap of the medium. The dynamics of these objects is quite rich and manifests for instance elastic reflections, or inelastic collisions where two solitons merge and propagate as a single solitary wave. We derive the dynamics of the slowly varying envelopes of the three fields (second harmonic pump and two-component signal) and study this new system theoretically. We show that it does present a threshold for nonlinear supratransmission that can be calculated from a series expansion approach with a very high accuracy. Specific physical implications of our theoretical predictions are illustrated on LiGaTe{sub 2} (LGT) crystals. Once irradiated by a cw laser beam of 10 {mu}m wavelength, at an incidence beyond the extinction angle, such crystals will transmit light, in the form of spatialsolitons generated in the nonlinear regime above the nonlinear supratransmission threshold.

Anghel-Vasilescu, P. [Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, D-01187 Dresden (Germany); Dorignac, J.; Geniet, F.; Leon, J. [Laboratoire Charles Coulomb, Departement de Physique Theorique, UMR 5221 CNRS-UM2, Universite Montpellier 2, F-34095 Montpellier Cedex 5 (France); Taki, A. [Laboratoire de Physique des Lasers, Atomes et Molecules, CNRS-INP-UMR8523, Universite des Sciences et Technologies de Lille, F-59655 Villeneuve d'Ascq (France)

The immobilization of functional units in the interlayer spaces of layered silicates and titanates is summarized from the viewpoint of how the spatial distribution of functional units in the interlayer affects the performance of the intercalation compounds. The ways of incorporating controlled amounts of functional units with controlled spatial distribution are also discussed. As a result of controlled spatial distribution of functional units in two-dimensional nanospace, one can achieve improved efficiency of photo-induced events (photoluminescence and photoinduced electron/energy transfer), molecular sieving and substrate/product selective catalytic reactions. PMID:24789673

Domain walls with oscillatory tails are commonplace in models of spatially extended nonlinear optical devices. Their interaction and locking at discrete distances lead to asymptotically stable spatial disorder. We show that noise in the presence of domain walls with oscillatory tails can suppress spatial disorder by privileging highly correlated dynamical states consisting of arrays of spatialsolitons. PMID:12484888

We have studied magnetotransport in the two-dimensional electron gas (2D EG) in a GaAs-(Al,Ga)As heterojunction consisting of two contiguous regions in series characterized by different resistivity tensors as a model for a realistic, inhomogeneous 2D EG. We observed effects of a magnetic field dependence of the in-plane band diagram and of macroscopic current redistributions. Under conditions where the first effect

G. L. J. A. Rikken; J. A. M. M. van Haaren; A. P. van Gelder; H. van Kempen; P. Wyder; H.-U. Habermeier; K. Ploog

We present results on the spatial distribution of copper vapour flux in the three-dimensional flow behaviour region under identical experimental conditions as a function of the temperature of a two-dimensional (2D) evaporating source. These experimental results clearly show that, with increasing source temperature, atomic collision processes along the length and the width of a 2D source differ, which results in

We find that the recently introduced model of self-trapping supported by a spatially growing strength of a repulsive nonlinearity gives rise to robust vortex-soliton tori, i.e., three-dimensional vortex solitons, with topological charges S?1. The family with S=1 is completely stable, while the one with S=2 has alternating regions of stability and instability. The families are nearly exactly reproduced in an analytical form by the Thomas-Fermi approximation. Unstable states with S=2 and 3 split into persistently rotating pairs or triangles of unitary vortices. Application of a moderate torque to the vortex torus initiates a persistent precession mode, with the torus' axle moving along a conical surface. A strong torque heavily deforms the vortex solitons, but, nonetheless, they restore themselves with the axle oriented according to the vectorial addition of angular momenta. PMID:24483996

A system for continuous variable quantum key distribution via a wavelength router is proposed. The Kerr type of light in the nonlinear microring resonator (NMRR) induces the chaotic behavior. In this proposed system chaotic signals are generated by an optical soliton or Gaussian pulse within a NMRR system. The parameters, such as input power, MRRs radii and coupling coefficients can change and plays important role in determining the results in which the continuous signals are generated spreading over the spectrum. Large bandwidth signals of optical soliton are generated by the input pulse propagating within the MRRs, which is allowed to form the continuous wavelength or frequency with large tunable channel capacity. The continuous variable QKD is formed by using the localized spatialsoliton pulses via a quantum router and networks. The selected optical spatial pulse can be used to perform the secure communication network. Here the entangled photon generated by chaotic signals has been analyzed. The continuous entangled photon is generated by using the polarization control unit incorporating into the MRRs, required to provide the continuous variable QKD. Results obtained have shown that the application of such a system for the simultaneous continuous variable quantum cryptography can be used in the mobile telephone hand set and networks. In this study frequency band of 500 MHz and 2.0 GHz and wavelengths of 775 nm, 2,325 nm and 1.55 ?m can be obtained for QKD use with input optical soliton and Gaussian beam respectively.

Kouhnavard, M.; Amiri, I. S.; Afroozeh, A.; Jalil, M. A.; Ali, J.; Yupapin, P. P.

Effects of recurrence and multiplication in the spatial distribution of the probability-flux density j\\u000a x(x, z) (or the quantum-mechanical current density ej\\u000a x(x, z), where e is the elementary charge), which arise from electron-wave interference in two-dimensional semiconductor nanostructures, are\\u000a analyzed, and the possibility of controlling these effects by the application of a dc transverse electric field is examined.\\u000a A

Using recent advances in the constrained-path auxiliary-field quantum Monte Carlo method, we study the ground state of the two-dimensional, single-band Hubbard model at intermediate interactions (2<=U/t <=8). In the first part of this study [1], we have determined the equation of state and also calculated the spin-spin correlation functions in square lattices up to size 16x16. Shell effects are eliminated and finite-size effects are greatly reduced by boundary condition integration. It was shown that, upon doping, the system separates into a region with antiferromagnetic (AF) order and a hole-containing region without AF order. In the second part, we study rectangular supercells up to 8x64 to examine the nature of this inhomogeneous phase, in particular to probe phase separation versus stripes and spin-density waves of long wave lengths. [1] Chia-Chen Chang and Shiwei Zhang, Phys. Rev. B 78, 165101 (2008)

This thesis investigates the dynamical and soliton-like behavior of spatially-partially incoherent light beams in non-instantaneous nonlinear materials. Self-trapping of incoherent beams and their coherence properties are studied in great detail. Two complimentary approaches are developed in order to explain the observed incoherent self-focusing behavior in biased photorefractive media; namely the coherent density approach and the self- consistent incoherent multimode method. It is shown that under appropriate initial conditions, bright as well as dark-like incoherent solitons are possible in saturable nonlinear media. Our numerical simulations have demonstrated that the coherence properties of these beams are significantly affected by the self-trapping process. More specifically, in the case of bright beams, we have found that the coherence length remains approximately constant around the center of the beam, whereas it increases at the margins. An exact (one/twodimensional) Gaussian solution was also obtained in the case where the nonlinearity is of the logarithmic type. These incoherent Gaussian solitons can exist as long as their spatial width is appropriately related to the strength of the nonlinearity and the width of the angular power spectrum of the incoherent source. Moreover, twodimensional incoherent solitons can be elliptical or circular depending on whether the angular power spectrum of the incoherent source is symmetric or not. Our analysis has demonstrated that dark incoherent solitons are possible only if a ?-phase shift is initially imposed on the wave front, and that they are in fact gray. In this case, the coherence length has been found to be higher within the dark notch, with a depression at the center. These dark soliton entities involve radiation modes as well as bound states. Depending on the initial conditions, an even or an odd number of incoherent dark-like structures can be obtained in a self-defocusing environment. It was found that over a wide range of parameters, the Y-splitting is approximately the same irrespective of spatial coherence. It is important to note that the behavior of bright/dark incoherent solitons is fundamentally different from that of their coherent counterparts. For example, unlike a coherent gray soliton, an incoherent dark soliton does not exhibit a transverse velocity in spite of its grayness. Furthermore, it is shown that the evolution of incoherent dark solitons in non-instantaneous nonlinear media is associated with strong ``phase- memory'' effects which are otherwise absent in the linear regime.

We investigated whether and how student performance on three types of spatial cognition tasks differs when worked with two-dimensional or stereoscopic representations. We recruited nineteen middle school students visiting a planetarium in a large Midwestern American city and analyzed their performance on a series of spatial cognition tasks in terms of response accuracy and task completion time. Results show that response accuracy did not differ between the two types of representations while task completion time was significantly greater with the stereoscopic representations. The completion time increased as the number of mental manipulations of 3D objects increased in the tasks. Post-interviews provide evidence that some students continued to think of stereoscopic representations as two-dimensional. Based on cognitive load and cue theories, we interpret that, in the absence of pictorial depth cues, students may need more time to be familiar with stereoscopic representations for optimal performance. In light of these results, we discuss potential uses of stereoscopic representations for science learning.

By using a rigorous plane-wave representation, we examine the diffracted fields generated by a Gaussian beam incident onto the planar upper boundary of a 2D periodic structure. We first determine a geometric profile for every diffracted beam by neglecting the amplitude variation of its plane-wave spectrum. We then account for the spectral variation and show that, with respect to that geometric profile, every actual diffracted beam exhibits spatial modifications in the form of 2D lateral displacements, focal shifts, angular deviations, and beam-width alterations. These effects are relatively large if the incidence conditions tend to generate grating resonances. The magnitudes of the beam modifications are illustrated by using a canonic grating model that consists of a planar surface whose impedance varies sinusoidally along its two orthogonal directions. We also develop accurate analytical expressions for the spatial modifications by expressing the spectral amplitude functions in terms of Padé approximants. We thus find that the 2D spatial effects exhibit greater complexity and include features that are absent in previously reported cases involving 1D periodic surfaces. PMID:17491635

Purpose To demonstrate reduced field-of-view (RFOV) single-shot fast spin echo (SS-FSE) imaging based on the use of two-dimensionalspatially-selective RF pulses. Materials and Methods 2DRF pulses were incorporated into a SS-FSE sequence for RFOV imaging in both phantoms and the human brain on a 1.5 T whole-body MR system with the aim of demonstrating improvements in terms of shorter scan time, reduced blurring and higher spatial resolution compared to full FOV imaging. Results For phantom studies, scan time gains of up to 4.2 fold were achieved as compared to the full FOV imaging. For human studies, the spatial resolution was increased by a factor of 2.5 (from 1.7 mm/pixel to 0.69 mm/pixel) for RFOV imaging within a scan time (0.7s) similar to full FOV imaging. A 2.2-fold shorter scan time along with a significant reduction of blurring was demonstrated in RFOV images compared to full FOV images for a target spatial resolution of 0.69 mm/pixel. Conclusion RFOV SS-FSE imaging using a 2DRF pulse shows advantages in scan time, blurring, and SAR reduction along with true spatial resolution increase compared to full FOV imaging. This approach is promising to benefit fast imaging applications such as image guided therapy.

Yuan, Jing; Zhao, Tzu-Cheng; Tang, Yi; Panych, Lawrence P.

Particulate composite reinforcements are good candidates for the fracture toughness of ceramics. In order to predict mechanical response of ceramic matrix composites, an efficient method capable of modelling their complex microstructure is needed. The purpose of this research is the development of such a model using fractal spatial particle distribution. A review of different toughness mechanisms for particulate composites and associated models for deriving their constitutive relationships is presented in chapter 2. These different toughening mechanisms as well constitutive properties depend on particle shape, size and spatial distribution, which lend themselves to a self-similar fractal based modelling approach. A self-similar distribution of particles linked to the fractal geometry is proposed. Fractal geometry provides an ideal tool for describing the randomness and disorder of the system. Its foundations are reviewed in chapter three with emphasis on iterated function systems that are subsequently used to obtain the particle configurations in the proposed model. For the sake of completeness, a review of fractal structure in science is given to illustrate possible applications. Derivation of the volume fraction associated with self similar distributions is provided in chapter 4. This is followed by a description of the numerical model and the boundary conditions. A Finite Element simulation is performed for different volume fractions, generators and number of particles for different displacements (two uniaxial and biaxial cases) and 2-D stress state cases. From these simulations the inverse distribution of the maximum principal stress is computed. Then the self similar models are compared with the model obtained by the Yang Teriari Gokhale (Y.T.G.) method and model obtained by only one iteration. Fractal dimension for real microstructure are computed and microstructure based on the fractal dimension and number of particle is simulated. It can be derived that the fractal dimension can be related to the average radius of circular particle in special cases. General conclusion and recommendation for future work brings this investigation to a close.

MR thermometry can be a very challenging application, as good resolution may be needed along spatial, temporal, and temperature axes. Given that the heated foci produced during thermal therapies are typically much smaller than the anatomy being imaged, much of the imaged field-of-view is not actually being heated and may not require temperature monitoring. In this work, many-fold improvements were obtained in terms of temporal resolution and/or 3D spatial coverage by sacrificing some of the in-plane spatial coverage. To do so, three fast-imaging approaches were jointly implemented with a spoiled gradient echo sequence: (1) two-dimensionalspatially selective RF excitation, (2) unaliasing by Fourier encoding the overlaps using the temporal dimension (UNFOLD), and (3) parallel imaging. The sequence was tested during experiments with focused ultrasound heating in ex vivo tissue and a tissue-mimicking phantom. Temperature maps were estimated from phase-difference images based on the water proton resonance frequency shift. Results were compared to those obtained from a spoiled gradient echo sequence sequence, using a t-test. Temporal resolution was increased by 24-fold, with temperature uncertainty less than 1°C, while maintaining accurate temperature measurements (mean difference between measurements, as observed in gel = 0.1°C ± 0.6; R = 0.98; P > 0.05). PMID:21337421

Mei, Chang-Sheng; Panych, Lawrence P; Yuan, Jing; McDannold, Nathan J; Treat, Lisa H; Jing, Yun; Madore, Bruno

MR thermometry can be a very challenging application, as good resolution may be needed along spatial, temporal as well as temperature axes. Given that the heated foci produced during thermal therapies are typically much smaller than the anatomy being imaged, much of the imaged FOV is not actually being heated and may not require temperature monitoring. In the present work, many-fold improvements were obtained in terms of temporal resolution and/or 3D spatial coverage by sacrificing some of the in-plane spatial coverage. To do so, three fast-imaging approaches were jointly implemented with a spoiled gradient echo sequence: 1) two-dimensionalspatially-selective RF excitation, 2) unaliasing by Fourier-encoding the overlaps using the temporal dimension (UNFOLD), and 3) parallel imaging. The sequence was tested during experiments with focused ultrasound heating in ex-vivo tissue and a tissue-mimicking phantom. Temperature maps were estimated from phase-difference images based on the water proton resonance frequency shift. Results were compared to those obtained from a spoiled gradient echo sequence, using a t-test. Temporal resolution was increased by 24-fold, with temperature uncertainty less than 1°C, while maintaining accurate temperature measurements (mean difference between measurements, as observed in gel, = 0.1°C ± 0.6; R = 0.98; P > 0.05).

Mei, Chang-Sheng; Panych, Lawrence P.; Yuan, Jing; McDannold, Nathan J.; Treat, Lisa H.; Jing, Yun; Madore, Bruno

A new approach recently developed by one of the authors has been utilised to study the effect of Raman perturbation on the propagation characteristics of spatialsoliton in an optical lattice. The time-dependent nature of perturbation effectively induces a spatio-temporal behaviour of the pulse. The variation of the amplitude, width, chirp and frequency of the pulse are obtained through the projection operator technique. Important consequences are seen to follow due to the mutual influence of the periodicity of the lattice and the strength of Raman perturbations. Optimum configurations are sorted out with the help of an external pumping at fixed spatial interval. It is observed that in the absence of any dispersion management, it is possible to restore the profile of the pulse by pumping at regular series of intervals.

We present a systematic investigation of ultrashort electromagnetic pulse propagation in metamaterials (MMs) with simultaneous cubic electric and magnetic nonlinearity. We predict that spatiotemporal electromagnetic solitons may exist in the positive-index region of a MM with focusing nonlinearity and anomalous group velocity dispersion (GVD), as well as in the negative-index region of the MM with defocusing nonlinearity and normal GVD. The experimental circumstances for generating and manipulating spatiotemporal electromagnetic solitons can be created by elaborating appropriate MMs. In addition, we find that, in the negative-index region of a MM, a spatial ring may be formed as the electromagnetic pulse propagates for focusing nonlinearity and anomalous GVD; while the phenomenon of temporal splitting of the electromagnetic pulse may appear for the same case except for the defocusing nonlinearity. Finally, we demonstrate that the nonlinear magnetization makes the sign of effective electric nonlinear effect switchable due to the combined action of electric and magnetic nonlinearity, exerting a significant influence on the propagation of electromagnetic pulses.

Zhang Jinggui; Wen Shuangchun; Xiang Yuanjiang; Wang Youwen; Luo Hailu [Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education, School of Computer and Communication, Hunan University, Changsha 410082 (China)

We present a new method for the determination of the two-dimensional (2D) projected spatial distribution of globular clusters (GCs) in external galaxies. This method is based on the K-Nearest Neighbor density estimator of Dressler, complemented by Monte-Carlo simulations to establish the statistical significance of the results. We apply this method to NGC 4261, a ''test galaxy'' where significant 2D anisotropy in the GC distribution has been reported. We confirm that the 2D distribution of GC is not azimuthally isotropic. Moreover, we demonstrate that the 2D distribution departures from the average GC radial distribution results in highly significant spiral-like or broken shell features. Overall, the same perturbations are found in ''red'' and ''blue'' GCs, but with some differences. In particular, we observe a central feature, roughly aligned with the minor axis of NGC 4261, composed of red and most luminous GCs. Blue and fainter GCs are more frequent at large radial distances and follow the spiral-like features of the overall density structure. These results suggest a complex merging history for NGC 4261.

D'Abrusco, R.; Fabbiano, G.; Zezas, A.; Mineo, S.; Fragos, T.; Kim, D.-W. [Harvard-Smithsonian Astrophysical Observatory, 60 Garden Street, Cambridge, MA 02138 (United States); Strader, J. [Department of Astronomy, Michigan State University, 567 Wilson Road, East Lansing, MI 48824-2320 (United States); Bonfini, P. [Physics Department and Institute of Theoretical and Computational Physics, University of Crete, 71003 Heraklion, Crete (Greece); Luo, B. [Department of Astronomy and Astrophysics, 525 Davey Lab, The Pennsylvania State University, University Park, PA 16802 (United States); King, A. [Department of Physics and Astronomy, University of Leicester, Leicester (United Kingdom)

Since 10 years spatial optical solitons are studied for application in optical steering and routing. We propose here another potential use of solitons: a localized spectral probe in colloids. We show the feasibility of this concept by collecting the fluorescence signal escaping from in a cell filled with a mixture of liquid crystal (5CB) and dye (quinizarin), excited either by a spatialsoliton obtained by thermal self-focusing or by a freely propagating beam. We find that the fluorescence signal collected at the output of the soliton is larger than the one collected on the same optical path in the linear regime. A model based on waveguide considerations confirms such a behavior. Finally we discuss how polystyrene particles can be detected in colloids by using spatialsolitons.

Finite-difference weighted essentially non-oscillatory (WENO) simulations of the reshocked two-dimensional single-mode Richtmyer-Meshkov instability using third-, fifth- and ninth-order spatial flux reconstruction and uniform spatial grid resolutions corresponding to 128, 256 and 512 points per initial perturbation wavelength are presented. The dependence of the density, vorticity, simulated density Schlieren and baroclinic production fields, mixing layer width, circulation deposition, mixing profiles, chemical products and mixing fractions, energy spectra, statistics, probability distribution functions, effective turbulent kinetic energy and enstrophy production/dissipation rates, numerical Reynolds numbers, and effective numerical viscosity on the order and resolution is comprehensively investigated to long evolution times. The results are interpreted using the computed implicit numerical diffusion arising from the truncation errors in the characteristic projection-based WENO method. It is quantitatively shown that simulations with higher order and higher resolution have lower numerical dissipation. The sensitivity of the quantities considered to the order and resolution is further amplified following reshock, when the energy deposition on the evolving interface by the second shock-interface interaction induces the formation of small-scale structures. Simulations using lower orders of reconstruction and on coarser grids preserve large-scale structures and flow symmetry to late times, while simulations using higher orders of reconstruction and on finer grids exhibit fragmentation of the structures, symmetry breaking and increased mixing. The investigation demonstrates that similar flow features are qualitatively and quantitatively captured by either approximately doubling the order or the resolution. Additionally, the computational scaling shows that increasing the order is more advantageous than doubling the resolution for the complex shock-driven hydrodynamic flow and WENO method considered here. The present investigation suggests that the ninth-order WENO method is well-suited for the simulation and analysis of complex multi-scale flows and mixing generated by shock-induced hydrodynamic instabilities.

We investigate total internal reflection of nonlocal spatial optical solitons at the interface between two differently oriented regions of a highly birefringent nematic liquid crystal. The solitons survive the interaction with an induced index mismatch and undergo nonspecular reflection, with an emerging angle differing appreciably from the incidence angle. PMID:17501056

Spatialsolitons in nematic liquid crystals are considered in the regime of local response of the crystal, such solitons having been called nematicons in previous experimental studies. In the limit of low light intensity and local material response, it is shown that the full governing equations reduce to a single, higher-order nonlinear Schrödinger equation. Modulation equations are derived for the

Cathy García Reinbert; Antonmaria A. Minzoni; Noel F. Smyth

Weighted essentially non-oscillatory (WENO) simulations of the reshocked two-dimensional single-mode Richtmyer-Meshkov instability using third-, fifth- and ninth-order spatial flux reconstruction and uniform grid resolutions corresponding to 128, 256 and 512 points per initial perturbation wavelength are presented. The dependence of the density, vorticity, simulated density Schlieren and baroclinic production fields, mixing layer width, circulation deposition, mixing profiles, production and mixing fractions, energy spectra, statistics, probability distribution functions, numerical turbulent kinetic energy and enstrophy production/dissipation rates, numerical Reynolds numbers, and numerical viscosity on the order and resolution is investigated to long evolution times. The results are interpreted using the implicit numerical dissipation in the characteristic projection-based, finite-difference WENO method. It is shown that higher order higher resolution simulations have lower numerical dissipation. The sensitivity of the quantities considered to the order and resolution is further amplified following reshock, when the energy deposition by the second shock-interface interaction induces the formation of small-scale structures. Lower-order lower-resolution simulations preserve large-scale structures and flow symmetry to late times, while higher-order higher-resolution simulations exhibit fragmentation of the structures, symmetry breaking and increased mixing. Similar flow features are qualitatively and quantitatively captured by either approximately doubling the order or the resolution. Additionally, the computational scaling shows that increasing the order is more advantageous than increasing the resolution for the flow considered here. The present investigation suggests that the ninth-order WENO method is well-suited for the simulation and analysis of complex multi-scale flows and mixing generated by shock-induced hydrodynamic instabilities.

We study theoretically the properties of waveguides induced by one-dimensional steady-state biased photovoltaic spatialsolitons, and show that the waveguides can be induced by both bright and dark spatialsolitons in the biased photovoltaic- photorefractive crystal such as LiNbO3. We also derive wave equations for the probe beam in the general condition and low-amplitude condition.

We have studied the electronic transport in a two-dimensional electron gas (2DEG) subjected to a spatially modulated magnetic field and electrostatic potential. Independent control of the magnetic field components parallel and perpendicular to the 2DEG plane allows us to manipulate the amplitude of the magnetic modulation independently of the normal field component relevant to the magnetotransport in the 2DEG. The

Mayumi Kato; Akira Endo; Shingo Katsumoto; Yasuhiro Iye

The pulse broadening by group velocity dispersion can be balanced by the narrowing effect of self-phase modulation to form temporal solitons. The identical nonlinear Schrodinger equation describes the one-transverse-dimension balancing of diffraction and ...

G. Khitrova H. M. Gibbs Y. Kawamura H. Iwamura T. Ikegami

In certain materials, the spontaneous spreading of a laser beam (owing to diffraction) can be compensated for by the interplay of optical intensity and material nonlinearity. The resulting non-diffracting beams are called 'spatialsolitons' (refs 1-3), and they have been observed in various bulk media. In nematic liquid crystals, solitons can be produced at milliwatt power levels and have been investigated for both practical applications and as a means of exploring fundamental aspects of light interactions with soft matter. Spatialsolitons effectively operate as waveguides, and so can be considered as a means of channelling optical information along the self-sustaining filament. But actual steering of these solitons within the medium has proved more problematic, being limited to tilts of just a fraction of a degree. Here we report the results of an experimental and theoretical investigation of voltage-controlled 'walk-off' and steering of self-localized light in nematic liquid crystals. We find not only that the propagation direction of individual spatialsolitons can be tuned by several degrees, but also that an array of direction-tunable solitons can be generated by modulation instability. Such control capabilities might find application in reconfigurable optical interconnects, optical tweezers and optical surgical techniques. PMID:15592407

We observe clamping of the output spatial light distribution of a waveguide array. Using a chirped pulse amplifier we reach peak intensities in the waveguides of ~24 GW/cm2. At this level, three photon absorption in the AlGaAs material clamps the discrete spatialsoliton to a set distribution. Further increase in intensity does not change the distribution. PMID:22330434

Hudson, Darren D; Kutz, J Nathan; Schibli, Thomas R; Christodoulides, Demetrios N; Morandotti, Roberto; Cundiff, Steven T

A coaxial backward wave oscillator with a two-dimensional Bragg structure mounted at the exit from the interaction space is studied theoretically and experimentally. Azimuthal wave fluxes arising in this structure permit one to synchronize radiation of different fractions of a tubular relativistic electron beam with a large diameter. A narrowband radiation of the 8-mm range with a megawatt level of power has been obtained in the experimental prototype of the backward wave oscillator. The prototype was implemented on the basis of the Saturn accelerator (300 keV/200 A/1 ?s), as the perimeter of the system constituted more than 15 wavelengths.

Ginzburg, N. S.; Zaslavskii, V. Yu.; Ilyakov, E. V.; Kulagin, I. S.; Peskov, N. Yu.; Sergeev, A. S.

The dispersive nature of the acousto-optical deflector (AOD) presents a challenge to applications of two sequential orthogonal AODs (a two-dimensional AOD) as XY scanners in multiphoton microscopy. Introducing a prism before the two-dimensional (2D) AOD allows both temporal and spatial dispersion to be compensated for simultaneously. A 90 fs laser pulse was broadened to 572 fs without compensation, and 143 fs with compensation. The ratio of long axis to short axis of the exiting laser beam spot was 3.50 without compensation and 1.14 with compensation. The insertion loss was 37%. Two-photon fluorescence microscopy used the compensated 2D AOD scanner to image a fluorescent microsphere, which improves signal intensity -15-fold compared with the uncompensated scanner. PMID:16625913

A new method for fast spectral-spatial electron paramagnetic resonance imaging (EPRI) is presented. To reduce the time of projections acquisition we propose to combine rapid scan of Zeeman magnetic field using high frequency sinusoidal modulation with simultaneously applied magnetic field gradients, whose amplitude is modulated at low frequency. The correctness of the method is confirmed by studies carried out on a phantom consisting of two LiPc samples. The spectral-spatial images from the acquired data are reconstructed using iterative algorithms. The proposed method allows to acquire the spectral-spatial image with 800 projections at 200ms. PMID:24705409

A new method for fast spectral-spatial electron paramagnetic resonance imaging (EPRI) is presented. To reduce the time of projections acquisition we propose to combine rapid scan of Zeeman magnetic field using high frequency sinusoidal modulation with simultaneously applied magnetic field gradients, whose amplitude is modulated at low frequency. The correctness of the method is confirmed by studies carried out on a phantom consisting of two LiPc samples. The spectral-spatial images from the acquired data are reconstructed using iterative algorithms. The proposed method allows to acquire the spectral-spatial image with 800 projections at 200 ms.

Czechowski, T.; Chlewicki, W.; Baranowski, M.; Jurga, K.; Szczepanik, P.; Szulc, P.; Kedzia, P.; Szostak, M.; Malinowski, P.; Wosinski, S.; Prukala, W.; Jurga, J.

We used an analysis based on a geographic information system (GIS) to determine the amount of rearing habitat and stranding area for subyearling fall chinook salmon Oncorhynchus tshawytscha in the Hanford Reach of the Columbia River at steady-state flows ranging from 1,416 to 11,328 m3/s. High-resolution river channel bathymetry was used in conjunction with a two-dimensional hydrodynamic model to estimate water velocities, depths, and lateral slopes throughout our 33-km study area. To relate the probability of fish presence in nearshore habitats to measures of physical habitat, we developed a logistic regression model from point electrofishing data. We only considered variables that were compatible with a GIS and therefore excluded other variables known to be important to juvenile salmonids. Water velocity and lateral slope were the only two variables included in our final model. The amount of available rearing habitat generally decreased as flow increased, with the greatest decreases occurring between 1,416 and 4,814 m3/s. When river discharges were between 3,682 and 7,080 m3/s, flow fluctuations of 566 m3/s produced the smallest change in available rearing area (from -6.3% to +6.8% of the total). Stranding pool area was greatly reduced at steady-state flows exceeding 4,531 m3/s, but the highest net gain in stranding area was produced by 850 m3/s decreases in flow when river discharges were between 5,381 and 5,664 m3/s. Current measures to protect rearing fall chinook salmon include limiting flow fluctuations at Priest Rapids Dam to 850 m3/s when the dam is spilling water and when the weekly flows average less than 4,814 m3/s. We believe that limiting flow fluctuations at all discharges would further protect subyearling fall chinook salmon.

A grid resolution sensitivity analysis using a two-dimensional flood inundation model has been presented in this paper. Simulations for 6 dam breaches located randomly in the United States were run at 10,30,60,90, and 120 meter resolutions. The dams represent a range of topographic conditions, ranging from 0% slope to 1.5% downstream of the dam. Using 10 meter digital elevation model (DEM) simulation results as the baseline, the coarser simulation results were compared in terms of flood inundation area, peak depths, flood wave travel time, daytime and nighttime population in flooded area, and economic impacts. The results of the study were consistent with previous grid resolution studies in terms of inundated area, depths, and velocity impacts. The results showed that as grid resolution is decreased, the relative fit of inundated area between the baseline and coarser resolution decreased slightly. This is further characterized by increasing over prediction as well as increasing under prediction with decreasing resolution. Comparison of average peak depths showed that depths generally decreased as resolution decreased, as well as the velocity. It is, however, noted that the trends in depth and velocity showed less consistency than the inundation area metrics. This may indicate that for studies in which velocity and depths must be resolved more accurately (urban environments when flow around buildings is important in the calculation of drag effects), higher resolution DEM data should be used. Perhaps the most significant finding from this study is the perceived insensitivity of socio-economic impacts to grid resolution. The difference in population at risk (PAR) and economic cost generally remained within 10% of the estimated impacts using the high resolution DEM. This insensitivity has been attributed to over estimated flood area and associated socio-economic impacts compensating for under estimated flooded area and associated socio-economic impacts. The United States has many dams that are classified as high-hazard potential that need an emergency action plan (EAP). It has been found that the development of EAPs for all high-hazard dams is handicapped due to funding limitations. The majority of the cost associated with developing an EAP is determining the flooded area. The results of this study have shown that coarse resolution dam breach studies can be used to provide an acceptable estimate of the inundated area and economic impacts, with very little computational cost. Therefore, the solution to limited funding may be to perform coarse resolution dam breach studies on high-hazard potential dams and use the results to help prioritize the order in which detailed EAPs should be developed.

