NaKV4O9·2H2O: a new 2D magnetic compound with a 1/5-depleted square lattice.
Cui, Meiyan; He, Zhangzhen; Wang, Nannan; Tang, Yingying; Guo, Wenbin; Zhang, Suyun; Wang, Lin; Xiang, Hongping
2016-03-15
A new vanadate compound NaKV4O9·2H2O is successfully synthesized by a conventional hydrothermal method. This compound crystallizes in the monoclinic system with the space group C2/c, showing a typical 2D layered structure built from VO5 pyramids, in which the layers are separated by Na(+), K(+), and H2O. The topology structure of magnetic V(4+) ions shows a quite interesting 1/5-depleted square lattice, which is quite similar to that of a famous low-dimensional quantum spin system CaV4O9. A structural and magnetic comparison confirmed that the title compound may exhibit a more pronounced 2D character with a large spin gap. PMID:26892907
Gao, Song; Fan, Rui Qing; Wang, Xin Ming; Wei, Li Guo; Song, Yang; Du, Xi; Xing, Kai; Wang, Ping; Yang, Yu Lin
2016-07-28
In this work, a rare 2D → 3D single-crystal-to-single-crystal transformation (SCSC) is observed in metal-organic coordination complexes, which is triggered by thermal treatment. The 2D two-fold interpenetrating square lattice layer [Cd(IBA)2]n (1) is irreversibly converted into a 3D four-fold interpenetrating diamond framework {[Cd(IBA)2(H2O)]·2.5H2O}n (2) (HIBA = 4-(1H-imidazol-1-yl)benzoic acid). Consideration is given to these two complexes with different interpenetrating structures and dimensionality, and their influence on photovoltaic properties are studied. Encouraged by the UV-visible absorption and HOMO-LUMO energy states matched for sensitizing TiO2, the two complexes are employed in combination with N719 in dye-sensitized solar cells (DSSCs) to compensate absorption in the ultraviolet and blue-violet region, offset competitive visible light absorption of I3(-) and reducing charge the recombination of injected electrons. After co-sensitization with 1 and 2, the device co-sensitized by 1/N719 and 2/N719 to yield overall efficiencies of 7.82% and 8.39%, which are 19.94% and 28.68% higher than that of the device sensitized only by N719 (6.52%). Consequently, high dimensional interpenetrating complexes could serve as excellent co-sensitizers and have application in DSSCs. PMID:27356177
Skyrmions in square-lattice antiferromagnets
NASA Astrophysics Data System (ADS)
Keesman, Rick; Raaijmakers, Mark; Baerends, A. E.; Barkema, G. T.; Duine, R. A.
2016-08-01
The ground states of square-lattice two-dimensional antiferromagnets with anisotropy in an external magnetic field are determined using Monte Carlo simulations and compared to theoretical analysis. We find a phase in between the spin-flop and spiral phase that shows strong similarity to skyrmions in ferromagnetic thin films. We show that this phase arises as a result of the competition between Zeeman and Dzyaloshinskii-Moriya interaction energies of the magnetic system. Moreover, we find that isolated (anti-)skyrmions are stabilized in finite-sized systems, even at higher temperatures. The existence of thermodynamically stable skyrmions in square-lattice antiferromagnets provides an appealing alternative over skyrmions in ferromagnets as data carriers.
Beam-Plasma Instabilities in a 2D Yukawa Lattice
Kyrkos, S.; Kalman, G. J.; Rosenberg, M.
2009-06-05
We consider a 2D Yukawa lattice of grains, with a beam of other charged grains moving in the lattice plane. In contrast to Vlasov plasmas, where the electrostatic instability excited by the beam is only longitudinal, here both longitudinal and transverse instabilities of the lattice phonons can develop. We determine and compare the transverse and longitudinal growth rates. The growth rate spectrum in wave number space exhibits remarkable gaps where no instability can develop. Depending on the system parameters, the transverse instability can be selectively excited.
Unitary quantum lattice gas representation of 2D quantum turbulence
NASA Astrophysics Data System (ADS)
Zhang, Bo; Vahala, George; Vahala, Linda; Soe, Min
2011-05-01
Quantum vortex structures and energy cascades are examined for two dimensional quantum turbulence (2D QT) using a special unitary evolution algorithm. The qubit lattice gas (QLG) algorithm, is employed to simulate the weakly-coupled Bose-Einstein condensate (BEC) governed by the Gross-Pitaevskii (GP) equation. A parameter regime is uncovered in which, as in 3D QT, there is a very short Poincare recurrence time. This short recurrence time is destroyed as the nonlinear interaction energy is increased. Energy cascades for 2D QT are considered to examine whether 2D QT exhibits the inverse cascades of 2D classical turbulence. In the parameter regime considered, the spectra analysis reveals no such dual cascades---dual cascades being a hallmark of 2D classical turbulence.
Cao, Tun; Wei, Chenwei; Mao, Libang; Li, Yang
2014-01-01
Giant chiroptical responses routinely occur in three dimensional chiral metamaterials (MMs), but their resonance elements with complex subwavelength chiral shapes are challenging to fabricate in the optical region. Here, we propose a new paradigm for obtaining strong circular conversion dichroism (CCD) based on extrinsic 2D chirality in multilayer achiral MMs, showing that giant chiroptical response can be alternatively attained without complex structures. Our structure consists of an array of thin Au squares separated from a continuous Au film by a GaAs dielectric layer, where the Au squares occupy the sites of a rectangular lattice. This structure gives rise to a pronounced extrinsically 2D-chiral effect (CCD) in the mid-infrared (M-IR) region under an oblique incidence, where the 2D-chiral effect is due to the mutual orientation of the Au squares array and the incident light propagation direction; the large magnitude of CCD due to the large difference between left-to-left and right-to-right circularly polarized reflectance conversion efficiencies. PMID:25501766
2-D weighted least-squares phase unwrapping
Ghiglia, Dennis C.; Romero, Louis A.
1995-01-01
Weighted values of interferometric signals are unwrapped by determining the least squares solution of phase unwrapping for unweighted values of the interferometric signals; and then determining the least squares solution of phase unwrapping for weighted values of the interferometric signals by preconditioned conjugate gradient methods using the unweighted solutions as preconditioning values. An output is provided that is representative of the least squares solution of phase unwrapping for weighted values of the interferometric signals.
2-D weighted least-squares phase unwrapping
Ghiglia, D.C.; Romero, L.A.
1995-06-13
Weighted values of interferometric signals are unwrapped by determining the least squares solution of phase unwrapping for unweighted values of the interferometric signals; and then determining the least squares solution of phase unwrapping for weighted values of the interferometric signals by preconditioned conjugate gradient methods using the unweighted solutions as preconditioning values. An output is provided that is representative of the least squares solution of phase unwrapping for weighted values of the interferometric signals. 6 figs.
2D barrier in a superconducting niobium square
Joya, Miryam R. Barba-ortega, J.; Sardella, Edson
2014-11-05
The presence of barriers changes the vortex structure in superconducting Nb square in presence of a uniform applied magnetic field. The Cooper pair configurations in a mesoscopics superconducting square of Nb with a barrier are calculated within the nonlinear Ginzburg Landau equations. We predict the nucleation of multi-vortex states into the sample and a soft entry of the magnetic field inside and around into the barrier. A novel and non-conventional vortex configurations occurs at determined magnetic field.
Optimization and Design of 2d Honeycomb Lattice Photonic Crystal Modulated by Liquid Crystals
NASA Astrophysics Data System (ADS)
Guo, Caihong; Zheng, Jihong; Gui, Kun; Zhang, Menghua; Zhuang, Songlin
2013-12-01
Photonic crystals (PCs) with infiltrating liquid crystals (LCs) have many potential applications because of their ability to continuously modulate the band-gaps. Using the plane-wave expansion method (PWM), we simulate the band-gap distribution of 2D honeycomb lattice PC with different pillar structures (circle, hexagonal and square pillar) and with different filling ratios, considering both when the LC is used as filling pillar material and semiconductors (Si, Ge) are used in the substrate, and when the semiconductors (Si, Ge) are pillar material and the LC is the substrate. Results show that unlike LC-based triangle lattice PC, optimized honeycomb lattice PC has the ability to generate absolute photonic band-gaps for fabricating optical switches. We provide optimization parameters for LC infiltrating honeycomb lattice PC structure based on simulation results and analysis.
Predicting non-square 2D dice probabilities
NASA Astrophysics Data System (ADS)
Pender, G. A. T.; Uhrin, M.
2014-07-01
The prediction of the final state probabilities of a general cuboid randomly thrown onto a surface is a problem that naturally arises in the minds of men and women familiar with regular cubic dice and the basic concepts of probability. Indeed, it was considered by Newton in 1664 (Newton 1967 The Mathematical Papers of Issac Newton vol I (Cambridge: Cambridge University Press) pp 60-1). In this paper we make progress on the 2D problem (which can be realized in 3D by considering a long cuboid, or alternatively a rectangular cross-sectioned dreidel). For the two-dimensional case we suggest that the ratio of the probabilities of landing on each of the two sides is given by \\frac{\\sqrt{{{k}^{2}}+{{l}^{2}}}-k}{\\sqrt{{{k}^{2}}+{{l}^{2}}}-l}\\frac{arctan \\frac{l}{k}}{arctan \\frac{k}{l}} where k and l are the lengths of the two sides. We test this theory both experimentally and computationally, and find good agreement between our theory, experimental and computational results. Our theory is known, from its derivation, to be an approximation for particularly bouncy or ‘grippy’ surfaces where the die rolls through many revolutions before settling. On real surfaces we would expect (and we observe) that the true probability ratio for a 2D die is a somewhat closer to unity than predicted by our theory. This problem may also have wider relevance in the testing of physics engines.
Phases of the infinite U Hubbard model on square lattices.
Liu, Li; Yao, Hong; Berg, Erez; White, Steven R; Kivelson, Steven A
2012-03-23
We apply the density matrix renormalization group to study the phase diagram of the infinite U Hubbard model on 2- to 6-leg ladders. Where the results are largely insensitive to the ladder width, we consider the results representative of the 2D square lattice. We find a fully polarized ferromagnetic Fermi liquid phase when n, the density of electrons per site, is in the range 1>n≳0.800. For n=3/4 we find an unexpected insulating checkerboard phase with coexisting bond-density order with 4 sites per unit cell and block-spin antiferromagnetic order with 8 sites per unit cell. For 3/4>n, all ladders with width >2 have unpolarized ground states. PMID:22540606
Compact polymers on decorated square lattices
NASA Astrophysics Data System (ADS)
Higuchi, Saburo
1999-05-01
A Hamiltonian cycle of a graph is a closed path that visits every vertex once and only once. It serves as a model of a compact polymer on a lattice. I study the number of Hamiltonian cycles, or equivalently the entropy of a compact polymer, on various lattices that are not homogeneous but with a sublattice structure. Estimates for the number are obtained by two methods. One is the saddle point approximation for a field theoretic representation. The other is the numerical diagonalization of the transfer matrix of a fully packed loop model in the zero fugacity limit. In the latter method, several scaling exponents are also obtained.
Quantum interference effects in particle transport through square lattices
NASA Astrophysics Data System (ADS)
Cuansing, E.; Nakanishi, H.
2004-12-01
We study the transport of a quantum particle through square lattices of various sizes by employing the tight-binding Hamiltonian from quantum percolation. Input and output semi-infinite chains are attached to the lattice either by diagonal point-to-point contacts or by a busbar connection. We find resonant transmission and reflection occurring whenever the incident particle’s energy is near an eigenvalue of the lattice alone (i.e., the lattice without the chains attached). We also find the transmission to be strongly dependent on the way the chains are attached to the lattice.
Quantum interference effects in particle transport through square lattices.
Cuansing, E; Nakanishi, H
2004-12-01
We study the transport of a quantum particle through square lattices of various sizes by employing the tight-binding Hamiltonian from quantum percolation. Input and output semi-infinite chains are attached to the lattice either by diagonal point-to-point contacts or by a busbar connection. We find resonant transmission and reflection occurring whenever the incident particle's energy is near an eigenvalue of the lattice alone (i.e., the lattice without the chains attached). We also find the transmission to be strongly dependent on the way the chains are attached to the lattice. PMID:15697469
Scaling of Greenwood Peierls conductance on a diluted square lattice
NASA Astrophysics Data System (ADS)
Schwalm, William; Schmitz, Albert
The modified rectangle lattice of Dhar is a bond-diluted square lattice. The structure is self-similar and finitely ramified, like a fractal. Nevertheless certain discrete Schrödinger equation Green functions for the modified rectangle are known in closed form in the infinite lattice limit and the spectrum is continuous. By standard transfer matrix renormalization methods we present a study scaling properties of the Greenwood Peierls conductance distribution across the lattice with one dimensional lead wires attached as a function of lattice size and of additional disorder of several types.
2D photonic crystals on the Archimedean lattices (tribute to Johannes Kepler (1571 1630))
NASA Astrophysics Data System (ADS)
Gajić, R.; class="cross-out">D. Jovanović,
2008-03-01
Results of our research on 2D Archemedean lattice photonic crystals are presented. This involves the calculations of the band structures, band-gap maps, equifrequency contours and FDTD simulations of electromagnetic propagation through the structures as well as an experimental verification of negative refraction at microwaves. The band-gap dependence on dielectric contrast is established both for dielectric rods in air and air-holes in dielectric materials. A special emphasis is placed on possibilities of negative refraction and left-handedness in these structures. Together with the familiar Archimedean lattices like square, triangular, honeycomb and Kagome' ones, we consider also, the less known, (3 2, 4, 3, 4) (ladybug) and (3, 4, 6, 4) (honeycomb-ring) structures.
Room Temperature Quantum Spin Hall Insulators with a Buckled Square Lattice
NASA Astrophysics Data System (ADS)
Luo, Wei; Xiang, Hongjun
Two-dimensional (2D) topological insulators (TIs), are excellent candidates for coherent spin transport related applications Currently, most known 2D TIs are based on a hexagonal lattice. Here, we propose that there exists the quantum spin Hall effect (QSHE) in a new tight-binding (TB) model for a two-orbital system with the buckled square lattices. We show that the band inversion is due to the hybridization between thepx andpyorbitals, while the spin-orbit coupling (SOC) induced nearest-neighbor effective hopping is responsible for a band gap opening at the Dirac cone. Through performing global structure optimization, we predict a new three-layer quasi-2D (Q2D) structure which has the lowest energy among all structures with the thickness less than 6.0 Å for the BiF system. It is identified to be a Q2D TI with a large band gap (0.69 eV). The electronic states of the Q2D BiF system near the Fermi level are mainly contributed by the middle Bi square lattice, which are sandwiched by two inert BiF2 layers. This is beneficial since the interaction between a substrate and the Q2D material may not change the topological properties of the system, as we demonstrate in the case of the NaF substrate. Our analysis shows that the low-energy physics of the Q2D BiF system can be qualitatively described by our newly proposed two-orbital TB model. Our study not only predicts a Q2D QSH insulator for realistic room temperature (RT) applications, but also provides a new lattice system for engineering topological states such as quantum anomalous Hall effect.
Enumeration of directed site animals on the decorated square lattices
NASA Astrophysics Data System (ADS)
Ali, Agha Afsar
1994-01-01
We study the problem of directed site lattice animals on decorated square lattice using its equivalence to the probabilistic cellular automata. By mapping this problem to a special case of a triangular Ising model in external field, we prove that the generating function of number of animals satisfy a quadratic equation, as was conjectured by Andrew Conway. The coupling constants of the latter satisfy the disorder condition, and it reduces to a problem already solved by Jaekel and Maillard. We also establish a connection of this problem with the problem of anisotropic directed bond percolation on a square lattice.
Fractional excitations in the square lattice quantum antiferromagnet
Christensen, N. B.; Nilsen, G. J.; Tregenna-Piggott, P.; Perring, T. G.; Enderle, M.; McMorrow, D. F.; Ivanov, D. A.; Rønnow, H. M.
2014-01-01
Quantum magnets have occupied the fertile ground between many-body theory and low-temperature experiments on real materials since the early days of quantum mechanics. However, our understanding of even deceptively simple systems of interacting spins-1/2 is far from complete. The quantum square-lattice Heisenberg antiferromagnet (QSLHAF), for example, exhibits a striking anomaly of hitherto unknown origin in its magnetic excitation spectrum. This quantum effect manifests itself for excitations propagating with the specific wave vector (π, 0). We use polarized neutron spectroscopy to fully characterize the magnetic fluctuations in the metal-organic compound CFTD, a known realization of the QSLHAF model. Our experiments reveal an isotropic excitation continuum at the anomaly, which we analyse theoretically using Gutzwiller-projected trial wavefunctions. The excitation continuum is accounted for by the existence of spatially-extended pairs of fractional S=1/2 quasiparticles, 2D analogues of 1D spinons. Away from the anomalous wave vector, these fractional excitations are bound and form conventional magnons. Our results establish the existence of fractional quasiparticles in the high-energy spectrum of a quasi-two-dimensional antiferromagnet, even in the absence of frustration. PMID:25729400
A note on the limitations of lattice least squares
NASA Technical Reports Server (NTRS)
Gillis, J. T.; Gustafson, C. L.; Mcgraw, G. A.
1988-01-01
This paper quantifies the known limitation of lattice least squares to ARX models in terms of the dynamic properties of the system being modeled. This allows determination of the applicability of lattice least squares in a given situation. The central result is that an equivalent ARX model exists for an ARMAX system if and only if the ARMAX system has no transmission zeros from the noise port to the output port. The technique used to prove this fact is a construction using the matrix fractional description of the system. The final section presents two computational examples.
Lattice Boltzmann Equation On a 2D Rectangular Grid
NASA Technical Reports Server (NTRS)
Bouzidi, MHamed; DHumieres, Dominique; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean invariance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions; (b) Poiseuille flow with an arbitrasy inclined angle with respect to the lattice orientation: and (c) a cylinder &symmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations.
Analysis of the antiferromagnetic phase transitions of the 2D Kondo lattice
NASA Astrophysics Data System (ADS)
Jones, Barbara
2010-03-01
The Kondo lattice continues to present an interesting and relevant challenge, with its interactions between Kondo, RKKY, and coherent order. We present our study[1] of the antiferromagnetic quantum phase transitions of a 2D Kondo-Heisenberg square lattice. Starting from the nonlinear sigma model as a model of antiferromagnetism, we carry out a renormalization group analysis of the competing Kondo-RKKY interaction to one-loop order in an ɛ-expansion. We find a new quantum critical point (QCP) strongly affected by Kondo fluctuations. Near this QCP, there is a breakdown of hydrodynamic behavior, and the spin waves are logarithmically frozen out. The renormalization group results allow us to propose a new phase diagram near the antiferromagnetic fixed point of this 2D Kondo lattice model. The T=0 phase diagram contains four phases separated by a tetracritical point, the new QCP. For small spin fluctuations, we find a stable local magnetic moment antiferromagnet. For stronger coupling, region II is a metallic quantum disordered paramagnet. We find in region III a paramagnetic phase driven by Kondo interactions, with possible ground states of a heavy fermion liquid or a Kondo driven spin-liquid. The fourth phase is a spiral phase, or a large-Fermi-surface antiferromagnetic phase. We will describe these phases in more detail, including possible experimental confirmation of the spiral phase. The existence of the tetracritical point found here would be expected to affect the phase diagram at finite temperatures as well. In addition, It is hoped that these results, and particularly the Kondo interaction paramagnetic phase, will serve to bridge to solutions starting from the opposite limit, of a Kondo effect leading to a heavy fermion ground state. Work in collaboration with T. Tzen Ong. [4pt] [1] T. Ong and B. A. Jones, Phys. Rev. Lett. 103, 066405 (2009).
Dipolar Fermions in Quasi-Two-Dimensional Square Lattice
NASA Astrophysics Data System (ADS)
Lai, Chen-Yen; Tsai, Shan-Wen
2013-03-01
Motivated by recent experimental realization of quantum degenerate dipolar Fermi gas, we study a system of ultralcold single- and two-species polar fermions in a double layer two-dimensional square lattice. The long-range anisotropic nature of dipole-dipole interaction has shown a rich phase diagram on a two dimensional square lattice*. We investigate how the interlayer coupling affects the monolayer system. Our study focuses on the regime where the fermions are closed to half-filling, which is when lattice effects play an important role. We find several correlated phases by using a functional renormalization group technique, which also provides estimates for the critical temperature of each phase. [*] S. G. Bhongale et. al. arXiv:1209.2671 and Phys. Rev. Lett. 108 145301 (2012).
Lattice Formulation of 2D SQCD with exact supersymmetry
Sugino, Fumihiko
2008-11-23
We construct a lattice model for two-dimensional N = (2,2) supersymmetric QCD (SQCD), with the matter multiplets belonging to the fundamental or anti-fundamental representation of the gauge group U(N) or SU(N). The construction is based on the topological field theory (twisted supercharge) formulation and exactly preserves one supercharge. In order to avoid the species doublers of the matter multiplets, we introduce the Wilson terms and the model is defined for the case of the number of the fundamental matters (n{sub +}) equal to that of the anti-fundamental matters (n{sub -}). If some of the matter multiplets decouple from the theory by sending the corresponding anti-holomorphic twisted masses to the infinity, we can analyze the general n{sub +}{ne}n{sub -} case, although the lattice model is defined for n{sub +} = n{sub -}. By computing the anomaly of the U(1){sub A} R-symmetry in the lattice perturbation, we see that the decoupling is achieved and the anomaly for n{sub +}{ne}n{sub -} is correctly obtained.