Judi, David R [Los Alamos National Laboratory; Mcpherson, Timothy N [Los Alamos National Laboratory; Burian, Steven J [UNIV OF UTAH

Minimally invasive surgery procedures benefit from a reduced size of endoscopic devices. A prospective path to implement miniaturized endoscopy is single optical-fiber-based spectrally encoded imaging. While simultaneous spectrally encoded inertial-scan-free imaging and laser microsurgery have been successfully demonstrated in a large table setup, a highly miniaturized optical design would promote the development of multipurpose endoscope heads. This paper presents a highly scalable, entirely transmissive axial design for a spectral 2D spatial disperser. The proposed design employs a grating prism and a virtual imaged phased array (VIPA). Based on semi-analytical device modeling, we performed a systematic parameter analysis to assess the spectral disperser's manufacturability and to obtain an optimum application-specific design. We found that, in particular, a low grating period combined with a high optical input bandwidth and low VIPA tilt showed favorable results in terms of a high spatial resolution, a small device diameter, and a large field of view. Our calculations reveal that a reasonable imaging performance can be achieved with system diameters of below 5 mm, which renders the proposed 2D spatial disperser design highly suitable for use in future endoscope heads that combine mechanical-scan-free imaging and laser microsurgery. PMID:24514122

We present the theory of plasmon excitation in a grating-gate transistor structure with spatially modulated 2D electron channel. The plasmon spectrum varies depending on the electron density modulation in the transistor channel. We report on the frequency ranges of plasmon mode excitation in the gated and ungated regions of the channel and on the interaction of these different types of plasmon modes. We show that a constructive influence of the ungated regions of the electron channel considerably increases the intensity of the gated plasmon resonances and reduces the plasmon-resonance linewidth in the grating-gated transistor structure.

Fateev, D. V., E-mail: FateevDV@yandex.ru; Popov, V. V. [Kotelnikov Institute of Radio Engineering and Electronics of RAS (Saratov Branch) (Russian Federation); Shur, M. S. [Rensselaer Polytechnic Institute, Department of Electrical, Computer, and System Engineering and Center for Integrated Electronics, CII9015 (United States)

Solitons dynamics in the frame of the extended nonlinear Schrödinger equation taking into account space stimulated Raman scattering (SSRS), synchronic spatial variation of inhomogeneous second-order dispersion (SOD), and self-phase modulation (SPM) is considered both analytically and numerically. Compensation of soliton Raman self-wave number down shift by synchronically increasing SOD and SPM is shown. Analytical soliton solution as a result of the equilibrium of SSRS and increasing both SOD and SPM is found. Regime of the dynamical equilibrium of SSRS and inhomogeneous media with periodical variation of soliton's parameters is found. Analytical and numerical results are in a good agreement.

We introduce a model for the condensate of dipolar atoms or molecules, in which the dipole-dipole interaction (DDI) is periodically modulated in space due to a periodic change of the local orientation of the permanent dipoles, imposed by the corresponding structure of an external field (the necessary field can be created, in particular, by means of magnetic lattices, which are available to the experiment). The system represents a realization of a nonlocal nonlinear lattice, which has a potential to support various spatial modes. By means of numerical methods and variational approximation (VA), we construct bright one-dimensional solitons in this system and study their stability. In most cases, the VA provides good accuracy and correctly predicts the stability by means of the Vakhitov-Kolokolov criterion. It is found that the periodic modulation may destroy some solitons, which exist in the usual setting with unmodulated DDI and can create stable solitons in other cases, not verified in the absence of modulations. Unstable solitons typically transform into persistent localized breathers. The solitons are often mobile, with inelastic collisions between them leading to oscillating localized modes.

Abdullaev, F. Kh.; Gammal, A.; Malomed, B. A.; Tomio, Lauro

In this paper, the torque, reorientation and the change in angular momentum of the light are firstly discussed. And moreover, the propagation of light beam (optical spatialsoliton beam) at the distance of a few millimeters in chiral nematic liquid crystal (CNLC) will be experimentally under study. In spite of the complex structure of these crystals, due to a self-focusing effect, by injection of infrared laser beam with a power of the order of a few tenths of milliwatts into CNLC an optical spatialsoliton beam is observed. In addition, we experimentally obtain the formation of splitting of a soliton beam into two soliton beams which have equal powers due to a saturation of the reorientational nonlinearity. As a matter of fact, this saturation of the reorientational nonlinearity can occur at one point of CNLC, due to the nonlocal nonlinearity. Hence this saturation of the reorientation nonlinearity can split one soliton beam to two soliton beams. This splitting can have a great potential interest for applications in all-optical signal processing, reconfigurable optical interconnects and switching.

We have found various families of two-dimensional spatiotemporal solitons in quadratically nonlinear waveguide arrays. The families of unstaggered odd, even, and twisted stationary solutions are thoroughly characterized and their stability against perturbations is investigated. We show that the twisted and even solitons display instability, while most of the odd solitons show remarkable stability upon evolution.

Two-dimensional turbulence models are compared with experimental measurements made using an array of instrumented towers. The spatial correlation coefficient, the two-point spectrum or cross spectrum, and the coherence function are discussed. The prediction techniques in general agree reasonably well with the experimental results. Measurements of the integral length scale however, do not correlate well with the prediction model.

Viability assessment following acute myocardial infarction (MI) is important to guide revascularization. Two-dimensional strain echocardiography (2DSE) was shown to predict viability but the methodology assumed strain in each segment is independent of contiguous segments. We tested the hypotheses that segmental strain post-MI are spatially correlated and that using Bayesian approach improves prediction of non-viable myocardium. 21 subjects (58±12 years, 6 females) with ?2 weeks MI underwent 2DSE and late gadolinium enhancement (LGE) cardiac magnetic resonance imaging within 48-hours of each other. The heart was divided into 16 segments and longitudinal, radial and circumferential strains were measured using software. Using similar segmentation, LGE was measured and segments with >50% LGE were considered nonviable. Spearman analyses assessed spatial correlation of strain and receiver operating characteristic curve analysis was used to determine prediction of non-viable myocardium without and with Bayesian logistic spatial conditionally autoregressive (CAR) model. There is significant spatial correlation in strain and LGE, especially in the apex. Longitudinal strain was the best predictor of non-viability and was impaired in non-viable myocardium (-12.1±0.6, -8.0±0.6 and -4.6±1% for 0, 1-50, >50% LGE, respectively, p<0.001). Use of CAR model improved the area under the curve for detection of non-viable myocardium (0.7 to 0.94). A CAR probabilistic score of 0.17 had 88% sensitivity and 86% specificity for detecting non-viable myocardium. In conclusion, longitudinal strain from 2DSE can predict myocardial viability following MI and exploiting spatial correlations in segmental strain using Bayesian CAR enhances the ability of 2D strain to predict non-viable myocardium.

Migrino, Raymond Q.; Ahn, Kwang Woo; Brahmbhatt, Tejas; Harmann, Leanne; Jurva, Jason; Pajewski, Nicholas

We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.

Zhang Jiefang; Meng Jianping; Wu Lei [Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua, Zhejiang 321004 (China); Li Yishen [Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Malomed, Boris A. [Department of Physical Electronics, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

The propagation of monochromatic radiation in a system of weakly coupled single-mode optical fibers with saturable amplification and absorption and Kerr nonlinearity of the refractive index is analyzed. Conditions of stability and bistability of plane-wave regimes are determined. Discrete dissipative optical solitons are found and their stability is studied. The hysteresis dependences of the peak intensity of the discrete solitons on the value of the Kerr nonlinearity and the input beam intensity are demonstrated. The numerical estimates of the parameters of the spatial dissipative discrete solitons are presented.

Within the framework of the study a twodimensional hydrodynamic high-resolution model of the energy, H2O, CO2 turbulent exchange was developed and applied to describe effect of the horizontal and vertical heterogeneity of a forest canopy on CO2exchange between soil surface, forest stand and the atmosphere under different weather conditions. Most attention in the study was paid to analyze the influence of forest clearing, windthrow of different sizes, forest edges, etc. on turbulent exchange rate and CO2 flux partitioning between forest overstorey, understorey and soil surface. The modeling experiments were provided under different wind conditions, thermal stratification of the atmospheric boundary layer, incoming solar radiation, etc. To quantify effect of spatial heterogeneity on total ecosystem fluxes the modeling results were compared with CO2 fluxes modeled for a spatially uniform forest canopy under similar ambient conditions. The averaged system of hydrodynamic equations is used for calculating the components of the mean velocity ?V = {V1, V2}: ( ( ) ) ?Vi+ V ?Vi= - 1-??P- - -?- ? E - K ?Vi-+ ?Vj- + F, ?Vi = 0, ?t j?xj ?0 ?xi ?xj ij ?xj ?xi i ?xi where E is the turbulent kinetic energy (TKE), K is the turbulent diffusivity, ?P is the deviation of pressure from the hydrostatic distribution and ?0?F is the averaged force of air flow interaction with vegetation. F? was parameterized as ?F = -cd ·LAD ·| | ||V?||·?V, where cd is the drag coefficient and LAD is the leaf area density. The turbulent diffusivity K can be expressed by means of TKE and the velocity of TKE dissipation ? as follows: K = C?E2?-1, where C? is the proportionality coefficient. One of the ways to obtain E and ? is to solve the additional system of two differential equations of diffusion-transport type: ( ) ( ) ?E- -?E- -?- -K-?E- ?-? ??- -?- K-?? -? ( 1 2 ) ?t +Vj?xj = ?xi ?E ?xi +PE - ?, ?t +Vj ?xj = ?xi ???xi +E C ?PE - C?? - ? ?, where ?E and ?? are the Prandtl numbers, PE is the TKE production by shear, C?1 and C?2 are the model constants. The term ?? = ?- E(C ?1 - C?2) · 12C?1/2c dLAD||? || |V |E describes the increase of TKE dissipation due to the interaction with vegetation elements. The function ? can be any of the following variables: ?, ?/ E, or El, where l is the mixing length. Detailed analysis of these equations performed by Sogachev (Sogachev, Panferov, 2006) showed that for ? = ?/ E the model is less sensible to the errors of the input data. Transfer equation for CO2 within and above a plant canopy can be written as: ( ) ?C- -?C- -?- -K-?C- ?t + Vj?xj = ?xi ?C ?xi + FC, where C is CO2 concentration, ?C is the Prandtl number, and the term FC describes the sources/sinks of CO2 in the vegetation and soil. For parameterization of the photosynthesis rate in the forest canopy the Monsi and Saeki approach (Monsi M., Saeki T., 1953) was applied. Stem respiration was ignored in the study. The CO2 emission from the soil surface into the atmosphere was assumed to be constant for entire forest area. This study was supported by grants of the Russian Foundation for Basic Research (RFBR 14-04-01568-a).

In Chap. 5 is given basic information concerning two-dimensional distributions of random variables. Starting from a classical\\u000a problem of the accuracy of artillery fire it is shown that, besides a traditional analytical procedure, components of a covariance\\u000a tensor may be transformed by means of their representation by Mohr circles. It is shown that this representation, used commonly\\u000a in mechanics of solids,

The evidence that double-negative media, with an effective negative permittivity and an effective negative permeability, can be manufactured to operate at frequencies ranging from microwave to optical is ushering in a new era of metamaterials. They are referred to here as 'left handed', even though a variety of names is evident from the literature. In anticipation of a demand for highly structured integrated practical waveguides, this paper addresses the impact of this type of medium upon waveguides that can be also nonlinear. After an interesting historical overview and an exposure of some straightforward concepts, a planar guide is investigated, in which the waveguide is a slab consisting of a left-handed medium sandwiched between a substrate and cladding that are simple dielectrics. The substrate and cladding display a Kerr-type nonlinear response. Because of the nonlinear properties of the Kerr media, the power flow direction can be controlled by the intensity of the electric field. A comprehensive finite-difference-time-domain (FDTD) analysis is presented that concentrates upon spatialsoliton behaviour. An interesting soliton-lens arrangement is investigated that lends itself to a novel cancellation effect.

The transverse stability of the planar solitons described by the fifth-order Korteweg-de Vries equation (Kawahara solitons) is studied. It is shown that the planar solitons are unstable with respect to bending if the coefficient at the fifth-derivative term is positive and stable if it is negative. This is in agreement with the dynamics of the two-dimensional Kawahara solitons.

A theory is presented to show that gray and dark solitons can exist in bulk polymers with two-photon isomerization (TPI) nonlinearity. The soliton FWHM, intensity and phase profiles are discussed in detail. In addition, the stability properties of these TPI solitons are also investigated by employing the stability criterion based on the renormalized momentum.

A broad definition of solitons and a discussion of their role in physics is given. Vortices and magnetic monopoles which are examples of topological solitons in two and three spatial dimensions are described in some detail. (BB)

We introduce a spectroscopic method that determines nonlinear quantum mechanical response functions beyond the optical diffraction limit and allows direct imaging of nanoscale coherence. In established coherent two-dimensional (2D) spectroscopy, four-wave-mixing responses are measured using three ingoing waves and one outgoing wave; thus, the method is diffraction-limited in spatial resolution. In coherent 2D nanoscopy, we use four ingoing waves and detect the final state via photoemission electron microscopy, which has 50-nanometer spatial resolution. We recorded local nanospectra from a corrugated silver surface and observed subwavelength 2D line shape variations. Plasmonic phase coherence of localized excitations persisted for about 100 femtoseconds and exhibited coherent beats. The observations are best explained by a model in which coupled oscillators lead to Fano-like resonances in the hybridized dark- and bright-mode response.

A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction.

In this Letter, we investigate the dynamics of Bose-Einstein Condensates (BECs) with spatially inhomogeneous interaction and generate bright solitons for the condensates by solving the associated mean field description governed by the Gross-Pitaevskii (GP) equation. We then investigate the properties of BECs in an optical lattice and periodic potential. We show that the GP equation in an optical lattice potential is integrable provided the interaction strength between the atoms varies periodically in space. The model discussed in the Letter offers the luxury of choosing the form of the lattice without destroying the integrability. Besides, we have also brought out the possible ramifications of the integrable model in the condensates of quasi-particles.

We theoretically demonstrate the realization of a complete canonical set of all-optical logic gates (AND, OR, NOT), with a persistent (stored) output, by combining propagative spatialsolitons in a photorefractive crystal and dissipative cavity solitons in a downstream broad-area vertical cavity surface emitting laser (VCSEL). The system uses same-color, optical-axis aligned input and output channels with fixed readout locations, while switching from one gate to another is achieved by simply varying the potential applied to the photorefractive crystal. The inputs are Gaussian beams launched in the photorefractive crystal and the output is a bistable, persistent soliton in the VCSEL with a 'robust' eye diagram and large signal-to-noise ratio (SNR). Fast switching and intrinsic parallelism suggest that high bit flow rates can be obtained. PMID:24664042

Columbo, L L; Rizza, C; Brambilla, M; Prati, F; Tissoni, G

In this paper we investigate the properties of self-induced transparency (SIT) solitons, propagating in a {Lambda}-type medium. We find that the interaction between SIT solitons can lead to trapping with their phases preserved in the ground-state coherence of the medium. These phases can be altered in a systematic way by the application of appropriate light fields, such as additional SIT solitons. Furthermore, multiple independent SIT solitons can be made to propagate as bisolitons through their mutual interaction with a separate light field. Finally, we demonstrate that control of the SIT soliton phase can be used to implement an optical exclusive-or (xor) gate.

Beeker, Willem P.; Lee, Chris J.; Boller, Klaus J. [Laser Physics and Nonlinear Optics Group, MESA Research Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500AE Enschede (Netherlands); Can, Edip [Physics of Fluids Group, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500AE Enschede (Netherlands)

Spatial rocking is a kind of resonant forcing able to convert a self-oscillatory system into a phase-bistable, pattern forming system, whereby the phase of the spatially averaged oscillation field locks to one of two values differing by ?. We propose the spatial rocking in an experimentally relevant system—the vertical-cavity surface-emitting laser (VCSEL)—and demonstrate its feasibility through analytical and numerical tools applied to a VCSEL model. We show phase bistability, spatial patterns, such as roll patterns, domain walls, and phase (dark-ring) solitons, which could be useful for optical information storage and processing purposes.

Fernandez-Oto, C.; de Valcárcel, G. J.; Tlidi, M.; Panajotov, K.; Staliunas, K.

An effective Nonlinear Schrodinger Equation for propagation is derived for optical dark and power law spatialsolitons at the subwavelength with a surface plasmonic interaction. Starting with Maxwell's Nonlinear Equations a model is proposed for TM polari...

We introduce a one-dimensional model of a cavity with the Kerr nonlinearity and saturated gain designed so as to hold solitons in the state of shuttle motion. The solitons are always unstable in the cavity bounded by the usual potential barriers, due to accumulation of noise generated by the linear gain. Complete stabilization of the shuttling soliton is achieved if the linear barrier potentials are replaced by nonlinear ones, which trap the soliton, being transparent to the radiation. The removal of the noise from the cavity is additionally facilitated by an external ramp potential. The stable dynamical regimes are found numerically, and their basic properties are explained analytically. PMID:24343015

Dynamics of solitons is considered in the framework of an extended nonlinear Schrödinger equation (NLSE), which is derived from a system of the Zakharov?s type for the interaction between high- and low-frequency (HF and LF) waves. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term, which is a known ingredient of the temporal-domain NLSE in optics. Inhomogeneity of the spatial second-order dispersion (SOD) and linear losses of HF waves was also included. It is shown that wavenumber downshift by the pseudo-SRS may be compensated by the upshift provided by SOD whose local strength is an exponentially decaying function of the coordinate. An analytical soliton solution with a permanent shape is found in an approximate form, and is verified by the comparison with numerical results.

Mycotoxins in agricultural commodities are a hazard to human and animal health. Their heterogeneous spatial distribution in bulk storage or transport makes it particularly difficult to design effective and efficient sampling plans. There has been considerable emphasis on identifying the different sources of uncertainty associated with mycotoxin concentration estimations, but much less on identifying the effect of the spatial location

M. Rivas Casado; D. J. Parsons; R. M. Weightman; N. Magan; S. Origgi

At low temperature, a quasi-one-dimensional ensemble of atoms with an attractive interaction forms a bright soliton. When exposed to a weak and smooth external potential, the shape of the soliton is hardly modified, but its center-of-mass motion is affected. We show that in a spatially correlated disordered potential, the quantum motion of a bright soliton displays Anderson localization. The localization length can be much larger than the soliton size and could be observed experimentally.

Sacha, Krzysztof; Zakrzewski, Jakub [Instytut Fizyki imienia Mariana Smoluchowskiego and Mark Kac Complex Systems Research Center, Uniwersytet Jagiellonski, ulica Reymonta 4, PL-30-059 Krakow (Poland); Laboratoire Kastler-Brossel, UPMC, ENS, CNRS, 4 Place Jussieu, F-75005 Paris (France); Mueller, Cord A. [Laboratoire Kastler-Brossel, UPMC, ENS, CNRS, 4 Place Jussieu, F-75005 Paris (France); Physikalisches Institut, Universitaet Bayreuth, D-95440 Bayreuth (Germany); Delande, Dominique [Laboratoire Kastler-Brossel, UPMC, ENS, CNRS, 4 Place Jussieu, F-75005 Paris (France)

Informed consent was obtained; the study was HIPAA compliant and institutional review board approved. Fourfold accelerated (FFA) two-dimensional (2D) sensitivity encoding (SENSE) (65 seconds) was prospectively compared with its nonaccelerated counterpart (4 minutes 20 seconds) for diagnostic image quality and sharpness of visualization of blood vessels at 1.5 T with three-dimensional (3D) intracranial contrast-enhanced magnetic resonance venography in 18 consecutive volunteers (10 men, eight women; mean age, 48.4 years) and two patients (55-year-old man, 30-year-old woman). Two readers compared FFA 2D SENSE results with results from its nonaccelerated counterpart; they rated visualization of large and medium sinuses as equivalent (P > .1) and that of small deep cerebral veins (P < .01) and superficial cerebral veins (P < .001) as superior. Overall diagnostic image quality ratings were excellent for 62% and 80% of nonaccelerated and FFA 2D SENSE results, respectively (P < .05). FFA 2D SENSE may become the method of choice for fast visualization of intracranial venous vasculature in clinical practice.

Hu, Houchun H.; Campeau, Norbert G.; Huston, John; Kruger, David G.; Haider, Clifton R.; Riederer, Stephen J.

A review is presented of the main features of localized structures - dissipative solitons - in optical systems with nonlinear amplification and absorption, without driving (holding) radiation, including cases with and without feedback. The focus is on two-dimensional laser solitons. For the case of cylindrically- symmetric intensity distributions, there is a discrete set of such solitons with different values of

Kodama and his colleagues presented a classification theorem for exact soliton solutions of the quasi-two-dimensional Kadomtsev-Petviashvili (KP) equation. The classification theorem is related to non-negative Grassmann manifold, Gr(N, M) that is parameterized by a unique chord diagram based on the derangement of the permutation group. The cord diagram can infer the asymptotic behavior of the solution with arbitrary number of line solitons. Here we present the realization of a variety of the KP soliton formations in the laboratory environment. The experiments are performed in a water tank designed and constructed for precision experiments for long waves. The tank is equipped with a directional-wave maker, capable of generating arbitrary-shaped multi-dimensional waves. Temporal and spatial variations of water-surface profiles are captured using the Laser Induces Fluorescent method - a nonintrusive optical measurement technique with sub-millimeter precision. The experiments yield accurate anatomy of the KP soliton formations and their evolution behaviors. Physical interpretations are discussed for a variety of KP soliton formations predicted by the classification theorem.

We propose a scheme for the lithography of arbitrary, two-dimensional nanostructures via matter-wave interference. The required quantum control is provided by a {pi}/2-{pi}-{pi}/2 atom interferometer with an integrated atom lens system. The lens system is developed such that it allows simultaneous control over the atomic wave-packet spatial extent, trajectory, and phase signature. We demonstrate arbitrary pattern formations with two-dimensional {sup 87}Rb wave packets through numerical simulations of the scheme in a practical parameter space. Prospects for experimental realizations of the lithography scheme are also discussed.

Gangat, A.; Pradhan, P.; Pati, G.; Shahriar, M.S. [Department of Electrical and Computer Engineering, Northwestern University, Evanston, Illinois 60208 (United States)

We consider the problem of formation and propagation of optical vortex solitons in hollow-core optical fibres filled with a cold atomic gas for the case of the Raman regime in the ?-scheme of interaction subject to the Lorentz local field effects and in the presence of optical and atomic perturbations. We shows that the coherent optical control by pump beam in such an atomic medium leads to effective development of dynamical equilibrium of diffraction, nonlinear and dissipative processes necessary to stabilize dissipative vortex solitons. We demonstrate that the generation of acoustic waves even with small amplitudes in the fiber can quickly destroy the soliton mode.

Gubin, M. Yu.; Prokhorov, A. V.; Gladush, M. G.; Leksin, A. Yu.; Arakelian, S. M.

The spatially distributed effects of riparian vegetation on fluvial hydrodynamics during low flows to large floods are poorly documented. Drawing on a LiDAR-derived, meter-scale resolution raster of vegetation canopy height as well as an existing algorithm to spatially distribute stage-dependent channel roughness, this study developed a meter-scale two-dimensional hydrodynamic model of ~ 28.3 km of a gravel/cobble-bed river corridor for flows ranging from 0.2 to 20 times bankfull discharge, with and without spatially distributed vegetation roughness. Results were analyzed to gain insight into stage-dependent and scale-dependent effects of vegetation on velocities, depths, and flow patterns. At the floodplain filling flow of 597.49 m3/s, adding spatially distributed vegetation roughness parameters caused 8.0 and 7.4% increases in wetted area and mean depth, respectively, while mean velocity decreased 17.5%. Vegetation has a strong channelization effect on the flow, increasing the difference between mid-channel and bank velocities. It also diverted flow away from densely vegetated areas. On the floodplain, vegetation stands caused high velocity preferential flow paths that were otherwise unaccounted for in the unvegetated model runs. For the river as a whole, as discharge increases, overall roughness increases as well, contrary to popular conception.

Abu-Aly, T. R.; Pasternack, G. B.; Wyrick, J. R.; Barker, R.; Massa, D.; Johnson, T.

Direct-detection laser radars can measure the range and the intensity returns from a target, with or without clutter, for each part of the target resolved in angle by the optical system. Because the ladar's angular resolution is in micro-radians, there are generally at least a few angular pixels 'on target.' In addition, for narrow pulse (approximately 1 ns) ladar systems, there may be ten or so sequential intensity measurements in range per pixel as the laser pulse propagates down the target's surface. The output image is, therefore, potentially a three dimensional 'cube' of intensity measurements and quantized in the range axis by the range-bin size or 'voxel' size. This is known as 'range resolved angle-angle-intensity' ladar. In a previous paper we transformed this 3D-matrix image into the spatial-frequency domain using 3D- Fourier transforms and followed conventional 2D template correlation techniques to perform target recognition and identification. During this previous study, it was noted that the 2D range-bins could be placed in sequence and 2D filtering used on these synthetic images. Results of 3D and 2D-sequence target correlators using the 'joint transform correlator,' 'the inverse filter,' the 'phase-only matched-filter,' the 'binary phase-only filter,' and the classical 'matched filter' are presented here. Far-field test data using conical shaped targets are used to study the 3D and 2D correlators, and the effects of laser speckle are discussed. Recent developments in negative-binomial driven shot- noise effects in range-resolved direct-detection ladar are reviewed as well. These 3D or 2D-sequence template correlators may supplement or refine less computationally intensive algorithms such as total signal; range-extent; x-z, y-z, and x-y plane image centroid estimation; and image moments.

Information on the Japanese National Aerospace Laboratory twodimensional transonic wind tunnel, completed at the end of 1979 is presented. Its construction is discussed in detail, and the wind tunnel structure, operation, test results, and future plans are presented.

The tensio-active properties of different types of polymerizable diesters can be used to synthesize two-dimensional model\\u000a networks at the interface between oil and water. — The adsorbed monolayers can be polymerized and crosslinked by UV-irradiation.\\u000a — The kinetics of surface gelation were systematically investigated by measuring the two-dimensional shear modulus and the\\u000a surface viscosity as a function of the reaction

We show experimentally optical bistability and the existence of bright and dark resonator solitons in the strong coupling regime between quantum-well excitons and the optical field in a semiconductor microcavity. The strong coupling results in a quasi-particle exciton-polariton, which gives access to positive and negative reactive and dissipative optical nonlinearities, as opposed to the usual room temperature semiconductor nonlinearities possessing essentially only one sign. The existence range and the properties of solitons can be varied widely by the detuning between polariton states and light frequency. PMID:18278097

A cloaking theory for a two-dimensional spin-(1/2) fermion is proposed. It is shown that the spinor of the two-dimensional fermion can be cloaked perfectly through controlling the fermion's energy and mass in a specific manner moving in an effective vector potential inside a cloaking shell. Different from the cloaking of three-dimensional fermions, the scaling function that determines the invisible region is uniquely determined by a nonlinear equation. It is also shown that the efficiency of the cloaking shell is unaltered under the Aharonov-Bohm effect.

Lin, De-Hone [Department of Physics, National Sun Yat-sen University, Kaohsiung, Taiwan (China)

We study analytically the properties of the optical absorption and the spatial weak-light solitons in a quantum dot molecule system with the interdot tunneling coupling (ITC). It is shown that, for the linear case, there exists tunneling induced transparency (TIT) in the context of a weak ITC, while the TIT can be replaced by Autler-Townes splitting in the presence of a strong ITC. For the nonlinear case, it is probable to realize the spatial optical solitons even under weak light intensity. Interestingly, we find that there appears transformation behavior between the bright and dark solitons by properly turning both the ITC strength and the detuning of the probe field. Meanwhile, the transformation condition of the bright and dark solitons is obtained. Additionally it is also found that the amplitude of the solitons first descends and then rises with the increasing of ITC strength. Our results may have potential applications for nonlinear optical experiments and optical telecommunication engineering in solid systems.

We demonstrate frequency-controlled angular steering of light-induced solitary waveguides using dual frequency nematic liquid crystals. Specially designed comb-shaped electrodes allow the maximization of the in-plane electro-optic angular deviation of the soliton Poynting vector, modulating the resulting walk-off up to an overall deflection of 13° when the frequency of the applied voltage goes from 1 to 100 kHz.

We demonstrate the existence of shape-preserving self-localized nonlinear modes in a two-dimensional photonic lattice with a flat-topped defect that covers several lattice sites. The balance of diffraction, defocusing nonlinearity, and optical potential induced by lattices with various forms of defects results in novel families of solitons featuring salient properties. We show that the soliton shape can be controlled by varying the shape of lattice defects. The existence domains of fundamental and vortex solitons in the semi-infinite gap expand with the defect amplitude. Vortex solitons in the semi-infinite gap with rectangular intensity distributions will break into dipole solitons when the propagation constant exceeds a critical value. In the semi-infinite and first-finite gaps, we find that lattices with rectangular defects can support stable vortex solitons which exhibit noncanonical phase structure.

Dong Liangwei [Institute of Information Optics of Zhejiang Normal University, Jinhua 321004 (China); Ye Fangwei [Department of Physics, Centre for Nonlinear Studies, and the Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Hoongkong Baptist University, Kowloon Tong (Hong Kong)

Solitons are localized concentrations of field energy, resulting from a balance of dispersive and nonlinear effects. They are ubiquitous in the natural sciences. In recent years optical solitons have arisen in new and exciting contexts that differ in many ways from the original context of coherent propagation in a uniform medium. We review recent developments in incoherent spatialsolitons and in gap solitons in periodic structures.

Bronski, Jared C.; Segev, Mordechai; Weinstein, Michael I.

Solitons are a special class of pulse-shaped waves that propagate in nonlinear dispersive media while maintaining their spatial confinement. They are found throughout nature where the proper balance between nonlinearity and dispersion is achieved. Examples of the soliton phenomena include shallow water waves, vibrations in a nonlinear spring-mass lattice, acoustic waves in plasma, and optical pulses in fiber optic cable.

Localized states in the discrete two-dimensional (2D) nonlinear Schrödinger equation is found: vortex solitons with an integer vorticity S. While Hamiltonian lattices do not conserve angular momentum or the topological invariant related to it, we demonstrate that the soliton's vorticity may be conserved as a dynamical invariant. Linear stability analysis and direct simulations concur in showing that fundamental vortex solitons, with S=1, are stable if the intersite coupling C is smaller than some critical value C((1))(cr). At C>C((1))(cr), an instability sets in through a quartet of complex eigenvalues appearing in the linearized equations. Direct simulations reveal that an unstable vortex soliton with S=1 first splits into two usual solitons with S=0 (in accordance with the prediction of the linear analysis), but then an instability-induced spontaneous symmetry breaking takes place: one of the secondary solitons with S=0 decays into radiation, while the other one survives. We demonstrate that the usual (S=0) 2D solitons in the model become unstable, at C>C((0))(cr) approximately 2.46C((1))(cr), in a different way, via a pair of imaginary eigenvalues omega which bifurcate into instability through omega=0. Except for the lower-energy S=1 solitons that are centered on a site, we also construct ones which are centered between lattice sites which, however, have higher energy than the former. Vortex solitons with S=2 are found too, but they are always unstable. Solitons with S=1 and S=0 can form stable bound states. PMID:11497724

We report the generation of three-dimensional bright spatial solitary waves by the breakup of an optical vortex in a saturable self-focusing nonlinear medium. An elliptical Gaussian beam from a Ti:sapphire laser containing a singly charged on-axis vortex was passed through a nonlinear medium consisting of rubidium vapor at low concentrations. The modulational instability resulted in the formation of a pair of out-of-phase solitonlike beams, which spiraled away from each other during propagation as a result of the repulsive nature of their interaction. The rate of rotation and separation of the two soliton beams could be controlled by the parameters of the medium and the laser intensity. Numerical analysis of the propagation based on a model nonlinearity corresponding to a strongly saturated two-level system showed good quantitative agreement with the experimental data. Copyright (c) 1995 Optical Society of America

Tikhonenko, Vladimir; Christou, Jason; Luther-Daves, Barry

Ultrathin crystalline films offer the possibility of exploring phase transitions in the crossover region between two and three dimensions. Second-order ferromagnetic phase transitions have been observed in monolayer magnetic films,, where surface anisotropy energy stabilizes the two-dimensional ferromagnetic state at finite temperature. Similarly, a number of magnetic materials have magnetic surface layers that show a second-order ferromagnetic-paramagnetic phase transition with

A. V. Bune; V. M. Fridkin; Stephen Ducharme; L. M. Blinov; S. P. Palto; A. V. Sorokin; S. G. Yudin; A. Zlatkin

The collision of spherical ion-acoustic solitons having different centers of symmetry is studied. Unlike one-dimensional collisions, the solitons are significantly changed by the collision. A new two-dimensional nonlinear object is found to be created. Remnants of the solitons that survive are found to be shifted in phase and reduced in amplitude.