Dynamical polarizability of the 2D pseudospin-1 dice lattice
NASA Astrophysics Data System (ADS)
Malcolm, John; Nicol, Elisabeth
The two-dimensional dice lattice is composed of three triangular sublattices whose low-energy excitation spectrum consists of Dirac-Weyl fermions with pseudospin-1. The energy dispersion has two Dirac cones, like the pseudospin-1/2 two-triangular-sublattice graphene, with an additional third band exactly at zero energy. We present theoretical results for the electronic dynamical polarization function in the material. This is a fundamental entity in many-body physics, renormalizing the Coulomb interaction through the dielectric function. From the polarization function we also obtain the Lindhard function, the plasmon branch, and can discuss other screening effects. These are constrasted with those of graphene.
Quantum spin Hall phase in 2D trigonal lattice.
Wang, Z F; Jin, Kyung-Hwan; Liu, Feng
2016-01-01
The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Here we show that a minimal basis of three orbitals (s, px, py) is required to produce a QSH phase via nearest-neighbour hopping in a two-dimensional trigonal lattice. Tight-binding model analyses and calculations show that the QSH phase arises from a spin-orbit coupling (SOC)-induced s-p band inversion or p-p bandgap opening at Brillouin zone centre (Γ point), whose topological phase diagram is mapped out in the parameter space of orbital energy and SOC. Remarkably, based on first-principles calculations, this exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ∼73 meV, facilitating the possible room-temperature measurement. Our results will extend the search for substrate supported QSH materials to new lattice and orbital types. PMID:27599580
On the squared eigenfunction symmetry of the Toda lattice hierarchy
NASA Astrophysics Data System (ADS)
Cheng, Jipeng; He, Jingsong
2013-02-01
The squared eigenfunction symmetry for the Toda lattice hierarchy is explicitly constructed in the form of the Kronecker product of the vector eigenfunction and the vector adjoint eigenfunction, which can be viewed as the generating function for the additional symmetries when the eigenfunction and the adjoint eigenfunction are the wave function and the adjoint wave function, respectively. Then after the Fay-like identities and some important relations about the wave functions are investigated, the action of the squared eigenfunction related to the additional symmetry on the tau function is derived, which is equivalent to the Adler-Shiota-van Moerbeke formulas.
NASA Astrophysics Data System (ADS)
Volčko, Dušan; Quader, Khandker F.
2012-12-01
We consider fermions on a 2D square lattice with a finite-range pairing interaction, and obtain signatures for unconventional pair-symmetry states, dx2-y2 and extended-s (s*), in the Bardeen-Cooper-Schrieffer-Bose-Einstein Condensation crossover region. We find that the fermion momentum distribution function, vk2, the ratio of the Bogoliubov coefficients, vk/uk, and the Fourier transform of vk2 are strikingly different for d and s* symmetries in the crossover region. The chemical potential and the gap functions for both pairing symmetries show several interesting features as a function of interaction. Fermionic atoms in 2D optical lattices may provide a way to test these signatures. We discuss current generation cold atom experiments that may be utilized.
A transfer-matrix study of directed lattice animals and directed percolation on a square lattice
NASA Astrophysics Data System (ADS)
Knežević, Dragica; Knežević, Milan
2016-03-01
We studied the large-scale properties of directed lattice animals and directed percolation on a square lattice. Using a transfer-matrix approach on strips of finite widths, we generated relatively long sequences of estimates for effective values of critical fugacity, percolation threshold and correlation length critical exponents. We applied two different extrapolation methods to obtain estimates for infinite systems. The precision of our final estimates is comparable to (or better than) the precision of the best currently available results.
Highly Compact Circulators in Square-Lattice Photonic Crystal Waveguides
Jin, Xin; Ouyang, Zhengbiao; Wang, Qiong; Lin, Mi; Wen, Guohua; Wang, Jingjing
2014-01-01
We propose, demonstrate and investigate highly compact circulators with ultra-low insertion loss in square-lattice- square-rod-photonic-crystal waveguides. Only a single magneto- optical square rod is required to be inserted into the cross center of waveguides, making the structure very compact and ultra efficient. The square rods around the center defect rod are replaced by several right-angled-triangle rods, reducing the insertion loss further and promoting the isolations as well. By choosing a linear-dispersion region and considering the mode patterns in the square magneto-optical rod, the operating mechanism of the circulator is analyzed. By applying the finite-element method together with the Nelder-Mead optimization method, an extremely low insertion loss of 0.02 dB for the transmitted wave and ultra high isolation of 46 dB∼48 dB for the isolated port are obtained. The idea presented can be applied to build circulators in different wavebands, e.g., microwave or Tera-Hertz. PMID:25415417
Highly compact circulators in square-lattice photonic crystal waveguides.
Jin, Xin; Ouyang, Zhengbiao; Wang, Qiong; Lin, Mi; Wen, Guohua; Wang, Jingjing
2014-01-01
We propose, demonstrate and investigate highly compact circulators with ultra-low insertion loss in square-lattice- square-rod-photonic-crystal waveguides. Only a single magneto- optical square rod is required to be inserted into the cross center of waveguides, making the structure very compact and ultra efficient. The square rods around the center defect rod are replaced by several right-angled-triangle rods, reducing the insertion loss further and promoting the isolations as well. By choosing a linear-dispersion region and considering the mode patterns in the square magneto-optical rod, the operating mechanism of the circulator is analyzed. By applying the finite-element method together with the Nelder-Mead optimization method, an extremely low insertion loss of 0.02 dB for the transmitted wave and ultra high isolation of 46 dB∼48 dB for the isolated port are obtained. The idea presented can be applied to build circulators in different wavebands, e.g., microwave or Tera-Hertz. PMID:25415417
Birefringent breakup of Dirac fermions on a square optical lattice
Kennett, Malcolm P.; Komeilizadeh, Nazanin; Kaveh, Kamran; Smith, Peter M.
2011-05-15
We introduce a lattice model for fermions in a spatially periodic magnetic field that also has spatially periodic hopping amplitudes. We discuss how this model might be realized with cold atoms in an artificial magnetic field on a square optical lattice. When there is an average flux of half a flux quantum per plaquette, the spectrum of low-energy excitations can be described by massless Dirac fermions in which the usually doubly degenerate Dirac cones split into cones with different ''speeds of light.'' These gapless birefringent Dirac fermions arise because of broken chiral symmetry in the kinetic energy term of the effective low-energy Hamiltonian. We characterize the effects of various perturbations to the low-energy spectrum, including staggered potentials, interactions, and domain-wall topological defects.
Square lattice honeycomb reactor for space power and propulsion
NASA Astrophysics Data System (ADS)
Gouw, Reza; Anghaie, Samim
2000-01-01
The most recent nuclear design study at the Innovative Nuclear Space Power and Propulsion Institute (INSPI) is the Moderated Square-Lattice Honeycomb (M-SLHC) reactor design utilizing the solid solution of ternary carbide fuels. The reactor is fueled with solid solution of 93% enriched (U,Zr,Nb)C. The square-lattice honeycomb design provides high strength and is amenable to the processing complexities of these ultrahigh temperature fuels. The optimum core configuration requires a balance between high specific impulse and thrust level performance, and maintaining the temperature and strength limits of the fuel. The M-SLHC design is based on a cylindrical core that has critical radius and length of 37 cm and 50 cm, respectively. This design utilized zirconium hydrate to act as moderator. The fuel sub-assemblies are designed as cylindrical tubes with 12 cm in diameter and 10 cm in length. Five fuel subassemblies are stacked up axially to form one complete fuel assembly. These fuel assemblies are then arranged in the circular arrangement to form two fuel regions. The first fuel region consists of six fuel assemblies, and 18 fuel assemblies for the second fuel region. A 10-cm radial beryllium reflector in addition to 10-cm top axial beryllium reflector is used to reduce neutron leakage from the system. To perform nuclear design analysis of the M-SLHC design, a series of neutron transport and diffusion codes are used. To optimize the system design, five axial regions are specified. In each axial region, temperature and fuel density are varied. The axial and radial power distributions for the system are calculated, as well as the axial and radial flux distributions. Temperature coefficients of the system are also calculated. A water submersion accident scenario is also analyzed for these systems. Results of the nuclear design analysis indicate that a compact core can be designed based on ternary uranium carbide square-lattice honeycomb fuel, which provides a relatively
Antiferromagnetic majority voter model on square and honeycomb lattices
NASA Astrophysics Data System (ADS)
Sastre, Francisco; Henkel, Malte
2016-02-01
An antiferromagnetic version of the well-known majority voter model on square and honeycomb lattices is proposed. Monte Carlo simulations give evidence for a continuous order-disorder phase transition in the stationary state in both cases. Precise estimates of the critical point are found from the combination of three cumulants, and our results are in good agreement with the reported values of the equivalent ferromagnetic systems. The critical exponents 1 / ν, γ / ν and β / ν were found. Their values indicate that the stationary state of the antiferromagnetic majority voter model belongs to the Ising model universality class.
Grid Cell Responses in 1D Environments Assessed as Slices through a 2D Lattice.
Yoon, KiJung; Lewallen, Sam; Kinkhabwala, Amina A; Tank, David W; Fiete, Ila R
2016-03-01
Grid cells, defined by their striking periodic spatial responses in open 2D arenas, appear to respond differently on 1D tracks: the multiple response fields are not periodically arranged, peak amplitudes vary across fields, and the mean spacing between fields is larger than in 2D environments. We ask whether such 1D responses are consistent with the system's 2D dynamics. Combining analytical and numerical methods, we show that the 1D responses of grid cells with stable 1D fields are consistent with a linear slice through a 2D triangular lattice. Further, the 1D responses of comodular cells are well described by parallel slices, and the offsets in the starting points of the 1D slices can predict the measured 2D relative spatial phase between the cells. From these results, we conclude that the 2D dynamics of these cells is preserved in 1D, suggesting a common computation during both types of navigation behavior. PMID:26898777
Bak–Tang–Wiesenfeld model on the square site-percolation lattice
NASA Astrophysics Data System (ADS)
Najafi, M. N.
2016-08-01
The Bak–Tang–Wiesenfeld (BTW) model is considered on the site-diluted square lattice, tuned by the occupancy probability p. Various statistical observables of the avalanches are analyzed in terms of p, e.g. the fractal dimension of their exterior frontiers, gyration radius, loop lengths and Green’s function. The model exhibits critical behavior for all amounts of p, and the exponents of the statistical observables are analyzed. We find a distinct universality class at p={p}c, which is unstable towards a p = 1 (BTW) fixed point. This universality class displays some common features such as a two-dimensional (2D) Ising universality class, e.g. the fractal dimension of loops in the thermodynamic limit is {D}Fp={pc}=1.38\\mp 0.01 which is compatible with the fractal dimension of geometrical spin clusters of the 2D critical Ising model (with {D}F{{Ising}}=\\tfrac{11}{8}).
Duality and Fisher zeros in the two-dimensional Potts model on a square lattice
NASA Astrophysics Data System (ADS)
Astorino, Marco; Canfora, Fabrizio
2010-05-01
A phenomenological approach to the ferromagnetic two-dimensional (2D) Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the q -state Potts model. The duality symmetry of the 2D Potts model together with the known results on its critical exponent α allows us to fix consistently the details of the proposed expression for the free energy. The agreement of the analytic ansatz with numerical data in the q=3 case is very good at high and low temperatures as well as at the critical point. It is shown that the q>4 cases naturally fit into the same scheme and that one should also expect a good agreement with numerical data. The limiting q=4 case is shortly discussed.
Pair interaction energy for a 12-electron 2D square Quantum Dot.
NASA Astrophysics Data System (ADS)
Nissenbaum, Daniel; Barbiellini, Bernardo; Bansil, Arun
2004-03-01
We have investigated a system of 12 electrons enclosed in a 2D square well representing a quantum dot. We employ a Jastrow-type wavefunction with Slater determinants and optimize the Jastrow parameter using the variational Monte Carlo method. We use the Metropolis algorithm to select a large distribution of configuration points and to perform a relatively noiseless calculation of the radial distribution function and to obtain insight into the contrast between the Fermi hole for the same-spin electrons and the Coulomb hole for the opposite-spin electrons. The calculated pair interaction energy provides a handle for constructing a model Hamiltonian useful for the study of spontaneous spin magnetization of the system. Work supported in part by the USDOE.
Dynamics and hysteresis in square lattice artificial spin ice
NASA Astrophysics Data System (ADS)
Wysin, G. M.; Moura-Melo, W. A.; Mól, L. A. S.; Pereira, A. R.
2013-04-01
Dynamical effects under geometrical frustration are considered in a model for artificial spin ice on a square lattice in two dimensions. Each island of the spin ice has a three-component Heisenberg-like dipole moment subject to shape anisotropies that influence its direction. The model has real dynamics, including rotation of the magnetic degrees of freedom, going beyond the Ising-type models of spin ice. The dynamics is studied using a Langevin equation solved via a second-order Heun algorithm. Thermodynamic properties such as the specific heat are presented for different couplings. A peak in specific heat is related to a type of melting-like phase transition present in the model. Hysteresis in an applied magnetic field is calculated for model parameters where the system is able to reach thermodynamic equilibrium.
Frustrated square lattice Heisenberg model and magnetism in Iron Telluride
NASA Astrophysics Data System (ADS)
Zaliznyak, Igor; Xu, Zhijun; Gu, Genda; Tranquada, John; Stone, Matthew
2011-03-01
We have measured spin excitations in iron telluride Fe1.1Te, the parent material of (1,1) family of iron-based superconductors. It has been recognized that J1-J2-J3 frustrated Heisenberg model on a square lattice might be relevant for the unusual magnetism and, perhaps, the superconductivity in cuprates [1,2]. Recent neutron scattering measurements show that similar frustrated model might also provide reasonable account for magnetic excitations in iron pnictide materials. We find that it also describes general features of spin excitations in FeTe parent compound observed in our recent neutron measurements, as well as in those by other groups. Results imply proximity of magnetic system to the limit of extreme frustration. Selection of spin ground state under such conditions could be driven by weak extrinsic interactions, such as lattice distortion, or strain. Consequently, different nonuniversal types of magnetic order could arise, both commensurate and incommensurate. These are not necessarily intrinsic to an ideal J1-J2-J3 model, but might result from lifting of its near degeneracy by weak extrinsic perturbations.
Thermodynamic properties of magnetic strings on a square lattice
NASA Astrophysics Data System (ADS)
Mol, Lucas; Oliveira, Denis Da Mata; Bachmann, Michael
2015-03-01
In the last years, spin ice systems have increasingly attracted attention by the scientific community, mainly due to the appearance of collective excitations that behave as magnetic monopole like particles. In these systems, geometrical frustration induces the appearance of degenerated ground states characterized by a local energy minimization rule, the ice rule. Violations of this rule were shown to behave like magnetic monopoles connected by a string of dipoles that carries the magnetic flux from one monopole to the other. In order to obtain a deeper knowledge about the behavior of these excitations we study the thermodynamics of a kind of magnetic polymer formed by a chain of magnetic dipoles in a square lattice. This system is expected to capture the main properties of monopole-string excitations in the artificial square spin ice. It has been found recently that in this geometry the monopoles are confined, but the effective string tension is reduced by entropic effects. To obtain the thermodynamic properties of the strings we have exactly enumerated all possible string configurations of a given length and used standard statistical mechanics analysis to calculate thermodynamic quantities. We show that the low-temperature behavior is governed by strings that satisfy ice rules. Financial support from FAPEMIG and CNPq (Brazilian agencies) are gratefully acknowledged.
NASA Astrophysics Data System (ADS)
Liu, Rongqiang; Zhao, Haojiang; Zhang, Yingying; Guo, Honghwei; Deng, Zongquan
2015-12-01
The plane wave expansion (PWE) method is used to calculate the band gaps of two-dimensional (2D) phononic crystals (PCs) with a hybrid square-like (HSL) lattice. Band structures of both XY-mode and Z-mode are calculated. Numerical results show that the band gaps between any two bands could be maximized by altering the radius ratio of the inclusions at different positions. By comparing with square lattice and bathroom lattice, the HSL lattice is more efficient in creating larger gaps.
NASA Astrophysics Data System (ADS)
Lee, Kang Il; Kang, Hwi Suk; Yoon, Suk Wang
2016-04-01
The present work reports a combined experimental and theoretical study on the acoustic band gaps in a two-dimensional (2D) phononic crystal (PC) consisting of periodic square arrays of stainless-steel cylinders with diameters of 1.0 mm and a lattice constant of 1.5 mm in water. The theoretical band structure of the 2D PC was calculated along the ΓX direction of the first Brillouin zone. The transmission and the reflection coefficients were obtained both experimentally and theoretically along the ΓX direction of the 2D PC. The 2D PC exhibited 5 band gaps at frequencies below 2.0 MHz, with the first Bragg gap being around a frequency of 0.5 MHz. To understand the band gaps in the 2D PC, we calculated the acoustic pressure fields at specific frequencies of interest for normal incidence, and we explained them from the perspective of acoustic diffraction gratings.
The effect of freestream turbulence on the wake of a 2D square prism
NASA Astrophysics Data System (ADS)
Lander, Daniel; Letchford, Chris; Amitay, Michael; Kopp, Gregory
2015-11-01
The effect of freestream turbulence (FST) on a 2 D square prism is investigated at ReD = 5 . 0 ×104 using long duration Time Resolved Particle Image Velocimetry (TR-PIV). Increasing the FST results in alterations to the flow field in the shear-layer and base regions and the origins of the apparent differences are discussed. The triple decomposition technique is employed to disintegrate changes attributable to the coherent and random components of the global wake stresses. In the presence of FST the vortex formation process is altered due to an increase reattachment time of the separating shear-layers on the trailing edge of the prism. This is accompanied by a transposition of the von-Kármán vorticies observed in the phase averaged flow field; a feature complementary to the narrowing and lengthening of the steady wake commonly observed in the literature. We wish to acknowledge financial support provided by the NSF under grant CMMI-1200987.
Influence of lattice defects on the ferromagnetic resonance behaviour of 2D magnonic crystals
NASA Astrophysics Data System (ADS)
Manzin, Alessandra; Barrera, Gabriele; Celegato, Federica; Coïsson, Marco; Tiberto, Paola
2016-02-01
This paper studies, from a modelling point of view, the influence of randomly distributed lattice defects (non-patterned areas and variable hole size) on the ferromagnetic resonance behaviour and spin wave mode profiles of 2D magnonic crystals based on Ni80Fe20 antidot arrays with hexagonal lattice. A reference sample is first defined via the comparison of experimental and simulated hysteresis loops and magnetoresistive curves of patterned films, prepared by self-assembly of polystyrene nanospheres. Second, a parametric analysis of the dynamic response is performed, investigating how edge, quasi-uniform and localized modes are affected by alterations of the lattice geometry and bias field amplitude. Finally, some results about the possible use of magnetic antidot arrays in frequency-based sensors for magnetic bead detection are presented, highlighting the need for an accurate control of microstructural features.
Influence of lattice defects on the ferromagnetic resonance behaviour of 2D magnonic crystals.
Manzin, Alessandra; Barrera, Gabriele; Celegato, Federica; Coïsson, Marco; Tiberto, Paola
2016-01-01
This paper studies, from a modelling point of view, the influence of randomly distributed lattice defects (non-patterned areas and variable hole size) on the ferromagnetic resonance behaviour and spin wave mode profiles of 2D magnonic crystals based on Ni80Fe20 antidot arrays with hexagonal lattice. A reference sample is first defined via the comparison of experimental and simulated hysteresis loops and magnetoresistive curves of patterned films, prepared by self-assembly of polystyrene nanospheres. Second, a parametric analysis of the dynamic response is performed, investigating how edge, quasi-uniform and localized modes are affected by alterations of the lattice geometry and bias field amplitude. Finally, some results about the possible use of magnetic antidot arrays in frequency-based sensors for magnetic bead detection are presented, highlighting the need for an accurate control of microstructural features. PMID:26911336
Influence of lattice defects on the ferromagnetic resonance behaviour of 2D magnonic crystals
Manzin, Alessandra; Barrera, Gabriele; Celegato, Federica; Coïsson, Marco; Tiberto, Paola
2016-01-01
This paper studies, from a modelling point of view, the influence of randomly distributed lattice defects (non-patterned areas and variable hole size) on the ferromagnetic resonance behaviour and spin wave mode profiles of 2D magnonic crystals based on Ni80Fe20 antidot arrays with hexagonal lattice. A reference sample is first defined via the comparison of experimental and simulated hysteresis loops and magnetoresistive curves of patterned films, prepared by self-assembly of polystyrene nanospheres. Second, a parametric analysis of the dynamic response is performed, investigating how edge, quasi-uniform and localized modes are affected by alterations of the lattice geometry and bias field amplitude. Finally, some results about the possible use of magnetic antidot arrays in frequency-based sensors for magnetic bead detection are presented, highlighting the need for an accurate control of microstructural features. PMID:26911336
NASA Astrophysics Data System (ADS)
Woods, Justin; Bhat, Vinayak; Farmer, Barry; Sklenar, Joseph; Teipel, Eric; Ketterson, John; Hastings, J. Todd; de Long, Lance
2015-03-01
Artificial spin ice (ASI) systems are composed of nanoscale ferromagnetic segments whose shape anisotropy dictates they behave as mesoscopic Ising spins. Most ASI have segments patterned on periodic lattices and a single vertex topology. We have continuously distorted 2D honeycomb and square lattices such that the pattern vertex spacings follow a Fibonacci chain sequence along primitive lattice directions. The Fibonacci distortion is related to the aperiodic translational symmetry of 2D artificial quasicrystals1 that cannot be viewed as continuous distortions of periodic lattices due to their forbidden (e.g., fivefold) rotational symmetries. In contrast, Fibonacci distortions of 2D periodic lattices can be ``turned on'' by control of the ratio of two lattice parameters d1 and d2. Distortions alter film segments such that pattern vertices are no longer equivalent and traditional spin ice rules are no longer strictly valid. We have performed OOMMF simulations of magnetization reversal for samples having different levels of distortion, and found the magnetic reversal to be dramatically slowed by small distortions (d1/d2 ~ 1). Research at Kentucky is supported by U.S. DoE Grant DE-FG02-97ER45653 and NSF Grant EPS-0814194.