Frederic Ze; Noah Hershkowitz; Chung Chan; K. E. Lonngren

We demonstrate that optical discrete solitons are possible in appropriately oriented biased photorefractive crystals. This can be accomplished in optically induced periodic waveguide lattices that are created via plane- wave interference. Our method paves the way towards the observation of entirely new families of discrete solitons. These include, for example, discrete solitons in two-dimensional self-focusing and defocusing lattices of different

Nikos K. Efremidis; Suzanne Sears; Demetrios N. Christodoulides; Jason W. Fleischer; Mordechai Segev

We study two-dimensionalsoliton-soliton vector pairs in media with self-focusing nonlinearities and defocusing cross interactions. The general properties of the stationary states and their stability are investigated. The different scenarios of instability are observed using numerical simulations. The quasistable propagation regime of the high-power vector solitons is revealed.

Yakimenko, A. I. [Department of Physics, Taras Shevchenko National University, Kiev 03022 (Ukraine); Institute for Nuclear Research, Kiev 03680 (Ukraine); Prikhodko, O. O.; Vilchynskyi, S. I. [Department of Physics, Taras Shevchenko National University, Kiev 03022 (Ukraine)

One of the main fields of solar research is the study of dynamic processes of small-scale structures. For this purpose, time sequences of spectroscopic and polarimetric information in two spatial dimensions with best achievable quality are needed. The present contribution deals with the ways to obtain images in small wavelength bands. Among these are image scanners and the MSDP (Multi-Channel Subtractive Double Pass Spectrograph). Further potential instruments are scanning Fabry-Perot interferometers (FPI). The principles of such instruments are discussed. The results obtained hitherto from the FPI in the Vacuum Tower Telescope at the Observatorio del Teide are promising. Small-band, two-dimensional spectroscopy with spatial resolution close to the telescopic diffraction limit seems possible in the near future.

An optical implementation of the two-dimensional (2-D) wavelet transform and inverse wavelet transform is performed in real time by the exploitation of a new multichannel system that processes the different daughter wavelets separately. The so-coined wavelet-processor system relies on a multichannel replication array generated that uses a Dammann grating and is able to handle every wavelet function. All channels process in parallel using a conventional 2-D correlator. Experimental results applying the Mexican-hat wavelet-decomposition technique are presented.

We address the stability problem for vortex solitons in two-dimensional media combining quadratic and self-defocusing cubic [ ?(2) : ?(3) - ] nonlinearities. We consider the propagation of spatial beams with intrinsic vorticity S in such bulk optical media. It was earlier found that the S=1 and S=2 solitons can be stable, provided that their power (i.e., transverse size) is large enough, and it was conjectured that all the higher-order vortices with S?3 are always unstable. On the other hand, it was recently shown that vortex solitons with S>2 and very large transverse size may be stable in media combining cubic self-focusing and quintic self-defocusing nonlinearities. Here, we demonstrate that the same is true in the ?(2) : ?(3) - model, the vortices with S=3 and S=4 being stable in regions occupying, respectively, ?3% and 1.5% of their existence domain. The vortex solitons with S>4 are also stable in tiny regions. The results are obtained through computation of stability eigenvalues, and are then checked in direct simulations, with a conclusion that the stable vortices are truly robust ones, easily self-trapping from initial beams with embedded vorticity. The dependence of the stability region on the ?(2) phase-mismatch parameter is specially investigated. We thus conclude that the stability of higher-order two-dimensional vortex solitons in narrow regions is a generic feature of optical media featuring the competition between self-focusing and self-defocusing nonlinearities. A qualitative analytical explanation to this feature is proposed.

Mihalache, D.; Mazilu, D.; Malomed, B. A.; Lederer, F.

Theoretical analysis to the defect mediated discrete solitons in one- and two-dimensional periodical waveguide lattices is presented. The waveguide arrays with these functional defects are assumed to respond to the light field as an optically induced photorefraction and they are patterned by a holographic technique. It is found that the spatial energy distributions of the solitary waves can be controlled by the defects in the waveguide arrays, and this gives rise to an additional freedom to externally shaping the light field distribution to a special shape.

Li Yongyao [State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275 (China); Department of Applied Physics, South China Agricultural University, Guangzhou 510642 (China); Pang Wei [Department of Experiment, Guangdong University of Technology, Guangzhou 510006 (China); Chen Yongzhu [State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275 (China); School of Electro-Mechanic Engineering, Guangdong Polytechnic Normal University, Guangzhou 510665 (China); Yu Zhiqiang; Zhou Jianying; Zhang Huarong [State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275 (China)

The state of the art of asymptotic theory is discussed with respect to incompressible two-dimensional separated flows. As an example, the flow over an indented flat plate is considered for two cases: a small separation bubble within the lower part of the boundary layer, and the 'catastrophic' separation of the whole boundary layer with a large recirculating eddy. Separation means failure of Prandtl's boundary layer theory, and alternate theories are required. An example of this is shown in the calculation of circulation in the dent according to triple-deck theory. The free-streamline theory approach is used to examine the indented flat plate and the flow past a circular cylinder. Attention is also given to flow control by continuous injection, combined forced and free convection, unsteady laminar flows, and laminar flows.

We present a comprehensive analytical theory of localized nonlinear excitations—dark solitons—supported by an incoherently pumped, spatially homogeneous exciton-polariton condensate. We show that, in contrast to dark solitons in conservative systems, these nonlinear excitations "relax" by blending with the background at a finite time, which critically depends on the parameters of the condensate. Our analytical results for trajectory and lifetime are in excellent agreement with direct numerical simulations of the open-dissipative mean-field model. In addition, we show that transverse instability of quasi-one-dimensional dark stripes in a two-dimensional open-dissipative condensate demonstrates features that are entirely absent in conservative systems, as creation of vortex-antivortex pairs competes with the soliton relaxation process.

Smirnov, Lev A.; Smirnova, Daria A.; Ostrovskaya, Elena A.; Kivshar, Yuri S.

This Ph.D. thesis pursues two goals: The study of the geometrical structure of two-dimensional quantum gravity and in particular its fractal nature. To address these questions we review the continuum formalism of quantum gravity with special focus on the scaling properties of the theory. We discuss several concepts of fractal dimensions which characterize the extrinsic and intrinsic geometry of quantum gravity. This work is partly based on work done in collaboration with Jan Ambjørn, Dimitrij Boulatov, Jakob L. Nielsen and Yoshiyuki Watabiki (1997). The other goal is the discussion of the discretization of quantum gravity and to address the so called quantum failure of Regge calculus. We review dynamical triangulations and show that it agrees with the continuum theory in two dimensions. Then we discuss Regge calculus and prove that a continuum limit cannot be taken in a sensible way and that it does not reproduce continuum results. This work is partly based on work done in collaboration with Jan Ambjørn, Jakob L. Nielsen and George Savvidy (1997).

We investigate classically spinning topological solitons in (2+1)- and (3+1)-dimensional models; more explicitely spinning sigma model solitons in 2+1 dimensions and Skyrme solitons in 2+1 and 3+1 dimensions. For example, such types of solitons can be used to describe quasiparticle excitations in ferromagnetic quantum Hall systems or to model spin and isospin states of nuclei. The standard way to obtain solitons with quantised spin and isospin is the semiclassical quantization procedure: One parametrizes the zero-mode space - the space of energy-degenerate soliton configurations generated from a single soliton by spatial translations and rotations in space and isospace - by collective coordinates which are then taken to be time-dependent. This gives rise to additional dynamical terms in the Hamiltonian which can then be quantized following semiclassical quantization rules. A simplification which is often made in the literature is to apply a simple adiabatic approximation to the (iso)rotational zero modes of the soliton by assuming that the soliton's shape is rotational frequency independent. Our numerical results on classically spinning arbitrarily deforming soliton solutions clearly show that soliton deformation cannot be ignored.

Battye, Richard A.; Haberichter, Mareike [Jodrell Bank Centre for Astrophysics, University of Manchester, Manchester M13 9PL (United Kingdom)

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schroedinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear ''ship-wave'' pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

El, G. A.; Khodorovskii, V. V. [Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU (United Kingdom); Kamchatnov, A. M. [Institute of Spectroscopy, Russian Academy of Sciences, 142190 Troitsk, Moscow Region (Russian Federation); Annibale, E. S.; Gammal, A. [Instituto de Fisica, Universidade de Sao Paulo, CP 66318, 05315-970 Sao Paulo, SP (Brazil)

A model of a two-dimensional optical waveguide with the Kerr nonlinearity and two transversal (cross-)Bragg gratings (BGs) is considered. Four waves trapped in the waveguide are coupled linearly by reflections on the cross-BG, and nonlinearly by self-phase-modulation, cross-phase-modulation, and four-wave-mixing. One-dimensional gap solitons (GSs) in the model are found by means of the variational approximation and numerical methods, the analytical and numerical results being in good agreement. The solitons fall into three distinct categories, which are identified as symmetric (S), anti-symmetric (anti-S), and asymmetric (aS) ones at the center of the bandgap, and those which are obtained by continuation of these three types in the general case. The stability of the GSs is studied in the spatial domain. All the solitons of the S and anti-S types are unstable (their instability modes are different), while the aS solitons have a well-defined stability region. The latter is identified by means of the Vakhitov-Kolokolov (VK) criterion, which is verified by direct simulations. It is demonstrated too that stable breathers, which are close to strongly asymmetric solitons, readily self-trap from a two-component input that corresponds to a physically relevant boundary condition in the spatial domain (the development of the instability of solitons of the S type gives rise to breathers of a different kind, in which the field periodically switches between two aS configurations that are mirror images to each other). Tilted spatialsolitons of the aS type are found too; they are stable for relatively small values of the tilt.

Quadratic spatial solitary waves are predicted and observed experimentally near degeneracy for Type II optical parametric amplification in bulk KTP, by seeding an intense pump optical field with a control signal at half the pump wave frequency. The self-trapping of light at the two wavelengths has been shown to be insensitive to phase, polarization and magnitude of the control input,

R. A. Fuerst; M. T. G. Canva; G. I. Stegeman; G. Leo; G. Assanto

A dynamic two-dimensional laser-beam-pattern steering technique using photorefractive holograms in conjunction with electrically addressed spatial light modulators is proposed and investigated. The experimental results demonstrate the dynamic steering of random combinations of basis beam patterns. The proposed method has the advantages of random beam-pattern combination, good beam intensity uniformity, and higher diffraction efficiency compared with conventional methods.

We study the collision of a gravitational wave pulse and a soliton wave on a spatially homogeneous background. This collision is described by an exact solution of Einstein's equations in a vacuum which is generated from a nondiagonal seed by means of a soliton transformation. The effect produced by the soliton on the amplitude and polarization of the wave is considered.

Unlike the thermodynamic equipartition of energy in conservative systems, turbulent equipartitions (TEP) describe strongly non-equilibrium systems such as turbulent plasmas. In turbulent systems, energy is no longer a good invariant, but one can utilize the conservation of other quantities, such as adiabatic invariants, frozen-in magnetic flux, entropy, or combination thereof, in order to derive new, turbulent quasi-equilibria. These TEP equilibria assume various forms, but in general they sustain spatially inhomogeneous distributions of the usual thermodynamic quantities such as density or temperature. This mechanism explains the effects of particle and energy pinch in tokamaks. The analysis of the relaxed states caused by turbulent mixing is based on the existence of Lagrangian invariants (quantities constant along fluid-particle or other orbits). A turbulent equipartition corresponds to the spatially uniform distribution of relevant Lagrangian invariants. The existence of such turbulent equilibria is demonstrated in the simple model of twodimensional electrostatically turbulent plasma in an inhomogeneous magnetic field. The turbulence is prescribed, and the turbulent transport is assumed to be much stronger than the classical collisional transport. The simplicity of the model makes it possible to derive the equations describing the relaxation to the TEP state in several limits.

Isichenko, M.B.; Yankov, V.V. [Univ. of California, Santa Barbara, CA (United States). Inst. for Theoretical Physics

The structure, dynamics, and thermodynamics of magnetic solitons in low-dimensional antiferromagnets (AFMs) are reviewed from a unified point of view. Primary attention is given to problems for which experimental data are available. The analysis is based on simple phenomenological equations describing the dynamics of AFMs in terms of a single antiferromagnetism vector, which have the form of a Lorentz-invariant sigma model (with the magnon phase velocity selected as the working velocity) in the simplest model of an AFM. The reduction in symmetry of an AFM in the presence of an external magnetic field or with allowance for Dzyaloshinskii interaction violates Lorentz invariance. The restructuring of one-dimensional solitons of the kink type at a finite velocity is discussed, along with its influence on the soliton thermodynamics of quasi-one-dimensional magnetic media. The soliton solutions are subjected to quasiclassical quantization. It is shown that the dynamics of the internal degrees of freedom of a kink in a homogeneous AFM has a quantum nature, which becomes conspicuous in the investigation of two-parameter solitons of the bion type in almost-easy-axis AFMs. Two-dimensional topological solitons such as localized and nonlocalized magnetic vortices are discussed together with their contribution to the thermodynamics of two-dimensional AFMs. The current status of the problem of observing magnetic solitons experimentally in quasi-two- dimensional AFMs are reviewed, and various possible directions of future research are considered.

By using a nonlinear waveguide array we experimentally demonstrate dynamic features of solitons in discrete systems. Spatialsolitons do not exhibit these properties in continuous systems. We experimentally recorded nonlinearly induced locking of an initially moving soliton at a single waveguide. We also show that discrete solitons can acquire transverse momentum and propagate at an angle with respect to the

R. Morandotti; U. Peschel; J. S. Aitchison; H. S. Eisenberg; Y. Silberberg

We study experimentally and numerically the equilibrium density profiles of a trapped two-dimensional {sup 87}Rb Bose gas and investigate the equation of state of the homogeneous system using the local density approximation. We find a clear discrepancy between in situ measurements and quantum Monte Carlo simulations, which we attribute to a nonlinear variation of the optical density of the atomic cloud with its spatial density. However, good agreement between experiment and theory is recovered for the density profiles measured after time of flight, taking advantage of their self-similarity in a two-dimensional expansion.

Rath, Steffen P.; Yefsah, Tarik; Guenter, Kenneth J.; Cheneau, Marc; Desbuquois, Remi; Dalibard, Jean [Laboratoire Kastler Brossel, CNRS, Universite Pierre et Marie Curie, Ecole Normale Superieure, 24 rue Lhomond, F-75005 Paris (France); Holzmann, Markus [Laboratoire de Physique Theorique de la Matiere Condensee, CNRS, Universite Pierre et Marie Curie, 4 Place Jussieu, F-75005 Paris, France, and Laboratoire de Physique et Modelisation des Milieux Condenses, CNRS, Universite Joseph Fourier, BP 166, F-38042 Grenoble (France); Krauth, Werner [Laboratoire de Physique Statistique, CNRS, Universite Pierre et Marie Curie, Universite Paris Diderot, Ecole Normale Superieure, 24 rue Lhomond, F-75005 Paris (France)

A scheme of semi-phenomenological quantization is proposed for the collision process of two equal size envelopes-solitons provided by nonlinear Schroedinger equation. The time advance due to two envelopes-solitons collision was determined. Considering the...

Two-dimensional (2D) equations describing the nonlinear interaction between upper-hybrid and dispersive magnetosonic waves are presented. Nonlocal nonlinearity in the equations results in the possibility of the existence of stable 2D nonlinear structures. A rigorous proof of the absence of collapse in the model is given. Different types of nonlinear localized structures such as fundamental solitons, radially symmetric vortices, nonrotating multisolitons (two-hump solitons, dipoles, and quadrupoles), and rotating multisolitons (azimuthons) have been found numerically. It is shown by direct numerical simulations that 2D fundamental solitons with a negative Hamiltonian are stable.

Lashkin, V. M. [Institute for Nuclear Research, Pr. Nauki 47, Kiev 03680 (Ukraine)

Light solitons in space spatialsoliton) have been under an intensive theoretical and experimental research in the last three decades. The solitons evolve from nonlinear changes in the refractive index of the material, due to the light intensity distribut...

Solutions to the scalar quasilinear equation with initial data given by a twodimensional Riemann problem are piecewise smooth if f/sub 1/ identical with f/sub 2/ identical with f, and f has at most one inflection point. We show the pieces of this solution can be classified and are expressible in terms of twodimensional non-linear waves in analogy with the non-linear rarefaction and shock waves of the Riemann problem in one spatial dimension. The twodimensional waves can be expressed in almost closed form. Explicit solutions are constructable from these waves. An application is illustrated by calculation of the interaction of water/oil banks in two phase incompressible flow in reservoirs.

Solitons are a special class of pulse-shaped waves that propagate in nonlinear dispersive media while maintaining their spatial confinement. They are found throughout nature where the proper balance between nonlinearity and dispersion is achieved. Examples of the soliton phenomena include shallow water waves, vibrations in a nonlinear spring-mass lattice, acoustic waves in plasma, and optical pulses in fiber optic cable. In electronics, the nonlinear transmission line (NLTL) serves as a nonlinear dispersive medium that propagates voltage solitons. Electrical solitons on the NLTL have been actively investigated over the last 40 years, particularly in the microwave domain, for sharp pulse generation applications and for high-speed RF and microwave sampling applications. In these past studies the NLTL has been predominantly used as a 2-port system where a high-frequency input is required to generate a sharp soliton output through a transient process. One meaningful extension of the past 2-port NLTL works would be to construct a 1-port self-sustained electrical soliton oscillator by properly combining the NLTL with an amplifier (positive active feedback). Such an oscillator would self-start by growing from ambient noise to produce a train of periodic soliton pulses in steady-state, and hence would make a self-contained soliton generator not requiring an external high-frequency input. While such a circuit may offer a new direction in the field of electrical pulse generation, there has not been a robust electrical soliton oscillator reported to date to the best of our knowledge. In this thesis we introduce the first robust electrical soliton oscillator, which is able to self-generate a stable, periodic train of electrical solitons. This new oscillator is made possible by combining the NLTL with a unique nonlinear amplifier that is able to "tame" the unruly dynamics of the NLTL. The principle contribution of this thesis is the identification of the key instability mechanisms of solitons in a closed-loop oscillator and the development of the necessary stabilizing mechanisms. Demonstration of the concepts developed were in the form of three prototypes: a low MHz discrete prototype, a microwave discrete prototype, and a chip-scale, GHz prototype.

We consider problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste. In two-dimensional bin packing problems these units are finite rectangles, and the objective is to pack all the items into the minimum number of units, while in two-dimensional strip packing problems there is a single standardized unit of given width,

It has recently been discovered that stabilization of two-dimensional (2D) solitons against the critical collapse in media with cubic nonlinearity by means of nonlinear lattices (NLs) is a challenging problem. We address the one-dimensional (1D) version of the problem, i.e., the nonlinear-Schrödinger equation (NLSE) with quintic or cubic-quintic (CQ) terms, the coefficients in front of which are periodically modulated in space. The models may be realized in optics and Bose-Einstein condensates (BECs). Stability diagrams for the solitons are produced by means of numerical methods and analytical approximations. It is found that the sinusoidal NL stabilizes solitons supported by the quintic-only nonlinearity in a narrow stripe in the respective parameter plane, contrary to the case of the cubic nonlinearity in 2D, where the stabilization of solitons by smooth spatial modulations is not possible at all. The stability region is much broader in the 1D CQ model, where higher-order solitons may be stable too.

The field equations with nonlinearity proportional to Vertical BarPSIVertical Barsup(- alpha )PSI, alpha >0 (model 1 of Simonov-Tjon) are solved in one spatial dimension with initial conditions corresponding to two colliding solitons. One or several breat...

We report the first observation of stationary necklacelike solitons. Such necklace structures were realized when a high-order vortex beam was launched appropriately into a two-dimensional optically induced photonic lattice. Our theoretical results obtained with continuous and discrete models show that the necklace solitons resulting from a charge-4 vortex have a pi phase difference between adjacent "pearls" and are formed in an octagon shape. Their stability region is identified. PMID:15903857

Yang, J; Makasyuk, I; Kevrekidis, P G; Martin, H; Malomed, B A; Frantzeskakis, D J; Chen, Zhigang

We report the first observation of stationary necklacelike solitons. Such necklace structures were realized when a high-order vortex beam was launched appropriately into a two-dimensional optically induced photonic lattice. Our theoretical results obtained with continuous and discrete models show that the necklace solitons resulting from a charge-4 vortex have a ? phase difference between adjacent “pearls” and are formed in an octagon shape. Their stability region is identified.

Yang, J.; Makasyuk, I.; Kevrekidis, P. G.; Martin, H.; Malomed, B. A.; Frantzeskakis, D. J.; Chen, Zhigang

The nonlinear evolution of oblique collisions is investigated experimentally on plane ion-acoustic solitons in two-dimensional space. Many of the observed characteristics of inelastic collisions of solitons are found to be similar to those of resonance interactions described by nonlinear ion-acoustic waves.

The dynamical properties of many-dimensional U(1) solitons have been studied by means of the computer simulations of the head-on collisions in the framework of some field-theoretical models with nondegenerate vacuum. A long-living bound state (two-dimensional bion) emerging from two interacting unstable soliton-like objects have been found. It has been shown, that the picture of soliton interactions is governed by the dispertion law Q(?) and is model independent.

The focus of this work is to demonstrate discrete solitons in arrays of coupled nonlinear waveguides or the controlled switching of optical information from one line to another. Results have been the successful creation of a linear array of over one hundr...

We report the existence of transversely stable soliton trains in optics. These stable soliton trains are found in two-dimensional square photonic lattices when they bifurcate from X-symmetry points with saddle-shaped diffraction inside the first Bloch band and their amplitudes are above a certain threshold. We also show that soliton trains with low amplitudes or bifurcated from edges of the first Bloch band ({Gamma} and M points) still suffer transverse instability. These results are obtained in the continuous lattice model and are further corroborated by the discrete model.

Yang Jianke [Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401 (United States)

A systems engineering study was conducted to leverage a new two-dimensional (2D) lander concept with a low per unit cost to enable scientific study at multiple locations with a single entry system as the delivery vehicle.

We investigate surface plasmon polariton (SPP) cavitiy modes on twodimensional Moire surfaces in the visible spectrum. Twodimensional hexagonal Moire surface can be recorded on a photoresist layer using Interference lithography (IL). Two sequential exposures at slightly different angles in IL generate one dimensional Moire surfaces. Further sequential exposure for the same sample at slightly different angles after turning the sample 60 degrees around its own axis generates twodimensional hexagonal Moire cavity. Spectroscopic reflection measurements have shown plasmonic band gaps and cavity states at all the azimuthal angles (omnidirectional cavity and band gap formation) investigated. The plasmonic band gap edge and the cavity states energies show six fold symmetry on the twodimensional Moire surface as measured in reflection measurements.

Conoscopic holography is an incoherent light holographic technique based on the properties of crystal optics. We present experimental results of the numerical reconstruction of a two-dimensional object from its conoscopic hologram. PMID:19798352

Large two-dimensional amorphous silicon image sensor arrays offer an advantage for high speed document scanning and medical X-ray imaging. We describe our page sized 200 spot per inch imager and the accompanying high speed readout electronics. The spatial resolution performance for white light and X-ray imaging is illustrated. We discuss how the important issues of noise and resolution depend on

X. D. Wu; R. Weisfield; S. Ready; R. Apte; M. Ngyuen; W. B. Jackson; P. Nylen

A two-dimensional sheet of anisotropic cardiac tissue is represented with the bidomain model, and the finite element method is used to solve the bidomain equations. When the anisotropy ratios of the intracellular and extracellular spaces are not equal, the injection of current into the tissue induces a transmembrane potential that has a complicated spatial dependence, including adjacent regions of depolarized and hyperpolarized tissue. This behavior may have important implications for the electrical stimulation of cardiac tissue and for defibrillation.

Strain rate images (SRI) of the beating heart have been proposed to identify non-contracting regions of myocardium. Initial attempts used spatial derivatives of tissue velocity (Doppler) signals. Here, an alternate method is proposed based on two-dimensional phase-sensitive speckle tracking applied to very high frame rate, real-time images. This processing can produce high resolution maps of the time derivative of the

K. Kaluzynski; Xunchang Chen; Stanislav Y. Emelianov; Andrei R. Skovoroda; Matthew O'Donnell

We investigate the magnetoresistance of a nonplanar two-dimensional electron gas (2DEG) fabricated by growth of a GaAs\\/(AlGa)As heterojunction on a wafer prepatterned with facets at 20° to the substrate. Applying a uniform magnetic field (B) produces a spatially nonuniform component of field perpendicular to the 2DEG. With the field in the plane of the substrate, the resistance measured across an

M. L. Leadbeater; C. L. Foden; J. H. Burroughes; M. Pepper; T. M. Burke; L. L. Wang; M. P. Grimshaw; D. A. Ritchie

We report, for the first time, ballistic magnetoresistance effects in a two-dimensional electron gas (2DEG) subjected to a spatially modulated periodic magnetic field. The periodic magnetic field is formed by the presence of superconducting stripes on the surface of the heterostructure with a 2DEG. We observe oscillatory magnetoresistance due to a commensurability effect between the classical cyclotron diameter and the period of magnetic modulation. The behavior is in agreement with existing theory with no adjustable parameters.

Carmona, H. A.; Geim, A. K.; Nogaret, A.; Main, P. C.; Foster, T. J.; Henini, M.; Beaumont, S. P.; Blamire, M. G.

We consider the effects of anisotropy on solitons of various types in two-dimensional nonlinear lattices, using the discrete nonlinear Schrödinger equation as a paradigm model. For fundamental solitons, we develop a variational approximation that predicts that broad quasicontinuum solitons are unstable, while their strongly anisotropic counterparts are stable. By means of numerical methods, it is found that, in the general case, the fundamental solitons and simplest on-site-centered vortex solitons ("vortex crosses") feature enhanced or reduced stability areas, depending on the strength of the anisotropy. More surprising is the effect of anisotropy on the so-called "super-symmetric" intersite-centered vortices ("vortex squares"), with the topological charge equal to the square's size : we predict in an analytical form by means of the Lyapunov-Schmidt theory, and confirm by numerical results, that arbitrarily weak anisotropy results in dramatic changes in the stability and dynamics in comparison with the degenerate, in this case, isotropic, limit. PMID:16383560

Kevrekidis, P G; Frantzeskakis, D J; Carretero-González, R; Malomed, B A; Bishop, A R

We study a quasi-two-dimensional superfluid Fermi gas where the confinement in the third direction is due to a strong harmonic trapping. We investigate the behavior of such a system when the chemical potential is varied and find strong modifications of the superfluid properties due to the discrete harmonic oscillator states. We show that such quasi-two-dimensional behavior can be created and observed with current experimental capabilities. PMID:16383804

We use soliton techniques of the two-dimensional reduced {beta}-function equations to obtain nontrivial string backgrounds from flat space. These solutions are characterized by two integers ({ital n},{ital m}) referring to the soliton numbers of the metric and axion-dilaton sectors, respectively. We show that the Nappi-Witten universe associated with the SL(2){times}SU(2)/SO(1,1){times}U(1) CFT coset arises as a (1,1) soliton in this fashion for certain values of the moduli parameters, while for other values of the soliton moduli we arrive at the SL(2)/SO(1,1){times}SO(1,1){sup 2} background. Ordinary four-dimensional black holes arise as two-dimensional (2,0) solitons, while the Euclidean wormhole background is described as a (0,2) soliton on flat space. The soliton transformations correspond to specific elements of the string Geroch group. These could be used as a starting point for exploring the role of {ital U} dualities in string compactifications to two dimensions. {copyright} {ital 1996 The American Physical Society.}

Bakas, I. [Theory Division, European Organization for Nuclear Research (CERN), 1211 Geneva 23, Switzerl] [Theory Division, European Organization for Nuclear Research (CERN), 1211 Geneva 23, Switzerl; [and Department of Physics, University of Patras, 26110 Patras (Greece)

The information transmitted (Ti) by the direction of two-dimensional (2-D) isometric forces at different stereoscopic depths was studied in 50 naive human subjects using an isometric manipulandum and random dot stereograms generated in a color display (Massey et al. 1988). Subjects viewed the display through appropriate color filters and perceived the image of a disk rotated about a horizontal axis on the frontal plane; the top of the disk was rotated around that axis by 15, 45, 60 and 80 degrees away from the subject. Each of these disks involved a different amount of stereoscopic depth perception which was lowest for the 15 degrees and highest for the 80 degrees tilt. Subjects were instructed to exert force in the direction of a visual target presented on the disk in a reaction time task. The instantaneous force exerted by the subjects on the manipulandum was shown on the disk in the form of a feedback cursor. Information transmitted, reaction time (RT) and systematic directional deviations were calculated. We found the following. (a) Ti increased with input information but at a lower rate; at the highest level of input information studied (5.91 bits), Ti was 4.1 bits at the 15 degrees tilt. This high value of Ti suggests that directional information for isometric force is processed very efficiently. However, this Ti was consistently lower than that transmitted by the direction of movement (Georgopoulos and Massay, 1988). (b) Ti did not differ significantly among the 15-60 degrees tilt but was 0.19 bits less for the 80 degrees tilt. RT did not differ among the 15-80 degrees tilts.(ABSTRACT TRUNCATED AT 250 WORDS) PMID:1850700

Massey, J T; Drake, R A; Lurito, J T; Georgopoulos, A P

We present simulation studies of the formation and dynamics of dark solitons and vortices in quantum electron plasmas. The electron dynamics in the latter is governed by a pair of equations comprising the nonlinear Schroedinger and Poisson system of equations, which conserves the number of electrons as well as their momentum and energy. The present governing equations in one spatial dimension admit stationary solutions in the form a dark envelope soliton. The dynamics of the latter reveals its robustness. Furthermore, we numerically demonstrate the existence of cylindrically symmetric two-dimensional quantum electron vortices, which survive during collisions. The nonlinear structures presented here may serve the purpose of transporting information at quantum scales in ultracold micromechanical systems and dense plasmas, such as those created during intense laser-matter interactions.

Shukla, P.K.; Eliasson, B. [Institut fuer Theoretische Physik IV, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)

We present a comprehensive analysis of how the properties of two-dimensional lattice (''discrete'') solitons in a Kerr medium are influenced by their peak intensity and width. We are able to quantitatively relate the Townes solution for solitons in a two-dimensional, homogeneous media to two distinct regimes of the lattice solitons: to narrow, high-intensity, highly nonlinear solitons and to broad, low-intensity, weakly nonlinear solitons, which experience the periodic potential as an effective homogeneous medium. Both regimes, although they support a different power flow and are affected by completely different diffraction dynamics, are thus traced back to the same physical phenomenon. They are separated by a range of unstable and stable solutions, directly caused by the periodicity of the lattice.