SIMULATIONS OF 2D AND 3D THERMOCAPILLARY FLOWS BY A LEAST-SQUARES FINITE ELEMENT METHOD. (R825200)
Numerical results for time-dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank-Nicolson scheme for time integration, Newton's method for linearization, and a least-squares finite element method, together with a matri...
Light trapping at Dirac point in 2D triangular Archimedean-like lattice photonic crystal.
Mao, Qiuping; Xie, Kang; Hu, Lei; Li, Qian; Zhang, Wei; Jiang, Haiming; Hu, Zhijia; Wang, Erlei
2016-04-20
Optical cavities and waveguides are critical parts of modern optical devices. Traditionally, optical cavities and waveguides rely on photonic bandgaps, or total internal reflection, to achieve light trapping. It has been reported that a novel light trapping, which exists in triangular and honeycomb lattices, is attributed to the so-called Dirac point. Our analysis reveals that 2D triangular Archimedean-like lattice photonic crystals also can support this Dirac mode with similar characteristics. This is a new type of localized mode with a different algebraic field profile at a different specified Dirac frequency, which is also beyond any complete photonic bandgap. The new wave localization has different features and can be applied to the design of new optical devices. PMID:27140119
Self-Assembly of Cubes into 2D Hexagonal and Honeycomb Lattices by Hexapolar Capillary Interactions
NASA Astrophysics Data System (ADS)
Soligno, Giuseppe; Dijkstra, Marjolein; van Roij, René
2016-06-01
Particles adsorbed at a fluid-fluid interface induce capillary deformations that determine their orientations and generate mutual capillary interactions which drive them to assemble into 2D ordered structures. We numerically calculate, by energy minimization, the capillary deformations induced by adsorbed cubes for various Young's contact angles. First, we show that capillarity is crucial not only for quantitative, but also for qualitative predictions of equilibrium configurations of a single cube. For a Young's contact angle close to 90°, we show that a single-adsorbed cube generates a hexapolar interface deformation with three rises and three depressions. Thanks to the threefold symmetry of this hexapole, strongly directional capillary interactions drive the cubes to self-assemble into hexagonal or graphenelike honeycomb lattices. By a simple free-energy model, we predict a density-temperature phase diagram in which both the honeycomb and hexagonal lattice phases are present as stable states.
Self-Assembly of Cubes into 2D Hexagonal and Honeycomb Lattices by Hexapolar Capillary Interactions.
Soligno, Giuseppe; Dijkstra, Marjolein; van Roij, René
2016-06-24
Particles adsorbed at a fluid-fluid interface induce capillary deformations that determine their orientations and generate mutual capillary interactions which drive them to assemble into 2D ordered structures. We numerically calculate, by energy minimization, the capillary deformations induced by adsorbed cubes for various Young's contact angles. First, we show that capillarity is crucial not only for quantitative, but also for qualitative predictions of equilibrium configurations of a single cube. For a Young's contact angle close to 90°, we show that a single-adsorbed cube generates a hexapolar interface deformation with three rises and three depressions. Thanks to the threefold symmetry of this hexapole, strongly directional capillary interactions drive the cubes to self-assemble into hexagonal or graphenelike honeycomb lattices. By a simple free-energy model, we predict a density-temperature phase diagram in which both the honeycomb and hexagonal lattice phases are present as stable states. PMID:27391753
Identifying topological edge states in 2D optical lattices using light scattering
NASA Astrophysics Data System (ADS)
Goldman, Nathan; Beugnon, Jérôme; Gerbier, Fabrice
2013-02-01
We recently proposed in a Letter [Phys. Rev. Lett. 108, 255303] a novel scheme to detect topological edge states in an optical lattice, based on a generalization of Bragg spectroscopy. The scope of the present article is to provide a more detailed and pedagogical description of the system - the Hofstadter optical lattice - and probing method. We first show the existence of topological edge states, in an ultra-cold gas trapped in a 2D optical lattice and subjected to a synthetic magnetic field. The remarkable robustness of the edge states is verified for a variety of external confining potentials. Then, we describe a specific laser probe, made from two lasers in Laguerre-Gaussian modes, which captures unambiguous signatures of these edge states. In particular, the resulting Bragg spectra provide the dispersion relation of the edge states, establishing their chiral nature. In order to make the Bragg signal experimentally detectable, we introduce a "shelving method", which simultaneously transfers angular momentum and changes the internal atomic state. This scheme allows to directly visualize the selected edge states on a dark background, offering an instructive view on topological insulating phases, not accessible in solid-state experiments.
Buckling in 2D periodic, soft and porous structures: effect of pore shape and lattice pattern
NASA Astrophysics Data System (ADS)
Shan, Sicong; Bertoldi, Katia; Shim, Jongmin; Overvelde, Johannes T. B.; Kang, Sung Hoon
2013-03-01
Adaptive structures allowing dramatic shape changes offer unique opportunities for the design of responsive and reconfigurable devices. Traditional morphing and foldable structures with stiff structural members and mechanical joints remains a challenge in manufacturing at small length scales. Soft structures where the folding mechanisms are induced by a mechanical instability represent a new class of novel adaptive materials which can be easily manufactured over a wide range of length scales. More specifically, soft porous structures with deliberately designed patterns can significantly change their architecture in response to diverse stimuli, opening avenues for reconfigurable devices that change their shapes to respond to their environment. While so far only two-dimensional periodic porous structures with circular holes arranged on a square or triangular lattice have been investigated, here we investigate both numerically and experimentally the effects of pore shape and lattice pattern on the macroscopic properties of the structures. Our results show that both the pore shape and lattice pattern can be used to effectively design desired materials and pave the way for the development of a new class of soft, active and reconfigurable devices over a wide range of length scales.
Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices
NASA Astrophysics Data System (ADS)
Piñeros, William D.; Baldea, Michael; Truskett, Thomas M.
2016-08-01
Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability.
Exact ground state for the four-electron problem in a 2D finite honeycomb lattice
NASA Astrophysics Data System (ADS)
Trencsényi, Réka; Glukhov, Konstantin; Gulácsi, Zsolt
2014-07-01
Working in a subspace with dimensionality much smaller than the dimension of the full Hilbert space, we deduce exact four-particle ground states in 2D samples containing hexagonal repeat units and described by Hubbard type of models. The procedure identifies first a small subspace ? in which the ground state ? is placed, than deduces ? by exact diagonalization in ?. The small subspace is obtained by the repeated application of the Hamiltonian ? on a carefully chosen starting wave vector describing the most interacting particle configuration, and the wave vectors resulting from the application of ?, till the obtained system of equations closes in itself. The procedure which can be applied in principle at fixed but arbitrary system size and number of particles is interesting on its own since it provides exact information for the numerical approximation techniques which use a similar strategy, but apply non-complete basis for ?. The diagonalization inside ? provides an incomplete image of the low lying part of the excitation spectrum, but provides the exact ?. Once the exact ground state is obtained, its properties can be easily analysed. The ? is found always as a singlet state whose energy, interestingly, saturates in the ? limit. The unapproximated results show that the emergence probabilities of different particle configurations in the ground state presents 'Zittern' (trembling) characteristics which are absent in 2D square Hubbard systems. Consequently, the manifestation of the local Coulomb repulsion in 2D square and honeycomb types of systems presents differences, which can be a real source in the differences in the many-body behaviour.
Electronic and geometrical properties of monoatomic and diatomic 2D honeycomb lattices. A DFT study
NASA Astrophysics Data System (ADS)
Rojas, Ángela; Rey, Rafael; Fonseca, Karen; Grupo de Óptica e Información Cuántica Team
Since the discovery of graphene by Geim and Novoselov at 2004, several analogous systems have been theoretically and experimentally studied, due to their technological interest. Both monoatomic lattices, such as silicine and germanene, and diatomic lattices (h-GaAs and h-GaN) have been studied. Using Density Functional Theory we obtain and confirm the chemical stability of these hexagonal 2D systems through the total energy curves as a function of interatomic distance. Unlike graphene, silicine and germanene, gapless materials, h-GaAs and h-GaN exhibit electronic gaps, different from that of the bulk, which could be interesting for the industry. On the other hand, the ab initio band structure calculations for graphene, silicene and germanene show a non-circular cross section around K points, at variance with the prediction of usual Tight-binding models. In fact, we have found that Dirac cones display a dihedral group symmetry. This implies that Fermi speed can change up to 30 % due to the orientation of the wave vector, for both electrons and holes. Traditional analytic studies use the Dirac equation for the electron dynamics at low energies. However, this equation assumes an isotropic, homogeneous and uniform space. Authors would like to thank the División de Investigación Sede Bogotá for their financial support at Universidad Nacional de Colombia. A. M. Rojas-Cuervo would also like to thank the Colciencias, Colombia.
Narasimhan, S L; Rajarajan, A K; Vardharaj, L
2012-09-21
We present an exact enumeration algorithm for identifying the native configuration--a maximally compact self-avoiding walk configuration that is also the minimum energy configuration for a given set of contact-energy schemes; the process is implicitly sequence-dependent. In particular, we show that the 25-step native configuration on a diamond lattice consists of two sheet-like structures and is the same for all the contact-energy schemes, {(-1, 0, 0); (-7, -3, 0); (-7, -3, -1); (-7, -3, 1)}; on a square lattice also, the 24-step native configuration is independent of the energy schemes considered. However, the designing sequence for the diamond lattice walk depends on the energy schemes used whereas that for the square lattice walk does not. We have calculated the temperature-dependent specific heat for these designed sequences and the four energy schemes using the exact density of states. These data show that the energy scheme (-7, -3, -1) is preferable to the other three for both diamond and square lattice because the associated sequences give rise to a sharp low-temperature peak. We have also presented data for shorter (23-, 21-, and 17-step) walks on a diamond lattice to show that this algorithm helps identify a unique minimum energy configuration by suitably taking care of the ground-state degeneracy. Interestingly, all these shorter target configurations also show sheet-like secondary structures. PMID:22998288
Existence and stability of PT-symmetric states in nonlinear two-dimensional square lattices
NASA Astrophysics Data System (ADS)
Xu, Haitao; Kevrekidis, P. G.; Pelinovsky, Dmitry E.
2016-07-01
Solitons and vortices symmetric with respect to simultaneous parity (P) and time reversing (T) transformations are considered on the square lattice in the framework of the discrete nonlinear Schrödinger equation. The existence and stability of such PT-symmetric configurations is analyzed in the limit of weak coupling between the lattice sites, when predictions on the elementary cell of a square lattice (i.e., a single square) can be extended to a large (yet finite) array of lattice cells. In particular, we find all examined vortex configurations are unstable with respect to small perturbations while a branch extending soliton configurations is spectrally stable. Our analytical predictions are found to be in good agreement with numerical computations.
NASA Astrophysics Data System (ADS)
Tsakiris, N.; Maragakis, M.; Kosmidis, K.; Argyrakis, P.
2010-10-01
We study the percolation properties of the growing clusters model on a 2D square lattice. In this model, a number of seeds placed on random locations on the lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The model exhibits a discontinuous transition for very low values of the seed concentration p and a second, nontrivial continuous phase transition for intermediate p values. Here we study in detail this continuous transition that separates a phase of finite clusters from a phase characterized by the presence of a giant component. Using finite size scaling and large scale Monte Carlo simulations we determine the value of the percolation threshold where the giant component first appears, and the critical exponents that characterize the transition. We find that the transition belongs to a different universality class from the standard percolation transition.
Lattice Boltzmann simulations of 2D laminar flows past two tandem cylinders
NASA Astrophysics Data System (ADS)
Mussa, Alberto; Asinari, Pietro; Luo, Li-Shi
2009-03-01
We apply the lattice Boltzmann equation (LBE) with multiple-relaxation-time (MRT) collision model to simulate laminar flows in two-dimensions (2D). In order to simulate flows in an unbounded domain with the LBE method, we need to address two issues: stretched non-uniform mesh and inflow and outflow boundary conditions. We use the interpolated grid stretching method to address the need of non-uniform mesh. We demonstrate that various inflow and outflow boundary conditions can be easily and consistently realized with the MRT-LBE. The MRT-LBE with non-uniform stretched grids is first validated with a number of test cases: the Poiseuille flow, the flow past a cylinder asymmetrically placed in a channel, and the flow past a cylinder in an unbounded domain. We use the LBE method to simulate the flow past two tandem cylinders in an unbounded domain with Re = 100. Our results agree well with existing ones. Through this work we demonstrate the effectiveness of the MRT-LBE method with grid stretching.
Phase Diagram of the Frustrated Square-Lattice Hubbard Model: Variational Cluster Approach
NASA Astrophysics Data System (ADS)
Misumi, Kazuma; Kaneko, Tatsuya; Ohta, Yukinori
2016-06-01
The variational cluster approximation is used to study the frustrated Hubbard model at half filling defined on the two-dimensional square lattice with anisotropic next-nearest-neighbor hopping parameters. We calculate the ground-state phase diagrams of the model in a wide parameter space for a variety of lattice geometries, including square, crossed-square, and triangular lattices. We examine the Mott metal-insulator transition and show that, in the Mott insulating phase, magnetic phases with Néel, collinear, and spiral orders appear in relevant parameter regions, and in an intermediate region between these phases, a nonmagnetic insulating phase caused by the quantum fluctuations in the geometrically frustrated spin degrees of freedom emerges.
NASA Astrophysics Data System (ADS)
Guillamon, I.; Vieira, S.; Suderow, H.; Cordoba, R.; Sese, J.; de Teresa, J. M.; Ibarra, R.
In two dimensional (2D) systems, theory has proposed that random disorder destroys long range correlations driving a transition to a glassy state. Here, I will discuss new insights into this issue obtained through the direct visualization of the critical behaviour of a 2D superconducting vortex lattice formed in a thin film with a smooth 1D thickness modulation. Using scanning tunneling microscopy at 0.1K, we have tracked the modification in the 2D vortex arrangements induced by the 1D thickness modulation while increasing the vortex density by three orders of magnitude. Upon increasing the field, we observed a two-step order-disorder transition in the 2D vortex lattice mediated by the appearance of dislocations and disclinations and accompanied by an increase in the local vortex density fluctuations. Through a detailed analysis of correlation functions, we find that the transition is driven by the incommensurate 1D thickness modulation. We calculate the critical points and exponents and find that they are well above theoretical expectation for random disorder. Our results show that long range 1D correlations in random potentials enhance the stability range of the ordered phase in a 2D vortex lattice. Work supported by Spanish MINECO, CIG Marie Curie Grant, Axa Research Fund and FBBVA.
NASA Astrophysics Data System (ADS)
Goldman, N.; Gerbier, F.; Lewenstein, M.
2013-07-01
We describe a scheme to engineer non-Abelian gauge potentials on a square optical lattice using laser-induced transitions. We emphasize the case of two-electron atoms, where the electronic ground state g is laser-coupled to a metastable state e within a state-dependent optical lattice. In this scheme, the alternating pattern of lattice sites hosting g and e states depicts a chequerboard structure, allowing for laser-assisted tunnelling along both spatial directions. In this configuration, the nuclear spin of the atoms can be viewed as a ‘flavour’ quantum number undergoing non-Abelian tunnelling along nearest-neighbour links. We show that this technique can be useful to simulate the equivalent of the Haldane quantum Hall model using cold atoms trapped in square optical lattices, offering an interesting route to realize Chern insulators. The emblematic Haldane model is particularly suited to investigate the physics of topological insulators, but requires, in its original form, complex hopping terms beyond nearest-neighbouring sites. In general, this drawback inhibits a direct realization with cold atoms, using standard laser-induced tunnelling techniques. We demonstrate that a simple mapping allows us to express this model in terms of matrix hopping operators that are defined on a standard square lattice. This mapping is investigated for two models that lead to anomalous quantum Hall phases. We discuss the practical implementation of such models, exploiting laser-induced tunnelling methods applied to the chequerboard optical lattice.
Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices.
Piñeros, William D; Baldea, Michael; Truskett, Thomas M
2016-08-01
Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability. PMID:27497576
Existence of featureless paramagnets on the square and the honeycomb lattices in 2+1 dimensions
NASA Astrophysics Data System (ADS)
Jian, Chao-Ming; Zaletel, Michael
2016-01-01
The peculiar features of quantum magnetism sometimes forbid the existence of gapped "featureless" paramagnets which are fully symmetric and unfractionalized. The Lieb-Schultz-Mattis theorem is an example of such a constraint, but it is not known what the most general restriction might be. We focus on the existence of featureless paramagnets on the spin-1 square lattice and the spin-1 and spin-1/2 honeycomb lattice with spin rotation and space group symmetries in 2+1 dimensions. Although featureless paramagnet phases are not ruled out by any existing theorem, field theoretic arguments disfavor their existence. Nevertheless, by generalizing the construction of Affleck, Kennedy, Lieb, and Tasaki to a class we call "slave-spin" states, we propose featureless wave functions for these models. The featurelessness of the spin-1 slave-spin states on the square and honeycomb lattice are verified both analytically and numerically, but the status of the spin-1/2 honeycomb state remains unclear.
Bias-free simulation of diffusion-limited aggregation on a square lattice
NASA Astrophysics Data System (ADS)
Loh, Yen Lee
We identify sources of systematic error in traditional simulations of the Witten-Sander model of diffusion-limited aggregation (DLA) on a square lattice. Based on semi-analytic solutions of the walk-to-line and walk-to-square first-passage problems, we develop an algorithm that reduces the simulation bias to below 10-12. We grow clusters of 108 particles on 65536 × 65536 lattices. We verify that lattice DLA clusters inevitably grow into anisotropic shapes, dictated by the anisotropy of the aggregation process. We verify that the fractal dimension evolves from the continuum DLA value, D = 1 . 71 , for small disk-shaped clusters, towards Kesten's bound of D = 3 / 2 for highly anisotropic clusters with long protruding arms.
Orso, G.; Stringari, S.; Menotti, C.
2006-11-10
We use Bogoliubov theory to calculate the beyond mean field correction to the equation of state of a weakly interacting Bose gas in the presence of a tight 2D optical lattice. We show that the lattice induces a characteristic 3D to 1D crossover in the behavior of quantum fluctuations. Using the hydrodynamic theory of superfluids, we calculate the corresponding shift of the collective frequencies of a harmonically trapped gas. We find that this correction can be of the order of a few percent and hence easily measurable in current experiments. The behavior of the quantum depletion of the condensate is also discussed.
Thermodynamics of the Hubbard model on stacked honeycomb and square lattices
NASA Astrophysics Data System (ADS)
Imriška, Jakub; Gull, Emanuel; Troyer, Matthias
2016-07-01
We present a numerical study of the Hubbard model on simply stacked honeycomb and square lattices, motivated by a recent experimental realization of such models with ultracold atoms in optical lattices. We perform simulations with different interlayer coupling and interaction strengths and obtain Néel transition temperatures and entropies. We provide data for the equation of state to enable comparisons of experiments and theory. We find an enhancement of the short-range correlations in the anisotropic lattices compared to the isotropic cubic lattice, in parameter regimes suitable for the interaction driven adiabatic cooling. Supplementary material in the form of one zip file available from the Jounal web page at http://dx.doi.org/10.1140/epjb/e2016-70146-y
Ising-like transitions in the O(n) loop model on the square lattice.
Fu, Zhe; Guo, Wenan; Blöte, Henk W J
2013-05-01
We explore the phase diagram of the O(n) loop model on the square lattice in the (x,n) plane, where x is the weight of a lattice edge covered by a loop. These results are based on transfer-matrix calculations and finite-size scaling. We express the correlation length associated with the staggered loop density in the transfer-matrix eigenvalues. The finite-size data for this correlation length, combined with the scaling formula, reveal the location of critical lines in the diagram. For n>2 we find Ising-like phase transitions associated with the onset of a checkerboardlike ordering of the elementary loops, i.e., the smallest possible loops, with the size of an elementary face, which cover precisely one-half of the faces of the square lattice at the maximum loop density. In this respect, the ordered state resembles that of the hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of n represents a softening of its particle-particle potentials. We also determine critical points in the range -2≤n≤2. It is found that the topology of the phase diagram depends on the set of allowed vertices of the loop model. Depending on the choice of this set, the n>2 transition may continue into the dense phase of the n≤2 loop model, or continue as a line of n≤2 O(n) multicritical points. PMID:23767498
Zharova, Yu. A. Fedulova, G. V.; Astrova, E. V.; Baldycheva, A. V.; Tolmachev, V. A.; Perova, T. S.
2011-08-15
Design and fabrication technology of a microcavity structure based on a double heterojunction in macroporous silicon is suggested. The fabrication process of a strip of a 2D photonic crystal constituted by a finite number of lattice periods and the technique for defect formation by local opening of macropores on the substrate side, followed by filling of these macropores with a nematic liquid crystal, are considered.
Classical and quantum transport on square lattices and disordered clusters in two dimensions
NASA Astrophysics Data System (ADS)
Cuansing, Eduardo C., Jr.
The transport of a particle through disordered clusters can be treated either classically or quantum mechanically, depending on the size of the systems involved. In this thesis we employ both treatments. In the classical part we extend ordinary site percolation on a square lattice to fully coordinated (FC) percolation and to iterated fully coordinated (IFC) percolation models. FC percolation comes about by adding a full coordination requirement to ordinary site percolation. In IFC percolation we iterate this requirement one more time. We find all three models to belong to the same universality class. We also find a developing Euclidean signature as we iterate the models from ordinary to FC and then to IFC percolation. In the quantum part we study the transmittance of a particle traversing through square lattices and through disordered clusters. The square lattices and disordered clusters are attached to two semi-infinite chains serving as the input and output leads. The leads and the clusters are coupled together through either point to point contacts or busbar connections. In transport through square lattices we find resonant transmission and reflection whenever the energy of the incident particle is close to a doubly-degenerate eigenvalue of the uncoupled lattice. We also find the transmission to be sensitive to the type of coupling chosen. In transport through disordered clusters we find the transmission to decrease as the clusters become larger. This hints that states are localized. Furthermore, we find the transmission to be independent of the coupling chosen in the presence of strong disorder. This independence is lost in weakly disordered clusters. We also find hints of localized-to-localized transitions as we vary the degree of disorder. However, the clusters we have been studying are still too small to make definite conclusions. We thus find it necessary to extend our analyses to larger-sized clusters.
One-dimensional crystal growth model on a square lattice substrate
NASA Astrophysics Data System (ADS)
Cheng, Yi; Lu, Chenxi; Yang, Bo; Tao, Xiangming; Wang, Jianfeng; Ye, Gaoxiang
2016-08-01
A one-dimensional crystal growth model along the preferential growth direction is established. The simulation model is performed on a square lattice substrate. First, particles are deposited homogeneously and, as a result, each of the lattice sites is occupied by one particle. In the subsequent stage, N nuclei are selected randomly on the substrate, then the growth process starts by adsorbing the surrounding particles along the preferential growth directions of the crystals. Finally, various one-dimensional crystals with different length and width form. The simulation results are in good agreement with the experimental findings.
Optical NOR logic gate design on square lattice photonic crystal platform
NASA Astrophysics Data System (ADS)
D'souza, Nirmala Maria; Mathew, Vincent
2016-05-01
We numerically demonstrate a new configuration of all-optical NOR logic gate with square lattice photonic crystal (PhC) waveguide using finite difference time domain (FDTD) method. The logic operations are based on interference effect of optical waves. We have determined the operating frequency range by calculating the band structure for a perfectly periodic PhC using plane wave expansion (PWE) method. Response time of this logic gate is 1.98 ps and it can be operated with speed about 513 GB/s. The proposed device consists of four linear waveguides and a square ring resonator waveguides on PhC platform.
NASA Astrophysics Data System (ADS)
Farmer, B.; Bhat, V. S.; Sklenar, J.; Teipel, E.; Woods, J.; Ketterson, J. B.; Hastings, J. T.; De Long, L. E.
2015-05-01
The static and dynamic magnetic responses of patterned ferromagnetic thin films are uniquely altered in the case of aperiodic patterns that retain long-range order (e.g., quasicrystals). We have fabricated permalloy wire networks based on periodic square antidot lattices (ADLs) distorted according to an aperiodic Fibonacci sequence applied to two lattice translations, d1 = 1618 nm and d2 = 1000 nm. The wire segment thickness is fixed at t = 25 nm, and the width W varies from 80 to 510 nm. We measured the DC magnetization between room temperature and 5 K. Room-temperature, narrow-band (9.7 GHz) ferromagnetic resonance (FMR) spectra were acquired for various directions of applied magnetic field. The DC magnetization curves exhibited pronounced step anomalies and plateaus that signal flux closure states. Although the Fibonacci distortion breaks the fourfold symmetry of a finite periodic square ADL, the FMR data exhibit fourfold rotational symmetry with respect to the applied DC magnetic field direction.
A novel snowdrift game model with edge weighting mechanism on the square lattice
NASA Astrophysics Data System (ADS)
Zhang, Juan-juan; Ning, Hong-yun; Yin, Zi-yu; Sun, Shi-wen; Wang, Li; Sun, Jun-qing; Xia, Cheng-yi
2012-06-01
We propose a novel snowdrift game model with edge weighting mechanism to explore the cooperative behaviors among the players on the square lattice. Based on the assumption of three types of weight distribution including uniform, exponential and power-law schemes, the cooperation level is largely boosted in contrast with the traditional snowdrift game on the unweighted square lattice. Extensive numerical simulations indicate that the fraction of cooperators greatly augments, especially for the intermediate range of cost-to-benefit ratio r. Furthermore, we investigate how the cooperative behaviors are affected by the undulation amplitude of weight distribution and noise strength of strategy selection, respectively. The simulation results will be conducive to further understanding and analyzing the emergence of cooperation, which is a ubiquitous phenomenon in social and biological science.
Surface plasmon resonance biosensor based on large size square-lattice photonic crystal fiber
NASA Astrophysics Data System (ADS)
Bing, Pibin; Li, Zhongyang; Yuan, Sheng; Yao, Jianquan; Lu, Ying
2016-04-01
A surface plasmon resonance biosensor based on large size square-lattice photonic crystal fiber has been designed and simulated by finite element method. The square-lattice airholes are first coated with a calcium fluoride layer to provide mode confinement, then a nanoscale gold layer is deposited to excite the plasmon mode, and finally, the sample is infiltrated into the holes. The numerical results reveal that the resonance properties are easily affected by many parameters. The refractive index resolution of corresponding sensor can reach 4.3 × 10-6 RIU when the optimum parameters are set as the radius of curvature of the airhole r = 2 μm, the thickness of the core struts c = 200 nm, the auxiliary dielectric layer s = 1 μm, and the gold film d = 40 nm. In addition, the effective area and nonlinear coefficient are calculated.
Soliton excitations and stability in a square lattice model of ferromagnetic spin system
NASA Astrophysics Data System (ADS)
Latha, M. M.; Anitha, T.
2015-12-01
We investigate the nature of nonlinear spin excitations in a square lattice model of ferromagnetic (FM) spin system with bilinear and biquadratic interactions. Using the coherent state ansatz combined with the Holstein-Primakoff (HP) bosonic representation of spin operators, the dynamics is found to be governed by a discrete nonlinear equation which possesses soliton solution. The modulational instability aspects of the soliton excitations are analysed for small perturbations in wave vectors.
Gubbiotti, G.; Tacchi, S.; Madami, M.; Carlotti, G.; Ding, J.; Adeyeye, A. O.
2015-06-29
The Brillouin light scattering technique has been exploited to study the angle-resolved spin wave band diagrams of squared Permalloy antidot lattice. Frequency dispersion of spin waves has been measured for a set of fixed wave vector magnitudes, while varying the wave vector in-plane orientation with respect to the applied magnetic field. The magnonic band gap between the two most dispersive modes exhibits a minimum value at an angular position, which exclusively depends on the product between the selected wave vector magnitude and the lattice constant of the array. The experimental data are in very good agreement with predictions obtained by dynamical matrix method calculations. The presented results are relevant for magnonic devices where the antidot lattice, acting as a diffraction grating, is exploited to achieve multidirectional spin wave emission.
Polymer model with annealed dilution on the square lattice: A transfer-matrix study
NASA Astrophysics Data System (ADS)
Serra, Pablo; Stilck, Jürgen F.
1994-02-01
We study a lattice model for equilibrium polymerization with annealed dilution. The model considered is an Ising lattice-gas monomer-solvent system where the polymers are represented by mutually and self-avoiding walks constrained to pass through sites occupied by monomers. Numerical results on the square lattice using transfer-matrix techniques and finite-size scaling are reported. The values obtained for the tricitical exponent νt are in agreement with the tricritical Ising exponent (8/11) for high values of the monomer fugacity, but the accuracy we obtained does not rule out the possibility of νt being equal to the critical self-avoiding-walk (SAW) value 3/4. Our results indicate that a crossover occurs in the tricritical behavior of the model. This crossover corroborates the equivalence between a particular limit of the diluted model and the self-attracting polymer system proposed recently.
The Lattice-Based Screen Set: A Square N -Color All-Orders Moiré-Free Screen Set.
Yung-Yao Chen; Kashti, Tamar; Fischer, Mani; Shaked, Doron; Ulichney, Robert; Allebach, Jan P
2016-04-01
Periodic clustered-dot screens are widely used for electrophotographic printers due to their print stability. However, moiré is a ubiquitous problem that arises in color printing due to the beating together of the clustered-dot, periodic halftone patterns that are used to represent different colorants. The traditional solution in the graphic arts and printing industry is to rotate identical square screens to angles that are maximally separated from each other. However, the effectiveness of this approach is limited when printing with more than four colorants, i.e., N -color printing, where N > 4 . Moreover, accurately achieving the angles that have maximum angular separation requires a very high-resolution plate writer, as is used in commercial offset printing. Commercially available high-end digital printers cannot achieve this resolution. In this paper, we propose a systematic way to design color screen sets for periodic, clustered-dot screens that offer more explicit control of the moiré properties of the resulting screens when used in color printing. We develop a principled approach for the moiré-free screen design that is called lattice-based screen design. The basic concept behind our approach is the creation of the screen set on a 2D lattice in the frequency domain, and then picking each fundamental frequency vector of the individual colorant planes in the created spectral lattice according to the desired properties. The lattice-based screen design offers more flexibility in designing N -color screen sets with different halftone geometries, and all of them are guaranteed to be all-orders moiré-free. We demonstrate the efficacy of our proposed method by introducing several new screen designs, and a comparison with published screen designs. PMID:26849865
Anomalous giant piezoresistance in AlAs 2D electron systems with antidot lattices.
Gunawan, O; Gokmen, T; Shkolnikov, Y P; De Poortere, E P; Shayegan, M
2008-01-25
An AlAs two-dimensional electron system patterned with an antidot lattice exhibits a giant piezoresistance effect at low temperatures, with a sign opposite to the piezoresistance observed in the unpatterned region. We suggest that the origin of this anomalous giant piezoresistance is the nonuniform strain in the antidot lattice and the exclusion of electrons occupying the two conduction-band valleys from different regions of the sample. This is analogous to the well-known giant magnetoresistance effect, with valley playing the role of spin and strain the role of magnetic field. PMID:18233015
2D and 3D Anilato-Based Heterometallic M(I)M(III) Lattices: The Missing Link.
Benmansour, Samia; Vallés-García, Cristina; Gómez-Claramunt, Patricia; Mínguez Espallargas, Guillermo; Gómez-García, Carlos J
2015-06-01
The similar bis-bidentate coordination mode of oxalato and anilato-based ligands is exploited here to create the first examples of 2D and 3D heterometallic lattices based on anilato ligands combining M(I) and a M(III) ions, phases already observed with oxalato but unknown with anilato-type ligands. These lattices are prepared with alkaline metal ions and magnetic chiral tris(anilato)metalate molecular building blocks: [M(III)(C6O4X2)3](3-) (M(III) = Fe and Cr; X = Cl and Br; (C6O4X2)(2-) = dianion of the 3,6-disubstituted derivatives of 2,5-dihydroxy-1,4-benzoquinone, H4C6O4). The new compounds include two very similar 2D lattices formulated as (PBu3Me)2[NaCr(C6O4Br2)3] (1) and (PPh3Et)2[KFe(C6O4Cl2)3](dmf)2 (2), both presenting hexagonal [M(I)M(III)(C6O4X2)3](2-) honeycomb layers with (PBu3Me)(+) in 1 or (PPh3Et)(+) and dmf in 2 inserted between them. Minor modifications in the synthetic conditions yield the novel 3D lattice (NEt3Me)[Na(dmf)][NaFe(C6O4Cl2)3] (3), in which hexagonal layers analogous to 1 and 2 are interconnected through Na(+) cations, and (NBu3Me)2[NaCr(C6O4Br2)3] (4), the first heterometallic 3D lattice based on anilato ligands. This compound presents two interlocked chiral 3D (10,3) lattices with opposite chiralities. Attempts to prepare 4 in larger quantities result in the 2D polymorph of compound 4 (4'). Magnetic properties of compounds 1, 3, and 4' are reported, and in all cases we observe, as expected, paramagnetic behaviors that can be satisfactorily reproduced with simple monomer models including a zero field splitting (ZFS) of the corresponding S = 3/2 for Cr(III) in 1 and 4' or S = 5/2 for Fe(III) in 3. PMID:25965415
Microscopy of a Quantum Gas in a 2D Optical Lattice
NASA Astrophysics Data System (ADS)
Bakr, Waseem; Peng, Amy; Tai, Ming; Ma, Ruichao; Jotzu, Gregor; Gillen, Jonathon; Foelling, Simon; Greiner, Markus
2010-03-01
Ultracold quantum gases in optical lattices provide a rich experimental toolbox for simulating the physics of condensed matter systems. With atoms in the lattice playing the role of electrons or Cooper pairs in real materials, it is possible to experimentally realize condensed matter Hamiltonians in a controlled way. To realize the full potential of such quantum simulations, we have created a quantum gas microscope (NA = 0.8) which can spatially resolve the atoms in the optical lattice at the single site level, and project arbitrary potential landscapes onto the atoms by combining the high resolution optics with static holographic masks or a spatial light modulator. The high resolution microscope operates with the atoms trapped in a two dimensional optical lattice at a distance of 10 microns from a glass surface that is part of the microscope. We have experimentally verified a resolution of ˜ 600 nm, providing the capability to study the phase diagram of the Bose Hubbard model by measuring occupation number at individual sites.
NASA Astrophysics Data System (ADS)
Eising, G.; Kooi, B. J.
2012-06-01
Growth and decay of clusters at temperatures below Tc have been studied for a two-dimensional Ising model for both square and triangular lattices using Monte Carlo (MC) simulations and the enumeration of lattice animals. For the lattice animals, all unique cluster configurations with their internal bonds were identified up to 25 spins for the triangular lattice and up to 29 spins for the square lattice. From these configurations, the critical cluster sizes for nucleation have been determined based on two (thermodynamic) definitions. From the Monte Carlo simulations, the critical cluster size is also obtained by studying the decay and growth of inserted, most compact clusters of different sizes. A good agreement is found between the results from the MC simulations and one of the definitions of critical size used for the lattice animals at temperatures T > ˜0.4 Tc for the square lattice and T > ˜0.2 Tc for the triangular lattice (for the range of external fields H considered). At low temperatures (T ≈ 0.2 Tc for the square lattice and T ≈ 0.1 Tc for the triangular lattice), magic numbers are found in the size distributions during the MC simulations. However, these numbers are not present in the critical cluster sizes based on the MC simulations, as they are present for the lattice animal data. In order to achieve these magic numbers in the critical cluster sizes based on the MC simulation, the temperature has to be reduced further to T ≈ 0.15 Tc for the square lattice. The observed evolution of magic numbers as a function of temperature is rationalized in the present work.
Zhang, Hai-Feng E-mail: lsb@nuaa.edu.cn; Liu, Shao-Bin E-mail: lsb@nuaa.edu.cn; Jiang, Yu-Chi
2014-09-15
In this paper, the tunable all-angle negative refraction and photonic band gaps (PBGs) in two types of two-dimensional (2D) plasma photonic crystals (PPCs) composed of homogeneous plasma and dielectric (GaAs) with square-like Archimedean lattices (ladybug and bathroom lattices) for TM wave are theoretically investigated based on a modified plane wave expansion method. The type-1 structure is dielectric rods immersed in the plasma background, and the complementary structure is named as type-2 PPCs. Theoretical simulations demonstrate that the both types of PPCs with square-like Archimedean lattices have some advantages in obtaining the higher cut-off frequency, the larger PBGs, more number of PBGs, and the relative bandwidths compared to the conventional square lattices as the filling factor or radius of inserted rods is same. The influences of plasma frequency and radius of inserted rod on the properties of PBGs for both types of PPCs also are discussed in detail. The calculated results show that PBGs can be manipulated by the parameters as mentioned above. The possibilities of all-angle negative refraction in such two types of PPCs at low bands also are discussed. Our calculations reveal that the all-angle negative phenomena can be observed in the first two TM bands, and the frequency range of all-angle negative refraction can be tuned by changing plasma frequency. Those properties can be used to design the optical switching and sensor.
NASA Astrophysics Data System (ADS)
Zhang, Hai-Feng; Liu, Shao-Bin; Jiang, Yu-Chi
2014-09-01
In this paper, the tunable all-angle negative refraction and photonic band gaps (PBGs) in two types of two-dimensional (2D) plasma photonic crystals (PPCs) composed of homogeneous plasma and dielectric (GaAs) with square-like Archimedean lattices (ladybug and bathroom lattices) for TM wave are theoretically investigated based on a modified plane wave expansion method. The type-1 structure is dielectric rods immersed in the plasma background, and the complementary structure is named as type-2 PPCs. Theoretical simulations demonstrate that the both types of PPCs with square-like Archimedean lattices have some advantages in obtaining the higher cut-off frequency, the larger PBGs, more number of PBGs, and the relative bandwidths compared to the conventional square lattices as the filling factor or radius of inserted rods is same. The influences of plasma frequency and radius of inserted rod on the properties of PBGs for both types of PPCs also are discussed in detail. The calculated results show that PBGs can be manipulated by the parameters as mentioned above. The possibilities of all-angle negative refraction in such two types of PPCs at low bands also are discussed. Our calculations reveal that the all-angle negative phenomena can be observed in the first two TM bands, and the frequency range of all-angle negative refraction can be tuned by changing plasma frequency. Those properties can be used to design the optical switching and sensor.
Lattice Boltzmann methods for some 2-D nonlinear diffusion equations:Computational results
Elton, B.H.; Rodrigue, G.H. . Dept. of Applied Science Lawrence Livermore National Lab., CA ); Levermore, C.D. . Dept. of Mathematics)
1990-01-01
In this paper we examine two lattice Boltzmann methods (that are a derivative of lattice gas methods) for computing solutions to two two-dimensional nonlinear diffusion equations of the form {partial derivative}/{partial derivative}t u = v ({partial derivative}/{partial derivative}x D(u){partial derivative}/{partial derivative}x u + {partial derivative}/{partial derivative}y D(u){partial derivative}/{partial derivative}y u), where u = u({rvec x},t), {rvec x} {element of} R{sup 2}, v is a constant, and D(u) is a nonlinear term that arises from a Chapman-Enskog asymptotic expansion. In particular, we provide computational evidence supporting recent results showing that the methods are second order convergent (in the L{sub 1}-norm), conservative, conditionally monotone finite difference methods. Solutions computed via the lattice Boltzmann methods are compared with those computed by other explicit, second order, conservative, monotone finite difference methods. Results are reported for both the L{sub 1}- and L{sub {infinity}}-norms.
Algebraic rings of integers and some 2D lattice problems in physics
NASA Astrophysics Data System (ADS)
Nanxian, Chen; Zhaodou, Chen; Shaojun, Liu; Yanan, Shen; Xijin, Ge
1996-09-01
This paper develops the Möbius inversion formula for the Gaussian integers and Eisenstein's integers, and gives two applications. The first application is to the two-dimensional arithmetic Fourier transform (AFT), which is suitable for parallel processing. The second application is to two-dimensional inverse lattice problems, and is illustrated with the recovery of interatomic potentials from the cohesive energy for monolayer graphite. The paper demonstrates the potential application in the physical science of integral domains other than the standard integers.
Bandgaps and directional properties of two-dimensional square beam-like zigzag lattices
Wang, Yan-Feng; Wang, Yue-Sheng; Zhang, Chuanzeng
2014-12-15
In this paper we propose four kinds of two-dimensional square beam-like zigzag lattice structures and study their bandgaps and directional propagation of elastic waves. The band structures are calculated by using the finite element method. Both the in-plane and out-of-plane waves are investigated simultaneously via the three-dimensional Euler beam elements. The mechanism of the bandgap generation is analyzed by studying the vibration modes at the bandgap edges. The effects of the geometry parameters of the xy- and z-zigzag lattices on the bandgaps are investigated and discussed. Multiple complete bandgaps are found owing to the separation of the degeneracy by introducing bending arms. The bandgaps are sensitive to the geometry parameters of the periodic systems. The deformed displacement fields of the harmonic responses of a finite lattice structure subjected to harmonic loads at different positions are illustrated to show the directional wave propagation. An extension of the proposed concept to the hexagonal lattices is also presented. The research work in this paper is relevant to the practical design of cellular structures with enhanced vibro-acoustics performance.
Bezuglova, G S; Chechin, G M; Goncharov, P P
2011-09-01
A group-theoretical approach for studying localized periodic and quasiperiodic vibrations in two- and three-dimensional lattice dynamical models is developed. This approach is demonstrated for the scalar models on the plane square lattice. The symmetry-determined invariant manifolds admitting existence of localized vibrations are found, and some types of discrete breathers are constructed on these manifolds. A general method using the apparatus of matrix representations of symmetry groups to simplify the standard linear stability analysis is discussed. This method allows one to decompose the corresponding system of linear differential equations with time-dependent coefficients into a number of independent subsystems whose dimensions are less than the full dimension of the considered system. PMID:22060521
Violation of the des Cloizeaux relation for self-avoiding walks on Sierpinski square lattices.
Marini, Francesco; Ordemann, Anke; Porto, Markus; Roman, H Eduardo
2006-11-01
The statistics of self-avoiding walks (SAWs) on deterministic fractal structures with infinite ramification, modeled by Sierpinski square lattices, is revisited in two and three dimensions using the reptation algorithm. The probability distribution function of the end-to-end distance of SAWs, consisting of up to 400 steps, is obtained and its scaling behavior at small distances is studied. The resulting scaling exponents are confronted with previous calculations for much shorter linear chains (20 to 30 steps) based on the exact enumeration (EE) technique. The present results coincide with the EE values in two dimensions, but differ slightly in three dimensions. A possible explanation for this discrepancy is discussed. Despite this, the violation of the so-called des Cloizeaux relation, a renormalization result that holds on regular lattices and on deterministic fractal structures with finite ramification, is confirmed numerically. PMID:17279872
Complex zeros of the 2 d Ising model on dynamical random lattices
NASA Astrophysics Data System (ADS)
Ambjørn, J.; Anagnostopoulos, K. N.; Magnea, U.