Eilenberger, Falk; Pertsch, Thomas [Institute for Applied Physics, Friedrich Schiller University, Max-Wien-Platz 1, D-07743 Jena (Germany); Szameit, Alexander [Physics Department and Solid State Institute, Technion-Israel Institute of Technology, 32000 Haifa (Israel)

We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman-Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite-Gaussian and three Laguerre-Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion. PMID:22660146

Shapira, Asia; Shiloh, Roy; Juwiler, Irit; Arie, Ady

In this paper we present results in the areas of shape matching of nonoccluded and occluded two-dimensional objects. Shape matching is viewed as a ``segment matching'' problem. Unlike the previous work, the technique is based on a stochastic labeling procedure which explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification. To reduce the computation time, the

Two-dimensional magnetic garnets exhibit complex and fascinating magnetic domain structures, like stripes, labyrinths, cells, and mixed states of stripes and cells. These patterns do change in a reversible way when the intensity of an externally applied magnetic field is varied. The main objective of this contribution is to present the results of a model that yields a rich pattern structure

J. R. Iglesias; S. Gonçalves; O. A. Nagel; Miguel Kiwi

Two-dimensional magnetic garnets exhibit complex and fascinating magnetic domain structures, like stripes, cells, mixed states of stripes and cells and labyrinths, which have challenged theorists for a long time. They change reversibly when the intensity of an externally applied magnetic field is varied. By Monte Carlo simulations we investigate the pattern formation and the thermodynamics of these systems as a

The purpose of this study was to develop a twodimensional mathematical model of an unrestrained, right, front seat, passenger car occupant, subjected to frontal collision. A 10 degrees of freedom linkage system made of 8 rigid segments connected with revolute joints was used as occupant model. Relative rotation between links were constrained by torsional springs, dampers, Coulomb frictions and

In an inhomogeneous magnetized plasma the transport of energy and particles perpendicular to the magnetic field is in general mainly caused by quasi two-dimensional turbulent fluid mixing. The physics of turbulence and structure formation is of ubiquitous importance to every magnetically confined laboratory plasma for experimental or industrial…

The report is the second in a series in the exact numerical calculations of the stability of viscous flows by the method of quasilinearization. It describes results for the growth or decay of Tollmien-Schlichting type disturbances in a two-dimensional Poi...

We investigate two-dimensional invisibility cloaking via transformation optics approach. The cloaking media possess much more singular parameters than those having been considered for three-dimensional cloaking in literature. Finite energy solutions for these cloaking devices are studied in appropriate weighted Sobolev spaces. We derive some crucial properties of the singularly weighted Sobolev spaces. The invisibility cloaking is then justified by decoupling

The base research project is on two-dimensional pho nonic band gap materials whose characteristic stop band can be tun ed by using an eccentric coating layer to the core scatterers. The host institution is the Polytechnic University of Valencia, Spain, whose 1995 article in the Nature magazine was considered by many as the article that started this field of endeavor.

A two-dimensional plasma actuator analysis code has been developed. A time-accurate Navier-Stokes CFD code was coupled with a time-dependent, phenomenological model of an alternating current, single dielectric barrier discharge plasma actuator. The accura...

Efficient browsing and retrieval of geographically referenced information requires the allocation of data on different storage devices for concurrent retrieval. By dividing a twodimensional space into tiles, a system can allow users to specify regions of interest using a query rectangle and then retrieving all information related to tiles overlapping with the query. In this paper, we derive the

A review is presented of the main features of localized structures - dissipative solitons - in optical systems with nonlinear amplification and absorption, without driving (holding) radiation, including cases with and without feedback. The focus is on two-dimensional laser solitons. For the case of cylindrically- symmetric intensity distributions, there is a discrete set of such solitons with different values of topological charge and different numbers of oscillations in the radial profiles of their amplitude and phase, within certain intervals of the system parameters. Even these simplest dissipative solitons have certain internal structures that become apparent in the distribution of the radiation energy flows. For weakly-coupled solitons whose tail overlap is only small, the distribution of energy flows in the vicinity of each constituent soliton is topologically similar to the distribution for individual solitons. In addition to weakly-coupled solitons, strongly coupled states exist in parameter domains overlapping with those for symmetric solitons. Symmetric structures are motionless, while asymmetric structures move and rotate. Strongly-coupled soliton states are characterized by asymmetric multi-humped intensity distributions. Rotation occurs even in the absence of radiation wavefront dislocations. We present examples of bifurcations of the phase portrait of energy flows during the transient process of the rotating structure formation, as well as different rotating chains of localized strongly-coupled laser vortices. Under conditions of modulation instability of homogeneous field distributions, new regimes arise, including localized structures with simultaneous rotation and pulsation, and "bio-solitons" with initial growth of structure like a labyrinth, with periodic separation of the fragments; then the fragments repeat the stages of growth and separation of new generations of fragments.

Environmental managers and protection agencies try to assess the magnitudes of earthquakes in regions of seismic activity. For several decades they have used the seismic b-values and Bouguer anomalies for evaluating the crustal character and stress regimes. We have analyzed geostatistically data on both variables to map their spatial distributions in the southeast of the Zagros of Iran. We found a strong correlation between the distribution of the b-value and the Bouguer gravity anomaly in the region. The large Bouguer gravity anomaly values and small b-values all accord with there being a thinner crustal root and a larger concentration of stress in the center. The small to moderate Bouguer gravity anomaly values and intermediate to large b-values accord with the thicker crustal root and the smaller concentration of stress in the northeast. We conclude the southeast of the Zagros, consists of heterogeneous crust, such that accounts for its varied tectonics.

Sarkarinejad, Khalil; Mehdi Zadeh, Rezvan; Webster, Richard

We examine the existence and stability of discrete spatialsolitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active defocusing media, where the gain exceeds damping in the low-amplitude limit. A new family of stable localized structures is found: these are bright and gray cavity solitons representing the connections between homogeneous and inhomogeneous states. Solitons of this type can be controlled by discrete diffraction and are stable when the bistability of homogenous states is absent. PMID:23164851

Prilepsky, Jaroslaw E; Yulin, Alexey V; Johansson, Magnus; Derevyanko, Stanislav A

Solitonic objects play a central role in gauge and string theory (as, e.g., monopoles, black holes, D-branes, etc.). Certain string backgrounds produce a noncommutative deformation of the low-energy effective field theory, which allows for new types of solitonic solutions. I present the construction, moduli spaces and dynamics of Moyal-deformed solitons, exemplified in the 2+1 dimensional Yang-Mills-Higgs theory and its Bogomolny system, which is gauge-fixed to an integrable chiral sigma model (the Ward model). Noncommutative solitons for various 1+1 dimensional integrable systems (such as sine-Gordon) easily follow by dimensional and algebraic reduction. Supersymmetric extensions exist as well and are related to twistor string theory.

The gamma sensitivity of a two-dimensional scintillation neutron detector based on position sensitive photomultipliers (Hamamatsu R2387 PM) has been minimized by a digital differential discrimination unit. Since the photomultiplier gain is position-dependent by [+-]25% a discrimination unit was developed where digital upper and lower discrimination levels are set due to the position-dependent photomultiplier gain obtained from calibration measurements. By this method narrow discriminator windows can be used to reduce the gamma background drastically without effecting the neutron sensitivity of the detector. The new discrimination method and its performance tested by neutron measurements will be described. Experimental results concerning spatial resolution and [gamma]-sensitivity are presented.

Kanyo, M.; Reinartz, R.; Schelten, J.; Mueller, K.D. (Research Center Juelich GmbH (Germany). Central Lab. for Electronics)

Two-dimensional optical strain measurements on high temperature test specimens are presented. This two-dimensional capability is implemented through a rotatable sensitive strain axis. Three components of surface strain can be measured automatically, from which the first and second principal strains are calculated. One- and two-dimensional strain measurements at temperatures beyond 750 C with a resolution of 15 microstrain are demonstrated. The system is based on a one-dimensional speckle shift technique. The speckle shift technique makes use of the linear relationship between surface strain and the differential shift of laser speckle patterns in the diffraction plane. Laser speckle is a phase effect that occurs when spatially coherent light interacts with an optically rough surface. Since speckle is generated by any diffusely reflecting surface, no specimen preparation is needed to obtain a good signal. Testing was done at room temperature on a flat specimen of Inconel 600 mounted in a fatigue testing machine. A load cell measured the stress on the specimen before and after acquiring the speckle data. Strain components were measured at 0 C (parallel to the load axis) and at plus or minus 45 C, and plots indicate the calculated values of the first and second principal strains. The measured values of Young's modulus and Poisson's ratio are in good agreement with handbook values. Good linearity of the principal strain moduli at high temperatures indicate precision and stability of the system. However, a systematic error in the high-temperature test setup introduced a scale factor in the slopes of the two-dimensional stress-strain curves. No high temperature effects, however, have been observed to degrade speckle correlation.

We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way, the ranking of nodes becomes twodimensional which paves the way for the development of two-dimensional search engines of a new type. Statistical properties of information flow on the PageRank-CheiRank plane are analyzed for networks of British, French and Italian universities, Wikipedia, Linux Kernel, gene regulation and other networks. A special emphasis is done for British universities networks using the large database publicly available in the UK. Methods of spam links control are also analyzed.

Ermann, L.; Chepelianskii, A. D.; Shepelyansky, D. L.

The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists ab aeterno. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. While PageRank highlights very well known nodes with many ingoing links, CheiRank highlights very communicative nodes with many outgoing links. In this way the ranking becomes two-dimensional. Using CheiRank and PageRank we analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.

A wealth of effort in photonics has been dedicated to the study and engineering of surface plasmonic waves in the skin of three-dimensional bulk metals, owing largely to their trait of subwavelength confinement. Plasmonic waves in two-dimensional conductors, such as semiconductor heterojunction and graphene, contrast the surface plasmonic waves on bulk metals, as the former emerge at gigahertz to terahertz and infrared frequencies well below the photonics regime and can exhibit far stronger subwavelength confinement. This review elucidates the machinery behind the unique behaviours of the two-dimensional plasmonic waves and discusses how they can be engineered to create ultra-subwavelength plasmonic circuits and metamaterials for infrared and gigahertz to terahertz integrated electronics. PMID:24567472

Yoon, Hosang; Yeung, Kitty Y M; Kim, Philip; Ham, Donhee

We review the status of solitons in superstring theory, with a view to understanding the strong coupling regime. These solitonic solutions are non-singular field configurations which solve the empty-space low-energy field equations (generalized, whenever possible, to all orders in ??), carry a non-vanishing topological “magnetic” charge and are stabilized by a topological conservation law. They are compared and contrasted with

Superdiffusion of two-dimensional (2D) liquids was studied using an equilibrium molecular dynamics simulation. At intermediate temperatures, the mean-squared displacement, probability distribution function (PDF), and velocity autocorrelation function (VACF) all indicate superdiffusion; the VACF has a long-time tail; and the PDF indicates no Lévy flights. These effects are predicted to occur in 2D dusty plasmas and other 2D liquids that can be modeled with a long-range repulsive potential.

Two-dimensional magnetic garnets exhibit complex and fascinating magnetic\\u000adomain structures, like stripes, labyrinths, cells and mixed states of stripes\\u000aand cells. These patterns do change in a reversible way when the intensity of\\u000aan externally applied magnetic field is varied. The main objective of this\\u000acontribution is to present the results of a model that yields a rich pattern\\u000astructure

J. R. Iglesias; S. Goncalves; O. A. Nagel; Miguel Kiwi

We report the design of quasi-two-dimensional artificial structures that acoustically behave as positive, single negative, double negative or density-near-zero metamaterials. The scattering units consist of a cavity drilled in one surface of a 2D waveguide and they have an inner structure whose geometrical parameters can be selected in order to obtain the desired dynamical behavior. Finally, we report the practical realization of two samples as well as their experimental characterization showing metamaterial features.

Torrent, D.; Graciá-Salgado, R.; García-Chocano, V. M.; Cervera, F.; Sánchez-Dehesa, J.

As part of a code validation effort supporting the proposed Yucca Mountain Nuclear Waste Repository, we simulate two-dimensional flow of basaltic lava using a multi-fluid, multi-phase continuum fluid dynamics code CFDLib. As a starting point, we look at flow in a straight conduit of circular cross-section. This can be compared with the one-dimensional simulations reported in a companion paper [1

A new type of simple and reliable two-dimensional fiber-optical accelerometer is developed to measure constant (dc) and variable (ac) accelerations simultaneously in two perpendicular directions (vector acceleration) with a linearity error of less than 0.1%. The sensor is based on a deflection of a uniform round elastic cantilever beam sensed by an optical lever and a continuous position optical sensor.

The coherent matter waves of a dipolar condensate in deep two-dimensional (2D) tilted and nontilted optical lattices are studied both analytically and numerically. It is shown that, in tilted lattices, by properly designing the sign and the magnitude of the contact interaction and the dipolar interaction, it is possible to control the decoherence of Bloch oscillations. Contrary to the usual short-range interacting Bose system, long-lived Bloch oscillations of the dipolar condensate are achieved when the dipolar interaction, the contact interaction, and the lattice dimension satisfy an analytical condition. Furthermore, we predict that, in untilted lattices, stable coherent 2D moving soliton and breather states of the dipolar condensate exist. This fact is very different from the purely short-range interacting Bose system (where the moving soliton cannot be stabilized in high-dimensional lattices). The dipolar interaction can lead to some novel phenomena that can not appear in short-range interacting BEC system.

Zhang Aixia; Xue Jukui [Physics and Electronics Engineering College, Northwest Normal University, Lanzhou 730070 (China)

We propose a scheme for stabilizing spatiotemporal solitons (STSs) in media with cubic self-focusing nonlinearity and "dispersion management," i.e., a layered structure inducing periodically alternating normal and anomalous group-velocity dispersion. We develop a variational approximation for the STS, and verify results by direct simulations. A stability region for the two-dimensional (2D) STS (corresponding to a planar waveguide) is identified. At the borders between this region and that of decay of the solitons, a more sophisticated stable object, in the form of a periodically oscillating bound state of two subpulses, is also found. In the 3D case (bulk medium), all the spatiotemporal pulses spread out or collapse. PMID:15324185

Matuszewski, M; Trippenbach, M; Malomed, B A; Infeld, E; Skorupski, A A

It is commonly held that a necessary condition for the existence of solitons in nonlinear-wave systems is that the soliton’s frequency (spatial or temporal) must not fall into the continuous spectrum of radiation modes. However, this is not always true. We present a new class of codimension-one solitons (i.e., those existing at isolated frequency values) that are embedded into the

A. R. Champneys; B. A. Malomed; J. Yang; D. J. Kaup

Spatialsolitons are localized structures that propagate through nonlinear media keeping their cross section unperturbed due to a balance between diffraction and nonlinearity. When they occur in optical cavities, they are called cavity solitons (CS). We present here a general method to obtain CS in any kind of lasers, including semiconductor lasers. We use the idea of \\

We investigate the routing of vortex beams in nonlocal media by means of coaxial, co-propagating spatial optical solitons. By introducing a refractive index perturbation in the form of a localized defect or a dielectric interface, the soliton waveguide can be curved and, therefore, can deviate the collinear vortex, effectively routing it, while preventing its destabilization and breakup. PMID:24487852

Assanto, Gaetano; Minzoni, Antonmaria A; Smyth, Noel F

We analyze two-component spatial optical vortex solitons supported by parametric wave mixing processes in a nonlinear bulk medium. We study two distinct cases of such localized waves, namely, parametric vortex solitons due to phase-matched second-harmonic generation in an optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a "halo-vortex," consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a "ring-vortex" soliton which is a vortex in a harmonic field that guides a ring-like localized mode of the fundamental-frequency field. PMID:11046495

We perform Young's double-slit experiment to study the spatial coherence properties of a two-dimensional dynamic condensate of semiconductor microcavity polaritons. The coherence length of the system is measured as a function of the pump rate, which confirms a spontaneous buildup of macroscopic coherence in the condensed phase. An independent measurement reveals that the position and momentum uncertainty product of the condensate is close to the Heisenberg limit. An experimental realization of such a minimum uncertainty wave packet of the polariton condensate opens a door to coherent matter-wave phenomena such as Josephson oscillation, superfluidity, and solitons in solid state condensate systems. PMID:17930529

We investigate the influence of the isospin asymmetry on the phase structure of quark matter near the chiral critical point systematically using a generalized version of Ginzburg-Landau approach. The effect has proven to be so profound that it brings about not only a shift of the critical point but also a rich variety of phases in its neighborhood. In particular, there shows up a phase with spatially varying charged pion condensate which we name the “solitonic pion condensate” in addition to the “chiral defect lattice” where the chiral condensate is partially destructed by periodic placements of two-dimensional wall-like defects. Our results suggest that there may be an island of solitonic pion condensate in the low temperature and high density side of QCD phase diagram.

Disclosed is the design of a high speed two-dimensional optical beam position detector which outputs the X and Y displacement and total intensity linearly. The experimental detector measures the displacement from DC to 123 MHz and the intensity of an optical spot in a similar way as a conventional quadrant photodiode detector. The design uses four discrete photodiodes and simple dedicated optics for the position decomposition which enables higher spatial accuracy and faster electronic processing than conventional detectors. Measurements of the frequency response and the spatial sensitivity demonstrate high suitability for atomic force microscopy, scanning probe data storage applications, and wideband wavefront sensing. The operation principle allows for position measurements up to 20 GHz and more in bandwidth.

Several features of the equilibrium and nonequilibrium statistical mechanics of a two-dimensional plasma in a uniform dc magnetic field are investigated. The charges are assumed to interact only through electrostatic potentials. The problem is considered both with and without the guiding-center approximation. With the guiding-center approximation, an appropriate Liouville equation and BBGKY hierarchy predict no approach to thermal equilibrium for the spatially uniform case. For the spatially nonuniform situation, a guiding-center Vlasov equation is discussed and solved in special cases. For the nonequilibrium, nonguiding-center case, a Boltzmann equation, and a Fokker-Planck equation are derived in the appropriate limits. The latter is more tractable than the former, and can be shown to obey conservation laws and an H-theorem, but contains a divergent integral which must be cut off on physical grounds. Several unsolved problems are posed.

Disclosed is the design of a high speed two-dimensional optical beam position detector which outputs the X and Y displacement and total intensity linearly. The experimental detector measures the displacement from DC to 123 MHz and the intensity of an optical spot in a similar way as a conventional quadrant photodiode detector. The design uses four discrete photodiodes and simple dedicated optics for the position decomposition which enables higher spatial accuracy and faster electronic processing than conventional detectors. Measurements of the frequency response and the spatial sensitivity demonstrate high suitability for atomic force microscopy, scanning probe data storage applications, and wideband wavefront sensing. The operation principle allows for position measurements up to 20 GHz and more in bandwidth.

Thiol capped gold nanoparticles (Au NPs) form a simple twodimensional (2D) liquid on water surface but this thin film is unstable under compression. Amphiphilic stearic acid (StA) molecules on water surface, on the other hand, form a complex and more stable 2D liquid. We have initiated a study on a mixture of StA and Au NPs in a monolayer through Surface Pressure (?) - Specific Molecular Area (A) isotherms and Brewster Angle Microscopy (BAM). A mixture of Stearic Acid and Au nanoparticles (10% by weight) produces a monolayer on water surface that acts as a 2D liquid with phases that are completely reversible with negligible hysteresis.

Two-dimensional magnetic garnets exhibit complex and fascinating magnetic domain structures, like stripes, cells, mixed states of stripes and cells and labyrinths, which have challenged theorists for a long time. They change reversibly when the intensity of an externally applied magnetic field is varied. By Monte Carlo simulations we investigate the pattern formation and the thermodynamics of these systems as a function of the intensity of the external magnetic field. Our simulations yield patterns which are similar to the ones observed experimentally. The ordering transition temperature, relaxation energy and average domain size of each configuration are computed. General trends, as functions of the model parameters, are presented and discussed.

Kiwi, M.; Iglesias, J. R.; Goncalves, S.; Nagel, O.

We have created an apparatus to quantitatively measure two-dimensional heat flow in a metal plate using a grid of temperature sensors read by a microcontroller. Real-time temperature data are collected from the microcontroller by a computer for comparison with a computational model of the heat equation. The microcontroller-based sensor array allows previously unavailable levels of precision at very low cost, and the combination of measurement and modeling makes for an excellent apparatus for the advanced undergraduate laboratory course.

We consider the morphology of two-dimensional cracks observed in experimental results obtained from paper samples and compare these results with the numerical simulations of the random fuse model (RFM). We demonstrate that the data obey multiscaling at small scales but cross over to self-affine scaling at larger scales. Next, we show that the roughness exponent of the random fuse model is recovered by a simpler model that produces a connected crack, while a directed crack yields a different result, close to a random walk. We discuss the multiscaling behaviour of all these models.

Alava, Mikko [Helsinki University of Technology, Helsinki, Finland; Nukala, Phani K [ORNL; Zapperi, Stefano [University of La Sapienza, Rome

Combined inclination/azimuth leaf angle distributions are important for accurate models of vegetation canopy reflectance. It is shown that appropriate mathematical representations can be constructed from beta distributions under most circumstances. This is illustrated by analyzing observational data on soybean leaves and balsam fir needles. There are some problems when the data is imprecise and when correlations between inclination and azimuth angle are induced by heliotropism. Otherwise, the two-dimensional beta-type distribution appears to be a versatile tool for describing complete inclination/azimuth leaf angle distributions.

A two-dimensional photon counting array in operation at Mount Stromlo is described and its performance discussed. The detector consists of a highly intensified Fairchild SL 62925 charge coupled device (CCD) where the spectral response of the system can be varied by the use of intensifiers which have different cathode types (S-20, S-25) as the first electron-emitting surface. The format of the external memory is 760 x 488 event-centered pixels. Prior frame subtraction is used to achieve counting rates of 5 Hz pixel with 3% coincidence correction. The advantages of photon-counting array systems over analog CCD detectors are discussed.

We investigate next-nearest-neighbor correlations of the contact number in simulations of polydisperse, frictionless packings in two dimensions. We find that disks with few contacting neighbors are predominantly in contact with disks that have many neighbors and vice versa at all packing fractions. This counterintuitive result can be explained by drawing a direct analogy to the Aboav-Weaire law in cellular structures. We find an empirical one parameter relation similar to the Aboav-Weaire law that satisfies an exact sum rule constraint. Surprisingly, there are no correlations in the radii between neighboring particles, despite correlations between contact number and radius.

Two-dimensional magnetic garnets exhibit complex and fascinating magnetic domain structures, like stripes, labyrinths, cells, and mixed states of stripes and cells. These patterns do change in a reversible way when the intensity of an externally applied magnetic field is varied. The main objective of this contribution is to present the results of a model that yields a rich pattern structure that closely resembles what is observed experimentally. Our model is a generalized two-dimensional Ising-like spin-1 Hamiltonian with long-range interactions, which also incorporates anisotropy and Zeeman terms. The model is studied numerically by means of Monte Carlo simulations. Changing the model parameters, stripes, labyrinth, and/or cellular domain structures are generated. For a variety of cases we display the patterns and determine the average size of the domains, the ordering transition temperature, specific heat, magnetic susceptibility, and hysteresis cycle. Finally, we examine the reversibility of the pattern evolution under variations of the applied magnetic field. The results we obtain are in good qualitative agreement with experiment.

Iglesias, J. R.; Gonçalves, S.; Nagel, O. A.; Kiwi, Miguel

We experimentally investigate the two-dimensional condensate (optical dropletlike) soliton formation and dynamics of the generated signal and probe beams in four-wave mixing (FWM) process with atomic coherence, under competition between the third- and fifth-order nonlinear susceptibilities. With such competing nonlinearities, mutual transformations among dropletlike fundamental, dipole, and azimuthally modulated vortex FWM solitons are observed. The influence of nonlinear competition on the photonic band gap is also investigated. All the results are obtained under low powers.

Two-dimensional difference gel electrophoresis (2D DIGE) is a modified form of 2D electrophoresis (2DE) that allows one to compare two or three protein samples simultaneously on the same gel. The proteins in each sample are covalently tagged with different color fluorescent dyes that are designed to have no effect on the relative migration of proteins during electrophoresis. Proteins that are common to the samples appear as "spots" with a fixed ratio of fluorescent signals, whereas proteins that differ between the samples have different fluorescence ratios. With the appropriate imaging system, difference gel electrophoresis (DIGE) is capable of reliably detecting as little as 0.2 fmol of protein, and protein differences down to ±15%, over a ?20,000-fold protein concentration range. DIGE combined with digital image analysis therefore greatly improves the statistical assessment of proteome variation. Here we describe a protocol for conducting DIGE experiments, which takes 2-3 days to complete. PMID:22585495

Flexible supercapacitors, as one of most promising emerging energy storage devices, are of great interest owing to their high power density with great mechanical compliance, making them very suitable as power back-ups for future stretchable electronics. Two-dimensional (2D) nanomaterials, including the quasi-2D graphene and inorganic graphene-like materials (IGMs), have been greatly explored to providing huge potential for the development of flexible supercapacitors with higher electrochemical performance. This review article is devoted to recent progresses in engineering 2D nanomaterials for flexible supercapacitors, which survey the evolution of electrode materials, recent developments in 2D nanomaterials and their hybrid nanostructures with regulated electrical properties, and the new planar configurations of flexible supercapacitors. Furthermore, a brief discussion on future directions, challenges and opportunities in this fascinating area is also provided. PMID:24614864

Array-based group-testing algorithms for case identification are widely used in infectious disease testing, drug discovery, and genetics. In this article, we generalize previous statistical work in array testing to account for heterogeneity among individuals being tested. We first derive closed-form expressions for the expected number of tests (efficiency) and misclassification probabilities (sensitivity, specificity, predictive values) for two-dimensional array testing in a heterogeneous population. We then propose two "informative" array construction techniques which exploit population heterogeneity in ways that can substantially improve testing efficiency when compared to classical approaches that regard the population as homogeneous. Furthermore, a useful byproduct of our methodology is that misclassification probabilities can be estimated on a per-individual basis. We illustrate our new procedures using chlamydia and gonorrhea testing data collected in Nebraska as part of the Infertility Prevention Project. PMID:22212007

McMahan, Christopher S; Tebbs, Joshua M; Bilder, Christopher R

Synthetic polymers exhibit diverse and useful properties and influence most aspects of modern life. Many polymerization methods provide linear or branched macromolecules, frequently with outstanding functional-group tolerance and molecular weight control. In contrast, extending polymerization strategies to two-dimensional periodic structures is in its infancy, and successful examples have emerged only recently through molecular framework, surface science and crystal engineering approaches. In this Review, we describe successful 2D polymerization strategies, as well as seminal research that inspired their development. These methods include the synthesis of 2D covalent organic frameworks as layered crystals and thin films, surface-mediated polymerization of polyfunctional monomers, and solid-state topochemical polymerizations. Early application targets of 2D polymers include gas separation and storage, optoelectronic devices and membranes, each of which might benefit from predictable long-range molecular organization inherent to this macromolecular architecture. PMID:23695626

A scanning probe microscope can provide very high resolution imaging, but only within a small scanning area. There is a high demand for compact long range positioners, so that distant locations on the same sample can be imaged and studied. We will present information on the design and operation of a piezoelectric driven two-dimensional micropositioner that can provide long range motion in the x- and z-directions. The z-direction motion can be used for coarse approach, while the x-direction motion can be used to scan along the sample surface. The device is build as one single unit, so it is extremely compact and rigid, and can provide a high resonance frequency platform for high performance scanning probe microscopy.

The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

The two-dimensional (2-D) structure of switch-off slow magnetosonic shocks is investigated using an electromagnetic hybrid (fluid electrons, kinetic ions) code. It is shown that the basic physical processes occurring at 1-D slow shocks are also operative in 2-D. Specifically, the interaction between the upstream ions and those streaming away from the shock results in the excitation of Alfven/ions-cyclotron (AIC) waves. Depending on the plasma parameters, these waves may either stay in the upstream or convect back into the shock resulting in a non-steady shock behavior which prevents the formation of a trailing wave train. Despite this similarity, some slow shocks which are steady in 1-D are found to be non-steady in 2-D. Fourier analysis of the waves downstream of non-steady shocks identifies them as AIC, demonstrating that the waves remain on the same branch as they convect from upstream into the downstream region.

Omidi, N.; Johnson, M.; Krauss-Varban, D.; Karimabadi, H.

Synthetic polymers exhibit diverse and useful properties and influence most aspects of modern life. Many polymerization methods provide linear or branched macromolecules, frequently with outstanding functional-group tolerance and molecular weight control. In contrast, extending polymerization strategies to two-dimensional periodic structures is in its infancy, and successful examples have emerged only recently through molecular framework, surface science and crystal engineering approaches. In this Review, we describe successful 2D polymerization strategies, as well as seminal research that inspired their development. These methods include the synthesis of 2D covalent organic frameworks as layered crystals and thin films, surface-mediated polymerization of polyfunctional monomers, and solid-state topochemical polymerizations. Early application targets of 2D polymers include gas separation and storage, optoelectronic devices and membranes, each of which might benefit from predictable long-range molecular organization inherent to this macromolecular architecture.

A hybrid simulation method is introduced and used to study two-dimensional single-asperity and multi-asperity contacts both quasistatically and dynamically. The method combines an atomistic treatment of the interfacial region with a finite-element method description of subsurface deformations. The dynamics in the two regions are coupled through displacement boundary conditions applied at the outer edges of an overlap region. The two solutions are followed concurrently but with different time resolution. The method is benchmarked against full atomistic simulations. Accurate results are obtained for contact areas, pressures, and static and dynamic friction forces. The time saving depends on the fraction of the system treated atomistically and is already more than a factor of 20 for the relatively small systems considered here. PMID:17155215

Luan, B Q; Hyun, S; Molinari, J F; Bernstein, N; Robbins, Mark O

The chemical compounds, which are present in the environment, increasingly cause bad effects on health. The most serious effects are tumors and various mutations at the cellular level. Such compounds, from the analytical point of view, can serve the function of biomarkers, constituting measurable changes in the organism's cells and biochemical processes occurring therein. The challenge of the twenty-first century is therefore searching for effective and reliable methods of identification of biomarkers as well as understanding bodily functions, which occur in living organisms at the molecular level. The irreplaceable tool for these examinations is proteomics, which includes both quality and quantity analysis of proteins composition, and also makes it possible to learn their functions and expressions. The success of proteomics examinations lies in the usage of innovative analytical techniques, such as electromigration technique, two-dimensional electrophoresis in polyacrylamide gel (2D PAGE), liquid chromatography, together with high resolution mass spectrometry and bio-informatical data analysis. Proteomics joins together a number of techniques used for analysis of hundreds or thousands of proteins. Its main task is not the examination of proteins inside the particular tissue but searching for the differences in the proteins' profile between bad and healthy tissues. These differences can tell us a lot regarding the cause of the sickness as well as its consequences. For instance, using the proteomics analysis it is possible to find relatively fast new biomarkers of tumor diseases, which in the future will be used for both screening and foreseeing the course of illness. In this chapter we focus on two-dimensional electrophoresis because as it seems, it may be of enormous importance when searching for biomarkers of cancer diseases.

A perturbation theory for dark solitons of the nonlinear Schrödinger equation is developed. The theory is based on the inverse scattering transform method. Equations describing dynamics discrete (solitonic) and continuous (radiative) scattering data in the presence of perturbations are derived for N -soliton case. Adiabatic equations for soliton parameters and the perturbation-induced radiative field are obtained. The problem of the absence of a threshold for the creation of dark solitons under the action of a perturbation is discussed. A temporal one-soliton pulse with random initial perturbation and a spatialsoliton with linear gain and two-photon absorption are considered as examples of application of the developed theory.

The paper was aimed to compare performance capabilities of two types of scintillation detectors commonly used for fast neutron imaging: twodimensional and linear ones. Best-case values of quantum efficiency, spatial resolution and capacity were estimated for detectors with plastic converter-screen in case of 14 MeV neutrons. For that there were examined nuclear reactions produced in converter-screen by fast neutrons, spatial distributions of energy release of emerged charged particles and amplitude distributions of scintillations generated by these particles. The paper shows that the efficiency of the linear detector is essentially higher and this detector provides potentially better spatial resolution in comparison with the twodimensional detector. But, the twodimensional detector surpasses the linear one in capacity. The presented results can be used for designing radiographic fast neutron detectors with organic scintillators.

Mikerov, V. I.; Koshelev, A. P.; Ozerov, O. V.; Sviridov, A. S.; Yurkov, D. I.

China Spallation Neutron Source (CSNS) was under construction since 2008. A two-dimensional thermal neutron detector with sensitive area of 200mm×200mm was constructed for the Reflect Spectrometer of CSNS. The detector was based on two-dimensional cathode strip readout MWPC, using 5.5atm3He+2.5atmC3H8 mixture as working gas, and the thickness of the gas volume was 16mm. A readout electronics system was also developed for the detector, which mainly consists of charge-sensitive preamplifiers, amplifiers, charge measurement modules and a 6U VME64x crate. The design maximum neutron count rate of the detector was 105 events per second and the calculated neutron detection efficiency was about 70% for A2 neutrons. A prototype of the detector had been constructed at first, which own an energy resolution (FWHM) of about 23% for 55Fe 5.9keV X-ray, and its spatial resolution (FWHM) along the anode wire direction was about 300?m in X-ray test. The detector was then tested by an Am-Be neutron source. The pulse height spectrum of the neutron signal was studied. The detector can work normally and has a good performance in neutron-gamma ray discrimination.

In this work we propose a prototype of the spectral vision system, which can be used to measure a color spectrum and two- dimensional spectral images. We first designed a low- dimensional broad band color filter set with a constraint of positive spectral values by the unsupervised neural network. Then we constructed a compact size optical setup for the spectral synthesizer, which can be used to synthesize the light corresponding to the spectral characteristics of the color filter. In the optical setup we implemented the color filters by the use of the liquid crystal spatial light modulator (LCSLM). In our experiments we illuminated a sample of a real world scene by the synthesized lights and detected the intensity images of the filtering process by the CCD- camera. The intensity images correspond to the optically calculated inner products between the color filters and a sample. The data obtained from the filtering process is only a few monochrome images and therefore convenient for storing and transmitting spectral images. From the detected inner products we reconstructed the sample's color spectra by the use of inverse matrix. We present experimental results of measuring a single color spectrum and two-dimensional spectral images.

Hauta-Kasari, Markku; Miyazawa, Kanae; Toyooka, Satoru; Parkkinen, Jussi P.

The successful implementation of a finite element model for computing shallow-water flow requires the identification and spatial discretization of a surface water region. Since no robust criterion or node spacing routine exists, which incorporates physical characteristics and subsequent responses into the mesh generation process, modelers are left to rely on crude gridding criteria as well as their knowledge of particular domains and their intuition. Two separate methods to generate a finite element mesh are compared for the Gulf of Mexico. A wavelength-based criterion and an alternative approach, which employs a localized truncation error analysis (LTEA), are presented. Both meshes have roughly the same number of nodes, although the distribution of these nodes is very different. Two-dimensional depth-averaged simulations of flow using a linearized form of the generalized wave continuity equation and momentum equations are performed with the LTEA-based mesh and the wavelength-to-gridsize ratio mesh. All simulations are forced with a single tidal constituent, M2. Use of the LTEA-based procedure is shown to produce a superior (i.e., less error) two-dimensional grid because the physics of shallow-water flow, as represented by discrete equations, are incorporated into the mesh generation process. Copyright

Hagen, S. C.; Westerink, J. J.; Kolar, R. L.; Horstmann, O.

A new method of observer design for shift-invariant two-dimensional digital systems is presented. The method is applicable to a large class of two-dimensional systems and the condition of applicability is very simple to test.

A method has been devised for the forward computation of magnetic anomalies due to two-dimensional (2-D) polygonal bodies with heterogeneously directed magnetization. The calculations are based on the equivalent line source approach wherein the source is subdivided into discrete elements that vary spatially in their magnetic properties. This equivalent dipole line method provides a fast and convenient means of representing and computing magnetic anomalies for bodies possessing complexly varying magnitude and direction of magnetization. The algorithm has been tested and applied to several generalized cases to verify the accuracy of the computation. The technique has also been used to model observed aeromagnetic anomalies associated with the structurally deformed, remanently magnetized Keweenawan volcanic rocks in eastern Lake Superior. This method is also easily adapted to the calculation of anomalies due to two and one-half-dimensional (2.5-D) and three-dimensional (3-D) heterogeneously magnetized sources.

Mariano, J.; Hinze, W.J. (Purdue Univ., West Lafayette, IN (United States). Dept. of Earth and Atmospheric Sciences)

We use a pin-grid electrode to introduce a corrugated electrical potential into a planar dielectric-barrier discharge (DBD) system, so that the amplitude of the applied electric field has the profile of a two-dimensional square lattice. The lattice potential provides a template for the spatial distribution of plasma filaments in the system and has pronounced effects on the patterns that can form. The positions at which filaments become localized within the lattice unit cell vary with the width of the discharge gap. The patterns that appear when filaments either overfill or underfill the lattice are reminiscent of those observed in other physical systems involving 2D lattices. We suggest that the connection between lattice-driven DBDs and other areas of physics may benefit from the further development of models that treat plasma filaments as interacting particles. PMID:22400753

The verification of a water quality model is the one procedure most needed by decision making evaluating a model predictions, but is often not adequate or done at all. The results of a properly conducted verification provide the decision makers with an estimate of the uncertainty associated with model predictions. Several statistical tests are available for quantifying of the performance of a model. Six methods of verification were evaluated using an application of the BETTER two-dimensional water quality model for Chickamauga reservoir. Model predictions for ten state variables were compared to observed conditions from 1989. Spatial distributions of the verification measures showed the model predictions were generally adequate, except at a few specific locations in the reservoir. The most useful statistics were the mean standard error of the residuals. Quantifiable measures of model performance should be calculated during calibration and verification of future applications of the BETTER model. 25 refs., 5 figs., 7 tabs.

Butkus, S.R. (Tennessee Valley Authority, Chattanooga, TN (USA). Water Quality Dept.)

In May 2002, the solar chromosphere was observed with a two-dimensional spectrometer which is mounted in the German Vacuum Tower Telescope (VTT) at the Observatorio del Teide/Tenerife. The aim of this observation was to investigate the fine structure of the solar chromosphere seen in H? . We took narrow-band filtergrams (Delta lambda ~ 72 mÅ) by scanning through this line. Broad-band images taken strictly simultaneously with the narrow-band filtergrams were restored by speckle methods. The instantaneous optical transfer function from this restoration procedure was used for the reconstruction of the narrow-band images. Some results of this high spatial resolution observation are presented below.

Faraday Cup (FC) and electron multiplier (EM) are of the most popular ion detector for mass spectrometer. FC is used for high-count-rate ion measurements and EM can detect from single ion. However, FC is difficult to detect lower intensities less than kilo-cps, and EM loses ion counts higher than Mega-cps. Thus, FC and EM are used complementary each other, but they both belong to zero-dimensional detector. On the other hand, micro channel plate (MCP) is a popular ion signal amplifier with two-dimensional capability, but additional detection system must be attached to detect the amplified signals. Two-dimensional readout for the MCP signals, however, have not achieve the level of FC and EM systems. A stacked CMOS active pixel sensor (SCAPS) has been developed to detect two-dimensional ion variations for a spatial area using semiconductor technology [1-8]. The SCAPS is an integrated type multi-detector, which is different from EM and FC, and is composed of more than 500×500 pixels (micro-detectors) for imaging of cm-area with a pixel of less than 20 µm in square. The SCAPS can be detected from single ion to 100 kilo-count ions per one pixel. Thus, SCAPS can be accumulated up to several giga-count ions for total pixels, i.e. for total imaging area. The SCAPS has been applied to stigmatic ion optics of secondary ion mass spectrometer, as a detector of isotope microscope [9]. The isotope microscope has capabilities of quantitative isotope images of hundred-micrometer area on a sample with sub-micrometer resolution and permil precision, and of two-dimensional mass spectrum on cm-scale of mass dispersion plane of a sector magnet with ten-micrometer resolution. The performance has been applied to two-dimensional isotope spatial distribution for mainly hydrogen, carbon, nitrogen and oxygen of natural (extra-terrestrial and terrestrial) samples and samples simulated natural processes [e.g. 10-17]. References: [1] Matsumoto, K., et al. (1993) IEEE Trans. Electron Dev. 40, 82-85. [2] Takayanagi et al. (1999) Proc. 1999 IEEE workshop on Charge-Coupled Devices and Advanced Image Sensors, 159-162. [3] Kunihiro et al. (2001) Nucl. Instrum. Methods Phys. Res. Sec. A 470, 512-519. [4] Nagashima et al. (2001) Surface Interface Anal. 31, 131-137. [5] Takayanagi et al. (2003) IEEE Trans. Electron Dev. 50, 70- 76. [6] Sakamoto and Yurimoto (2006) Surface Interface Anal. 38, 1760-1762. [7] Yamamoto et al. (2010) Surface Interface Anal. 42, 1603-1605. [8] Sakamoto et al. (2012) Jpn. J. Appl. Phys. 51, 076701. [9] Yurimoto et al. (2003) Appl. Surf. Sci. 203-204, 793-797. [10] Nagashima et al. (2004) Nature 428, 921-924. [11] Kunihiro et al. (2005) Geochim. Cosmochim. Acta 69, 763-773. [12] Nakamura et al. (2005) Geology 33, 829-832. [13] Sakamoto et al. (2007) Science 317, 231-233. [14] Greenwood et al. (2008) Geophys. Res. Lett., 35, L05203. [15] Greenwood et al. (2011) Nature Geoscience 4, 79-82. [16] Park et al. (2012) Meteorit. Planet. Sci. 47, 2070-2083. [17] Hashiguchi et al. (2013) Geochim. Cosmochim. Acta. 122, 306-323.

Spectra extraction is an important procedure in reducing raw data of fiber-fed spectrographs. The flux of fiber on each wavelength will be obtained by extracting spectra from a two-dimensional image of fiber-fed spectrographs. Spectra extraction affects the later spectrum data processing procedures directly, and its accuracy guarantees the scientific value of spectra. The extraction algorithm is described for extracting one-dimensional object spectra from a two-dimensional spectrum image of LAMOST in this paper. The principle of spectra extraction based on the weighted least square method and polynomial fitting is presented in detail as well as fiber spatial profile. The raw data of fiber-fed spectrographs consist of a collection of spectra distributed along a certain axis of a two-dimensional frame. For each wavelength, spectrum expands along the cross-dispersion axis and covers some width, which is called spatial profile. The profile is considered Gassian function in the paper. According to Guassian spatial profile character of the fiber and experiments, the scope of sampling point is well selected in this paper. The good scope of sampling point solves the problem that the fibers' flux extracted is negative. The least square method is often used for scientific computing. To fit Guassian spatial profile of fiber the weighted least square method is used for spectra extraction of LAMOST, and then the flux of fiber on each wavelength is obtained further. The existence of noise is usually a problem in data processing. In reducing raw data of fiber-fed spectrographs, strong noise will distort fiber spatial profile seriously. It will lead the bad extraction results from the spectrum image and can't meet the scientific demand. In frequency domain, the spectra energy lies in the low frequency, but the noise energy lies in the high frequency on the contrary. So the improved extraction algorithm based on spectrum analysis in frequency domain is proposed against the affection of strong noise in this paper. In the first step, it filters the sharp noise out by Fast Fourier Transformer and low-pass filter, and gets a more accurate spatial profile, which has less affection of noise. Then the spectra are extracted with existing algorithm in the later step. The cut-off frequency in improved spectrum extraction is a fatal parameter, and the iteration algorithm for selecting cut-off frequency is described in detail. Finally the improvement is tested with the simulated data provided by LAMOST 2d-pipeline system, the results demonstrate the improved spectrum extraction can remove sharp noise effectively and does not twist the original spatial profile. More accurate extraction results are also achieved. Furthermore, the improvement in extreme cases of 5.6 magnitudes difference between neighborhood fibers is tested, and the results also demonstrate the feasibility and effectiveness of the proposed method.

Today scientists must deal with complex samples that either cannot be adequately separated using one-dimensional chromatography or that require an inordinate amount of time for separation. For these cases we need two-dimensional chromatography because it takes far less time to generate a peak capacity n{sub c} twice in a row than to generate a peak capacity n{sub c}{sup 2} once. Liquid chromatography has been carried out successfully on thin layers of adsorbents and along tubes filled with various adsorbents. The first type of separation sorts out the sample components in a physical separation space that is the layer of packing material. The analysis time is the same for all the components of the sample while their migration distance increases with decreasing retention. The resolution between two components having a certain separation factor (a) increases with increasing migration distance, i.e., from the strongly to the weakly retained compounds. In the second type of separation, the sample components are eluted from the column and separated in the time space, their migration distances are all the same while their retention times increase from the unretained to the strongly retained compounds. Separation efficiency varies little with retention, as long as the components are eluted from the column. We call these two types of separation the chromatographic separations in space (LC{sup x}) and the chromatographic separations in time (LC{sup t}), respectively. In principle, there are four ways to combine these two modes and do two-dimensional chromatographic separations, LC{sup t} x LC{sup t}, LC{sup x} x LC{sup t}, LC{sup t} x LC{sup x}, and LC{sup x} x LC{sup x}. We review, discuss and compare the potential performance of these combinations, their advantages, drawbacks, problems, perspectives and results. Currently, column-based combinations (LC{sup t} x LC{sup t}) are the most actively pursued. We suggest that the combination LC{sup x} x LC{sup t} shows exceptional promise because it permits the simultaneous second-dimension separations of all the fractions separated in the first-dimension, thus providing remarkable time saving.

Guiochon, Georges A [ORNL; Marchetti, Nicola [University of Tennessee, Knoxville (UTK); Mriziq, Khaled S [ORNL; Shalliker, R. Andrew [University of Western Sydney, Australia

There are numerous types of self-consistent simulations that treat plasmas according to some approximations. The fluid codes are used to study global and macroscopic processes in space plasmas. Nonlinear microscopic processes in space plasmas are studied with kinetic simulation codes. Numerical methods for kinetic simulations fall into two groups. One is particle-in-cell (PIC) method which follows motions of individual particles in a self-consistent electromagnetic field. However, a limitation on the number of particles gives rise to numerical thermal fluctuations. Another approach is Vlasov method which follows spatial and temporal development of distribution functions in the position-velocity phase space. In contrast to PIC codes, numerical noise is substantially suppressed. However, Vlasov codes require huge computer resources to represent distribution functions and Vlasov simulation techniques are still developing. Owing to the rapid advancement of recent computer technology, Vlasov code simulation would be more essential in the near future. In the present study, a new two-and-half-dimensional and fully electromagnetic Vlasov simulation code is developed in which phase-space distribution functions are defined in five-dimensional position-velocity phase space (x,y,vx,vy,vz). The Vlasov equation in two-dimensional configuration and three-dimensional velocity spaces is solved with a non-oscillatory and conservative scheme, and the full set of Maxwell’s equations are self-consistently solved based on the implicit Finite Difference Time Domain (FDTD) method. The Geospace Environment Modeling (GEM) magnetic reconnection challenge is chosen as a benchmark test of our two-dimensional Vlasov code. The result is compared with the past simulation results with Darwin-Vlasov, explicit PIC and implicit PIC codes. The present simulation with a very-low spatial resolution gives a high growth rate of magnetic flux, which is in agreement with the results of the GEM reconnection challenge.

Instead of fluid type dark matter (DM), axion-like scalar fields with a periodic self-interaction or some truncations of it are analyzed as a model of galaxy halos. It is probed if such cold Bose–Einstein type condensates could provide a viable soliton type interpretation of the DM ‘bullets’ observed by means of gravitational lensing in merging galaxy clusters. We study solitary waves for two self-interacting potentials in the relativistic Klein–Gordon equation, mainly in lower dimensions, and visualize the approximately shape-invariant collisions of two ‘lump’ type solitons. -- Highlights: •An axion model of dark matter is considered. •Collision of axion type solitons are studied in a twodimensional toy model. •Relations to dark matter collisions in galaxy clusters are proposed.

Castañeda Valle, David, E-mail: casvada@gmail.com; Mielke, Eckehard W., E-mail: ekke@xanum.uam.mx

In order to assess reproducibility of quantitative planimetry, three physicians trained in two-dimensional echocardiography performed five successive studies on one another over 2 weeks (30 total studies). Then each physician traced each study (90 total tracings) for left ventricular and atrial volumes and ejection fraction by means of a modification of Simpson's rule, and left ventricular mass and average wall thickness by means of a truncated ellipsoid formula. Calculation of intertechnician variability, intertracer variability, and 95% confidence limits showed that measurements of volumes were less reproducible than measurements of ejection fraction, average wall thickness, and mass. Mean intertracer variability of 15% exceeded mean intertechnician variability of 11%; this disparity was magnified in the subject who was technically difficult to image. Ninety-five percent confidence limits were: ejection fraction +/- 7%, average wall thickness +/- 9%, left ventricular mass +/- 12%, left ventricular end-diastolic volume +/- 11%, stroke volume +/- 14%, left ventricular end-systolic volume +/- 15%, and left atrial volume +/- 19%. Reproducible planimetry data can be obtained in normal hearts with the use of a protocol for quantitative imaging and planimetry. PMID:3341178

Himelman, R B; Cassidy, M M; Landzberg, J S; Schiller, N B

Monolayers of rare gas atoms adsorbed onto the basal planes of graphite play the same prototype role in two dimensions that rare gas liquids and solids do in three dimensions. In recent experiments such novel phenomena as continuous melting, the lack of true crystallinity in two dimensions, orientationally ordered fluid phases, and melting from a solid to a reentrant fluid with decreasing temperature have been observed. Because the forces in these rare gas monolayers are simple and well understood, by studying them the investigator can examine a direct interface between experiment and first principles. In order to understand the phases and phase transitions that occur in such materials, it is necessary to consider the geometrical matching of the rare gas overlayer to the graphite substrate. It turns out that in two dimensions both the local and the long-distance behavior are important. These two-dimensional rare gas solids may be effectively probed with synchrotron x-ray techniques, and the results of a series of synchrotron x-ray scattering studies of these solids are presented. PMID:17792141

A time-dependent Ginzburg-Landau model of plastic deformation in two-dimensional solids is presented. The fundamental dynamic variables are the displacement field u and the lattice velocity v=delta(u)/delta(t). Damping is assumed to arise from the shear viscosity in the momentum equation. The elastic energy density is a periodic function of the shear and tetragonal strains, which enables the formation of slips at large strains. In this work we neglect defects such as vacancies, interstitials, or grain boundaries. The simplest slip consists of two edge dislocations with opposite Burgers vectors. The formation energy of a slip is minimized if its orientation is parallel or perpendicular to the flow in simple shear deformation and if it makes angles of +/-pi/4 with respect to the stretched direction in uniaxial stretching. High-density dislocations produced in plastic flow do not disappear even if the flow is stopped. Thus large applied strains give rise to structurally disordered states, which are metastable due to the Peierls potential. We divide the elastic energy into an elastic part due to affine deformation and a defect part. The latter represents degree of disorder and is nearly constant in plastic flow under cyclic straining. PMID:14754207

In this talk I will present our results for the fluctuation conductivity (FC) in disordered two-dimensional superconductors placed in a perpendicular magnetic field. In our works [1,2] we finally derived the complete solution in the temperature-magnetic field phase diagram. The obtained expressions allow both to perform straightforward (numerical) calculation of the FC surface ??(T,H) and to get all 27 asymptotic expressions in the seven qualitatively different domains of the phase diagram. This surface becomes in particular non-trivial at low temperatures, where it is trough-shaped and close to the quantum phase transition non-monotonic, in agreement with experimental findings. I will show our main results and demonstrate how these can be used as a high precision tool (fluctuoscope) to determine the critical temperature, critical magnetic field, and dephasing time from experimental data in superconducting films. [4pt] [1] A. Glatz, A. A. Varlamov, and V. M. Vinokur, EuroPhys. Lett. 94, 47005 (2011).[0pt] [2] A. Glatz, A. A. Varlamov, and V. M. Vinokur, Phys. Rev. B 84, 104510 (2011).

This study is concerned with how the attractor dimension of the two-dimensional Navier-Stokes equations depends on characteristic length scales, including the system integral length scale, the forcing length scale, and the dissipation length scale. Upper bounds on the attractor dimension derived by Constantin, Foias and Temam are analysed. It is shown that the optimal attractor-dimension estimate grows linearly with the domain area (suggestive of extensive chaos), for a sufficiently large domain, if the kinematic viscosity and the amplitude and length scale of the forcing are held fixed. For sufficiently small domain area, a slightly “super-extensive” estimate becomes optimal. In the extensive regime, the attractor-dimension estimate is given by the ratio of the domain area to the square of the dissipation length scale defined, on physical grounds, in terms of the average rate of shear. This dissipation length scale (which is not necessarily the scale at which the energy or enstrophy dissipation takes place) can be identified with the dimension correlation length scale, the square of which is interpreted, according to the concept of extensive chaos, as the area of a subsystem with one degree of freedom. Furthermore, these length scales can be identified with a “minimum length scale” of the flow, which is rigorously deduced from the concept of determining nodes.

A new two-dimensional micro-flow magnetophoresis device was constructed in a superconducting magnet (10 T) using triangular shaped pole pieces, which could apply a magnetic strength, B(dB/dx), in the range of ca. 0-14,000 T(2) m(-1) across a capillary cell. Polystyrene particles with diameters of 1, 3, and 6 ?m were used as test samples in a paramagnetic medium of 1 M MnCl(2) to evaluate the performance of this method. Microparticles migrated across the capillary along the edge of the pole pieces, and then flowed through the gap in the pole piece at a position defined as the migration distance, depending on the magnetic susceptibility and the size of particles as well as the flow rate. The most effective flow rate to exhibit the largest resolution among the particles was theoretically predicted and experimentally confirmed. By this method, the magnetic susceptibilities of individual deoxygenated and non-deoxygenated red blood cells were measured from the relative migration distance. PMID:22618326

The figure is a simplified depiction of a proposed spectrometer optical unit that would be suitable for incorporation into a remote-sensing instrumentation system. Relative to prior spectrometer optical assemblies, this unit would be compact and simple, largely by virtue of its predominantly two-dimensional character. The proposed unit would be a combination of two optical components. One component would be an arrayed-waveguide grating (AWG) an integrated-optics device, developed for use in wavelength multiplexing in telecommunications. The other component would be a diffraction grating superimposed on part of the AWG. The function of an AWG is conceptually simple. Input light propagates along a single-mode optical waveguide to a point where it is split to propagate along some number (N) of side-by-side waveguides. The lengths of the optical paths along these waveguides differ such that, considering the paths in a sequence proceeding across the array of waveguides, the path length increases linearly. These waveguides launch quasi-free-space waves into a planar waveguide-coupling region. The waves propagate through this region to interfere onto an array of output waveguides. Through proper choice of key design parameters (waveguide lengths, size and shape of the waveguide coupling region, and lateral distances between waveguides), one can cause the input light to be channeled into wavelength bins nominally corresponding to the output waveguides.

Using a combined analytical/molecular dynamics approach, we study the current fluctuation spectra and longitudinal and transverse collective mode dispersions of the classical two-dimensional (point) dipole system (2DDS) characterized by the {phi}{sub D}(r)={mu}{sup 2}/r{sup 3} repulsive interaction potential; {mu} is the electric dipole strength. The interest in the 2DDS is twofold. First, the quasi-long-range 1/r{sup 3} interaction makes the system a unique classical many-body system, with a remarkable collective mode behavior. Second, the system may be a good model for a closely spaced semiconductor electron-hole bilayer, a system that is in the forefront of current experimental interest. The longitudinal collective excitations, which are of primary interest for the liquid phase, are acoustic at long wavelengths. At higher wave numbers and for sufficiently high coupling strength, we observe the formation of a deep minimum in the dispersion curve preceded by a sharp maximum; this is identical to what has been observed in the dispersion of the zero-temperature bosonic dipole system, which in turn emulates so-called roton-maxon excitation spectrum of the superfluid {sup 4}He. The analysis we present gives an insight into the emergence of this apparently universal structure, governed by strong correlations. We study both the liquid and the crystalline solid state. We also observe the excitation of combination frequencies, resembling the roton-roton, roton-maxon, etc. structures in {sup 4}He.

Golden, Kenneth I.; Kalman, Gabor J.; Hartmann, Peter; Donko, Zoltan [Department of Mathematics and Statistics, Department of Physics, University of Vermont, Burlington, Vermont 05401 (United States); Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467 (United States); Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary and Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467 (United States)

We proposed and investigated a novel adaptive two-dimensional (2-D) microgas chromatography system, which consists of one 1st-dimensional column, multiple parallel 2nd-dimensional columns, and a decision-making module. The decision-making module, installed between the 1st- and 2nd-dimensional columns, normally comprises an on-column nondestructive vapor detector, a flow routing system, and a computer that monitors the detection signal from the detector and sends out the trigger signal to the flow routing system. During the operation, effluents from the 1st-dimensional column are first detected by the detector and, then, depending on the signal generated by the detector, routed to one of the 2nd-dimensional columns sequentially for further separation. As compared to conventional 2-D GC systems, the proposed adaptive GC scheme has a number of unique and advantageous features. First and foremost, the multiple parallel columns are independent of each other. Therefore, their length, stationary phase, flow rate, and temperature can be optimized for best separation and maximal versatility. In addition, the adaptive GC significantly lowers the thermal modulator modulation frequency and hence power consumption. Finally, it greatly simplifies the postdata analysis process required to reconstruct the 2-D chromatogram. In this paper, the underlying working principle and data analysis of the adaptive GC was first discussed. Then, separation of a mixture of 20 analytes with various volatilities and polarities was demonstrated using an adaptive GC system with a single 2nd-dimensional column. Finally, an adaptive GC system with dual 2nd-dimensional columns was employed, in conjunction with temperature ramping, in a practical application to separate a mixture of plant emitted volatile organic compounds with significantly shortened analysis time. PMID:22468727

Liu, Jing; Khaing Oo, Maung Kyaw; Reddy, Karthik; Gianchandani, Yogesh B; Schultz, Jack C; Appel, Heidi M; Fan, Xudong

The method of ultrafast twodimensional infrared (2D IR) vibrational echo spectroscopy is described. Three ultrashort IR pulses tuned to the frequencies of the vibrational transitions of interest are directed into the sample. The interaction of these pulses with the molecular vibrational oscillators produces a polarization that gives rise to a fourth pulse, the vibrational echo. The vibrational echo pulse is combined with another pulse, the local oscillator, for heterodyne detection of the signal. For fixed time between the second and third pulses, the waiting time, the first pulse is scanned. Two Fourier transforms of the data yield a 2D IR spectrum. The waiting time is increased, and another spectrum is obtained. The change in the 2D IR spectra with increased waiting time provides information on the time evolution of the structure of the molecular system under observation. In a 2D IR chemical exchange experiment, two species A and B, are undergoing chemical exchange. A's are turning into B's, and B's are turning into A's, but the overall concentrations of the species are not changing. The kinetics of the chemical exchange on the ground electronic state under thermal equilibrium conditions can be obtained 2D IR spectroscopy. A vibration that has a different frequency for the two species is monitored. At very short time, there will be two peaks on the diagonal of the 2D IR spectrum, one for A and one for B. As the waiting time is increased, chemical exchange causes off-diagonal peaks to grow in. The time dependence of the growth of these off-diagonal peaks gives the chemical exchange rate. The method is applied to organic solute-solvent complex formation, orientational isomerization about a carbon-carbon single bond, migration of a hydrogen bond from one position on a molecule to another, protein structural substate interconversion, and water hydrogen bond switching between ions and water molecules.

Two-dimensional gel isoelectric focusing (2-D gel IEF) is presented as the combination of the same separation method used consecutively in two directions of the same gel. In this new method, after completion of IEF process in the first dimension the gel was cut into the separate strips, each containing selected analytes together with the appropriate part of the original broad pH gradient, and the strips were rotated by 90 degrees (with regard to the first IEF) and left to diffuse overnight. After diffusion the strips were subjected to the second IEF. During the second IEF, the corresponding narrow part of pH gradient in each strip was restored again, however, now along the strip. The progress of the separation process can be monitored visually by using colored low-molecular-weight isoelectric point (pI) markers loaded into the gel simultaneously with proteins. The unique properties of IEF, focusing and resolution power were enhanced by using the same technique twice. Two forms of beta-lactoglobulin (pI values 5.14 and 5.31, respectively) non-separated in the first IEF were successfully separated in the second dimension at relatively low voltage (330 V) with the resolution power comparable to the high-resolution gels requiring the high voltage during the run and long separation time. Glucose oxidase loaded as diluted solution into ten positions across the gel was finally focused into a single band during 2-D gel IEF. Since the first and second IEF are carried out on the same gel, no losses and contamination of analyte occur. The suggested method can be used for separation/fractionation of complex biological mixtures, similarly as other multidimensional separation techniques applied in proteomics, and can be followed by further processing, e.g., mass spectrometry analysis. The focusing properties of IEF could be useful especially in separation of mixtures, where components are at low concentration levels. PMID:16100746

A two-dimensional full wavefield inversion for direct imaging of compressional wave and out-of-plane standing wave (SH) velocity distribution is developed, tested and implemented. The inversion is base on the finite difference solution of the full two-dimension scalar wave equation in the time-distance domain and operates on wide-aperture, common-shot data. The computational kernel fully utilizes the reverse-time image reconstruction principles. No travel-time picking and phase identification are required for full waveform inversion. For each shot records, gradients of misfit function (Frechét derivative) are dynamically determined by cross-correlation of the recorded forward propagating wavefield and backward propagating residual wavefield at each time step. Convergence to local minima can be avoided by gradually increasing the wavenumber bandwidth in the estimated velocity distribution and to increase the inversion resolution as iterations proceed. Synthetic examples show that the effects of the multiples, scattering, artificial boundary reflection waves, or noise do not contaminate the final results and convergences successfully to the correct solution. Using full two-way waveform approach for seismic imaging simplifies un-necessary skeleton seismic processing procedures. Furthermore, the resolution of inversion result is limited by the bandwidth of field recordings, source wavelet and dominant frequency. Convergence rate and stability of our in-house development of inversion algorithm is highly depends on step length and the complexity of subsurface structure associate with the steepest decent direction. For land data, near-surface effects including topography, lateral velocity variation, source and receiver static corrections are automatically included. For marine seismic data, multiples generated by water layer can be effectively suppressed through wavefield based seismic processing approach.

We show that many twodimensional domain patterns observed in Monte Carlo\\u000asimulations can be obtained from the many soliton solutions of the imaginary\\u000atime Sine Gordon equation. This opens the door to analytic physical\\u000aunderstanding of the micromagnetics in ultra-thin films.

This thesis is dedicated to the study of the structural, dynamical and thermal properties of finite two-dimensional systems of classical particles. In its first part, we study the structures and the vibrational properties of particles of confined systems in the zero temperature case. Specifically, the ordered configurations of a monolayer of interacting magnetic dipoles confined in a circular parabolic potential are investigated as a function of the dipole moment of the particles. Despite the circular confinement, we find very asymmetric ordered structures, like chains and Y-shaped configurations, when a magnetic field is applied parallel to the plane of the particles. Besides, we analyze the dynamic of particles through the study of the normal-mode spectrum. It is studied as a function of the magnetic field and the strength of the dipole moment of the particles. The translational and rotational components of the normal mode spectrum are obtained and investigated in details. In the second part of the thesis, we study the structural dependence of the two-dimensional systems on the temperature. Specifically, we systematically investigate the melting of a finite size binary system consisting of two types of particles having different charges and/or masses, confined in a two-dimensional parabolic trap. It is found that two types of particles melt at different temperatures; e.g., particles with smaller charge melt first. In addition, a remarkable temperature induced spatial separation of the two types of particles is observed. We also study the melting of a competing interacting potential system of classical particles confined in a circular parabolic trap. The particles interact through a short-range attractive, and long-range repulsive, potential. Different behaviors of the melting temperature are found depending on the strength of the attractive part of the interparticle potential. The melting of a system consisting of small bubbles takes place through a two-step melting process. A reentrant behavior and a thermally induced structural phase transition are observed in a small region of a space diagram of the main parameters of the system. A hysteresis effect in the configuration of the particles is observed as a function of temperature.