1998-04-01
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2 d quantum gravity for complex magnetic field and for complex temperature. We compute the zeros by using the exact solution coming from a two matrix model and by Monte Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional patterns in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of singularities near the critical point.
Furman, Eric M.; Anghaie, Samim
1999-01-22
A computational analysis is conducted to determine the optimum thermal-hydraulic design parameters for a square-lattice honeycomb nuclear rocket engine core that will incorporate ternary carbide based uranium fuels. Recent studies at the Innovative Nuclear Space Power and Propulsion Institute (INSPI) have demonstrated the feasibility of processing solid solution, ternary carbide fuels such as (U, Zr, Nb)C, (U, Zr, Ta)C, (U, Zr, Hf)C and (U, Zr, W)C. The square-lattice honeycomb design provides high strength and is amenable to the processing complexities of these ultrahigh temperature fuels. A parametric analysis is conducted to examine how core geometry, fuel thickness and the propellant flow area effect the thermal performance of the nuclear rocket engine. The principal variables include core size (length and diameter) and fuel element dimensions. The optimum core configuration requires a balance between high specific impulse and thrust level performance, and maintaining the temperature and strength limits of the fuel. A nuclear rocket engine simulation code is developed and used to examine the system performance as well as the performance of the main reactor core components. The system simulation code was originally developed for analysis of NERVA-Derivative and Pratt and Whitney XNR-2000 nuclear thermal rockets. The code is modified and adopted to the square-lattice geometry of the new fuel design. Thrust levels ranging from 44,500 to 222,400 N (10,000 to 50,000 lbf) are considered. The average hydrogen exit temperature is kept at 2800 K, which is well below the melting point of these fuels. For a nozzle area ratio of 300 and a thrust chamber pressure of 4.8 Mpa (700 psi), the specific impulse is 930 s. Hydrogen temperature and pressure distributions in the core and the fuel maximum temperatures are calculated.
Hubbard Model study of Off Diagonally Confined fermions in a 2D Optical Lattice
NASA Astrophysics Data System (ADS)
Cone, Dave; Chiesa, Simone; Scalettar, Richard; Batrouni, George
2010-03-01
We report Quantum Monte Carlo simulations of a Hubbard Hamiltonian which incorporates a proposed new method for confining atoms in an optical lattice employing an inhomogeneous array of hopping matrix elements which trap atoms by going to zero at the lattice edges. This has been termed ``Off Diagonal Confinement (ODC)'' [1] to distinguish it from the more conventional use of a parabolic trap coupling to (diagonal) density operators. It has the advantage of producing systems which, while still being inhomogeneous, are entirely in the Mott phase, and allow simulations which are free of the sign problem at low temperatures. We analyze the effects of using ODC traps on the local density, density fluctuation, spin, and pairing correlation functions. Finally, we will discuss the advantages and importance of this new confinement technique for modeling correlated systems. Research supported by the Department of Energy, Office of Science SCIDAC program, DOE-DE-FC0206ER25793. [1] V.G. Rousseau et al., arXiv:0909.3543
Modeling Selective Local Interactions with Memory: Motion on a 2D Lattice.
Weinberg, Daniel; Levy, Doron
2014-06-15
We consider a system of particles that simultaneously move on a two-dimensional periodic lattice at discrete times steps. Particles remember their last direction of movement and may either choose to continue moving in this direction, remain stationary, or move toward one of their neighbors. The form of motion is chosen based on predetermined stationary probabilities. Simulations of this model reveal a connection between these probabilities and the emerging patterns and size of aggregates. In addition, we develop a reaction diffusion master equation from which we derive a system of ODEs describing the dynamics of the particles on the lattice. Simulations demonstrate that solutions of the ODEs may replicate the aggregation patterns produced by the stochastic particle model. We investigate conditions on the parameters that influence the locations at which particles prefer to aggregate. This work is a two-dimensional generalization of [Galante & Levy, Physica D, http://dx.doi.org/10.1016/j.physd.2012.10.010], in which the corresponding one-dimensional problem was studied. PMID:25045193
Anomalous supersolidity in a weakly interacting dipolar Bose mixture on a square lattice
NASA Astrophysics Data System (ADS)
Wilson, Ryan M.; Shirley, Wilbur E.; Natu, Stefan S.
2016-01-01
We calculate the mean-field phase diagram of a zero-temperature, binary Bose mixture on a square optical lattice, where one species possesses a non-negligible dipole moment. Remarkably, this system exhibits supersolidity for anomalously weak dipolar interaction strengths, which are readily accessible with current experimental capabilities. The supersolid phases are robust, in that they occupy large regions in the parameter space. Further, we identify a first-order quantum phase transition between supersolid and superfluid phases. Our results demonstrate the rich features of the dipolar Bose mixture, and suggest that this system is well suited for exploring supersolidity in the experimental setting.
NASA Astrophysics Data System (ADS)
Lu, Tsan-Wen; Lin, Pin-Tso; Sio, Kuan-Un; Lee, Po-Tsung
2010-05-01
We propose a point-shifted D0 nanocavity formed by locally modulating four central air holes in square lattice photonic crystal for optical sensing application. Three defect modes in this nanocavity, including monopole, whispering-gallery, and dipole modes, are identified in experiments. We also apply a chemical treatment on InGaAsP surface to form a 1-octadecanethiol linking monolayer, which enables the following protein adsorption. In experiments, the wavelength shifts of lasing modes in the D0 nanocavity due to the protein adsorption are observed and agree with the simulation results. This can be a practical tool for label-free molecule detection in biomedical researches.
Interference based square lattice photonic crystal logic gates working with different wavelengths
NASA Astrophysics Data System (ADS)
D'souza, Nirmala Maria; Mathew, Vincent
2016-06-01
We propose a new configuration of interference based OR, XOR, NOT and AND optical logic gates on a two dimensional square lattice photonic crystal (PhC) platform. The working of these devices was analyzed by the FDTD method and the operating frequency range was explored using the plane wave expansion method. The XOR and NOT gates have high contrast ratio which is more than 35 dB between high and low logic states, for a particular wavelength. All these devices are operating with multiple wavelengths. The impact of structural parameter like radius on the operating wavelength and Contrast Ratio (CR) was analyzed. It is found that the optimization of structural parameters makes it possible to obtain the operating wavelength allowed by band structure. These proposed devices were made up of linear waveguides and square ring resonator waveguides, without using nonlinear materials, optical amplifiers and external phase shifters.
Nambu monopoles interacting with lattice defects in a two-dimensional artificial square spin ice
NASA Astrophysics Data System (ADS)
Silva, R. C.; Lopes, R. J. C.; Mól, L. A. S.; Moura-Melo, W. A.; Wysin, G. M.; Pereira, A. R.
2013-01-01
The interactions between an excitation (similar to a pair of Nambu monopoles connected by their associated string) and a lattice defect are studied in an artificial two-dimensional square spin ice. This is done by considering a square array of islands containing only one island different from all others. This difference is incorporated in the magnetic moment (spin) of the “imperfect” island and several cases are studied, including the special situation in which this distinct spin is zero (vacancy). We show that the two extreme points of a defective island behave like two opposite magnetic charges. Then, the effective interaction between a pair of Nambu monopoles with the defective island is a problem involving four magnetic charges (two pairs of opposite poles) and a string. We also sketch the configuration of the field lines of these four charges to confirm this picture. The influence of the string on this interaction decays rapidly with the string distance from the defect.
TOPICAL REVIEW: Statistical mechanics of directed models of polymers in the square lattice
NASA Astrophysics Data System (ADS)
Janse van Rensburg, E. J.
2003-04-01
Directed square lattice models of polymers and vesicles have received considerable attention in the recent mathematical and physical sciences literature. These are idealized geometric directed lattice models introduced to study phase behaviour in polymers, and include Dyck paths, partially directed paths, directed trees and directed vesicles models. Directed models are closely related to models studied in the combinatorics literature (and are often exactly solvable). They are also simplified versions of a number of statistical mechanics models, including the self-avoiding walk, lattice animals and lattice vesicles. The exchange of approaches and ideas between statistical mechanics and combinatorics have considerably advanced the description and understanding of directed lattice models, and this will be explored in this review. The combinatorial nature of directed lattice path models makes a study using generating function approaches most natural. In contrast, the statistical mechanics approach would introduce partition functions and free energies, and then investigate these using the general framework of critical phenomena. Generating function and statistical mechanics approaches are closely related. For example, questions regarding the limiting free energy may be approached by considering the radius of convergence of a generating function, and the scaling properties of thermodynamic quantities are related to the asymptotic properties of the generating function. In this review the methods for obtaining generating functions and determining free energies in directed lattice path models of linear polymers is presented. These methods include decomposition methods leading to functional recursions, as well as the Temperley method (that is implemented by creating a combinatorial object, one slice at a time). A constant term formulation of the generating function will also be reviewed. The thermodynamic features and critical behaviour in models of directed paths may be
Yang Xuefeng; Cui Jian; Zhang Yuan; Liu Yue
2012-07-15
The dispersion relations of the externally and thermally (naturally) excited dust lattice modes (both longitudinal and transverse) in two-dimensional Debye-Yukawa complex plasma crystals are investigated. The dispersion relations are calculated numerically by taking the neutral gas damping effects into account and the numerical results are in agreement with the experimental data given by Nunomura et al.[Phys. Rev. E 65, 066402 (2002)]. It is found that for the mode excited by an external disturbance with a real frequency, the dispersion properties are changed at a critical frequency near where the group velocity of the mode goes to zero. Therefore, the high frequency branch with negative dispersion cannot be reached. In contrast, for the thermally excited mode, the dispersion curve can extend all the way to the negative dispersion region, while a 'cut-off' wave number exists at the long wavelength end of the dispersion in the transverse mode.
RVB signatures in the spin dynamics of the square-lattice Heisenberg antiferromagnet
NASA Astrophysics Data System (ADS)
Ghioldi, E. A.; Gonzalez, M. G.; Manuel, L. O.; Trumper, A. E.
2016-03-01
We investigate the spin dynamics of the square-lattice spin-\\frac{1}{2} Heisenberg antiferromagnet by means of an improved mean-field Schwinger boson calculation. By identifying both, the long-range Néel and the RVB-like components of the ground state, we propose an educated guess for the mean-field magnetic excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this magnetic excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low- and high-energy spectral weight features of the experimental spectrum. In particular, the anomalous spectral weight depletion at (π,0) found in recent inelastic neutron scattering experiments can be attributed to the interference of the triplet bond excitations of the RVB component of the ground state. We conclude that the Schwinger boson theory seems to be a good candidate to adequately interpret the dynamic properties of the square-lattice Heisenberg antiferromagnet.
Particulate nature of blood determines macroscopic rheology: a 2-D lattice Boltzmann analysis.
Sun, Chenghai; Munn, Lance L
2005-03-01
Historically, predicting macroscopic blood flow characteristics such as viscosity has been an empirical process due to the difficulty in rigorously including the particulate nature of blood in a mathematical representation of blood rheology. Using a two-dimensional lattice Boltzmann approach, we have simulated the flow of red blood cells in a blood vessel to estimate flow resistance at various hematocrits and vessel diameters. By including white blood cells (WBCs) in the flow, we also calculate the increase in resistance due to white cell rolling and adhesion. The model considers the blood as a suspension of particles in plasma, accounting for cell-cell and cell-wall interactions to predict macroscopic blood rheology. The model is able to reproduce the Fahraeus-Lindqvist effect, i.e., the increase in relative apparent viscosity as tube size increases, and the Fahraeus effect, i.e., tube hematocrit is lower than discharge hematocrit. In addition, the model allows direct assessment of the effect of WBCs on blood flow in the microvasculature, reproducing the dramatic increases in flow resistance as WBCs enter short capillary segments. This powerful and flexible model can be used to predict blood flow properties in any vessel geometry and with any blood composition. PMID:15613630
Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions
NASA Astrophysics Data System (ADS)
Lloyd, Seth; Terhal, Barbara M.
2016-02-01
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a model for universal quantum computation with time-independent two-qubit ZZ and XX+YY interactions on an (almost) planar grid. The effective Hamiltonian is arrived at by a single use of first-order perturbation theory avoiding the use of perturbation gadgets. The dynamics and spectral properties of the effective Hamiltonian can be fully determined as it corresponds to a particular realization of a mapping between a quantum circuit and a Hamiltonian called the space-time circuit-to-Hamiltonian construction. Because of the simple interactions required, and because no higher-order perturbation gadgets are employed, our construction is potentially realizable using superconducting or other solid-state qubits.
Zhou, Benhu Zeng, Yangsu; Zhou, Benliang; Zhou, Guanghui; Ouyang, Tao
2015-03-14
We theoretically investigate spin-dependent Seebeck effects for a system consisting of a narrow graphene nanoribbon (GNR) contacted to square lattice ferromagnetic (FM) electrodes with noncollinear magnetic moments. Both zigzag-edge graphene nanoribbons (ZGNRs) and armchair-edge graphene nanoribbons (AGNRs) were considered. Compared with our previous work with two-dimensional honeycomb-lattice FM leads, a more realistic model of two-dimensional square-lattice FM electrodes is adopted here. Using the nonequilibrium Green's function method combining with the tight-binding Hamiltonian, it is demonstrated that both the charge Seebeck coefficient S{sub C} and the spin-dependent Seebeck coefficient S{sub S} strongly depend on the geometrical contact between the GNR and the leads. In our previous work, S{sub C} for a semiconducting 15-AGNR system near the Dirac point is two orders of magnitude larger than that of a metallic 17-AGNR system. However, S{sub C} is the same order of magnitude for both metallic 17-AGNR and semiconducting 15-AGNR systems in the present paper because of the lack of a transmission energy gap for the 15-AGNR system. Furthermore, the spin-dependent Seebeck coefficient S{sub S} for the systems with 20-ZGNR, 17-AGNR, and 15-AGNR is of the same order of magnitude and its maximum absolute value can reach 8 μV/K. The spin-dependent Seebeck effects are not very pronounced because the transmission coefficient weakly depends on spin orientation. Moreover, the spin-dependent Seebeck coefficient is further suppressed with increasing angle between the relative alignments of magnetization directions of the two leads. Additionally, the spin-dependent Seebeck coefficient can be strongly suppressed for larger disorder strength. The results obtained here may provide valuable theoretical guidance in the experimental design of heat spintronic devices.
A hierarchical lattice spring model to simulate the mechanics of 2-D materials-based composites
NASA Astrophysics Data System (ADS)
Brely, Lucas; Bosia, Federico; Pugno, Nicola
2015-07-01
In the field of engineering materials, strength and toughness are typically two mutually exclusive properties. Structural biological materials such as bone, tendon or dentin have resolved this conflict and show unprecedented damage tolerance, toughness and strength levels. The common feature of these materials is their hierarchical heterogeneous structure, which contributes to increased energy dissipation before failure occurring at different scale levels. These structural properties are the key to exceptional bioinspired material mechanical properties, in particular for nanocomposites. Here, we develop a numerical model in order to simulate the mechanisms involved in damage progression and energy dissipation at different size scales in nano- and macro-composites, which depend both on the heterogeneity of the material and on the type of hierarchical structure. Both these aspects have been incorporated into a 2-dimensional model based on a Lattice Spring Model, accounting for geometrical nonlinearities and including statistically-based fracture phenomena. The model has been validated by comparing numerical results to continuum and fracture mechanics results as well as finite elements simulations, and then employed to study how structural aspects impact on hierarchical composite material properties. Results obtained with the numerical code highlight the dependence of stress distributions on matrix properties and reinforcement dispersion, geometry and properties, and how failure of sacrificial elements is directly involved in the damage tolerance of the material. Thanks to the rapidly developing field of nanocomposite manufacture, it is already possible to artificially create materials with multi-scale hierarchical reinforcements. The developed code could be a valuable support in the design and optimization of these advanced materials, drawing inspiration and going beyond biological materials with exceptional mechanical properties.
Entanglement Properties of a Quantum Lattice-Gas Model on Square and Triangular Ladders
NASA Astrophysics Data System (ADS)
Tanaka, Shu; Tamura, Ryo; Katsura, Hosho
2014-03-01
In this paper, we review the entanglement properties of a quantum lattice-gas model according to our previous paper [S. Tanaka, R. Tamura, and H. Katsura, Phys. Rev. A 86, 032326 (2012)]. The ground state of the model under consideration can be exactly obtained and expressed by the Rokhsar-Kivelson type quantum superposition. The reduced density matrices of the model on square and triangular ladders are related to the transfer matrices of the classical hard-square and hard-hexagon models, respectively. In our previous paper, we investigated the entanglement properties including the entanglement entropy, the entanglement spectrum, and the nested entanglement entropy. We found that the entanglement spectra are critical when parameters are chosen so that the corresponding classical model is critical. In order to further investigate the entanglement properties, we also considered the nested entanglement entropy. As a result, the entanglement properties of the model on square and triangular ladders are described by the critical phenomena of the Ising model and the three-state ferromagnetic Potts model in two dimension, respectively.
Beyond classical nucleation theory: A 2-D lattice-gas automata model
NASA Astrophysics Data System (ADS)
Hickey, Joseph
Nucleation is the first step in the formation of a new phase in a thermodynamic system. The Classical Nucleation Theory (CNT) is the traditional theory used to describe this phenomenon. The object of this thesis is to investigate nucleation beyond one of the most significant limitations of the CNT: the assumption that the surface tension of a nucleating cluster of the new phase is independent of the cluster's size and has the same value that it would have in the bulk of the new phase. In order to accomplish this, we consider a microscopic, two-dimensional Lattice Gas Automata (LGA) model of precipitate nucleation in a supersaturated system, with model input parameters Ess (solid particle-to-solid particle bonding energy), Esw (solid particle-to-water particle bonding energy), eta (next-to-nearest neighbour bonding coeffiicent in solid phase), and Cin (initial solute concentration). The LGA method was chosen for its advantages of easy implementation, low memory requirements, and fast computation speed. Analytical results for the system's concentration and the crystal radius as functions of time are derived and the former is fit to the simulation data in order to determine the system's equilibrium concentration. A mean first-passage time (MFPT) technique is used to obtain the nucleation rate and critical nucleus size from the simulation data. The nucleation rate and supersaturation are evaluated using a modification to the CNT that incorporates a two-dimensional, radius-dependent surface tension term. The Tolman parameter, delta, which controls the radius-dependence of the surface tension, decreases (increases) as a function of the magnitude of Ess (Esw), at fixed values of eta and Esw (Ess). On the other hand, delta increases as eta increases while E ss and Esw are held constant. The constant surface tension term of the CNT, Sigma0, increases (decreases) with increasing magnitudes of Ess (Esw) fixed values of Esw (Ess), and increases as eta is increased. Together
NASA Astrophysics Data System (ADS)
Teo, Selin H. G.; Liu, A. Q.; Yu, M. B.; Singh, J.
2006-05-01
This paper reports fabrication and demonstration of optical intersections in two-dimensional (2D) rod-type photonic crystal (PhC) structures. High resolution and aspect ratio 2D square lattice PhC waveguide intersections were designed and fabricated for application at the optical communication wavelengths centered at 1550 nm. In the silicon processing front, challenges resolved to overcome issues of drastically reduced process windows caused by the dense PhC rods arrays with critical dimensions (CDs) reduced to only a few hundred nanometers were addressed not only in terms of critical process flow design but also in the development of each processing module. In the lithographic process of deep ultraviolet laser system working at 248 nm, PhC rods of sub-lithographic wavelength CDs (115 nm in radii) were realized in high resolution, even near periphery regions where proximity errors were prone. In the deep etching module, stringent requirements on etch angle control and low sidewall scallops (undulations arising from time multiplexed etch and passivation actions) were satisfied, to prevent catastrophic etch failures, and enable optical quality facets. The successfully fabricated PhCs were also monolithically integrated with large scale optical testing fiber grooves that enabled macro optical fiber assisted coupling to the micro scale PhC devices. In the optical experiments, the transmission and crosstalk properties for the PhC intersection devices with different rod radii at the center of the PhC optical waveguides crossings were measured with repeatability. The properties of the PhC intersections were therefore optimized and verified to correspond well with first principle finite difference time domain simulations.
Ao, L; Pham, A; Xiao, H Y; Zu, X T; Li, S
2016-03-14
We have systematically investigated the effects of different vacancy defects in 2D d(0) materials SnS2 and ZrS2 using first principles calculations. The theoretical results show that the single cation vacancy and the vacancy complex like V-SnS6 can induce large magnetic moments (3-4 μB) in these single layer materials. Other defects, such as V-SnS3, V-S, V-ZrS3 and V-ZrS6, can result in n-type conductivity. In addition, the ab initio studies also reveal that the magnetic and conductive properties from the cation vacancy and the defect complex V-SnS6 can be modified using the compressive/tensile strain of the in-plane lattices. Specifically, the V-Zr doped ZrS2 monolayer can be tuned from a ferromagnetic semiconductor to a metallic/half-metallic material with decreasing/increasing magnetic moments depending on the external compressive/tensile strains. On the other hand, the semiconducting and magnetic properties of V-Sn doped SnS2 is preserved under different lattice compression and tension. For the defect complex like V-SnS6, only the lattice compression can tune the magnetic moments in SnS2. As a result, by manipulating the fabrication parameters, the magnetic and conductive properties of SnS2 and ZrS2 can be tuned without the need for chemical doping. PMID:26888010
Topological phase transitions with non-Abelian gauge potentials on square lattices
NASA Astrophysics Data System (ADS)
Chen, Yao-Hua; Li, Jian; Ting, C. S.