The dynamical interaction between filaments and motor proteins is known for their propensity to selforganize into spatiotemporal patterns. Since the filaments are polar in the sense that motors define a direction of motion on them, motors might induce, under certain conditions, a spatially homogeneous polar filament orientation. We show that the latter two-dimensional anisotropic state itself may become unstable with

Victor Ruhle; Falko Ziebert; Ronny Peter; Walter Zimmermann

An analysis method based on a multidomain pseudospectral method is proposed for calculating the band diagrams of two-dimensional photonic crystals and is shown to possess excellent numerical convergence behavior and accuracy. The proposed scheme utilizes the multidomain Chebyshev collocation method. By applying Chebyshev-Lagrange interpolating polynomials to the approximation of spatial derivatives at collocation points, the Helmholtz equation is converted into

Investigated the development among fourth-graders of two-dimensional space concepts within a mathematics unit on grids, coordinates, and rectangles. Found that students' knowledge of grid and coordinate systems related to levels of competence in number sense, spatial-geometric relationships, and the ability to discriminate and integrate the two…

Sarama, Julie; Clements, Douglas H.; Swaminathan, Sudha; McMillen, Sue; Gonzalez Gomez, Rosa M.

A means of upscaling the effective saturated hydraulic conductivity, $\\\\langle$ K $\\\\rangle$, based on spatial variation in the saturated hydraulic conductivity (K) field is essential for the application of flow and transport models to practical problems. Multifractals are inherently scaling and thus may offer solutions to this dilemma. Random two-dimensional geometrical multifractal fields (multifractal Sierpinski carpets with a scale factor

S. R. Koirala; E. Perfect; R. W. Gentry; J. W. Kim

A means of upscaling the effective saturated hydraulic conductivity, $\\\\langle$K$\\\\rangle$, based on spatial variation in the saturated hydraulic conductivity (K) field is essential for the application of flow and transport models to practical problems. Multifractals are inherently scaling and thus may offer solutions to this dilemma. Random two-dimensional geometrical multifractal fields (multifractal Sierpinski carpets with a scale factor b =

S. R. Koirala; E. Perfect; R. W. Gentry; J. W. Kim

The purpose of this work is the development and testing of a new family of methods for calculating the spatial dependence of the neutron density in nuclear systems described in two-dimensional Cartesian geometry. The energy and angular dependence of the n...

Cellular structures like honeycombs or reticulated micro-frames are widely used in sandwich construction because of their superior structural static and dynamic properties. The aim of this study is to evaluate the dynamic behavior of two-dimensional cellular structures, with the focus on the effect of the geometry of unit cells on the dynamics of the propagation of elastic waves within the structure. The characteristics of wave propagation for the considered class of cellular solids are analyzed through the finite element model of the unit cell and the application of the theory of periodic structures. This combined analysis yields the phase constant surfaces, which define the directions of waves propagating in the plane of the structure for the assigned frequency values. The analysis of iso-frequency contour lines in the phase constant surfaces allows the prediction of the location and extension of angular ranges, and therefore regions within the structures where waves do not propagate. The performance of honeycomb grids of regular hexagonal topology is compared with that of grids of various geometries, with the emphasis on configurations featuring a negative Poisson's ratio behavior. The harmonic response of the considered structures at specified frequencies confirms the predictions from the analysis of the phase constant surfaces and demonstrates the strongly spatially-dependent characteristics of periodic cellular structures. The numerical results presented indicate the potentials of the phase constant surfaces as tools for the evaluation of the wave propagation characteristics of this class of two-dimensional periodic structures. Optimal design configurations can be identified in order to achieve the desired transmissibility levels in specified directions and to obtain efficient vibration isolation capabilities. The findings from the presented investigations and the described analysis methodology will provide invaluable guidelines for the prototyping of future concepts of honeycombs or cellular structures with enhanced vibro-acoustics performance.

Ruzzene, Massimo; Scarpa, Fabrizio; Soranna, Francesco

The dynamical behavior of single-component two-dimensional colloidal crystals confined in a slit geometry is studied by Langevin dynamics simulation of a simple model. The colloids are modeled as pointlike particles, interacting with the repulsive part of the Lennard-Jones potential, and the fluid molecules in the colloidal suspension are not explicitly considered. Considering a crystalline strip of triangular lattice structure with n=30 rows, the (one-dimensional) walls confining the strip are chosen as two rigidly fixed crystalline rows at each side, commensurate with the lattice structure and, thus, stabilizing long-range order. The case when the spacing between the walls is incommensurate with the ideal triangular lattice is also studied, where (due to a transition in the number of rows, n ? n-1) the confined crystal is incommensurate with the confining boundaries, and a soliton staircase forms along the walls. It is shown that mean-square displacements (MSDs) of particles as a function of time show an overshoot and then saturate at a horizontal plateau in the commensurate case, the value of the plateau being largest in the center of the strip. Conversely, when solitons are present, MSDs are largest in the rows containing the solitons, and all MSDs do not settle down at well-defined plateaus in the direction parallel to the boundaries, due to the lack of positional long-range order in ideal two-dimensional crystals. The MSDs of the solitons (which can be treated like quasiparticles at very low temperature) have also been studied and their dynamics are found to be about an order of magnitude slower than that of the colloidal particles themselves. Finally, transport of individual colloidal particles by diffusion processes is studied: both standard vacancy-interstitial pair formation and cooperative ring rotation processes are identified. These processes require thermal activation, with activation energies of the order of 10T(m) (T(m) being the melting temperature of the crystal), while the motions due to long-wavelength phonons decrease only linearly in temperature. PMID:23214781

Wilms, Dorothea; Virnau, Peter; Snook, Ian K; Binder, Kurt

The dynamical behavior of single-component two-dimensional colloidal crystals confined in a slit geometry is studied by Langevin dynamics simulation of a simple model. The colloids are modeled as pointlike particles, interacting with the repulsive part of the Lennard-Jones potential, and the fluid molecules in the colloidal suspension are not explicitly considered. Considering a crystalline strip of triangular lattice structure with n=30 rows, the (one-dimensional) walls confining the strip are chosen as two rigidly fixed crystalline rows at each side, commensurate with the lattice structure and, thus, stabilizing long-range order. The case when the spacing between the walls is incommensurate with the ideal triangular lattice is also studied, where (due to a transition in the number of rows, n?n-1) the confined crystal is incommensurate with the confining boundaries, and a soliton staircase forms along the walls. It is shown that mean-square displacements (MSDs) of particles as a function of time show an overshoot and then saturate at a horizontal plateau in the commensurate case, the value of the plateau being largest in the center of the strip. Conversely, when solitons are present, MSDs are largest in the rows containing the solitons, and all MSDs do not settle down at well-defined plateaus in the direction parallel to the boundaries, due to the lack of positional long-range order in ideal two-dimensional crystals. The MSDs of the solitons (which can be treated like quasiparticles at very low temperature) have also been studied and their dynamics are found to be about an order of magnitude slower than that of the colloidal particles themselves. Finally, transport of individual colloidal particles by diffusion processes is studied: both standard vacancy-interstitial pair formation and cooperative ring rotation processes are identified. These processes require thermal activation, with activation energies of the order of 10Tm (Tm being the melting temperature of the crystal), while the motions due to long-wavelength phonons decrease only linearly in temperature.

Wilms, Dorothea; Virnau, Peter; Snook, Ian K.; Binder, Kurt

We study two-dimensional (2D) solitons in the mean-field models of ultracold gases with long-range quadrupole-quadrupole interaction (QQI) between particles. The condensate is loaded into a deep optical-lattice (OL) potential, therefore the model is based on the 2D discrete nonlinear Schrödinger equation with contact on site and long-range intersite interactions, which represent the QQI. The quadrupoles are built as pairs of electric dipoles and antidipoles orientated perpendicular to the 2D plane to which the gas is confined. Because the quadrupoles interact with the local gradient of the external field, they are polarized by an inhomogeneous dc electric field that may be supplied by a tapered capacitor. Shapes, stability, mobility, and collisions of fundamental discrete solitons are studied by means of systematic simulations. In particular, threshold values of the norm, which are necessary for the existence of the solitons, are found and anisotropy of their static and dynamical properties is explored. As concerns the mobility and collisions, we analyze such properties for discrete solitons on 2D lattices with long-range intersite interactions. Estimates demonstrate that the setting can be realized under experimentally available conditions, predicting solitons built of ˜10000 particles.

Li, Yongyao; Liu, Jingfeng; Pang, Wei; Malomed, Boris A.

The formation and evolution of ion acoustic solitons in Earth's auroral upward current region are studied using one- and two-dimensional (2D) electrostatic particle-in-cell simulations. The one-dimensional simulations are confined to processes that occur in the auroral cavity and include four plasma populations: hot electrons, H{sup +} and O{sup +} anti-earthward ion beams, and a hot H{sup +} background population. Ion acoustic solitons are found to form for auroral-cavity ion beams consistent with acceleration through double-layer (DL) potentials measured by FAST. A simplified one-dimensional model simulation is then presented in order to isolate the mechanisms that lead to the formation of the ion acoustic soliton. Results of a two-dimensional simulation, which include both the ionosphere and the auroral cavity, separated by a low-altitude DL, are then presented in order to confirm that the soliton forms in a more realistic 2D geometry. The 2D simulation is initialized with a U-shaped potential structure that mimics the inferred shape of the low altitude transition region based on observations. In this simulation, a soliton localized perpendicular to the geomagnetic field is observed to form and reside next to the DL. Finally, the 2D simulation results are compared with FAST data and it is found that certain aspects of the data can be explained by assuming the presence of an ion acoustic soliton.

Main, D. S.; Scholz, C. [Department of Physics, John Brown University, Siloam Springs, Arkansas 72761 (United States); Newman, D. L. [Center for Integrated Plasma Studies, University of Colorado, Boulder, Colorado 80309 (United States); Ergun, R. E. [Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado 80303 (United States)

Ultra-fast x-ray imaging is of great importance for diagnosing laser-driven inertial confinement fusion (ICF) plasmas. Typical required spatial and temporal resolutions are 10 micrometer and 10 ps, respectively. We have developed variety of one- (1D) and two-dimensional (2D) image sampling technique for ultrafast time-resolved x-ray imaging with x-ray streak cameras. Moire imaging of an x-ray-backlit target has been developed as

A new type of two-dimensional neutron scintillation detector with high spatial resolution based on a position-sensitive photomultiplier has been investigated. With a 6Li glass scintillator a spatial resolution of 1.0 mm was measured. The integral linearity over the detection area of 55 × 45 mm2 is <=1.5 mm. The detector homogeneity is within 10% at a discriminator level at 60%

R. Kurz; R. Reinartz; S. Widdau; J. Schelten; A. Scholz; W. Schäfer

Neurons in primary visual cortex are widely considered to be oriented filters or energy detectors that perform one-dimensional feature analysis. The main deviations from this picture are generally thought to include gain controls and modulatory influences. Here we investigate receptive field (RF) properties of single neurons with localized two-dimensional stimuli, the two-dimensional Hermite functions (TDHs). TDHs can be grouped into distinct complete orthonormal bases that are matched in contrast energy, spatial extent, and spatial frequency content but differ in two-dimensional form, and thus can be used to probe spatially specific nonlinearities. Here we use two such bases: Cartesian TDHs, which resemble vignetted gratings and checkerboards, and polar TDHs, which resemble vignetted annuli and dartboards. Of 63 isolated units, 51 responded to TDH stimuli. In 37/51 units, we found significant differences in overall response size (21/51) or apparent RF shape (28/51) that depended on which basis set was used. Because of the properties of the TDH stimuli, these findings are inconsistent with simple feedforward nonlinearities and with many variants of energy models. Rather, they imply the presence of nonlinearities that are not local in either space or spatial frequency. Units showing these differences were present to a similar degree in cat and monkey, in simple and complex cells, and in supragranular, infragranular, and granular layers. We thus find a widely distributed neurophysiological substrate for two-dimensionalspatial analysis at the earliest stages of cortical processing. Moreover, the population pattern of tuning to TDH functions suggests that V1 neurons sample not only orientations, but a larger space of two-dimensional form, in an even-handed manner.

Victor, Jonathan D.; Mechler, Ferenc; Repucci, Michael A.; Purpura, Keith P.; Sharpee, Tatyana

Sub-resolution assist features are an important tool for improving process robustness for one-dimensional pattern features at advanced manufacturing process nodes. However, sub-resolution assist feature development efforts have not generally considered optimization for process robustness with two-dimensional pattern features. This generally arises both from conservatively placing SRAFs to avoid the possibility of imaging, and from a desire to simplify SRAF placement rules. By studying two-dimensional features using a manufacturing sensitivity model, one can gain insight into the capabilities of SRAFs regarding two-dimensional pattern features. These insights suggest new methodologies for shaping assist features to enhance two-dimensional feature robustness. In addition, a manufacturing sensitivity model form can be employed to optimize the placement of multiple competing SRAFs in localized two-dimensional regions. Initial studies demonstrate significant pullback reduction for two-dimensional features once SRAF placement has been optimized using the manufacturing sensitivity model form.

Melvin, Lawrence S., III; Painter, Benjamin D.; Barnes, Levi D.

Theoretical results on spatial optical bright solitons excited in arrays of nonlinear defocusing\\u000awaveguides, that result from the photovoltaic effect in a photorefractive material, are presented. The existence\\u000aof four types of stationary discrete bright staggered solitons, on-site, inter-site, twisted inter-site, and\\u000atwisted on-site solitons, is shown both analytically and numerically, and their stability properties are\\u000ainvestigated. The maximum Hamiltonian

It is commonly held that a necessary condition for the existence of solitons in nonlinear-wave systems is that the soliton's frequency (spatial or temporal) must not fall into the continuous spectrum of radiation modes. However, this is not always true. We present a new class of codimension-one solitons (i.e., those existing at isolated frequency values) that are embedded into the

We consider experimentally three-wave resonant nonlinear interactions of fields propagating in nonlinear media. We investigate the spatial dynamics of two diffractionless beams at frequency omega1, omega2 which mix to generate a field at the sum frequency omega3. If the generated field at omega3 can sustain a soliton, it decays into solitons at omega1, omega2. We report the experimental evidence of the transition from steady frequency wave generation to solitonic decay in nonlinear optics. PMID:19654796

Baronio, Fabio; Conforti, Matteo; Andreana, Marco; Couderc, Vincent; De Angelis, Costantino; Wabnitz, Stefan; Barthélémy, Alain; Degasperis, Antonio

By using the difference formula for approximations of two-dimensional continued fractions, the method of fundamental inequalities, the Stieltjes–Vitali theorem, and generalizations of divided and inverse differences, we estimate the accuracy of approximations of two-dimensional continued fractions with complex elements by their convergents and obtain estimates for the real and imaginary parts of remainders of two-dimensional continued fractions. We also prove

Two-dimensional recursive filters are conveniently described in terms of two-dimensional z transforms. The designer of these filters faces two fundamental problems, their stability and their synthesis. Stability is determined by the location of the zero-valued region of the filter's denominator polynomial. A conjecture based on a one-dimensional stability theorem leads to a useful empirical stabilization procedure. Two-dimensional recursive filters can

The effects of critical layer nonlinearity are considered on spatially growing oblique instability waves on nominally two-dimensional shear layers between parallel streams. The analysis shows that three-dimensional effects cause nonlinearity to occur at much smaller amplitudes than it does in two-dimensional flows. The nonlinear instability wave amplitude is determined by an integro-differential equation with cubic type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. The numerical solutions always end in a singularity at a finite downstream distance.

The theory and application of the RAZOR two-dimensional, continuous energy lattice physics code are discussed. RAZOR solves the continuous energy neutron transport equation in one- and two-dimensional geometries, and calculates equivalent few-group diffusion theory constants that rigorously account for spatial and spectral self-shielding effects. A dual energy resolution slowing down algorithm is used to reduce computer memory and disk storage requirements for the slowing down calculation. Results are presented for a 2D BWR pin cell depletion benchmark problem.

Zerkle, M.L.; Abu-Shumays, I.K.; Ott, M.W.; Winwood, J.P.

We consider single interval Rényi and entanglement entropies for a twodimensional conformal field theory on a circle at nonzero temperature. Assuming that the finite size of the system introduces a unique ground state with a nonzero mass gap, we calculate the leading corrections to the Rényi and entanglement entropy in a low temperature expansion. These corrections have a universal form for any twodimensional conformal field theory that depends only on the size of the mass gap and its degeneracy. We analyze the limits where the size of the interval becomes small and where it becomes close to the size of the spatial circle. PMID:24836236

We consider single interval Rényi and entanglement entropies for a twodimensional conformal field theory on a circle at nonzero temperature. Assuming that the finite size of the system introduces a unique ground state with a nonzero mass gap, we calculate the leading corrections to the Rényi and entanglement entropy in a low temperature expansion. These corrections have a universal form for any twodimensional conformal field theory that depends only on the size of the mass gap and its degeneracy. We analyze the limits where the size of the interval becomes small and where it becomes close to the size of the spatial circle.

The method of lines is used to transform the initial/boundary-value problem associated with the two-dimensional sine-Gordon equation in two space variables into a second-order initial-value problem. The finite-difference methods are developed by replacing the matrix-exponential term in a recurrence relation with rational approximants. The resulting finite-difference methods are analyzed for local truncation error, stability and convergence. To avoid solving the nonlinear system a predictor-corrector scheme using the explicit method as predictor and the implicit as corrector is applied. Numerical solutions for cases involving the most known from the bibliography line and ring solitons are given.

We report on a high-temperature perturbation expansion study of the superfluid-density spatial correlation function of a Ginzburg-Landau-model superconducting film in a magnetic field. We have derived a closed form which expresses the contribution to the correlation function from each graph of the perturbation theory in terms of the number of Euler paths around appropriate subgraphs. We have enumerated all graphs appearing out to 12th order in the expansion and have evaluated their contributions to the correlation function. Low-temperature correlation functions, obtained using Pade approximants, are in good agreement with Monte Carlo simulation results and show that the vortex liquid becomes strongly correlated at temperatures well above the vortex solidification temperature. We have also evaluated the high-temperature expansion for the free energy of the Ginzburg-Landau model to 13th order, two orders further than in previous work.

Hu, J.; MacDonald, A.H. (Department of Physics, Indiana University, Bloomington, Indiana 47405 (United States)); McKay, B.D. (Computer Science Department, Australian National University, Canberra, Australian Capital Territory 0200 (Australia))

The finite element ablation and thermal response (FEAtR, hence forth called FEAR) design and analysis program simulates the one, two, or three-dimensional ablation, internal heat conduction, thermal decomposition, and pyrolysis gas flow of thermal protection system materials. As part of a code validation study, two-dimensional axisymmetric results from FEAR are compared to thermal response data obtained from an arc-jet stagnation test in this paper. The results from FEAR are also compared to the two-dimensional axisymmetric computations from the two-dimensional implicit thermal response and ablation program under the same arcjet conditions. The ablating material being used in this arcjet test is phenolic impregnated carbon ablator with an LI-2200 insulator as backup material. The test is performed at the NASA, Ames Research Center Interaction Heating Facility. Spatially distributed computational fluid dynamics solutions for the flow field around the test article are used for the surface boundary conditions.

There is a gap in the electromagnetic spectrum where the microwave region is located when considering broadband two-dimensional spectroscopy. We introduce two-dimensional chirped-pulse Fourier transform microwave (CP-FTMW) spectroscopy as a way to directly identify coherences between coupled rotational levels. The theory and application of these experiments is a direct extension of traditional two-dimensional NMR techniques. Several different pulse sequences will

Amanda J. Shirar; Kelly M. Hotopp; David S. Wilcox; Brian C. Dian

Langevin dynamics simulations are used to study the effect of shear on a two-dimensional colloidal crystal (with implicit solvent) confined by structured parallel walls. When walls are sheared very slowly, only two or three crystalline layers next to the walls move along with them, while the inner layers of the crystal are only slightly tilted. At higher shear velocities, this inner part of the crystal breaks into several pieces with different orientations. The velocity profile across the slit is reminiscent of shear banding in flowing soft materials, where liquid and solid regions coexist; the difference, however, is that in the latter case the solid regions are glassy while here they are crystalline. At even higher shear velocities, the effect of the shearing becomes smaller again. Also the effective temperature near the walls (deduced from the velocity distributions of the particles) decreases again when the wall velocity gets very large. When the walls are placed closer together, thereby introducing an incommensurability between the periodicity of the confined crystal and the walls, a structure containing a soliton staircase arises in simulations without shear. Introducing shear increases the disorder in these systems until no solitons are visible anymore. Instead, similar structures like in the case without mismatch result. At high shear rates, configurations where the incommensurability of the crystalline structure is compensated by the creation of holes become relevant. PMID:23005095

Langevin dynamics simulations are used to study the effect of shear on a two-dimensional colloidal crystal (with implicit solvent) confined by structured parallel walls. When walls are sheared very slowly, only two or three crystalline layers next to the walls move along with them, while the inner layers of the crystal are only slightly tilted. At higher shear velocities, this inner part of the crystal breaks into several pieces with different orientations. The velocity profile across the slit is reminiscent of shear banding in flowing soft materials, where liquid and solid regions coexist; the difference, however, is that in the latter case the solid regions are glassy while here they are crystalline. At even higher shear velocities, the effect of the shearing becomes smaller again. Also the effective temperature near the walls (deduced from the velocity distributions of the particles) decreases again when the wall velocity gets very large. When the walls are placed closer together, thereby introducing an incommensurability between the periodicity of the confined crystal and the walls, a structure containing a soliton staircase arises in simulations without shear. Introducing shear increases the disorder in these systems until no solitons are visible anymore. Instead, similar structures like in the case without mismatch result. At high shear rates, configurations where the incommensurability of the crystalline structure is compensated by the creation of holes become relevant.

Understanding coherent synchrotron radiation (CSR) effects in a bunch compressor requires an accurate model accounting for the realistic beam shape and parameters. We extend the well-known 1D CSR analytic model into two dimensions and develop a simple numerical model based on the Liénard-Wiechert formula for the CSR field of a coasting beam. This CSR numerical model includes the 2D spatial dependence of the field in the bending plane and is accurate for arbitrary beam energy. It also removes the singularity in the space charge field calculation present in a 1D model. Good agreement is obtained with 1D CSR analytic result for free electron laser (FEL) related beam parameters but it can also give a more accurate result for low-energy/large spot size beams and off-axis/transient fields. This 2D CSR model can be used for understanding the limitation of various 1D models and for benchmarking fully electromagnetic multidimensional particle-in-cell simulations for self-consistent CSR modeling.

Huang, Chengkun; Kwan, Thomas J. T.; Carlsten, Bruce E.

Nonlinear propagation of twodimensional dust-acoustic solitary waves in a magnetized quantum dusty plasma whose constituents are electrons, ions, and negatively charged heavy dust particles are investigated using quantum hydrodynamic model. The Zakharov-Kuznetsov (ZK) equation is derived by using reductive perturbation technique (RPT). The higher order inhomogeneous ZK-type differential equation is obtained for the correction to ZK- soliton. The dynamical equation for dressed soliton is solved by using renormalization method. The effects of obliqueness ( l x ) of the wave vector, magnetic field strength ( B 0), quantum parameter for ions ( H i ), soliton velocity ( ?) and Fermi temperature ratio ( ?) on amplitudes and widths of the ZK-soliton and as well as of the dressed soliton are investigated. The conditions for the validity of the higher order correction are described. Suitable parameter ranges for the existence of compressive and rarefactive dressed solitons are also discussed.

The distribution of complex temperature zeros of the partition function of the two-dimensional Ising model in the absence of a magnetic field is investigated. For anisotropic square and triangular lattices the distribution function is two-dimensional and satisfies a partial differential equation derived from a generalized scaling theory. Corresponding results for the isotropic square, triangular and honeycomb lattices are also presented.

Two-dimensional quantum models which obey the property of shape invariance are built in the framework of polynomial two-dimensional supersymmetric quantum mechanics. They are obtained using the expressions for known one-dimensional shape invariant potentials. The constructed Hamiltonians are integrable with symmetry operators of fourth order in momenta, and they are not amenable to the conventional separation of variables.

Cannata, F. [INFN, Via Irnerio 46, 40126 Bologna (Italy); Ioffe, M. V. [Saint-Petersburg State University, 198504 St.-Petersburg (Russian Federation); Nishnianidze, D. N. [Saint-Petersburg State University, 198504 St.-Petersburg (Russian Federation); Akaki Tsereteli State University, 4600 Kutaisi (Georgia)

MOHR accepts the values of stress on a two-dimensional element and draws Mohr's Circle for the two-dimensional stress problem. After drawing Mohr's Circle, the user can display the principal stress element, the maximum shear stress element, and an element...

We consider the confined modes in dual-state two-dimensional waveguides in which each slab segment of waveguides can support two vertically confined modes with different effective indices. A matrix formulation is developed to extend the conventional effective-index method to investigate the two-dimensional confinement in multistate waveguides. The results are presented and discussed. PMID:19829532

The linear bicharacteristic scheme (LBS) was originally developed to improve unsteady solutions in computational acoustics and aeroacoustics. The LBS has previously been extended to treat lossy materials for one-dimensional problems. It is a classical leapfrog algorithm, but is combined with upwind bias in the spatial derivatives. This approach preserves the time-reversibility of the leapfrog algorithm, which results in no dissipation, and it permits more flexibility by the ability to adopt a characteristic based method. The use of characteristic variables allows the LBS to include the Perfectly Matched Layer boundary condition with no added storage or complexity. The LBS offers a central storage approach with lower dispersion than the Yee algorithm, plus it generalizes much easier to nonuniform grids. It has previously been applied to two and three-dimensional free-space electromagnetic propagation and scattering problems. This paper extends the LBS to the two-dimensional case. Results are presented for point source radiation problems, and the FDTD algorithm is chosen as a convenient reference for comparison.

In this paper, we demonstrate that two-dimensional (2D) periodic patterns of polyelectrolyte multilayers (PEMs) can be used as surface templates for assembling highly ordered 2D colloidal microarrays. We report detailed structural features of the 2D colloid crystals produced by depositing silica microspheres onto periodic micrometer-scale PEM patterns arrayed in a square or hexagonal lattice with a pattern pitch (approximately) twice the pattern diameter. Analysis of the images of these 2D colloid monolayers reveals that the distributions of the distances by which the adsorbed particles deviate from the corresponding PEM pattern centers are typically bell-shaped, with the majority of the deposited particles located within a relatively short distance from the respective pattern centers. We show that this behavior reflects the effect of the electrostatic focusing force that (occurs because of the finite size of the PEM pattern and) becomes effective when the depositing particle approaches the pattern site to a small distance. Also, in these 2D colloid crystals, the orientations of the off-center displacements of the deposited particles are strongly correlated spatially over the entire sample size. We present experimental evidence that this unusually long-ranged orientational correlation is due to the close spacing of the patterns, which causes an overlap of the excluded volumes between the neighboring deposited particles. PMID:18433154

A Raman chemical mapping investigation was conducted in the visible spectral region using an automated Spex 14018 double monochromator in concert with a moving twodimensional (2D) Hadamard encoding mask. The 2D Hadamard encoding mask combined with conventional Raman spectrometry was used to create chemical maps of heterogeneous liquid and solid samples. The 2D Hadamard encoding mask is based on the cyclic S{sub 255} matrix as a 15{times}17 array. It is mounted vertically and is moved from one encodement pattern to the next by an automated translation stage in concert with scans by the Spex monochromator. The moving 2D mechanical mask was used to spatially encode incident laser radiation or the Raman scattered radiation collected from a sample area illuminated by an argon ion laser operated at 514.5nm. The encoded radiation was decoded by a fast Hadamard transform that resulted in the assignment of a conventional Raman spectrum for each of the 255 {open_quotes}pixels{close_quotes} comprising the mask area. The Raman scattering intensity, plotted with respect to pixel coordinates, resulted in a chemical map of the illuminated sample area. The data demonstrates the utility of the moving 2D Hadamard encoding mask for Raman chemical mapping. {copyright} {ital 1998 American Institute of Physics.}

DeVerse, R.A.; Mangold, T.A.; Hammaker, R.M.; Fateley, W.G. [Department of Chemistry, Kansas State University, Manhattan , Kansas 66506-3701 (United States)

A Raman chemical mapping investigation was conducted in the visible spectral region using an automated Spex 14018 double monochromator in concert with a moving twodimensional (2D) Hadamard encoding mask. The 2D Hadamard encoding mask combined with conventional Raman spectrometry was used to create chemical maps of heterogeneous liquid and solid samples. The 2D Hadamard encoding mask is based on the cyclic S255 matrix as a 15×17 array. It is mounted vertically and is moved from one encodement pattern to the next by an automated translation stage in concert with scans by the Spex monochromator. The moving 2D mechanical mask was used to spatially encode incident laser radiation or the Raman scattered radiation collected from a sample area illuminated by an argon ion laser operated at 514.5nm. The encoded radiation was decoded by a fast Hadamard transform that resulted in the assignment of a conventional Raman spectrum for each of the 255 ``pixels'' comprising the mask area. The Raman scattering intensity, plotted with respect to pixel coordinates, resulted in a chemical map of the illuminated sample area. The data demonstrates the utility of the moving 2D Hadamard encoding mask for Raman chemical mapping.

Deverse, R. A.; Mangold, T. A.; Hammaker, R. M.; Fateley, W. G.

Soap film flows provide a very convenient laboratory model for studies of two-dimensional (2-D) hydrodynamics including turbulence. For a gravity-driven soap film channel with a grid of equally spaced cylinders inserted in the flow, we have measured the simultaneous velocity and thickness fields in the irregular flow downstream from the cylinders. The velocity field is determined by a modified digital particle image velocimetry method and the thickness from the light scattered by the particles in the film. From these measurements, we compute the decay of mean energy, enstrophy, and thickness fluctuations with downstream distance, and the structure functions of velocity, vorticity, thickness fluctuation, and vorticity flux. From these quantities we determine the microscale Reynolds number of the flow R{sub {lambda}}{approx}100 and the integral and dissipation scales of 2D turbulence. We also obtain quantitative measures of the degree to which our flow can be considered incompressible and isotropic as a function of downstream distance. We find coarsening of characteristic spatial scales, qualitative correspondence of the decay of energy and enstrophy with the Batchelor model, scaling of energy in {ital k} space consistent with the k{sup {minus}3} spectrum of the Kraichnan{endash}Batchelor enstrophy-scaling picture, and power-law scalings of the structure functions of velocity, vorticity, vorticity flux, and thickness. These results are compared with models of 2-D turbulence and with numerical simulations. {copyright} {ital 1999 American Institute of Physics.}

Vorobieff, P.; Rivera, M.; Ecke, R.E. [Center for Nonlinear Studies and Condensed Matter and Thermal Physics Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)] [Center for Nonlinear Studies and Condensed Matter and Thermal Physics Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

In magnetized plasmas, a turbulent cascade occurs in phase space at scales smaller than the thermal Larmor radius ('sub-Larmor scales') [Tatsuno et al., Phys. Rev. Lett. 103, 015003 (2009)]. When the turbulence is restricted to two spatial dimensions perpendicular to the background magnetic field, two independent cascades may take place simultaneously because of the presence of two collisionless invariants. In the present work, freely decaying turbulence of two-dimensional electrostatic gyrokinetics is investigated by means of phenomenological theory and direct numerical simulations. A dual cascade (forward and inverse cascades) is observed in velocity space as well as in position space, which we diagnose by means of nonlinear transfer functions for the collisionless invariants. We find that the turbulence tends to a time-asymptotic state, dominated by a single scale that grows in time. A theory of this asymptotic state is derived in the form of decay laws. Each case that we study falls into one of three regimes (weakly collisional, marginal, and strongly collisional), determined by a dimensionless number D{sub *}, a quantity analogous to the Reynolds number. The marginal state is marked by a critical number D{sub *}=D{sub 0} that is preserved in time. Turbulence initialized above this value become increasingly inertial in time, evolving toward larger and larger D{sub *}; turbulence initialized below D{sub 0} become more and more collisional, decaying to progressively smaller D{sub *}.

Tatsuno, T. [Department of Physics and IREAP, University of Maryland, College Park, Maryland 20742 (United States); Department of Communication Engineering and Informatics, University of Electro-Communications, Chofu, Tokyo 182-8585 (Japan); Plunk, G. G. [Department of Physics and IREAP, University of Maryland, College Park, Maryland 20742 (United States); Max-Planck-Institut fuer Plasmaphysik, 17491 Greifswald (Germany); Barnes, M. [Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Dorland, W. [Department of Physics and IREAP, University of Maryland, College Park, Maryland 20742 (United States); Howes, G. G. [Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242 (United States); Numata, R. [Department of Physics and IREAP, University of Maryland, College Park, Maryland 20742 (United States); Graduate School of Simulation Studies, University of Hyogo, Kobe, Hyogo 650-0047 (Japan)

By using a nonlinear waveguide array we experimentally demonstrate dynamic features of solitons in discrete systems. Spatialsolitons do not exhibit these properties in continuous systems. We experimentally recorded nonlinearly induced locking of an initially moving soliton at a single waveguide. We also show that discrete solitons can acquire transverse momentum and propagate at an angle with respect to the waveguide direction, when the initial excitation is not centered on a waveguide. This is to our knowledge the first time that the effect of the Peierls-Nabarro potential has been observed in a macroscopic system.

Morandotti, R.; Peschel, U.; Aitchison, J. S.; Eisenberg, H. S.; Silberberg, Y.

In this work, we study three higher-dimensional Virasoro integrable models, namely the (3+1)-dimensional Nizhnik-Novikov-Veselov equation, the (3+1)-dimensional breaking soliton equation, and a (3+1)-dimensional extended breaking soliton equation. The three equations are among the Virasoro integrable models. We use the simplified form of the Hirota's method to establish multiple soliton solutions for each equation. We determine the constraint conditions between the coefficients of the spatial variables to guarantee the existence of the multiple soliton solutions for each model.

We consider a mixture consisting of two species of spherical nanoparticles dispersed in a liquid medium. We show that with an appropriate choice of refractive indices and particle diameters, it is possible to observe the phenomenon of optical soliton bistability in two spatial dimensions in a broad beam power range. Previously, this possibility was ruled out in the case of a single-species colloid. As a particular example, we consider the system of hydrophilic silica particles and gas bubbles generated in the process of electrolysis in water. The interaction of two soliton beams can lead to switching of the lower branch solitons to the upper branch, and the interaction of solitons from different branches is phase independent and always repulsive.

Matuszewski, Michal [Nonlinear Physics Center, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200 (Australia)

The properties of molecular aggregates, coupled clusters of small molecules, are often challenging to unravel because of their inherent complexity and disordered environments. Their structure-function relationships are often far from obvious. However, their ability to efficiently channel excitation energy over remarkable distances, as is the case in photosynthetic light harvesting, is a compelling motivation to investigate them. Understanding and subsequently mimicking the processes in photosynthesis, for example, will set the stage for considerable advances in using light harvesting to fuel renewable energy technologies. Two-dimensional (2D) electronic spectroscopy is emerging as a nonlinear optical technique that provides significant insight into the interactions and dynamics of complex molecular systems. In addition to spectrally resolving excitation and emission energies over significant bandwidths with femtosecond resolution, this technique has already enabled discoveries about the structure and dynamics of photosynthetic light-harvesting complexes and other aggregates. Multiple capabilities unique to 2D electronic spectroscopy enable such findings. For example, the spectral resolution of excitation and emission combined with the ability to eliminate the effects of static disorder can reveal the homogeneous line width of a transition and the different dynamic contributions to it. Twodimensional spectroscopy is also sensitive to electronic coherence and has been employed to identify and characterize coherent excitation energy transfer dynamics in photosynthetic systems and conjugated polymers. The presence of cross-peaks, signals for which excitation and emission occur at different wavelengths, provides multiple forms of information. First, it allows the identification of states in congested spectra and reveals correlations between them. Second, we can track excitation energy flow from origin to terminus through multiple channels simultaneously. Finally, 2D electronic spectroscopy is uniquely sensitive to intermolecular electronic coupling through the sign and amplitude of the cross-peaks. This feature makes it possible to reveal spatial molecular configurations by probing electronic transitions. Another means of "resolving" these angstrom-scale arrangements is to manipulate the probing laser pulse polarizations. In this way, we can isolate and modulate specific processes in order to retrieve structural information. In this Account, we demonstrate these capabilities through a close collaboration between experiments and modeling on isolated photosynthetic pigment-protein complexes and also on J-aggregates. Each of the probed systems we describe offers insights that have both increased the utility of 2D electronic spectroscopy and led to discoveries about the molecular aggregates' dynamics and underlying structure. PMID:19691358

Ginsberg, Naomi S; Cheng, Yuan-Chung; Fleming, Graham R

The oscillatory behaviour of the solar chromosphere was studied from observations of a quiet region at disk centre using various diagnostic tools. The two-dimensional spectrometer in the Vacuum Tower Telescope/Tenerife (Spain) served to obtain a spatially highly resolved time series of ``white-light'' images and narrow-band filtergrams in the Na D_2 line. With a tunable Fabry-Perot interferometer, this line was scanned taking 30 images (i.e. a ``scan'') around the line core with wavelength steps of 30 m Angstroms and a spectral resolution of about 200 000. From these images, line profiles were derived for every pixel in the field of view. With each such narrow-band scan, a scan of ``white-light'' images was taken strictly simultaneously. The whole time series comprises (2x) 128 scans. Every 56 s, a new pair of scans was started with two CCDs, thus the observation covers nearly two hours. Finally, after correlation and other reduction procedures, a field size of 69\\farcs4 x 50\\farcs4 remained with 0\\farcs2/pixel on the CCD-chips. In the data reduction, new images were created representing the minimum intensity (I) of each line profile in the field of view, and also velocity (V) maps (derived from the Doppler shifts of the line profiles) for all 128 scans. >From these images, power spectra and diagnostic diagrams were computed. In the subsequent analysis, a distinction between network and intra-network regions was made where this seemed appropriate. One- and two-dimensional (V-I) phase and coherence spectra were analysed with regard to oscillations and to the nature of the waves leaving their marks in these diagrams. Several noteworthy results also raised the question of the actual line formation height of Na D_2, among them being the non-detection of a chromospheric eigenmode. While an explanation for a conspicuous 70(deg) plateau in a small region of the phase spectra already exists, the suspected reason behind the decreasing phase difference from about -60(deg) for the f-mode down to ~ -120(deg) for higher modes is still subject to some speculation. Moreover, the data gave evidence of gravity waves, probably discovered for the first time in a V-I phase spectrum of Na D_2.

We present a general review of some aspects of the dynamics of topological solitons in 1 and 2 dimensions. We discuss some recent work on the scattering of solitons on potential obstructions and in the presence of some external fields.

Brizhik, L. S.; Eremko, A. A.; Ferreira, L. A.; Piette, B. M.. A. G.; Zakrzewski, W. J.

A number of logic functions and mathematical operations were implemented in the laboratory based on soliton collisions in photo- refractive media. In addition to the usual NAND and AND logic gates, soliton collisions do transfer information and two succes...

G. Stageman D. Christodoulides P. Prucnell M. Segev K. Squier

The theory of Lee and Pang (1987), who obtained solutions for soliton stars composed of zero-temperature fermions and bosons, is applied here to quark soliton stars. Model soliton stars based on a simple physical model of the proton are computed, and the properties of the solitons are discussed, including the important problem of the existence of a limiting mass and thus the possible formation of black holes of primordial origin. It is shown that there is a definite mass limit for ponderable soliton stars, so that during cooling a soliton star might reach a stage beyond which no equilibrium configuration exists and the soliton star probably will collapse to become a black hole. The radiation of ponderable soliton stars may alter the short-wavelength character of the cosmic background radiation, and may be observed as highly redshifted objects at z of about 100,000.

Optical dark solitons described by the generalized nonlinear Schrodinger equation are discussed, and the criterion of soliton instability is presented. This analytical criterion is confirmed numerically for an exactly solvable model of nonlinear saturation.

A method is reported for determining the two-dimensional distribution of refractive-index changes in Ti-diffused LiNbO3 strip waveguides. The measurement process was as follows. Distributions of diffused Ti concentration in LiNbO3 were measured using an x-ray microanalyzer. Using calibration curves the Ti concentrations were then converted into refractive-index changes. To obtain high spatial resolution in the two-dimensional XMA measurement the electron

By nature discrete solitons represent self-trapped wavepackets in nonlinear periodic structures and result from the interplay between lattice diffraction (or dispersion) and material nonlinearity. In optics, this class of self-localized states has been successfully observed in both one-and two-dimensional nonlinear waveguide arrays. In recent years such lattice structures have been implemented or induced in a variety of material systems including those with cubic (Kerr), quadratic, photorefractive, and liquid-crystal nonlinearities. In all cases the underlying periodicity or discreteness leads to new families of optical solitons that have no counterpart whatsoever in continuous systems. In the first part of this dissertation, a theoretical investigation of linear and nonlinear optical wave propagation in semi-infinite waveguide arrays is presented. In particular, the properties and the stability of surface solitons at the edge of Kerr (AlGaAs) and quadratic (LiNbO3) lattices are examined. Hetero-structures of two dissimilar semi-infinite arrays are also considered. The existence of hybrid solitons in these latter types of structures is demonstrated. Rabi-type optical transitions in z-modulated waveguide arrays are theoretically demonstrated. The corresponding coupled mode equations, that govern the energy oscillations between two different transmission bands, are derived. The results are compared with direct beam propagation simulations and are found to be in excellent agreement with coupled mode theory formulations. In the second part of this thesis, the concept of parity-time-symmetry is introduced in the context of optics. More specifically, periodic potentials associated with PT-symmetric Hamiltonians are numerically explored. These new optical structures are found to exhibit surprising characteristics. These include the possibility of abrupt phase transitions, band merging, non-orthogonality, non-reciprocity, double refraction, secondary emissions, as well as power oscillations. Even though gain/loss is present in this class of periodic potentials, the propagation eigenvalues are entirely real. This is a direct outcome of the PT-symmetry. Finally, discrete solitons in PT -symmetric optical lattices are examined in detail.

Treating the two-dimensional Minkowski space as a Wick rotated version of the complex plane, we characterize the causal automorphisms in the two-dimensional Minkowski space as the Märzke-Wheeler maps of a certain class of observers. We also characterize the differentiable causal automorphisms of this space as the Minkowski conformal maps whose restriction to the time axis belongs to the class of observers mentioned above. We answer a recently raised question about whether causal automorphisms are characterized by their wave equation. As another application of the theory, we give a proper time formula for accelerated observers which solves the twin paradox in two-dimensional Minkowski spacetime.

An experimental technique is developed to study acoustic transmission in one and twodimensional modulated structures by employing third sound of a superfluid helium film. In particular, the Penrose lattice, which is a twodimensional quasiperiodic structure, is studied. In two dimensions, the scattering of third sound is weaker than in one dimension. Nevertheless, the authors find that the transmission spectrum in the Penrose lattice, which is a twodimensional prototype of the quasicrystal, is observable if the helium film thickness is chosen around 5 atomic layers. The transmission spectra in the Penrose lattice are explained in terms of dynamical theory of diffraction.

Komuro, T.; Kawashima, H., Shirahama, K.; Kono, K. [Univ. of Tokyo, Tokyo (Japan)

A substantial improvement in resolution has been achieved for the computation of jump discontinuities in gas dynamics using the method of front tracking. The essential feature of this method is that a lower dimensional grid is fitted to and follows the discontinuous waves. At the intersection points of these discontinuities, two-dimensional Riemann problems occur. In this paper we study such two-dimensional Riemann problems from both numerical and theoretical points of view. Specifically included is a numerical solution for the Mach reflection, a general classification scheme for two-dimensional elementary waves, and a discussion of problems and conjectures in this area.

The classic examples of optical phenomena resulting in the appearance of solitons are self-focusing, self-induced transparency, and parametric three-wave interaction. To date, the list of the fields of nonlinear optics and models where solitons play an important role has significantly expanded. Now long-lived or stable solitary waves are called solitons, including, for example, dissipative, gap, parametric, and topological solitons. This review considers nonlinear optics models giving rise to the appearance of solitons in a narrow sense: solitary waves corresponding to the solutions of completely integrable systems of equations basic for the models being discussed. (review)

Maimistov, Andrei I [Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Region (Russian Federation)

Two-dimensional photonic crystals (PC) have emerged as promising building blocks for integrated optics systems. Photonic crystal devices exploit defects, in an otherwise periodic lattice designed to exhibit a wide photonic bandgap (PBG), to form resonant ...

The paper discusses the development of a two-dimensional turbulentkinetic energy - dissipation rate (k-epsilon) turbulence model inthe form of vorticity and stream functions. his turbulence modelprovides the distribution of turbulent kinematic viscosity, used tocalculate the effe...

The Surface Evolver program, which is an interactive program for the study of surfaces shaped by surface tension and other energies, has been evaluated for simulation of two-dimensional grain growth. Examples have demonstrated that the grain structure evo...

A computer algorithm has been discovered for unwrapping two-dimensional Phase data and producing perfect contour maps without holes or dark bands of erroneous contour lines. The method employs local, temporary unwrapping within single grid squares of rect...

Introduces a method for two-dimensional kinematics measurements by hanging marbles with long strings. Describes experimental procedures for conservation of momentum and obtaining the coefficient of restitution. Provides diagrams and mathematical expressions for the activities. (YP)

Chebyshev pseudospectral methods are used to compute twodimensional smooth compressible flows. Grid refinement tests show that spectral accuracy can be obtained. Filtering is not needed if resolution is sufficiently high and if boundary conditions are carefully prescribed.

Kopriva, D. A.; Zang, T. A.; Salas, M. D.; Hussaini, M. Y.

A two-dimensional finite difference analysis is applied to surface diffusion-controlled instabilities of plates. Plates can evolve into cylinders, or if the plates have longitudinal internal boundaries, they may split into two segments. The evolution proc...

An experiment using a time-dependent, two-dimensional photochemical model of the troposphere to model the vertical and zonal distribution of ozone and its precursors is presented. The experiment examines two cases. Case I simulates vertical transport due ...

A standard model for hydrodynamic dispersion has been added to TOUGH2- The dispersion model, intended for use with the EOS7 fluid properties module, accounts for the effects of hydrodynamic dispersion and molecular diffusion in two-dimensional rectangular...

Several queuing problems lead to Markov chains with jumps of unbounded length, particularly with geometric behavior in one or more directions. In the present paper the equilibrium behavior is analyzed for two-dimensional nearest neighbor random walks, whi...

A two-dimensional numerical model for DFB semiconductor laser simulation is developed and presented. In this model the transverse carrier transport and longitudinal spatial\\/spectral hole-burning effects in a bulk DFB laser are accounted for rigorously. Comparison with simplified models is made. Methods for improving the accuracy of steady-state and small-signal analyses by the simplified models are proposed and verified

This study reports a microfluidic chip integrated with an arrayed immunoassay for surface plasmon resonance (SPR) phase imaging of specific bio-samples. The SPR phase imaging system uses a surface-sensitive optical technique to detect two-dimensional (2D) spatial phase variation caused by rabbit immunoglobulin G (IgG) adsorbed on an anti-rabbit IgG film. The microfluidic chip was fabricated by using micro-electro-mechanical-systems (MEMS) technology

Kuo-Hoong Lee; Yuan-Deng Su; Shean-Jen Chen; Fan-Gang Tseng; Gwo-Bin Lee

The thermal relaxation process for a spatially uniform twodimensional plasma in a uniform dc magnetic field is simulated numerically. Thermal relaxation times are defined in terms of the time necessary for the numerically computer Boltzman H-function to decrease through a given part of the distance to its minimum value. Dependence of relaxation time on two parameters is studied: number of particles per Debye square and ratio of gyrofrequency to plasma frequency.

In this paper a two-dimensional (2D) diffraction tomographic (DT) algorithm based on the first order Born approximation is proposed for through-the-wall radar imaging (TWRI). The spectral expansion of the three-layered background medium Green’s function is employed to derive a linear relation between the spatial Fourier transforms of the image and the scattered field. Then the image can be efficiently reconstructed

The goal of this research was achieved by self-consistently modeling the discharge characteristics of the radially-convergent cylindrical inertial electrostatic confinement (RC-IEC) fusion device using a Monte Carlo numerical approach. The model (called MCP) is time-independent and spatiallytwo-dimensional with three dimensions in energy and direction. Multiple particle species and collisions with background neutral gas are taken into account, and the

By exposing two-dimensional crystals to tunable substrate potentials one can selectively manipulate the crystal’s phonon band structure. We explore this idea and study the overdamped lattice dynamics of colloidal crystals subject to commensurate substrate potentials with sinusoidal modulations in up to two spatial directions. We furthermore show that the mean-square displacement of colloids in the crystal can be understood as the Laplace transform of the phonon spectrum and discuss how our results can best be verified experimentally.

We report the design of a new family of two-dimensional codes for fiber-optic CDMA networks. These newly designed temporary\\/spatial single-pulse-per-row (T\\/S SPR) codes have out-of-phase autocorrelation zero and cross correlation equal to one. Optical orthogonal codes (OOCs) have the lowest out-of-phase autocorrelation and cross-correlation values (both equal to one) among the one-dimensional codes. We compare the performance of our codes

E. S. Shivaleela; Kumar N. Sivarajan; A. Selvarajan

A simple method for implementing an asymmetrical two-dimensional magnetic lattice is proposed. The asymmetrical two-dimensional magnetic lattice is created by periodically distributing nonzero magnetic minima across the surface of a magnetic thin film, where the magnetic patterns are formed by milling n×n square holes on the surface of the film. The method is proposed for trapping and confining quantum degenerate

Ahmed Abdelrahman; Mikhail Vasiliev; Kamal Alameh; Peter Hannaford

A two-dimensional Ising-like model with spin 1 and long-range interactions is studied numerically through a Monte Carlo simulation. The goal of the simulation is to describe pattern formations and critical temperature of two-dimensional magnetic structures. Three sets of parameters are considered, that give rise to stripes, labyrinths or cellular domain structures. We determine for each configuration the transition ordering temperatures,

J. R. Iglesias; O. A. Nagel; S. Gonçalves; M. Kiwi

A two-dimensional Ising-like model with spin 1 and long-range interactions is studied numerically through a Monte Carlo simulation. The goal of the simulation is to describe pattern formations and critical temperature of two-dimensional magnetic structures. Three sets of parameters are considered, that give rise to stripes, labyrinths or cellular domain structures. We determine for each configuration the transition ordering temperatures, the relaxation of the energy, the hysteresis cycle, and the average size of the domains.

Iglesias, J. R.; Nagel, O. A.; Gonçalves, S.; Kiwi, M.

String theories with two-dimensional space-time target spaces are characterized by the existence of a ``ground ring'' of operators of spin (0, 0). By understanding this ring, one can understand the symmetries of the theory and illuminate the relation of the critical string theory to matrix models. The symmetry groups that arise are, roughly, the area-preserving diffeomorphisms of a two-dimensional phase

I explore the possibility of finding an equivalent string representation of\\u000atwo dimensional QCD. I develop the large N expansion of the ${\\\\rm QCD_2}$\\u000apartition function on an arbitrary twodimensional Euclidean manifold. If this\\u000ais related to a two-dimensional string theory then many of the coefficients of\\u000athe ${1\\\\over N}$ expansion must vanish. This is shown to be true

During the session on ``Introductory College Physics Textbooks'' at the 2007 Summer Meeting of the AAPT, there was a brief discussion about whether introductory physics should begin with one-dimensional motion or two-dimensional motion. Here we present the case that by starting with two-dimensional motion, we are able to introduce a considerable amount of physics even before discussing the constant acceleration formulas or Newton's laws.

A two-dimensional quasi-crystal with an eightfold rotational axis has been found in rapidly solidified V-Ni-Si and Cr-Ni-Si alloys by means of transmission electron microscopy. The electron-diffraction pattern taken along this axis shows no periodicity, but a clear eightfold orientation symmetry. The corresponding high-resolution electron-microscopic image agrees well with the two-dimensional eightfold quasi-lattice consisting of squares and 45 deg rhombi.

We determine the effective dipolar interaction between single domain two-dimensional ferromagnetic particles (islands or dots), taking into account their finite size. The first correction term decays as 1\\/D5, where D is the distance between particles. If the particles are arranged in a regular two-dimensional array and are magnetized in plane, we show that the correction term reinforces the antiferromagnetic character

In this work the two-dimensional analysis of continuous casting of low carbon steel was presented. The interaction between moved ingot, copper mould and transport rolls was modeling. The influence of liquid steel ferrostatic pressure and coupled between temperature and deformation fields were taken into consideration.For thermal analysis (with phase change), the two-dimensional unsteady-state heat conduction equation with enthalpy convention was

The superintegrability of three different two-dimensional oscillators is studied: (i) a nonlinear oscillator dependent on a parameter {lambda} (two-dimensional version of the oscillator of Lakshmanan and Mathews), (ii) a nonlinear oscillator related to the Riccati equation, and (iii) the standard harmonic oscillator on constant curvature spaces. They can be considered as nonlinear deformations, or curvature-dependent versions, of the linear harmonic oscillator.

Carinena, J. F., E-mail: jfc@unizar.es; Ranada, M. F. [Universidad de Zaragoza, Departamento de Fisica Teorica, Facultad de Ciencias (Spain)], E-mail: mfran@unizar.es; Santander, M. [Universidad de Valladolid, Departamento de Fisica Teorica, Facultad de Ciencias (Spain)], E-mail: msn@fta.uva.es

We study the quantum phase transitions in the two-dimensional spin-orbit models in terms of fidelity susceptibility and reduced fidelity susceptibility. An order-to-order phase transition is identified by fidelity susceptibility in the two-dimensional Heisenberg XXZ model with Dzyaloshinsky-Moriya interaction on a square lattice. The finite size scaling of fidelity susceptibility shows a power-law divergence at criticality, which indicates the quantum phase

This paper considers throughput and memory requirements in architectures which operate on two-dimensional (2D) digital signals. We present a novel technique for retiming a 2D data-flow graph to meet a given throughput constraint while keeping the memory required by the architecture low. This technique, which we call orthogonal two-dimensional retiming, is posed as two linear programming problems which can be

This dissertation considers a method for processing two-dimensional (2-D) signals (e.g. imagery) by transformation to a coordinate space where the 2-D operation separates into orthogonal 1-D operations. After processing, the 2-D output is reconstructed by a second coordinate transformation. This approach is based on the Radon transform, which maps a two-dimensional Cartesian representation of a signal into a series of

We construct two-dimensional gauge theories with N = (4,4) supersymmetry from branes of type IIA string theory. Quantum effects in the two-dimensional gauge theory are analyzed by embedding the IIA brane construction into M-theory. We find that the Coulomb branch of one theory and the Higgs branch of a mirror theory become equivalent at strong coupling. A relationship to the

We construct two-dimensional gauge theories with N= (4,4) supersymmetry from branes of type IIA string theory. Quantum effects in the two-dimensional gauge theory are analyzed by embedding the IIA brane construction into M-theory. We find that the Coulomb branch of one theory and the Higgs branch of a mirror theory become equivalent at strong coupling. A relationship to the decoupling

Chapter 1 discusses the quantum mechanical formalism used for describing the interaction between magnetic dipoles that dictates the appearance of a spectrum. The NMR characteristics of liquids and liquid crystals are stressed. Chapter 2 reviews the theory of multiple quantum and twodimensional NMR. Properties of typical spectra and phase cycling procedures are discussed. Chapter 3 describes a specific application of heteronuclear double quantum coherence to the removal of inhomogeneous broadening in liquids. Pulse sequences have been devised which cancel out any contribution from this inhomogeneity to the final spectrum. An interpretation of various pulse sequences for the case of /sup 13/C and /sup 1/H is given, together with methods of spectral editing by removal or retention of the homo- or heteronuclear J coupling. The technique is applied to a demonstration of high resolution in both frequency and spatial dimensions with a surface coil. In Chapter 4, multiple quantum filtered 2-D spectroscopy is demonstrated as an effective means of studying randomly deuterated molecules dissolved in a nematic liquid crystal. Magnitudes of dipole coupling constants have been determined for benzene and hexane, and their signs and assignments found from high order multiple quantum spectra. For the first time, a realistic impression of the conformation of hexane can be estimated from these results. Chapter 5 is a technical description of the MDB DCHIB-DR11W parallel interface which has been set up to transfer data between the Data General Nova 820 minicomputer, interfaced to the 360 MHz spectrometer, and the Vax 11/730. It covers operation of the boards, physical specifications and installation, and programs for testing and running the interface.

A computerized system was developed for real time acquisition, enhanced processing, analysis, and display of cross-sectional images of the left ventricle derived by two-dimensional echocardiography (2DE). The new methodology couples a standard medical imaging computer system to the video output of any current 2DE unit, uses a 128 x 128 or 64 x 64 matrix window and stores the real time 30 frames/sec digitized images on a magnetic disk. Computerized beat-to-beat and frame-by-frame processing employs space-time smoothing the automatic detection of endocardial interfaces by standard threshold and second derivative techniques. Multiple views are displayed in real time with 256 levels of gray and color. The methodology was used to analyze and graphically display frame-by-frame changes throughout the cardiac cycle. In addition, regional wall motion and thickness were analyzed in 12 sectors of individual cross-sections using a standardized angular subdivision originating at the center of area and indexed by an external reference point. An algorithm was developed to correct cross-sectional interference definition from the commonly used trailing-to-leading edge to the more valid leading-to-leading outline technique. Computerized analysis of spatial and temporal variations of cardiac contraction were demonstrated in several clinical and experimental applications, including bicycle exercise testing, investigation of acute myocardial infarction, and assessment of interventions. Initial evaluation indicates that the new real time computerized digital acquisition and data analysis represents a major advances toward quantitation of left ventricular function using 2DE. PMID:7234656

Garcia, E; Gueret, P; Bennett, M; Corday, E; Zwehl, W; Meerbaum, S; Corday, S; Swan, H J; Berman, D

The history of application of optical solitons for high speed communications presents an interesting example of how an abstract mathematical concept has been put into practical use. The historical development introduced in this manuscript is divided into five stages: (1) historical background and the discovery of the optical soliton, (2) the idea and demonstration of all optical soliton transmission systems, (3) identification of possible problems, (4) demonstration of soliton control and (5) discovery of dispersion managed optical solitons (DMS). Although there are many interesting related subjects such as modulational instability, dark solitons, and spatialsolitons, the manuscript focuses only on the subject of primarily theoretical developments of soliton based communications in fibers. (c) 2000 American Institute of Physics. PMID:12779400

In this paper we describe a concept for dosimetric treatment plan verification using two-dimensional ionization chamber arrays. Two different versions of the 2D-ARRAY (PTW-Freiburg, Germany) will be presented, a matrix of 16x16 chambers (chamber cross section 8 mmx8 mm; the distance between chamber centers, 16 mm) and a matrix of 27x27 chambers (chamber cross section 5 mmx5 mm; the distance between chamber centers is 10 mm). The two-dimensional response function of a single chamber is experimentally determined by scanning it with a slit beam. For dosimetric plan verification, the expected two-dimensional distribution of the array signals is calculated via convolution of the planned dose distribution, obtained from the treatment planning system, with the two-dimensional response function of a single chamber. By comparing the measured two-dimensional distribution of the array signals with the expected one, a distribution of deviations is obtained that can be subjected to verification criteria, such as the gamma index criterion. As an example, this verification method is discussed for one sequence of an IMRT plan. The error detection capability is demonstrated in a case study. Both versions of two-dimensional ionization chamber arrays, together with the developed treatment plan verification strategy, have been found to provide a suitable and easy-to-handle quality assurance instrument for IMRT.

Poppe, Bjoern; Blechschmidt, Arne; Djouguela, Armand; Kollhoff, Ralf; Rubach, Antje; Willborn, Kay C.; Harder, Dietrich [Klinik fuer Strahlentherapie und Internistische Onkologie, Pius-Hospital, Oldenburg, Germany, and Carl-von-Ossietzky-Universitaet Oldenburg, Oldenburg (Germany); Carl-von-Ossietzky-Universitaet Oldenburg, Oldenburg (Germany); Klinik fuer Strahlentherapie und Internistische Onkologie, Pius-Hospital, Oldenburg (Germany); Georg-August-Universitaet Goettingen, Goettingen (Germany)

Solitary waves have consistently captured the imagination of scientists, ranging from fundamental breakthroughs in spectroscopy and metrology enabled by supercontinuum light, to gap solitons for dispersionless slow-light, and discrete spatialsolitons in lattices, amongst others. Recent progress in strong-field atomic physics include impressive demonstrations of attosecond pulses and high-harmonic generation via photoionization of free-electrons in gases at extreme intensities of 1014 W/cm2. Here we report the first phase-resolved observations of femtosecond optical solitons in a semiconductor microchip, with multiphoton ionization at picojoule energies and 1010 W/cm2 intensities. The dramatic nonlinearity leads to picojoule observations of free-electron-induced blue-shift at 1016 cm?3 carrier densities and self-chirped femtosecond soliton acceleration. Furthermore, we evidence the time-gated dynamics of soliton splitting on-chip, and the suppression of soliton recurrence due to fast free-electron dynamics. These observations in the highly dispersive slow-light media reveal a rich set of physics governing ultralow-power nonlinear photon-plasma dynamics.

Husko, Chad A.; Combrie, Sylvain; Colman, Pierre; Zheng, Jiangjun; De Rossi, Alfredo; Wong, Chee Wei

The ion acoustic soliton in weakly a relativistic electron-positron-ion plasma with finite ion temperature have been investigated. Such plasmas is frequently occur in astrophysical environment. Using reductive perturbation method we have derived the twodimensional Kadomtsev- Petviashvili(KP) equation to study the characteristics of ion-acoustic soliton in three component plasma at different plasma temperature. The soliton solution of KP equation is

The existence and stability of solitons in Bose-Einstein condensates with attractive interatomic interactions, described by the Gross-Pitaevskii equation with a three-dimensional (3D) periodic potential, are investigated in a systematic form. We find a one-parameter family of stable 3D solitons in a certain interval of values of their norm, provided that the strength of the potential exceeds a threshold value. The minimum number of Li7 atoms in the stable solitons is 60, and the energy of the soliton at the stability threshold is ?6 recoil energies in the lattice. The respective energy versus norm diagram features two cuspidal points, resulting in a typical swallowtail pattern, which is a generic feature of 3D solitons supported by quasi-two-dimensional or fully dimensional lattice potentials.

Mihalache, D.; Mazilu, D.; Lederer, F.; Malomed, B. A.; Crasovan, L.-C.; Kartashov, Y. V.; Torner, L.

The existence and stability of solitons in Bose-Einstein condensates with attractive interatomic interactions, described by the Gross-Pitaevskii equation with a three-dimensional (3D) periodic potential, are investigated in a systematic form. We find a one-parameter family of stable 3D solitons in a certain interval of values of their norm, provided that the strength of the potential exceeds a threshold value. The minimum number of {sup 7}Li atoms in the stable solitons is 60, and the energy of the soliton at the stability threshold is {approx_equal}6 recoil energies in the lattice. The respective energy versus norm diagram features two cuspidal points, resulting in a typical swallowtail pattern, which is a generic feature of 3D solitons supported by quasi-two-dimensional or fully dimensional lattice potentials.

Mihalache, D. [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, 08034 Barcelona (Spain); Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller Universitaet Jena, Max-Wien-Platz 1, D-077743 Jena (Germany); Horia Hulubei National Institute of Physics and Nuclear Engineering, Department of Theoretical Physics, P.O. Box MG-6, Bucharest (Romania); Mazilu, D. [Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller Universitaet Jena, Max-Wien-Platz 1, D-077743 Jena (Germany); Horia Hulubei National Institute of Physics and Nuclear Engineering, Department of Theoretical Physics, P.O. Box MG-6, Bucharest (Romania); Lederer, F. [Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller Universitaet Jena, Max-Wien-Platz 1, D-077743 Jena (Germany); Malomed, B.A. [Department of Interdisciplinary Studies, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Crasovan, L.-C. [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, 08034 Barcelona (Spain); Horia Hulubei National Institute of Physics and Nuclear Engineering, Department of Theoretical Physics, P.O. Box MG-6, Bucharest (Romania); Kartashov, Y.V.; Torner, L. [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, 08034 Barcelona (Spain)

Various effects associated with ionospheric heating are investigated by numerically solving the modified Zakharov (1972) equations. It is shown that, for typical ionospheric parameters, the modulational instability is more important than the parametric decay instability in the spatial region of strongest heater electric field. It is concluded that the modulational instability leads to the formation of solitons, as originally predicted by Petviashvili (1976).