2013-11-01
We investigate the topological phase transition on interacting square lattices via the non-Abelian potential by employing the real-space cellular dynamical mean-field theory combining with the continuous-time Monte Carlo method. For a weak on-site Hubbard interaction, a topological band insulating state with a pair of gapless edge states is induced by a next-nearest-neighbor hopping. A phase transition from the metallic phase to the Mott insulating phase is observed when the interaction is increased. These two phases can be distinguished by detecting whether a bulk gap in the K-dependent spectral function exists. The whole phase diagrams as functions of the interaction, next-nearest-neighbor hopping energy, and temperature are presented. The experimental setup to observe these new interesting phase transitions is also discussed.
Interfaces, strings, and a soft mode in the square lattice quantum dimer model
NASA Astrophysics Data System (ADS)
Banerjee, D.; Bögli, M.; Hofmann, C. P.; Jiang, F.-J.; Widmer, P.; Wiese, U.-J.
2014-12-01
The quantum dimer model on the square lattice is a U(1 ) gauge theory that addresses aspects of the physics of high-Tc superconductors. Using a quantum Monte Carlo method, we show that the theory exists in a confining columnar valence bond solid phase. The interfaces separating distinct columnar phases display plaquette order, which, however, is not realized as a bulk phase. Static "electric" charges are confined by flux tubes that consist of multiple strands, each carrying a fractionalized flux 1/4 . A soft pseudo-Goldstone mode (which becomes exactly massless at the Rokhsar-Kivelson point) extends deep into the columnar phase, with potential implications for high-Tc physics.
Magneto-optical response in the arbitrary-Chern number topological phase on square lattice
NASA Astrophysics Data System (ADS)
Wang, Yi-Xiang
2016-07-01
In this work, we investigate the magneto-optical response in the arbitrary-Chern number topological phase. Based on the Dirac theory, we derive the analytic expressions for the magneto-optical response. More importantly, we construct the model on the possible square lattice and make the numerical calculations with the exact diagonalization method. We find the analytical and numerical results are in good agreement with each other. For the optical absorption spectrum, the low-energy absorptive peaks and the corresponding hopping processes are distinct in different Chern number phases, heavily depending on the filling factor of the system. While for the optical Hall conductivities, the physical mechanisms are revealed for the dichroism of the absorption peaks in response to the right- and left-circularly polarized light. We discuss the feasibility of these results in experiment.
Low-energy singlet excitations in spin-1/2 Heisenberg antiferromagnet on square lattice
NASA Astrophysics Data System (ADS)
Aktersky, A. Yu.; Syromyatnikov, A. V.
2016-05-01
We present an approach based on a dimer expansion which describes low-energy singlet excitations (singlons) in spin-1/2 Heisenberg antiferromagnet on simple square lattice. An operator ("effective Hamiltonian") is constructed whose eigenvalues give the singlon spectrum. The "effective Hamiltonian" looks like a Hamiltonian of a spin-1/2 magnet in strong external magnetic field and it has a gapped spectrum. It is found that singlet states lie above triplet ones (magnons) in the whole Brillouin zone except in the vicinity of the point (π , 0), where their energies are slightly smaller. Based on this finding, we suggest that a magnon decay is possible near (π , 0) into another magnon and a singlon which may contribute to the dip of the magnon spectrum near (π , 0) and reduce the magnon lifetime. It is pointed out that the singlon-magnon continuum may contribute to the continuum of excitations observed recently near (π , 0).
Phase transition of anisotropic frustrated Heisenberg model on the square lattice.
Hu, Ai-Yuan; Wang, Huai-Yu
2016-01-01
We have investigated the J_{1}-J_{2} Heisenberg model with exchange anisotropy on a square lattice and focused on possible AF1-AF2 phase transition below the Néel point and its dependence on the exchange anisotropy, where AF1 and AF2 represent Néel state and collinear state, respectively. We use the double-time Green's-function method and adopt the random-phase approximation. The less the exchange anisotropy, the stronger the quantum fluctuation of the system will be. Both the Néel state and collinear state can exist and have the same Néel temperature for arbitrary anisotropy and spin quantum number S when J_{2}/J_{1}=0.5. Under such parameters, the calculated free energies show that there may occur a first-order phase transition between the Néel state and collinear state for an arbitrary S when anisotropy is not strong. PMID:26871025
Magnetic correlations and pairing in the 1/5-depleted square lattice Hubbard model.
Khatami, Ehsan; Singh, Rajiv R P; Pickett, Warren E; Scalettar, Richard T
2014-09-01
We study the single-orbital Hubbard model on the 1/5-depleted square-lattice geometry, which arises in such diverse systems as the spin-gap magnetic insulator CaV4O9 and ordered-vacancy iron selenides, presenting new issues regarding the origin of both magnetic ordering and superconductivity in these materials. We find a rich phase diagram that includes a plaquette singlet phase, a dimer singlet phase, a Néel and a block-spin antiferromagnetic phase, and stripe phases. Quantum Monte Carlo simulations show that the dominant pairing correlations at half filling change character from d wave in the plaquette phase to extended s wave upon transition to the Néel phase. These findings have intriguing connections to iron-based superconductors, and suggest that some physics of multiorbital systems can be captured by a single-orbital model at different dopings. PMID:25238374
Effect of dominant three-body interaction in two-dimensional square lattice
NASA Astrophysics Data System (ADS)
Liang, Ying; Guo, Huaiming
2012-12-01
The effect of dominant three-body interaction to hard-core boson Hubbard model is studied on a two-dimensional square lattice. In terms of quantum Monte Carlo method, it is shown explicitly a ρ = 2/3 solid phase with coexistence of charge-density-wave and bond orders appears due to the presence of the dominant three-body interaction. For strong three-body interaction, the ρ = 2/3 solid phase appears between superfluid phases and shrinks as decreasing the strength of the three-body interaction, forming a lobe structure in the phase diagram. For weak three-body interactions, superfluid phase exists for the whole range of hard-core densities except the full filled case, where the system is a Mott insulator.
Spin transport in the frustrated anisotropic two-dimensional ferromagnet in the square lattice
NASA Astrophysics Data System (ADS)
Lima, L. S.
2016-08-01
We use the SU(3) Schwinger boson formalism together with the Kubo theory of the linear response to study the spin transport in the two-dimensional S=1 frustrated anisotropic Heisenberg ferromagnet in a square lattice with easy-plane single-ion anisotropy and considering the second-neighbor interaction in the diagonal and the third-neighbor interaction (J1-J2-J3 model). The AC spin conductivity σreg(ω) is determined for several values of the critical single-ion parameter D, and the frustration parameters J2 and J3. We have calculated the dynamic structure factor too, S(q → , ω), for this model and obtained a behaviour exponentially decreasing for the damping Γq with the decreasing of q = | q → | towards q → 0.
Zhang, Wan; Li, Shu-Guang; An, Guo-Wen; Fan, Zhen-Kai; Bao, Ya-Jie
2014-04-10
A novel design of Au-filled photonic crystal fiber (PCF) with square lattice has been proposed in this paper. The resonance strength of the surface plasmon mode and the impacts of structural parameters of the PCF on the polarization filter characteristics are studied through the finite element method. Numerical results show that the sizes of Au wires and the symmetry of the air holes near the fiber core have a great effect on the polarization filter characteristics. In the optimization process, it was found that the resonance strengths can reach 279.10 and 399.18 dB/cm at wavelengths of 1.02 μm and 1.55 μm, respectively, which can be applied in many polarization filter devices. PMID:24787416
Two-dimensional XXZ -Ising model on a square-hexagon lattice
NASA Astrophysics Data System (ADS)
Valverde, J. S.; Rojas, Onofre; de Souza, S. M.
2009-04-01
We study a two-dimensional XXZ -Ising model on a square-hexagon (denoted for simplicity by 4-6) lattice with spin 1/2. The phase diagram at zero temperature is discussed, where five states are found, two types of ferrimagnetic states, two types of antiferromagnetic states, and one ferromagnetic state. To solve this model, we have mapped onto the eight-vertex model with union Jack interaction term, and it was verified that the model cannot be completely mapped onto eight-vertex model. However, by imposing an exact solution condition, we have found the region where the XXZ -Ising model on 4-6 lattice is exactly soluble with one free parameter, particularly for the case of symmetric eight-vertex model condition. In this manner we have explored the properties of the system and have analyzed the interacting competition parameters which preserve the region where there is an exact solution. Unfortunately the present model does not satisfy the free fermion condition of the eight-vertex model, unless for a trivial solution. Even so, we are able to discuss the critical point region, beyond the region of exact resolvability.
NASA Astrophysics Data System (ADS)
Jazaeri, S.; Amiri-Simkooei, A. R.; Sharifi, M. A.
2012-02-01
GNSS ambiguity resolution is the key issue in the high-precision relative geodetic positioning and navigation applications. It is a problem of integer programming plus integer quality evaluation. Different integer search estimation methods have been proposed for the integer solution of ambiguity resolution. Slow rate of convergence is the main obstacle to the existing methods where tens of ambiguities are involved. Herein, integer search estimation for the GNSS ambiguity resolution based on the lattice theory is proposed. It is mathematically shown that the closest lattice point problem is the same as the integer least-squares (ILS) estimation problem and that the lattice reduction speeds up searching process. We have implemented three integer search strategies: Agrell, Eriksson, Vardy, Zeger (AEVZ), modification of Schnorr-Euchner enumeration (M-SE) and modification of Viterbo-Boutros enumeration (M-VB). The methods have been numerically implemented in several simulated examples under different scenarios and over 100 independent runs. The decorrelation process (or unimodular transformations) has been first used to transform the original ILS problem to a new one in all simulations. We have then applied different search algorithms to the transformed ILS problem. The numerical simulations have shown that AEVZ, M-SE, and M-VB are about 320, 120 and 50 times faster than LAMBDA, respectively, for a search space of dimension 40. This number could change to about 350, 160 and 60 for dimension 45. The AEVZ is shown to be faster than MLAMBDA by a factor of 5. Similar conclusions could be made using the application of the proposed algorithms to the real GPS data.
Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2005-10-01
A numerical model of the lattice Boltzmann method (LBM) utilizing least-squares finite-element method in space and the Crank-Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility. PMID:16383571
Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice. I
NASA Astrophysics Data System (ADS)
Katomeris, G.; Selva, F.; Pichard, J.-L.
2003-02-01
In 1969, Andreev and Lifshitz have conjectured the existence of a supersolid phase taking place at zero temperature between the quantum liquid and the solid. In this and a succeeding paper, we re-visit this issue for a few polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. This paper is restricted to the magic number of particles N = 4 for which a square Wigner molecule is formed when U increases and to the size L = 6 suitable for exact numerical diagonalizations. When the Coulomb energy to kinetic energy ratio rs = UL/(2t) reaches a value rsF 10, there is a level crossing between ground states of different momenta. Above rsF, the mesoscopic crystallization proceeds through an intermediate regime ( rsF < rs < rsW 28) where unpaired fermions with a reduced Fermi energy co-exist with a strongly paired, nearly solid assembly. We suggest that this is the mesoscopic trace of the supersolid proposed by Andreev and Lifshitz. When a random substrate is included, the level crossing at rsF is avoided and gives rise to a lower threshold rsF(W) < rsF where two usual approximations break down: the Wigner surmise for the distribution of the first energy excitation and the Hartree-Fock approximation for the ground state.
NASA Astrophysics Data System (ADS)
Jurčišinová, E.; Jurčišin, M.
2016-02-01
We investigate the second order phase transitions of the ferromagnetic spin-1 Ising model on pure Husimi lattices built up from elementary squares with arbitrary values of the coordination number. It is shown that the critical temperatures of the second order phase transitions are driven by a single equation simultaneously on all such lattices. It is also shown that for arbitrary given value of the coordination number this equation is equivalent to the corresponding polynomial equation. The explicit form of these polynomial equations is present for the lattices with the coordination numbers z = 4 , 6, and 8. It is proven that, at least for the small values of the coordination number, the positions of the critical temperatures are uniquely determined. In addition, it is shown that the properties of all phases of the model are also driven by the corresponding single equations simultaneously on all pure Husimi lattices built up from elementary squares. The spontaneous magnetization of the model is investigated in detail.
NASA Astrophysics Data System (ADS)
Masrour, R.; Jabar, A.; Benyoussef, A.; Hamedoun, M.
2016-07-01
In this work, we have studied and compared the magnetic properties of Ising spins-5/2 and 3/2 systems on decorated square and triangular lattices using the Monte Carlo simulations. The transition temperature of the two-dimensional decorated square and triangular lattices has been obtained. The effect of the exchange interactions and crystal field on the magnetization is investigated. The magnetic coercive field and saturation magnetization of the two-dimensional decorated square and triangular lattices have been obtained.
An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice
Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.; Petzold, Linda R.
2014-01-01
We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.
Statistics of opinion domains of the majority-vote model on a square lattice
NASA Astrophysics Data System (ADS)
Peres, Lucas R.; Fontanari, José F.
2010-10-01
The existence of juxtaposed regions of distinct cultures in spite of the fact that people’s beliefs have a tendency to become more similar to each other’s as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we study an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors’ opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size L and that they interact with their nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with L2 whereas the size of the largest cluster grows with lnL2 . The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model—Axelrod’s model—we found that these opinion domains are unstable to the effect of a thermal-like noise.
The dynamic critical properties of the spin-2 Ising model on a bilayer square lattice
NASA Astrophysics Data System (ADS)
Temizer, Ümüt; Yarar, Semih; Tülek, Mesimi
2016-05-01
The spin-2 Ising model is investigated for the ferromagnetic/ferromagnetic (FM/FM), antiferromagnetic/ferromagnetic (AFM/FM) and antiferromagnetic/antiferromagnetic (AFM/AFM) interactions on the two-layer square lattice by using the Glauber-type stochastic dynamics. The system is in contact with a heat bath at temperature T, and the exchange of energy with the heat bath occurs via one-spin flip. By employing the Master equation and Glauber transition rates, the dynamic equations of the system are obtained. These equations are solved by using the numerical methods. First, we investigate the average order parameters as a function of the time to find the phases in the system. Then, the temperature-dependence of the dynamic order parameters is examined to obtain the dynamic phase transition temperatures. The dynamic phase diagrams are presented on the different planes. According to the values of the system parameters, a variety of dynamic critical points such as tricritical point, triple point, quadruple point, critical end point, double critical end point, zero-temperature critical point, multicritical point and tetracritical point are obtained. The reentrant behavior is seen in the system for the AFM/AFM interaction. Finally, we also investigate the influence of the oscillating field frequency on the dynamic phase diagrams in detail.
Anomalous Phonon Dispersion of an Ultracold - Mixture in a Square Optical Lattice
NASA Astrophysics Data System (ADS)
Koinov, Zlatko; Pahl, Shanna; Mendoza, Rafael
2015-05-01
A necessary condition for the damping of the long-wavelength excitations of the superfluid phase (referred to as superfluid phonons) due to the three-particle process is to have an anomalous phonon dispersion. The existence of anomalous phonon dispersion has been confirmed in superfluid . There are no experimental data suggesting that this phenomenon exists in superfluid Fermi gases. To the best of our knowledge, the existence of anomalous dispersion has been theoretically predicted only in atomic spin balanced Fermi gas close to the unitarity limit. The numerical results reported here suggest that the anomalous long-wavelength dispersion can be realized in mass and spin imbalanced atomic Fermi gases away from the unitary limit. In particular, the numerical solution of the Bethe-Salpeter equation in a weak-coupling regime shows that the long-wavelength part of the collective-mode dispersion of the superfluid Fulde-Ferrell phase of a mixture of population-imbalanced Lithium-6 and Potassium-40 atoms in a square lattice at some values of polarization, interacting strength and temperature initially bends upward before bending over.
NASA Astrophysics Data System (ADS)
Zhao, Sheng-Dong; Wang, Yue-Sheng
2016-05-01
The negative refraction behavior and imaging effect for acoustic waves in a kind of two-dimensional square chiral lattice structure are studied in this paper. The unit cell of the proposed structure consists of four zigzag arms connected through a thin circular ring at the central part. The relation of the symmetry of the unit cell and the negative refraction phenomenon is investigated. Using the finite element method, we calculate the band structures and the equi-frequency surfaces of the system, and confirm the frequency range where the negative refraction is present. Due to the rotational symmetry of the unit cell, a phase difference is induced to the waves propagating from a point source through the structure to the other side. The phase difference is related to the width of the structure and the frequency of the source, so we can get a tunable deviated imaging. This kind of phenomenon is also demonstrated by the numerical simulation of two Gaussian beams that are symmetrical about the interface normal with the same incident angle, and the different negative refractive indexes are presented. Based on this special performance, a double-functional mirror-symmetrical slab is proposed for realizing acoustic focusing and beam separation. xml:lang="fr"
Search for the Heisenberg spin glass on rewired square lattices with antiferromagnetic interaction
NASA Astrophysics Data System (ADS)
Surungan, Tasrief; Bansawang B., J.; Tahir, Dahlang
2016-03-01
Spin glass (SG) is a typical magnetic system with frozen random spin orientation at low temperatures. The system exhibits rich physical properties, such as infinite number of ground states, memory effect, and aging phenomena. There are two main ingredients considered to be pivotal for the existence of SG behavior, namely, frustration and randomness. For the canonical SG system, frustration is led by the presence of competing interaction between ferromagnetic (FM) and antiferromagnetic (AF) couplings. Previously, Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)], reported the SG properties of the AF Ising spins on scale free network (SFN). It is a new type of SG, different from the canonical one which requires the presence of both FM and AF couplings. In this new system, frustration is purely caused by the topological factor and its randomness is related to the irregular connectvity. Recently, Surungan et. al. [Journal of Physics: Conference Series, 640, 012001 (2015)] reported SG bahavior of AF Heisenberg model on SFN. We further investigate this type of system by studying an AF Heisenberg model on rewired square lattices. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter to search for the existence of SG phase.
Numerical study of a three-state host-parasite system on the square lattice.
Hasegawa, Takehisa; Konno, Norio; Masuda, Naoki
2011-04-01
We numerically study the phase diagram of a three-state host-parasite model on the square lattice motivated by population biology. The model is an extension of the contact process, and the three states correspond to an empty site, a host, and a parasite. We determine the phase diagram of the model by scaling analysis. In agreement with previous results, three phases are identified: the phase in which both hosts and parasites are extinct (S(0)), the phase in which hosts survive but parasites are extinct (S(01)), and the phase in which both hosts and parasites survive (S(012)). We argue that both the S(0)-S(01) and S(01)-S(012) boundaries belong to the directed percolation class. In this model, it has been suggested that an excessively large reproduction rate of parasites paradoxically extinguishes hosts and parasites and results in S(0). We show that this paradoxical extinction is a finite size effect; the corresponding parameter region is likely to disappear in the limit of infinite system size. PMID:21599235
Properties of the multicritical point of ±J Ising spin glasses on the square lattice
NASA Astrophysics Data System (ADS)
Lessa, Jean C.; de Queiroz, S. L. A.
2006-10-01
We use numerical transfer-matrix methods to investigate properties of the multicritical point of binary Ising spin glasses on a square lattice, whose location we assume to be given exactly by a conjecture advanced by Nishimori and Nemoto. We calculate the two largest Lyapunov exponents, as well as linear and nonlinear zero-field uniform susceptibilities, on strip of widths 4⩽L⩽16 sites, from which we estimate the conformal anomaly c , the decay-of-correlations exponent η , and the linear and nonlinear susceptibility exponents γ/ν and γnl/ν , with the help of finite-size scaling and conformal invariance concepts. Our results are c=0.46(1) ; 0.187≲η≲0.196 ; γ/ν=1.797(5) ; γnl/ν=5.59(2) . A direct evaluation of correlation functions on the strip geometry, and of the statistics of the zeroth moment of the associated probability distribution, gives η=0.194(1) , consistent with the calculation via Lyapunov exponents. Overall, these values tend to be inconsistent with the universality class of percolation, though by small amounts. The scaling relation γnl/ν=2γ/ν+d (with space dimensionality d=2 ) is obeyed to rather good accuracy, thus showing no evidence of multiscaling behavior of the susceptibilities.
NASA Astrophysics Data System (ADS)
Zenine, N.; Boukraa, S.; Hassani, S.; Maillard, J.-M.
2005-10-01
We present a simple, but efficient, way to calculate connection matrices between sets of independent local solutions, defined at two neighbouring singular points, of Fuchsian differential equations of quite large orders, such as those found for the third and fourth contribution (χ(3) and χ(4)) to the magnetic susceptibility of the square lattice Ising model. We deduce all the critical behaviours of the solutions χ(3) and χ(4), as well as the asymptotic behaviour of the coefficients in the corresponding series expansions. We confirm that the newly found quadratic singularities of the Fuchsian ODE associated with χ(3) are not singularities of the particular solution χ(3) itself. We use the previous connection matrices to get the exact expressions of all the monodromy matrices of the Fuchsian differential equation for χ(3) (and χ(4)) expressed in the same basis of solutions. These monodromy matrices are the generators of the differential Galois group of the Fuchsian differential equations for χ(3) (and χ(4)), whose analysis is just sketched here. As far as the physics implications of the solutions are concerned, we find challenging qualitative differences when comparing the corrections to scaling for the full susceptibility χ at high temperature (respectively low temperature) and the first two terms χ(1) and χ(3) (respectively χ(2) and χ(4)).
NASA Astrophysics Data System (ADS)
Zenine, N.; Boukraa, S.; Hassani, S.; Maillard, J.-M.
2006-06-01
We first study the properties of the Fuchsian ordinary differential equations for the three and four-particle contributions χ(3) and χ(4) of the square lattice Ising model susceptibility. An analysis of some mathematical properties of these Fuchsian differential equations is sketched. For instance, we study the factorization properties of the corresponding linear differential operators, and consider the singularities of the three and four-particle contributions χ(3) and χ(4), versus the singularities of the associated Fuchsian ordinary differential equations, which actually exhibit new ''Landau-like'' singularities. We sketch the analysis of the corresponding differential Galois groups. In particular we provide a simple, but efficient, method to calculate the so-called ''connection matrices'' (between two neighboring singularities) and deduce the singular behaviors of χ(3) and χ(4). We provide a set of comments and speculations on the Fuchsian ordinary differential equations associated with the n-particle contributions χ(n) and address the problem of the apparent discrepancy between such a holonomic approach and some scaling results deduced from a Painlevé oriented approach.
Asymptotic behavior for a version of directed percolation on a square lattice
NASA Astrophysics Data System (ADS)
Chen, Lung-Chi
2011-02-01
We consider a version of directed bond percolation on a square lattice whose vertical edges are directed upward with probabilities pv and horizontal edges are directed rightward with probabilities ph and 1 in alternate rows. Let τ(M,N) be the probability that there is a connected directed path of occupied edges from (0,0) to (M,N). For each ph∈[0,1], pv=(0,1) and aspect ratio α=M/N fixed, it was established (Chen and Wu, 2006) [9] that there is an αc=[1-pv2-ph(1]/2pv2 such that, as N→∞, τ(M,N) is 1, 0, and 1/2 for α>αc, α<αc, and α=αc, respectively. In particular, for ph=0 or 1, the model reduces to the Domany-Kinzel model (Domany and Kinzel, 1981 [7]). In this article, we investigate the rate of convergence of τ(M,N) and the asymptotic behavior of τ(Mn-,N) and τ(Mn+,N), where Mn-/N↑αc and Mn+/N↓αc as N↑∞. Moreover, we obtain a susceptibility on the rectangular net {(m,n)∈Z+×Z+:0≤m≤M and 0≤n≤N}. The proof is based on the Berry-Esseen theorem.
Analysis of the phase transition for the Ising model on the frustrated square lattice
NASA Astrophysics Data System (ADS)
Kalz, Ansgar; Honecker, Andreas; Moliner, Marion
2011-11-01
We analyze the phase transition of the frustrated J1-J2 Ising model with antiferromagnetic nearest- and strong next-nearest-neighbor interactions on the square lattice. Using extensive Monte Carlo simulations we show that the nature of the phase transition for 1/2
NASA Astrophysics Data System (ADS)
Indrani, Murugan; Ramasubramanian, Ramasamy; Fronczek, Frank R.; Vasanthacharya, N. Y.; Kumaresan, Sudalaiandi
2009-08-01
Three distinct coordination complexes, viz., [Co(imi) 2(tmb) 2] ( 1) [where imi = imidazole], {[Ni(tmb) 2(H 2O) 3]·2H 2O} n ( 2) and [Cu 2(μ-tmb) 4(CH 3OH) 2] ( 3), have been synthesized hydrothermally by the reactions of metal acetates, 2,4,6-trimethylbenzoic acid (Htmb) and with or without appropriate amine. The Ni analogue of 1 and the Co analogue of 2 have also been synthesized. X-ray single-crystal diffraction suggests that complex 1 represents discrete mononuclear species and complex 2 represents a 1D chain coordination polymer in which the Ni(II) ions are connected by the bridging water molecules. Complex 3 represents a neutral dinuclear complex. In 1, the central metal ions are associated by the carboxylate moiety and imidazole ligands, whereas the central metal atom is coordinated to the carboxylate moiety and the respective solvent molecules in 2 and 3. In 3, the four 2,4,6-trimethylbenzoate moieties act as a bridge connecting two copper (II) ions and the O atoms of methanol coordinate in an anti arrangement to form a square pyramidal geometry, with the methanol molecule at the apical position. In all the three structures the central metal atom sits on a crystallographic inversion centre. In all the cases, the coordination entities are further organized via hydrogen bonding interactions to generate multifarious supramolecular networks. Complexes 1, 2 and 3 have also been characterized by spectroscopic (UV/Vis and IR) and thermal analysis (TGA). In addition, the complexes were found to exhibit antimicrobial activity.The magnetic susceptibility measurements, measured from 8 to 300 K, revealed antiferromagnetic interactions between the Co(II) ions in compound 1 and the Ni(II) ions in 1a, respectively.
Control of the third dimension in copper-based square-lattice antiferromagnets
NASA Astrophysics Data System (ADS)
Goddard, Paul A.; Singleton, John; Franke, Isabel; Möller, Johannes S.; Lancaster, Tom; Steele, Andrew J.; Topping, Craig V.; Blundell, Stephen J.; Pratt, Francis L.; Baines, C.; Bendix, Jesper; McDonald, Ross D.; Brambleby, Jamie; Lees, Martin R.; Lapidus, Saul H.; Stephens, Peter W.; Twamley, Brendan W.; Conner, Marianne M.; Funk, Kylee; Corbey, Jordan F.; Tran, Hope E.; Schlueter, J. A.; Manson, Jamie L.
2016-03-01
Using a mixed-ligand synthetic scheme, we create a family of quasi-two-dimensional antiferromagnets, namely, [Cu (HF2) (pyz) 2] ClO4 [pyz = pyrazine], [Cu L2(pyz) 2] (ClO4)2 [L = pyO = pyridine-N-oxide and 4-phpy-O = 4-phenylpyridine-N-oxide. These materials are shown to possess equivalent two-dimensional [Cu(pyz)2] 2 + nearly square layers, but exhibit interlayer spacings that vary from 6.5713 to 16.777 Å, as dictated by the axial ligands. We present the structural and magnetic properties of this family as determined via x-ray diffraction, electron-spin resonance, pulsed- and quasistatic-field magnetometry and muon-spin rotation, and compare them to those of the prototypical two-dimensional magnetic polymer Cu(pyz) 2(ClO4)2 . We find that, within the limits of the experimental error, the two-dimensional, intralayer exchange coupling in our family of materials remains largely unaffected by the axial ligand substitution, while the observed magnetic ordering temperature (1.91 K for the material with the HF2 axial ligand, 1.70 K for the pyO and 1.63 K for the 4-phpy-O) decreases slowly with increasing layer separation. Despite the structural motifs common to this family and Cu(pyz) 2(ClO4)2 , the latter has significantly stronger two-dimensional exchange interactions and hence a higher ordering temperature. We discuss these results, as well as the mechanisms that might drive the long-range order in these materials, in terms of departures from the ideal S =1 /2 two-dimensional square-lattice Heisenberg antiferromagnet. In particular, we find that both spin-exchange anisotropy in the intralayer interaction and interlayer couplings (exchange, dipolar, or both) are needed to account for the observed ordering temperatures, with the intralayer anisotropy becoming more important as the layers are pulled further apart.
NASA Astrophysics Data System (ADS)
Velarde, M. G.; Ebeling, W.; Chetverikov, A. P.
2013-01-01
We study the thermal excitation of intrinsic localized modes in the form of solitons in 1d and 2d anharmonic lattices at moderately high temperatures. Such finite-amplitude fluctuations form long-living dynamical structures with life-time in the pico-second range thus surviving a relatively long time in comparison to other thermal fluctuations. Further we discuss the influence of such long-living fluctuations on the dynamics of added excess free electrons. The atomic lattice units are treated as quasi-classical objects interacting by Morse forces and stochastically moving according to Langevin equations. In 2d the atoms are initially organized in a triangular lattice. The electron distributions are in a first estimate represented by equilibrium adiabatic distributions in the actual polarization fields. Computer simulations show that in 2d systems such excitations are moving with supersonic velocities along lattice rows oriented with the cristallographic axes. By following the electron distributions we have also been able to study the excitations of solectron type (electron-soliton dynamic bound states) and estimate their life times.
Fefelov, V F; Gorbunov, V A; Myshlyavtsev, A V; Myshlyavtseva, M D
2010-10-01
A model of homonuclear dimer adsorption in terms of two possible molecule orientations with respect to the surface on a square lattice has been constructed and studied. The dimers can occupy one or two sites on the lattice. The thermodynamics of this system has been studied by transfer-matrix and Monte Carlo methods. The phase diagram has been constructed. It was shown that in the vicinity of the tricritical point the coverage as a function of chemical potential possesses a minimum. This phenomenon seems to be the common one for molecules with several ways of adsorption. PMID:21230282
NASA Astrophysics Data System (ADS)
Salas, Jesús; Sokal, Alan D.
2011-09-01
We study, using transfer-matrix methods, the partition-function zeros of the square-lattice q-state Potts antiferromagnet at zero temperature (= square-lattice chromatic polynomial) for the boundary conditions that are obtained from an m× n grid with free boundary conditions by adjoining one new vertex adjacent to all the sites in the leftmost column and a second new vertex adjacent to all the sites in the rightmost column. We provide numerical evidence that the partition-function zeros are becoming dense everywhere in the complex q-plane outside the limiting curve {B}_{infty}(sq) for this model with ordinary (e.g. free or cylindrical) boundary conditions. Despite this, the infinite-volume free energy is perfectly analytic in this region.
NASA Astrophysics Data System (ADS)
Wu, Ya-Jie; Li, Ning; He, Jing; Kou, Su-Peng
2016-03-01
In this paper, based on mean-field approach and random-phase-approximation, we study the magnetic properties of the repulsive Haldane-Hubbard model on a square lattice. We find antiferromagnetic order driven topological spin density waves beyond Landau’s symmetry-breaking paradigm, for which the effective low energy physics is determined by Chern-Simons-Hopf gauge field theories with different K matrices.
Córcoles, A.D.; Magesan, Easwar; Srinivasan, Srikanth J.; Cross, Andrew W.; Steffen, M.; Gambetta, Jay M.; Chow, Jerry M.
2015-01-01
The ability to detect and deal with errors when manipulating quantum systems is a fundamental requirement for fault-tolerant quantum computing. Unlike classical bits that are subject to only digital bit-flip errors, quantum bits are susceptible to a much larger spectrum of errors, for which any complete quantum error-correcting code must account. Whilst classical bit-flip detection can be realized via a linear array of qubits, a general fault-tolerant quantum error-correcting code requires extending into a higher-dimensional lattice. Here we present a quantum error detection protocol on a two-by-two planar lattice of superconducting qubits. The protocol detects an arbitrary quantum error on an encoded two-qubit entangled state via quantum non-demolition parity measurements on another pair of error syndrome qubits. This result represents a building block towards larger lattices amenable to fault-tolerant quantum error correction architectures such as the surface code. PMID:25923200
All-optical controllable channel-drop filters in two-dimensional square-lattice photonic crystals
NASA Astrophysics Data System (ADS)
Fasihi, K.
2016-05-01
A novel all-optical controllable channel-drop filter in photonic crystals (PC) of square lattice is presented. We show that using a resonant-cavity-based add-drop filter with a wavelength-selective reflection feedback and a single-control switching module which is based on nonlinear PC microcavities, the dropped channel can be routed to the drop port or returned to the bus waveguide. Using the temporal coupled-mode theory and two-dimensional nonlinear finite-difference time-domain method, the performance of the proposed device is investigated and the simulation results show the validity of the proposed design.
NASA Astrophysics Data System (ADS)
Inui, Norio
1998-12-01
We investigate numerically the percolation probability of the asymmetric directed-bond percolation on the square lattice with two parameters p and q based on Guttmann and Enting's procedure (1996 Phys. Rev. Lett. 76 344). A series in the form of 0305-4470/31/48/001/img1 is derived by using the finite transfer-matrix method. The denominator of 0305-4470/31/48/001/img2 is directly calculated from the determinant of the transfer matrix and it leads to a proof that poles all lies on the unit circle in the complex q plane. The solvability of the bond directed percolation is also discussed.
Core-shell structured square mixed-spin 1 and 1/2 Ising nanowire on the Bethe lattice
NASA Astrophysics Data System (ADS)
Albayrak, Erhan
2016-03-01
The square Ising nanowire is constructed by adding square nanoparticles consisting of one spin-1 at the center and four spin-1/2 at the corners along a straight line in both directions. Therefore, this system may be taken to be equivalent to Bethe lattice of coordination number two and can be solved in terms of the exact recursion relations. This core-shell structured model is studied by using ferromagnetic exchange interactions between surface spins (Js), between core spins (Jc) and between surface and core spins (Jsc) and crystal field interaction (D) at the sites of spin-1. The phase diagrams of the model are obtained in terms of these parameters by varying the temperature on the possible planes. It is found that the model presents both second- and first-order phase transitions and tricritical points for the appropriate values of these parameters.
Physical significance of least mean squares criterion in nonstationary lattice predictors
NASA Astrophysics Data System (ADS)
Martinelli, G.; Orlandi, G.; Prinaricotti, L.; Ragazzini, S.
1985-06-01
An acoustical nonstationary model of the vocal tract is discussed. The effectiveness of the nonstationary lattice predictor in recovering the model is illustrated. The reflection coefficients are linearly decomposed on a function basis and the weights of the linear combinations are the new parameters of the model. Parameters are determined by an algorithm similar to Burg's by minimizing the sum of the variances of the forward and backward residuals. Synthetic signals of good approximation are obtained in two examples.
NASA Astrophysics Data System (ADS)
Rodrigues, Nathann T.; Oliveira, Tiago J.
2014-10-01
We study a generalized interacting self-avoiding walk (ISAW) model with nearest- and next nearest-neighbor (NN and NNN) interactions on square and cubic lattices. In both dimensions, the phase diagrams show coil and globule phases separated by continuous transition lines. Along these lines, we calculate the metric νt, crossover ϕt and entropic γt exponents, all of them in good agreement with the exact values of the Θ universality class. Therefore, the introduction of NNN interactions does not change the class of the ISAW model, which still exists even for repulsive forces. The growth parameters μt are shown to change monotonically with temperature along the Θ-lines. In the square lattice, the Θ-line has an almost linear behavior, which was not found in the cubic one. Although the region of repulsive NNN interactions, with attractive NN ones, leads to stiff polymers, no evidence of a transition to a crystalline phase was found.
NASA Astrophysics Data System (ADS)
Lebovka, Nikolai I.; Tarasevich, Yuri Yu.; Dubinin, Dmitri O.; Laptev, Valeri V.; Vygornitskii, Nikolai V.
2015-12-01
The jamming and percolation for two generalized models of random sequential adsorption (RSA) of linear k -mers (particles occupying k adjacent sites) on a square lattice are studied by means of Monte Carlo simulation. The classical RSA model assumes the absence of overlapping of the new incoming particle with the previously deposited ones. The first model is a generalized variant of the RSA model for both k -mers and a lattice with defects. Some of the occupying k adjacent sites are considered as insulating and some of the lattice sites are occupied by defects (impurities). For this model even a small concentration of defects can inhibit percolation for relatively long k -mers. The second model is the cooperative sequential adsorption one where, for each new k -mer, only a restricted number of lateral contacts z with previously deposited k -mers is allowed. Deposition occurs in the case when z ≤(1 -d ) zm where zm=2 (k +1 ) is the maximum numbers of the contacts of k -mer, and d is the fraction of forbidden contacts. Percolation is observed only at some interval kmin≤k ≤kmax where the values kmin and kmax depend upon the fraction of forbidden contacts d . The value kmax decreases as d increases. A logarithmic dependence of the type log10(kmax) =a +b d , where a =4.04 ±0.22 ,b =-4.93 ±0.57 , is obtained.
NASA Astrophysics Data System (ADS)
Laflorencie, Nicolas; Luitz, David J.; Alet, Fabien
2015-09-01
Using a modified spin-wave theory which artificially restores zero sublattice magnetization on finite lattices, we investigate the entanglement properties of the Néel ordered J1-J2 Heisenberg antiferromagnet on the square lattice. Different kinds of subsystem geometries are studied, either corner-free (line, strip) or with sharp corners (square). Contributions from the nG=2 Nambu-Goldstone modes give additive logarithmic corrections with a prefactor nG/2 independent of the Rényi index. On the other hand, π /2 corners lead to additional (negative) logarithmic corrections with a prefactor lqc which does depend on both nG and the Rényi index q , in good agreement with scalar field theory predictions. By varying the second neighbor coupling J2 we also explore universality across the Néel ordered side of the phase diagram of the J1-J2 antiferromagnet, from the frustrated side 0
Parity-time-symmetry breaking in two-dimensional photonic crystals: Square lattice
NASA Astrophysics Data System (ADS)
Mock, Adam
2016-06-01
We consider theoretically materials whose electromagnetic properties possess parity-time (PT ) symmetry and are periodic in two dimensions. When designed for optical frequencies such structures are commonly known as two-dimensional (2D) photonic crystals. With the addition of PT symmetry the optical modes of 2D photonic crystals exhibit thresholdless spontaneous PT -symmetry breaking near the Brillouin zone boundary, which is analogous to what has previously been studied in PT -symmetric structures with one-dimensional periodicity. Consistent with previous work, we find that spontaneous PT -symmetry breaking occurs at band crossings in the photonic dispersion diagram. Due to the extra spatial degree of freedom in 2D periodic systems, their band structures contain more band crossings and higher-order degeneracies than their one-dimensional counterparts. This work provides a comprehensive theoretical analysis of spontaneous PT -symmetry breaking at these points in the band structure. We find that, as in the case of one-dimensional structures, photonic band gaps exist at k =0 . We also find that at points of degeneracy with order higher than 2, bands merge pairwise to form broken-PT -symmetry supermodes. If the degeneracy order is even, this means multiple pairs of bands can form distinct (nondegenerate) broken-symmetry supermodes. If the order of degeneracy is odd, at least one of the bands will have protected PT symmetry. At other points of degeneracy, we find that the PT symmetry of the modes may be protected and we provide a spatial mode symmetry argument to explain this behavior. Finally, we identify a point at which two broken-PT -symmetry supermodes become degenerate, creating a point of fourfold degeneracy in the broken-PT -symmetry regime.
Nematic phase in the J1-J2 square-lattice Ising model in an external field
NASA Astrophysics Data System (ADS)
Guerrero, Alejandra I.; Stariolo, Daniel A.; Almarza, Noé G.
2015-05-01
The J1-J2 Ising model in the square lattice in the presence of an external field is studied by two approaches: the cluster variation method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined, and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter κ =J2/|J1| which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.
NASA Astrophysics Data System (ADS)
Bouchiat, Marie-Anne; Bouchiat, Claude
2012-10-01
We have constructed the geometric phases emerging from the non-trivial topology of a space-dependent magnetic field B(r), interacting with the spin magnetic moment of a neutral particle. Our basic tool, adapted from a previous work on Berry’s phases, is the space-dependent unitary transformation {U}({\\mathbf {r}}), which leads to the identity, {U}({\\mathbf {r}})^{\\dag }\\, {\\mathbf {S}}\\,{\\bm \\cdot}\\, {\\mathbf {B}}({\\mathbf {r}}) \\, {U}({\\mathbf {r}}) = \\vert {\\mathbf {B}}({\\mathbf {r}}) \\vert \\, S_z, at each point r. In the ‘rotated’ Hamiltonian \\widehat{ H}, \\frac{ \\partial }{\\partial {\\mathbf {r}}} is replaced by the non-Abelian covariant derivative \\frac{ \\partial }{\\partial {\\mathbf {r}}}- \\frac{i}{\\hbar } {A}({\\mathbf {r}}) where {A}({\\mathbf {r}}) = i \\hbar \\, {U}^{\\dag }\\,{\\bm\\cdot}\\, \\frac{ \\partial }{\\partial {\\mathbf {r}}} {U} can be written as A1(r)Sx + A2(r)Sy + A3(r)Sz. The Abelian differentials Ak(r)·dr are given in terms of the Euler angles defining the orientation of B(r). The non-Abelian field {A}({\\mathbf {r}}) transforms as a Yang-Mills field; however, its vanishing ‘curvature’ reveals its purely geometric character. We have defined a perturbation scheme based upon the assumption that in \\widehat{ H} the longitudinal field A3(r) dominates the transverse field A1, 2(r) contributions, evaluated to second order. The geometry embedded in both the vector field A3(r) and the geometric magnetic field \\mathbf { B}_3 ({\\mathbf {r}}) = \\frac{ \\partial }{\\partial {\\mathbf {r}}}\\wedge {{\\mathbf {A}}}_3({\\mathbf {r}}) is described by their associated Aharonov-Bohm phase. As an illustration we study the physics of cold 171Yb atoms dressed by overlaying two circularly polarized stationary waves with orthogonal directions, which form a 2D square optical lattice. The frequency is tuned midway between the two hyperfine levels of the (6s6p)3P1 states to protect the optical B(r) field generated by the
Tuning Pore Size in Square-Lattice Coordination Networks for Size-Selective Sieving of CO2.