Nicholson, D. R.; Payne, G. L.; Downie, R. M.; Sheerin, J. P.

In higher dimensional quantum field theory, irreducible representations of the Poincaré group are associated with particles. Their counterpart in two-dimensional massless models are "waves" introduced by Buchholz. In this paper we show that waves do not interact in two-dimensional Möbius covariant theories and in- and out-asymptotic fields coincide. We identify the set of the collision states of waves with the subspace generated by the chiral components of the Möbius covariant net from the vacuum. It is also shown that Bisognano-Wichmann property, dilation covariance and asymptotic completeness (with respect to waves) imply Möbius symmetry. Under natural assumptions, we observe that the maps which give asymptotic fields in Poincaré covariant theory are conditional expectations between appropriate algebras. We show that a two-dimensional massless theory is asymptotically complete and noninteracting if and only if it is a chiral Möbius covariant theory.

We introduce an analytically solvable model of two-dimensional continuous attractor neural networks (CANNs). The synaptic input and the neuronal response form Gaussian bumps in the absence of external stimuli, and enable the network to track external stimuli by its translational displacement in the two-dimensional space. Basis functions of the two-dimensional quantum harmonic oscillator in polar coordinates are introduced to describe the distortion modes of the Gaussian bump. The perturbative method is applied to analyze its dynamics. Testing the method by considering the network behavior when the external stimulus abruptly changes its position, we obtain results of the reaction time and the amplitudes of various distortion modes, with excellent agreement with simulation results.

By analogy to the three dimensional optical bottle beam, we introduce the plasmonic bottle beam: a twodimensional surface wave which features a lattice of plasmonic bottles, i.e. alternating regions of bright focii surrounded by low intensities. The two-dimensional bottle beam is created by the interference of a non-diffracting beam, a cosine-Gaussian beam, and a plane wave, thus giving rise to a non-diffracting complex intensity distribution. By controlling the propagation constant of the cosine-Gauss beam, the size and number of plasmonic bottles can be engineered. The twodimensional lattice of hot spots formed by this new plasmonic wave could have applications in plasmonic trapping.

We construct two-dimensional gauge theories with N = (4,4) supersymmetry from branes of type IIA string theory. Quantum effects in the two-dimensional gauge theory are analyzed by embedding the IIA brane construction into M-theory. We find that the Coulomb branch of one theory and the Higgs branch of a mirror theory become equivalent at strong coupling. A relationship to the decoupling limit of the type IIA and IIB 5-branes in Matrix theory is shown. T-duality between the ALE metric and the wormhole metric of Callan, Harvey, and Strominger is discussed from a brane perspective and some puzzles regarding string duality resolved. We comment on the existence of a quantum Higgs branch in two-dimensional theories. Branes prove to be useful tools in analyzing singular conformal field theories.

We show that broad-area cascade lasers with no absorbing intracavity elements support the spontaneous formation of two-dimensional bright localized structures in a dark background. These cavity solitons consist of islands of two-photon emission embedded in a background of single-photon emission. We discuss the mechanisms through which these structures are formed and interact, along with their properties and stability.

Vilaseca, R.; Torrent, M. C.; Garcia-Ojalvo, J.; Brambilla, M.; San Miguel, M.

The effects of two-dimensional spin diffusion on spin extraction in lateral semiconductor spin valves have been investigated experimentally and theoretically. A ferromagnetic collector terminal of variable size is placed between the ferromagnetic electron spin injector and detector of a conventional lateral spin valve for spin extraction. It is observed that transverse spin diffusion beneath the collector terminal plays an important role along with the conventional longitudinal spin diffusion in describing the overall transport of spin carriers. Two-dimensional spin diffusion reduces the perturbation of the channel electrochemical potentials and improves spin extraction.

We have developed a network model for two-dimensional phase-locked arrays of coupled lasers that provides a basis for modeling arrays incorporating mixed coupling schemes. With this network approach we show that the modes of two-dimensional arrays that are evanescently coupled in the lateral direction and injection coupled in the longitudinal direction can be expressed in terms of the eigenvalues of matrices separately representing the lateral and longitudinal coupling. As an example, the modes and grating-coupled near-field patterns of a 3 x 3 array injection coupled through surface-emitting second-order Bragg reflectors are determined explicitly. PMID:19749813

We present a detailed discussion of the complimentary fields of the application of two-dimensional infrared (2D-IR) spectroscopy in comparison with two-dimensional nuclear magnetic resonance (2D-NMR) spectroscopy. Transient 2D-IR (T2D-IR) spectroscopy of nonequilibrium ensembles is probably one of the most promising strengths of 2D-IR spectroscopy, as the possibilities of 2D-NMR spectroscopy are limited in this regime. T2D-IR spectroscopy uniquely combines ultrafast

A kind of two-dimensional hadamard transform spectrometer was developed. A grating was used for chromatic dispersion of orders and a prism was used for spectral dispersion. Quite different from traditional CCD detection method, a digital micromirror device (DMD) was applied for optical modulation, and a simple point detector was used as the sensor. Compared with traditional two-dimensional spectrometer, it has the advantage of high resolution and signal-noise-ratio, which was proved by theoretical calculation and computer simulation. PMID:22870674

We report a hybrid mesophase consisting of magnetic nanorods confined between the non-ionic surfactant bilayers of a lamellar phase. The magnetic field-induced ordering of the nanorods was measured experimentally and modeled by a two-dimensional Onsager theory including the third virial coefficient. The nanorods are strongly confined in layers, with no orientational coupling from one layer to the next. At high volume concentration they exhibit spontaneous in-plane orientational ordering and form a stack of independent two-dimensional nematic systems. This isotropic-nematic transition is first-order. PMID:24628202

Slyusarenko, Kostyantyn; Constantin, Doru; Davidson, Patrick

We report a hybrid mesophase consisting of magnetic nanorods confined between the non-ionic surfactant bilayers of a lamellar phase. The magnetic field-induced ordering of the nanorods was measured experimentally and modeled by a two-dimensional Onsager theory including the third virial coefficient. The nanorods are strongly confined in layers, with no orientational coupling from one layer to the next. At high volume concentration they exhibit spontaneous in-plane orientational ordering and form a stack of independent two-dimensional nematic systems. This isotropic-nematic transition is first-order.

Slyusarenko, Kostyantyn; Constantin, Doru; Davidson, Patrick

An accurate approach for reconstructing a time-dependent two-dimensional signal from non-synchronized time series recorded at points located on a grid is discussed. The method, denoted as correlation sampling, improves the standard conditional sampling approach commonly employed in the study of turbulence in magnetoplasma devices. Its implementation is illustrated in the case of an artificial time-dependent signal constructed using a fractal algorithm that simulates a fluctuating surface. A statistical method is also discussed for distinguishing coherent (i.e., collective) from purely random (noisy) behavior for such two-dimensional fluctuating phenomena.

Reactive transport in porous media is typically modeled approximating key processes occurring at the pore-scale through a set of continuum- (or Darcy-) scale partial differential equations, the advection dispersion reaction equation (ADRE) being a widely used model. Such formulations hold under a set of assumptions which are not always met in the context of laboratory and/or field scale applications. These hypotheses involve spatial scale separation and restrictions on the magnitude of dimensionless parameters, such as the Damköhler and the Péclet numbers, characterizing the process. In this context, direct measurements and micro-scale numerical simulations are key to (1) assess the validity of upscaled continuum formulations, and (2) quantify the ability of such models to capture the key features of the process dynamics. Here, we focus on the simulation of a homogeneous irreversible bimolecular reaction of the kind A + B ? C. We analyze the evolution of the process in the presence of different pore scale geometrical settings, upon performing numerical pore-scale simulations in ordered and disordered twodimensional arrays of cylinders. The selected pore scale geometries are characterized by different porosities and by the presence of large cavities and regions with different relative importance of diffusive and advective processes. A particle tracking methodology is employed to study the system dynamics and simulations are performed for a wide range of the Péclet and Damköhler numbers. The evolution of the features of the reactive transport process is analyzed on different observation scales. Our results show that the reactive transport process attains an asymptotic regime for which the reaction is limited by (effective) dispersion. The influence of the pore scale geometry on the asymptotic and pre-asymptotic behavior of the reaction rate globally observed in the domain is quantitatively analyzed. Local mixing features and related characteristic scales are also discussed. In particular, the influence of local velocity distributions and medium geometrical setting on the reaction process is documented. These results provide a framework to discuss the appropriateness of continuum scale formulations which can be employed to describe the target geochemical system. The impact of Péclet and Damköhler numbers and of the pore space geometry on the characterization of the parameters introduced in continuum scale formulations of the system is discussed. Recently an alternative continuum formulation of the system has been provided on the basis of a volume averaging analysis of the reactive transport process analyzed. Here the validity of this formulation is discussed, in comparison with the standard ADRE formulation. We assess (i) the influence of the reactive process on the (upscaled) hydrodynamic dispersion coefficient and (ii) the ability of the continuum modeling strategies considered to represent the effect of pore scale incomplete mixing processes.

Porta, G.; Chaynikov, S.; Thovert, J.; Riva, M.; Guadagnini, A.; Adler, P. M.

A new finite element code has been developed for simulation of the dynamics of two-dimensional incompressible magnetohydrodynamic flows. The solution scheme used in spatial discretization is the Galerkin weighted-residual finite-element method, incorporating the mixed interpolation technique, and a combination of the penalty and pseudocompressibility methods for implementing the incompressibility constraint. An implicit and stable theta-weighting finite difference scheme is used for integration in time, and a non-iterative time-level averaging method is employed for treatment of nonlinear terms. The code has been extensively benchmarked against known analytical solutions in magnetohydrodynamics and has been found to produce highly accurate results. The tearing-mode instability of a magnetic-field-reversing current sheet in the presence of coplanar stagnation-point flow, in which the unperturbed equilibrium state is an exact solution of the steady-state dissipative MHD equations, has been examined by use of the code. Simulation results indicate stability for sufficiently small values of the viscous Lundquist number, S_nu, or the resistive Lundquist number, S_eta : a curve in the S_nu -S_eta plane separating the stable and unstable regions has been found. In the unstable regime, the results show occurrence of multiple x-line reconnection along the center of the current sheet at x = 0. Small-scale structures of vorticity and current density near the x-point reconnection sites are observed and are found to be consistent with results obtained by Matthaeus (1982). Average linear growth rates are estimated for modest values of S_eta. In the range S_eta<=500, the number of magnetic islands is found to be independent of Seta, which implies that there exists a single dominant wavelength of the tearing-mode in this range. The stretching of magnetic islands which is present in this configuration but not in the perpendicular flow and field configuration examined by Phan and Sonnerup (1991), caused a substantial decrease in linear growth rate relative to that obtained by those authors. It is of particular interest that, unlike most simulations of the tearing-mode, no symmetry conditions are imposed on the perturbations; nevertheless they develop in an anti -symmetric manner.

The authors consider a chain of elastic (Hertzian) grains that repel upon contact according to the potential V = a{delta}{sup u}, u > 2, where {delta} is the overlap between the grains. They present numerical and analytical results to show that an impulse initiated at an end of a chain of Hertzian grains in contact eventually propagates as a soliton for all n > 2 and that no solitons are possible for n {le} 2. Unlike continuous, they find that colliding solitons in discrete media initiative multiple weak solitons at the point of crossing.

The structure of nontopological solutions of Einstein field equations as proposed by Friedberg, Lee, and Pang (1987) is examined. This analysis incorporates finite temperature effects and pair creation. Quarks are assumed to be the only species that exist in interior of soliton stars. The possibility of primordial creation of soliton stars in the incomplete decay of the degenerate vacuum in early universe is explored. Because of dominance of pair creation inside soliton stars, the luminosity of soliton stars is not determined by its radiative transfer characteristics, and the surface temperature of soliton stars can be the same as its interior temperature. It is possible that soliton stars are intense X-ray radiators at large distances. Soliton stars are nearly 100 percent efficient energy converters, converting the rest energy of baryons entering the interior into radiation. It is possible that a sizable number of baryons may also be trapped inside soliton stars during early epochs of the universe. In addition, if soliton stars exist they could assume the role played by massive black holes in galactic centers.

For a wide range of electron filling we study the spin density wave states in the Hubbard model on a square lattice within a Hartree-Fock approximation. It is shown that the incommensurate helical spin density wave states appear for whole region of the electron filling and, especially, that the commensurate helical spin density wave state with wave vector (?, 0) is stable near the quarter-filling. We examine also the relative stability of the soliton and the vortex lattice states to the helical spin density wave states and obtain the results that near the half-filling case the soliton lattice states are stable states for intermediate interaction strength and that the vortex lattice states do not appear as the stable state, except one particular state with the wind-mill spin structure at the quarter-filling.

We study semianalytically soliton dynamics in a soliton based communication line for which the amplifier spacing is larger than the soliton period (referred to as the quasi-adiabatic regime). This regime allows us to overcome the limit on the soliton dura...

Traditional waste stabilisation pond (WSP) models encounter problems predicting pond performance because they cannot account for the influence of pond features, such as inlet structure or pond geometry, on fluid hydrodynamics. In this study, twodimensional (2-D) computational fluid dynamics (CFD) models were compared to experimental residence time distributions (RTD) from literature. In one of the three geometries simulated, the

Computer simulation is a growing field of research and plasma physics is one of the important areas where it is being applied today. This report describes the particle method of simulating a two-dimensional electrostatic plasma. The methods used to discre...

The twodimensional (2D) energy of the hydrogen molecule is calculated by the Heitler-London method. The 2D integrals (which are more localized compared to 3D ones) are performed in the light of the 3D Slater integrals. Such a 2D system for doped semicond...

How single neurons self-organize to form a complex functional system, the neural network, is a fundamental question in developmental neuroscience, computation science, and pattern formation. Two-dimensional in vitro invertebrate preparations offer an attractive model system to tackle this question due to the large size of the neurons, and their ability to grow in relative isolation as well as to develop

Numerical simulation has become an indispensable tool for the interpretation of pulse EPR experiments. In this work it is shown how automatic orientation selection, grouping of operator factors, and direct selection and elimination of coherences can be used to improve the efficiency of time-domain simulations of one- and two-dimensional electron spin echo envelope modulation (ESEEM) spectra. The program allows for

We present an mvestlgaUon of the massless, two-dimensional, interacting field theories Their basic property is their invanance under an lnfimte-dlmenslonal group of conformal (analytic) transformations It is shown that the local fields forlmng the operator algebra can be classified according to the irreducible representations of Vtrasoro algebra, and that the correlation functions are bmlt up of the \\

The pair correlation functions and the mean squared displacements of charged dust particles were studied experimentally for quasi-two-dimensional (2D) nonideal systems. The experiments were carried out in a plasma of a capacitive radio-frequency (RF-) discharge in argon for monolayers of monodispersed (melamine formaldehyde) spheres. A comparison with the existing theoretical and numerical data is presented.

Vaulina, O. S.; Vasilieva, E. V.; Petrov, O. F.; Fortov, V. E.

Two-dimensional materials, e.g. graphene and molybdenum disulfide (MoS(2)), have attracted great interest in recent years. Identification of the thickness of two-dimensional materials will improve our understanding of their thickness-dependent properties, and also help with scientific research and applications. In this paper, we propose to use optical imaging as a simple, quantitative and universal way to identify the thickness of two-dimensional materials, i.e. mechanically exfoliated graphene, nitrogen-doped chemical vapor deposition grown graphene, graphene oxide and mechanically exfoliated MoS(2). The contrast value can easily be obtained by reading the red (R), green (G) and blue (B) values at each pixel of the optical images of the sample and substrate, and this value increases linearly with sample thickness, in agreement with our calculation based on the Fresnel equation. This method is fast, easily performed and no expensive equipment is needed, which will be an important factor for large-scale sample production. The identification of the thickness of two-dimensional materials will greatly help in fundamental research and future applications. PMID:23154446

A twodimensional numerical model of an optically gated GaAs MESFET with non uniform channel doping has been developed. This is done to characterize the device as a photo detector. First photo induced voltage (V op ) at the Schottky gate is calculated for estimating the channel profile. Then Poisson's equation for the device is solved numerically under dark and

In the literature, now one-dimensional models of MIS solar cells, emphasizing the interface properties, are described, while in practice the structures are two-dimensional. Two types are considered: thin-film MIS solar cells with a transparent front-elect...

H. J. Pauwels, P. De Visschere, L. Vandendriessche

In recent paper (K. Ito, el al., Jpn. J. Appl. Phys. 40, 2558 (2001)), we present a fast and sufficiently accurate procedure to construct the potential and the electric field distribution from the observed electron density distribution in two-dimensional ...

Antenna-coupled microbolometers are known for having short time constants and high responsivity, but their small dimensions make them unsuitable for imaging applications where a typical pixel area is generally greater than 20 × 20 µm2. In this paper a twodimensional array of antenna-coupled microbolometers is demonstrated as an area receiver. Using the response of microbolometers to visible frequencies a

F. J. González; M. A. Gritz; C. Fumeaux; G. D. Boreman

A new system, that of matrix grammars, for two-dimensional pattern processing, is introduced. A hierarchy, induced on Chomsky's is found. Language operations such as union, catenation (row and column), Kleene's closure (row and column), and homomorphisms are investigated. It is found that the smallest class of these languages may serve as the class of regular arrays, which is defined as

New excitation schemes, based on the use adiabatic pulses, for single scan two-dimensional NMR experiments (Frydman et al., Proc. Nat. Acad. Sci. 2002, 99, 15 858-15 862) are introduced. The advantages are discussed. Applications in homo- and heteronuclear experiments are presented. PMID:14519020

Because the size and weight of main propulsion and auxiliary systems are inversely proportional to the ease in which heat or energy is exchanged, a major thrust of the research and development program of the U.S. Navy is toward the design and development of equipment that perform at higher efficiency with a reduction in size and weight. In particular, one area of great interest is the reduction in size and weight of steam condensers. The heat-transfer effectiveness is governed by the amount of surface and the overall resistance to the flow of heat. Filmwise condensation of steam on externally-finned tubes is a very complex process. Recent experiments have shown that enhancement ratios (ratio of steam-side heat-transfer coefficient to that of a smooth tube having the same diameter) exceeded the area enhancement produced by the fins. Moreover, the enhancement ratios for fully flooded tubes exceed the values predicted by a simple, one-dimensional conduction model by a factor of 2 to 4. A new two-dimensional conduction model was developed, which showed that the one-dimensional model overpredicted the two-dimensional results for high conductivity tube-metals such as copper by as much as 13%. The two-dimensional model also showed that variations in fin thickness or spacing can result in an overprediction by the one-dimensional model of the two-dimensional results by as much as twenty-two percent.

We look into the inner structure of a two-dimensional dilatonic evaporating black hole. We establish and employ the homogenous approximation for the black-hole interior. Two kinds of spacelike singularities are found inside the black hole, and their structure is investigated. We also study the evolution of spacetime from the horizon to the singularity.

Two graphynes, 6(H2),14,18 graphyne and 6BN,6,12 graphyne, that contain the heteroatoms hydrogen or boron and nitrogen, respectively, are shown to feature Dirac points in their band structure according to first-principles electronic structure calculations. This shows that the existence of Dirac points in the band structure of two-dimensional materials is neither restricted to graphene nor to other two-dimensional all-carbon materials. 6(H2),14,18 graphyne and 6BN,6,12 graphyne belong to the rectangular two-dimensional space groups pmm and pm, respectively, and thus exhibit completely different symmetries than graphene. 6BN,6,12 graphyne features a Dirac cone with a band gap originating from an avoided crossing of its valence and conduction band at the Dirac point due to missing reflection symmetry. The examples of 6(H2),14,18 graphyne and 6BN,6,12 graphyne suggest that a wealth of two-dimensional materials with various chemical compositions and with electronic properties equally amazing as those of graphene is awaiting discovery.

We present a performance evaluation of eight two-dimensional phase unwrapping methods with respect to correct phase unwrapping and execution times. The evaluated methods are block least squares (BLS), adaptive integration (AI), quality guided path following (QUAL), mask cut (MCUT), multigrid (MGRID), preconditioned conjugate gradient (PCG), Flynn s (FLYNN), and Liang s (LIANG). This set included integration- (path following), least-squares-, L

Exact transfer function, ETF, is two-dimensional transfer function that constitutes basis of improved frequency-domain-convolution algorithm for processing synthetic-aperture-radar, SAR data. ETF incorporates terms that account for Doppler effect of motion of radar relative to scanned ground area and for antenna squint angle. Algorithm based on ETF outperforms others.

Chang, Chi-Yung; Jin, Michael Y.; Curlander, John C.

Monopole vortices, obeying the homogeneous Hasegawa-Mima equation or the convective cell equation in magnetized plasmas are considered. It is shown that two-dimensional perturbations of single vortices in the plane perpendicular to the external magnetic field do not grow in time. It is also argued that three-dimensional perturbations will not lead to an instability of monopoles.

Two-dimensional magnetic recording (TDMR) is a novel recording architecture intended to support densities beyond those of conventional recording systems. The gains from TDMR come primarily from more powerful coding and signal processing algorithms that allow the bits to be packed more tightly on the disk, and yet be retrieved with acceptable error rates. In this paper, we present some preliminary

Kheong Sann Chan; Rathnakumar Radhakrishnan; Kwaku Eason; M. R. Elidrissi; Jim J. Miles; Bane Vasic; Anantha Raman Krishnan

We have developed a two-dimensional, multibeam, binary optic based scanner for transmission/receiver functions for LADAR and other applications under a Small Business Innovation Research (SBIR) contract from Eglin Air Force Base. Multibeam scan provides many unique advantages including: increased data rate for pulsed lasers; increased scan coverage; and programmable broadcasting for optical interconnect applications.

We calculate the properties of dislocation waves in a two-dimensional Coulomb lattice. Hybridization of states with core location at different points in the lattice leads to a substantial lowering of the dislocation energy. At rs=37, this lowering is comparable to the elastic core energy. The mass of the dislocation waves for motion in the direction of the Burgers vector is

For a two-dimensional discrete cosine transform (DCT) image coding system, there have been different assumptions concerning the distributions of the transform coefficients. This paper presents results of distribution tests that indicate that for many images the statistics of the coefficients are best approximated by a Gaussian distribution for the DC coefficient and a Laplacian distribution for the other coefficients. Furthermore,

A Raman chemical mapping investigation was conducted in the visible spectral region using an automated Spex 14018 double monochromator in concert with a moving twodimensional (2D) Hadamard encoding mask. The 2D Hadamard encoding mask combined with conventional Raman spectrometry was used to create chemical maps of heterogeneous liquid and solid samples. The 2D Hadamard encoding mask is based on

R. A. DeVerse; T. A. Mangold; R. M. Hammaker; W. G. Fateley

This report describes the theoretical backgrounds and the algorithns for the calculation of the two-dimensional hydrodynamic potential coefficients of ship-like cross sections in deep water. The close-fit multi-parameter conformal mapping method, used to ...

Usually, an iterative procedure based on two-dimensional rotations is employed to find the varimax solution in factor analysis. A matrix is given where this procedure does not yield the maximum value of the varimax criterion. However, random orthogonal transformations of some matrices and subsequent varimax-rotation using the iterative procedure seem to indicate that usually no local maxima exist.

The main purpose of this paper is to develop a gridless method for unsteady flow simulation. A quadrantal point infilling strategy is developed to generate point and combine clouds of points automatically. A point-moving algorithm is introduced to ensure the clouds of points following the movements of body boundaries. A dual time method for solving the two-dimensional Euler equations in

We study the fractal structure of the surface in two-dimensional quantum Regge calculus by performing Monte Carlo simulation with up to 200,000 triangles. The correct scaling behavior has been observed for the type of loop attached to a baby universe, when the scale-invariant measure is taken as the measure of the link-length integration.

Mobility and diffusion-ordered two-dimensional nuclear magnetic resonance spectroscopy experiments have been developed for the analysis of mixtures. In the mobility -ordered experiments, the full range of positive and negative electrophoretic mobilities is displayed in one dimension and chemical shifts are displayed in the other. A concentric cylindrical tube electrophoresis chamber was designed to reduce the effective pathlength for current and

In ARO STTR Phase 1 program, we have demonstrated the concept and developed a real-time, two-dimensional THz wave imaging system. The THz imaging system uses electro-optic crystals and is capable of time-domain far-infrared spectroscopy across a frequency...

Wind-tunnel experiments and a theoretical model concerning the flow structure and pollutant diffusion over two-dimensional valleys of varying aspect ratio are described and compared. hree model valleys were used, having small, medium, and steep slopes. Measurements of mean and tu...

Off-axis, two-dimensional designs for free electron lasers that maintain correspondence of a light beam with a "synchronous electron" at an optimal transverse radius r>0 to achieve increased beam trapping efficiency and enhanced laser beam wavefront control so as to decrease optical beam diffraction and other deleterious effects.

Prosnitz, Donald (Walnut Creek, CA); Haas, Roger A. (Pleasanton, CA)

Off-axis, two-dimensional designs for free electron lasers are described that maintain correspondence of a light beam with a synchronous electron at an optimal transverse radius r > 0 to achieve increased beam trapping efficiency and enhanced laser beam wavefront control so as to decrease optical beam diffraction and other deleterious effects.

The paper presents a prefiltering technique for antialiasing twodimensional continuous curves which enables the correct handling of the geometry (self-intersections, small loops, cusps, curves with high and small radius of curvature, etc.) using a generic class of filters. Moreover, the technique allows for rendering curves of arbitrary thickness and can be optimally tuned to the bits used for image

A twodimensional model for the chordwise flow near the wing tip of the tilt rotor in hover is presented. The airfoil is represented by vortex panels and the rotor is modeled by doublet panels. The rotor slipstream and the airfoil wake are simulated by fr...

In signal-processing problems where two signals are combined by convolution, homomorphic filtering techniques may be useful. The techniques are applied to the problem when a signal and noise are combined by convolution, and the case of the two-dimensional...

The possibility of using an oblique detonation wave ramjet as a power plant for a hypersonic vehicle is examined. The performance of a model of a twodimensional oblique detonation wave ramjet is analyzed in terms of thrust, lift and fuel consumption.

The microstructure of a two-dimensional cell growth model at each fraction transformed along Rosiwal's line is characterized. Rosiwal's line cut grains and yields chord intercepts. By the use of probability theory we derive the mean number of chord intercepts per unit length as well as the dependence of the distribution density of the length of these chord intercepts on the

We derive a new scale length for two-dimensional (2-D) effects in MOSFETs and discuss its significance. This derivation properly takes into account the difference in permittivity between the Si channel and the gate insulator, and thus permits an accurate understanding of the effects of using insufficiently scaled oxide or thicker higher permittivity gate insulators. The theory shows that the utility

The first determination of non-linear superflow dissipation in a truly two-dimensional helium film is reported. Superfluid velocities were measured using third sound resonance on a closed superfluid film. The predicted power law dissipation function, with exponent of approximately eight, is observed at three temperatures in a film of 0.58 mobile superfluid layers.

The method of multiple scales is used to analyze the wave propagation in two-dimensional hard-walled ducts with sinusoidal walls. For traveling waves, resonance occurs whenever the wall wavenumber is equal to the difference of the wavenumbers of any two duct acoustic modes. The results show that neither of these resonating modes could occur without strongly generating the other.

Two-dimensional (2D) materials, graphene, hexagonal boron nitride (h-BN) and transition metal dichalcogenides (TMD) have been investigated by means of Scanning Transmission Electron Microscopy (STEM), in particular via High Angle Annular Dark Field (HAADF) imaging technique. They are compared in terms of their structure and durability under intense electron beams.

Zan, R.; Ramasse, Q. M.; Jalil, R.; Georgiou, T.; Bangert, U.; Novoselov, K. S.

Interacting orbital degrees of freedom in a Mott insulator are essentially directional and frustrated. In this Letter, the effect of dilution in a quantum-orbital system with this kind of interaction is studied by analyzing a minimal orbital model which we call the two-dimensional quantum compass model. We find that the decrease of the ordering temperature due to dilution is stronger

We present a fast algorithm for two-dimensional median filtering. It is based on storing and updating the gray level histogram of the picture elements in the window. The algorithm is much faster than conventional sorting methods. For a window size of m × n, the computer time required is 0(n).

Properties of two-dimensional O2 adsorbed on graphite are calculated in the extremely low-coverage delta region and for monolayers, with use of pattern-recognition optimization and Monte Carlo techniques. Equilibrium configurations and orientations, orientational order-disorder, melting, and dissociation transitions are predicted at various O2 densities. Phase characteristics, including a plastic crystallite phase, are compared with experiment.

A twodimensional spouted bed laboratory combustor has been designed and constructed with the objective of studying the interaction among the gas flow, particle flow, and combustion. The facility, designed for a maximum thermal power of 20 kW, has a quart...

Two-dimensional materials, e.g. graphene and molybdenum disulfide (MoS2), have attracted great interest in recent years. Identification of the thickness of two-dimensional materials will improve our understanding of their thickness-dependent properties, and also help with scientific research and applications. In this paper, we propose to use optical imaging as a simple, quantitative and universal way to identify the thickness of two-dimensional materials, i.e. mechanically exfoliated graphene, nitrogen-doped chemical vapor deposition grown graphene, graphene oxide and mechanically exfoliated MoS2. The contrast value can easily be obtained by reading the red (R), green (G) and blue (B) values at each pixel of the optical images of the sample and substrate, and this value increases linearly with sample thickness, in agreement with our calculation based on the Fresnel equation. This method is fast, easily performed and no expensive equipment is needed, which will be an important factor for large-scale sample production. The identification of the thickness of two-dimensional materials will greatly help in fundamental research and future applications.

A two-dimensional cellular complex is a partition of a surface into a finite number of elements—faces (open disks), edges (open arcs), and vertices (points). The topology of a cellular complex is the abstract incidence and adjacency relations among its elements. Here we describe a program that, given only the topology of a cellular complex, computes a geometric realization of the

Luis A. P. Lozada; Candido Ferreira Xavier De Mendonça Neto; R. M. Rosi; Jorge Stolfi

A solution of the least-squares two-dimensional phase-unwrapping problem is presented that is simpler to understand and implement than previously published solutions. It extends the phase function to a periodic function using a mirror reflection, and the resulting equation is solved using the Fourier transform

Some problems encountered in the computation of the steady two-dimensional flow of a viscous incompressible fluid past a cylinder in an unbounded field are discussed. They are mainly concerned with the correct satisfaction of the boundary conditions at large distances from the cylinder. It is shown that this is a particularly crucial matter in the case of asymmetrical flows and

It is shown that in the two-dimensional VHP-model the Boltzmann equation for the case of spatially homogeneous, isotropic in velocities distribution functions can always be reduced to a linear second-order differential equation. The general structure of the solution, including the case of slowly decaying distributions nonuniquely determined by initial conditions, is found.

It is shown that in the two-dimensional VHP-model the Boltzmann equation for the case of spatially homogeneous, isotropic in velocities distribution functions can always be reduced to a linear second-order differential equation. The general structure of the solution, including the case of slowly decaying distributions nonuniquely determined by initial conditions, is found.

We demonstrate robust, stable, mobile, quasi-one-dimensional, dark-in-bright dipolar Bose-Einstein-condensate (BEC) solitons with a notch in the central plane formed due to dipolar interaction for repulsive contact interaction. At medium velocity the head-on collision of two such solitons is found to be quasielastic with practically no deformation. A proposal for creating dipolar dark-in-bright solitons in laboratories by phase imprinting is also discussed. A rich variety of such solitons can be formed in dipolar binary BECs, where one can have a dark-in-bright soliton coupled to a bright soliton or two coupled dark-in-bright solitons. The findings are illustrated using numerical simulation in three spatial dimensions by employing realistic interaction parameters for a dipolar 164Dy BEC and a binary 164Dy-162Dy BEC.