Chen, Kai-Jie; Madden, David G; Pham, Tony; Forrest, Katherine A; Kumar, Amrit; Yang, Qing-Yuan; Xue, Wei; Space, Brian; Perry, John J; Zhang, Jie-Peng; Chen, Xiao-Ming; Zaworotko, Michael J
2016-08-22
Porous materials capable of selectively capturing CO2 from flue-gases or natural gas are of interest in terms of rising atmospheric CO2 levels and methane purification. Size-exclusive sieving of CO2 over CH4 and N2 has rarely been achieved. Herein we show that a crystal engineering approach to tuning of pore-size in a coordination network, [Cu(quinoline-5-carboxyate)2 ]n (Qc-5-Cu) ena+bles ultra-high selectivity for CO2 over N2 (SCN ≈40 000) and CH4 (SCM ≈3300). Qc-5-Cu-sql-β, a narrow pore polymorph of the square lattice (sql) coordination network Qc-5-Cu-sql-α, adsorbs CO2 while excluding both CH4 and N2 . Experimental measurements and molecular modeling validate and explain the performance. Qc-5-Cu-sql-β is stable to moisture and its separation performance is unaffected by humidity. PMID:27439315
Niu, Xue-jiao; Dong, Li-fang; Liu, Ying; Wang, Qian; Feng, Jian-yu
2016-02-01
Square super-lattice pattern with surface discharge consisting of central spots and dim spots is firstly observed in the mixture of argon and air by using a dielectric barrier discharge device with water electrodes. By observing the image, it is found that the central spot is located at the centriod of its surrounding four dim spots. The short-exposure image recorded by a high speed video camera shows that the dim spot results from the surface discharges (SDs). The brightness of the central spot and is quite different from that of the dim spot, which indicates that the plasma states of the central spot and the dim spot may be differentiated. The optical emission spectrum method is used to further study the several plasma parameters of the central spot and the dim spot in different argon content. The emission spectra of the N₂ second positive band (C³IIu --> B³ IIg) are measured, from which the molecule vibration temperatures of the central spot and the dim spot are calculated respectively. The broadening of spectral line 696.57 nm (2P₂-->1S₅) is used to study the electron densities of the central spot and the dim spot. It is found that the molecule vibration temperature and electron density of the dim spot are higher than those of the central spot in the same argon content The molecule vibration temperature and electron density of the central spot and the dim spot increase with the argon content increasing from 90% to 99.9%. The surface discharge induced by the volume discharge (VD) has the determinative effect on the formation of the dim spot The experimental results above play an important role in studying the formation mechanism of surface discharg&of square super-lattice pattern with surface discharge. In addition, the studies exert an influence on the application of surface discharge and volume discharge in different fields. PMID:27209733
Hierarchical mean-field approach to the J1-J2 Heisenberg model on a square lattice
NASA Astrophysics Data System (ADS)
Isaev, Leonid; Ortiz, Gerardo; Dukelsky, Jorge
2009-03-01
We study the quantum phase diagram and excitation spectrum of the frustrated J1-J2 spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying relevant degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers and other degrees of freedom, and show that only the symmetric plaquette covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) plaquette crystal, connected with the neighbouring N'eel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the N'eel and columnar phases. Our results suggest that the quantum phase transition between N'eel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.
Hierarchical mean-field approach to the J1-J2 Heisenberg model on a square lattice
NASA Astrophysics Data System (ADS)
Isaev, L.; Ortiz, G.; Dukelsky, J.
2009-01-01
We study the quantum phase diagram and excitation spectrum of the frustrated J1-J2 spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying relevant degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry-preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers, and other degrees of freedom, and show that only the symmetric plaquette covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) plaquette crystal, connected with the neighboring Néel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the Néel and columnar phases. Our results suggest that the quantum phase transition between Néel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.
Lebovka, Nikolai I; Tarasevich, Yuri Yu; Dubinin, Dmitri O; Laptev, Valeri V; Vygornitskii, Nikolai V
2015-12-01
The jamming and percolation for two generalized models of random sequential adsorption (RSA) of linear k-mers (particles occupying k adjacent sites) on a square lattice are studied by means of Monte Carlo simulation. The classical RSA model assumes the absence of overlapping of the new incoming particle with the previously deposited ones. The first model is a generalized variant of the RSA model for both k-mers and a lattice with defects. Some of the occupying k adjacent sites are considered as insulating and some of the lattice sites are occupied by defects (impurities). For this model even a small concentration of defects can inhibit percolation for relatively long k-mers. The second model is the cooperative sequential adsorption one where, for each new k-mer, only a restricted number of lateral contacts z with previously deposited k-mers is allowed. Deposition occurs in the case when z≤(1-d)z(m) where z(m)=2(k+1) is the maximum numbers of the contacts of k-mer, and d is the fraction of forbidden contacts. Percolation is observed only at some interval k(min)≤k≤k(max) where the values k(min) and k(max) depend upon the fraction of forbidden contacts d. The value k(max) decreases as d increases. A logarithmic dependence of the type log(10)(k(max))=a+bd, where a=4.04±0.22,b=-4.93±0.57, is obtained. PMID:26764641
NASA Astrophysics Data System (ADS)
Yang, PeiPei; Wen, Zhi; Dou, RuiFeng; Liu, Xunliang
2016-08-01
Flow and heat transfer through a 2D random porous medium are studied by using the lattice Boltzmann method (LBM). For the random porous medium, the influence of disordered cylinder arrangement on permeability and Nusselt number are investigated. Results indicate that the permeability and Nusselt number for different cylinder locations are unequal even with the same number and size of cylinders. New correlations for the permeability and coefficient b‧Den of the Forchheimer equation are proposed for random porous medium composed of Gaussian distributed circular cylinders. Furthermore, a general set of heat transfer correlations is proposed and compared with existing experimental data and empirical correlations. Our results show that the Nu number increases with the increase of the porosity, hence heat transfer is found to be accurate considering the effect of porosity.
Qi, Cong; He, Yurong; Yan, Shengnan; Tian, Fenglin; Hu, Yanwei
2013-01-01
Considering interaction forces (gravity and buoyancy force, drag force, interaction potential force, and Brownian force) between nanoparticles and a base fluid, a two-phase Lattice Boltzmann model for natural convection of nanofluid is developed in this work. It is applied to investigate the natural convection in a square enclosure (the left wall is kept at a high constant temperature (TH), and the top wall is kept at a low constant temperature (TC)) filled with Al2O3/H2O nanofluid. This model is validated by comparing numerical results with published results, and a satisfactory agreement is shown between them. The effects of different nanoparticle fractions and Rayleigh numbers on natural convection heat transfer of nanofluid are investigated. It is found that the average Nusselt number of the enclosure increases with increasing nanoparticle volume fraction and increases more rapidly at a high Rayleigh number. Also, the effects of forces on nanoparticle volume fraction distribution in the square enclosure are studied in this paper. It is found that the driving force of the temperature difference has the biggest effect on nanoparticle volume fraction distribution. In addition, the effects of interaction forces on flow and heat transfer are investigated. It is found that Brownian force, interaction potential force, and gravity-buoyancy force have positive effects on the enhancement of natural convective heat transfer, while drag force has a negative effect. PMID:23374509
NASA Astrophysics Data System (ADS)
Rangel, Rafael; Negruz, Marcos
2016-04-01
In this work, we derive an analytical procedure that allows us to write the multidimensional washboard ratchet potential (MDWBP) U f for a two-dimensional Josephson junction array. The array has an applied perpendicular magnetic field. The magnetic field is given in units of the quantum flux per plaquette or frustration of the form {f}=\\frac{{M}}{{N}}[{{{Φ }}}0], where Φ0 is the flux quantum. The derivation is done under the assumption that the checkerboard pattern ground state or unit cell of a two-dimensional Josephson junction array is preserved under current biasing. The resistively and capacitively shunted Josephson junction model with a white noise term describes the dynamics for each junction in the array. The multidimensional potential is the unique expression of the collective effects that emerge from the array in contrast to the single junction. The first step in the procedure is to write the equation for the phases for the unit cell. In doing this, one takes into account the constraints imposed for the gauge invariant phases due to frustration. Second, and the key idea of the procedure, is to perform a variable transformation from the original systems of stochastic equations to a system of variables where the condition for the equality of mixed second partial happens. This is achieved via Poincaré's theorem for differential forms. In this way, we find to a nonlinear matrix equation (equation (9) in the text), that permits us to find the new coordinate variables x f where the potential exists. The transformation matrix also permits the correct transformation of the original white noise terms of each junction to the intensities in the x f variables. The commensurate symmetries of the ground state pinned vortex lattice leads to discrete symmetries to the part of the washboard potential that does not contain a tilt due to the external bias current (equation (11) in the text). In this work we apply the procedure for the important cases f=\\frac{1
Competing orders in a dipolar Bose-Fermi mixture on a square optical lattice: mean-field perspective
NASA Astrophysics Data System (ADS)
Scaramazza, Jasen A.; Kain, Ben; Ling, Hong Y.
2016-07-01
We consider a mixture of a two-component Fermi gas and a single-component dipolar Bose gas in a square optical lattice and reduce it into an effective Fermi system where the Fermi-Fermi interaction includes the attractive interaction induced by the phonons of a uniform dipolar Bose-Einstein condensate. Focusing on this effective Fermi system in the parameter regime that preserves the symmetry of D4, the point group of a square, we explore, within the Hartree-Fock-Bogoliubov mean-field theory, the phase competition among density wave orderings and superfluid pairings. We construct the matrix representation of the linearized gap equation in the irreducible representations of D4. We show that in the weak coupling regime, each matrix element, which is a four-dimensional (4D) integral in momentum space, can be put in a separable form involving a 1D integral, which is only a function of temperature and the chemical potential, and a pairing-specific "effective" interaction, which is an analytical function of the parameters that characterize the Fermi-Fermi interactions in our system. We analyze the critical temperatures of various competing orders as functions of different system parameters in both the absence and presence of the dipolar interaction. We find that close to half filling, the dx2 - y2-wave pairing with a critical temperature in the order of a fraction of Fermi energy (at half filling) may dominate all other phases, and at a higher filling factor, the p-wave pairing with a critical temperature in the order of a hundredth of Fermi energy may emerge as a winner. We find that tuning a dipolar interaction can dramatically enhance the pairings with dxy- and g-wave symmetries but not enough for them to dominate other competing phases.
Percolation and jamming of linear k-mers on a square lattice with defects: Effect of anisotropy.
Tarasevich, Yuri Yu; Burmistrov, Andrei S; Shinyaeva, Taisiya S; Laptev, Valeri V; Vygornitskii, Nikolai V; Lebovka, Nikolai I
2015-12-01
Using the Monte Carlo simulation, we study the percolation and jamming of oriented linear k-mers on a square lattice that contains defects. The point defects with a concentration d are placed randomly and uniformly on the substrate before deposition of the k-mers. The general case of unequal probabilities for orientation of depositing of k-mers along different directions of the lattice is analyzed. Two different relaxation models of deposition that preserve the predetermined order parameter s are used. In the relaxation random sequential adsorption (RRSA) model, the deposition of k-mers is distributed over different sites on the substrate. In the single-cluster relaxation (RSC) model, the single cluster grows by the random accumulation of k-mers on the boundary of the cluster (Eden-like model). For both models, a suppression of growth of the infinite (percolation) cluster at some critical concentration of defects d(c) is observed. In the zero-defect lattices, the jamming concentration p(j) (RRSA model) and the density of single clusters p(s) (RSC model) decrease with increasing length k-mers and with a decrease in the order parameter. For the RRSA model, the value of d(c) decreases for short k-mers (k<16) as the value of s increases. For k=16 and 32, the value of d(c) is almost independent of s. Moreover, for short k-mers, the percolation threshold is almost insensitive to the defect concentration for all values of s. For the RSC model, the growth of clusters with ellipselike shapes is observed for nonzero values of s. The density of the clusters p(s) at the critical concentration of defects d(c) depends in a complex manner on the values of s and k. An interesting finding for disordered systems (s=0) is that the value of p(s) tends towards zero in the limits of the very long k-mers, k→∞, and very small critical concentrations d(c)→0. In this case, the introduction of defects results in a suppression of k-mer stacking and in the formation of empty or loose
Praveen, E. Satyanarayana, S. V. M.
2014-04-24
Traditional definition of phase transition involves an infinitely large system in thermodynamic limit. Finite systems such as biological proteins exhibit cooperative behavior similar to phase transitions. We employ recently discovered analysis of inflection points of microcanonical entropy to estimate the transition temperature of the phase transition in q state Potts model on a finite two dimensional square lattice for q=3 (second order) and q=8 (first order). The difference of energy density of states (DOS) Δ ln g(E) = ln g(E+ ΔE) −ln g(E) exhibits a point of inflexion at a value corresponding to inverse transition temperature. This feature is common to systems exhibiting both first as well as second order transitions. While the difference of DOS registers a monotonic variation around the point of inflexion for systems exhibiting second order transition, it has an S-shape with a minimum and maximum around the point of inflexion for the case of first order transition.
NASA Astrophysics Data System (ADS)
Ramazanov, M. K.; Murtazaev, A. K.; Magomedov, M. A.
2016-05-01
The thermodynamic and critical properties, and phase transitions of two-dimensional Ising model on a square lattice with competing interactions are investigated by the Monte Carlo method. Estimations are made for the magnitude relations of the next-nearest-neighbor and nearest-neighbor exchange interactions r=J2/J1 in the value ranges of 0.1≤r≤1.0. The anomalies of thermodynamic observables are shown to be present in this model on the interval 0.45≤r≤0.5. The phase diagram for the dependence of the critical temperature on a value of next-nearest neighbor interaction is plotted. A phase transition for all values in the interval 0.45≤r≤0.5 is shown to be a second order. Our data show that the temperature of the heat capacity maximum at r=0.5 tends to a finite value. The static critical exponents of the heat capacity α, susceptibility γ, order parameter β, correlation length ν, and the Fisher exponent η are calculated by means of the finite-size scaling theory. It is found that the change in next-nearest neighbor interaction value in the range 0.7≤r≤1.0 leads to nonuniversal critical behavior.
NASA Astrophysics Data System (ADS)
Šimkovic, Fedor; Liu, Xuan-Wen; Deng, Youjin; Kozik, Evgeny
2016-08-01
We obtain a complete and numerically exact in the weak-coupling limit (U →0 ) ground-state phase diagram of the repulsive fermionic Hubbard model on the square lattice for filling factors 0
Magnetic excitation spectrum of the square lattice S=1/2 Heisenberg antiferromagnet K2V3O8
NASA Astrophysics Data System (ADS)
Lumsden, M. D.; Nagler, S. E.; Sales, B. C.; Tennant, D. A.; McMorrow, D. F.; Lee, S.-H.; Park, S.
2006-12-01
We have explored the magnetic excitation spectrum of the S=1/2 square lattice Heisenberg antiferromagnet, K2V3O8 , using both triple-axis and time-of-flight inelastic neutron scattering. The long-wavelength spin waves are consistent with the previously determined Hamiltonian for this material. A small energy gap of 72±9μeV is observed at the antiferromagnetic zone center and the near-neighbor exchange constant is determined to be 1.08±0.03meV . A finite ferromagnetic interplanar coupling is observed along the crystallographic c axis with a magnitude of Jc=-0.0036±0.0006meV . However, upon approaching the zone boundary, the observed excitation spectrum deviates significantly from the expectation of linear spin wave theory resulting in split modes at the (π/2,π/2) zone boundary point. The effects of magnon-phonon interaction, orbital degrees of freedom, multimagnon scattering, and dilution/site randomness are considered in the context of the mode splitting. Unfortunately, no fully satisfactory explanation of this phenomenon is found and further theoretical and experimental work is needed.
Ashley, Carlee E; Dunphy, Darren R; Jiang, Zhang; Carnes, Eric C; Yuan, Zhen; Petsev, Dimiter N; Atanassov, Plamen B; Velev, Orlin D; Sprung, Michael; Wang, Jin; Peabody, David S; Brinker, C Jeffrey
2011-04-18
The rapid assembly of icosohedral virus-like particles (VLPs) into highly ordered (domain size > 600 nm), oriented 2D superlattices directly onto a solid substrate using convective coating is demonstrated. In-situ grazing-incidence small-angle X-ray scattering (GISAXS) is used to follow the self-assembly process in real time to characterize the mechanism of superlattice formation, with the ultimate goal of tailoring film deposition conditions to optimize long-range order. From water, GISAXS data are consistent with a transport-limited assembly process where convective flow directs assembly of VLPs into a lattice oriented with respect to the water drying line. Addition of a nonvolatile solvent (glycerol) modified this assembly pathway, resulting in non-oriented superlattices with improved long-range order. Modification of electrostatic conditions (solution ionic strength, substrate charge) also alters assembly behavior; however, a comparison of in-situ assembly data between VLPs derived from the bacteriophages MS2 and Qβ show that this assembly process is not fully described by a simple Derjaguin-Landau-Verwey-Overbeek model alone. PMID:21425464
Pérez-Montoto, Lázaro G; Santana, Lourdes; González-Díaz, Humberto
2009-11-01
We introduce here a new class of invariants for MD trajectories based on the spectral moments pi(k)(L) of the Markov matrix associated to lattice network-like (LN) graph representations of Molecular Dynamics (MD) trajectories. The procedure embeds the MD energy profiles on a 2D Cartesian coordinates system using simple heuristic rules. At the same time, we associate the LN with a Markov matrix that describes the probabilities of passing from one state to other in the new 2D space. We construct this type of LNs for 422 MD trajectories obtained in DNA-drug docking experiments of 57 furocoumarins. The combined use of psoralens+ultraviolet light (UVA) radiation is known as PUVA therapy. PUVA is effective in the treatment of skin diseases such as psoriasis and mycosis fungoides. PUVA is also useful to treat human platelet (PTL) concentrates in order to eliminate Leishmania spp. and Trypanosoma cruzi. Both are parasites that cause Leishmaniosis (a dangerous skin and visceral disease) and Chagas disease, respectively; and may circulate in blood products collected from infected donors. We included in this study both lineal (psoralens) and angular (angelicins) furocoumarins. In the study, we grouped the LNs on two sets; set1: DNA-drug complex MD trajectories for active compounds and set2: MD trajectories of non-active compounds or no-optimal MD trajectories of active compounds. We calculated the respective pi(k)(L) values for all these LNs and used them as inputs to train a new classifier that discriminate set1 from set2 cases. In training series the model correctly classifies 79 out of 80 (specificity=98.75%) set1 and 226 out of 238 (Sensitivity=94.96%) set2 trajectories. In independent validation series the model correctly classifies 26 out of 26 (specificity=100%) set1 and 75 out of 78 (sensitivity=96.15%) set2 trajectories. We propose this new model as a scoring function to guide DNA-docking studies in the drug design of new coumarins for anticancer or antiparasitic
Dea-Ayuela, María Auxiliadora; Pérez-Castillo, Yunierkis; Meneses-Marcel, Alfredo; Ubeira, Florencio M; Bolas-Fernández, Francisco; Chou, Kuo-Chen; González-Díaz, Humberto
2008-08-15
The toxicity and inefficacy of actual organic drugs against Leishmaniosis justify research projects to find new molecular targets in Leishmania species including Leishmania infantum (L. infantum) and Leishmaniamajor (L. major), both important pathogens. In this sense, quantitative structure-activity relationship (QSAR) methods, which are very useful in Bioorganic and Medicinal Chemistry to discover small-sized drugs, may help to identify not only new drugs but also new drug targets, if we apply them to proteins. Dyneins are important proteins of these parasites governing fundamental processes such as cilia and flagella motion, nuclear migration, organization of the mitotic splinde, and chromosome separation during mitosis. However, despite the interest for them as potential drug targets, so far there has been no report whatsoever on dyneins with QSAR techniques. To the best of our knowledge, we report here the first QSAR for dynein proteins. We used as input the Spectral Moments of a Markov matrix associated to the HP-Lattice Network of the protein sequence. The data contain 411 protein sequences of different species selected by ClustalX to develop a QSAR that correctly discriminates on average between 92.75% and 92.51% of dyneins and other proteins in four different train and cross-validation datasets. We also report a combined experimental and theoretic study of a new dynein sequence in order to illustrate the utility of the model to search for potential drug targets with a practical example. First, we carried out a 2D-electrophoresis analysis of L. infantum biological samples. Next, we excised from 2D-E gels one spot of interest belonging to an unknown protein or protein fragment in the region M<20,200 and pI<4. We used MASCOT search engine to find proteins in the L. major data base with the highest similarity score to the MS of the protein isolated from L. infantum. We used the QSAR model to predict the new sequence as dynein with probability of 99.99% without
Manson, J.; Stone, K; Southerland, H; Lancaster, T; Steele, A; Warter, M; Blundell, S; Pratt, F; Baker, P; et al,
2009-01-01
X-ray powder diffraction and magnetic susceptibility measurements show that Ag(pyz){sub 2}(S{sub 2}O{sub 8}) consists of 2D square nets of Ag{sup 2+} ions resulting from the corner-sharing of axially elongated AgN{sub 4}O{sub 2} octahedra and exhibits characteristic 2D antiferromagnetism. Nevertheless, {mu}{sup +}SR measurements indicate that Ag(pyz){sub 2}(S{sub 2}O{sub 8}) undergoes 3D magnetic ordering below 7.8(3) K.
NASA Astrophysics Data System (ADS)
Kumar, Ajit; Verma, Sanjay K.; Alvi, P. A.; Jasrotia, Dinesh
2016-04-01
The nanospatial morphological features of [ZnCl]- [C5H4NCH3]+ hybrid derivative depicts 28 nm granular size and 3D spreader shape packing pattern as analyzed by FESEM and single crystal XRD structural studies. The organic moiety connect the inorganic components through N-H+…Cl- hydrogen bond to form a hybrid composite, the replacement of organic derivatives from 2-methylpyridine to 2-Amino-5-choloropyridine results the increase in granular size from 28nm to 60nm and unit cell packing pattern from 3D-2D lattice dimensionality along ac plane. The change in optical energy direct band gap value from 3.01eV for [ZnCl]- [C5H4NCH3]+ (HM1) to 3.42eV for [ZnCl]- [C5H5ClN2]+ (HM2) indicates the role of organic moiety in optical properties of hybrid materials. The photoluminescence emission spectra is observed in the wavelength range of 370 to 600 nm with maximum peak intensity of 9.66a.u. at 438 nm for (HM1) and 370 to 600 nm with max peak intensity of 9.91 a.u. at 442 nm for (HM2), indicating that the emission spectra lies in visible range. PL excitation spectra depicts the maximum excitation intensity [9.8] at 245.5 nm for (HM1) and its value of 9.9 a.u. at 294 nm, specify the excitation spectra lies in UV range. Photoluminescence excitation spectra is observed in the wavelength range of 280 to 350 nm with maximum peak intensity of 9.4 a.u. at 285.5 nm and 9.9 a.u. at 294 and 297 nm, indicating excitation in the UV spectrum. Single crystal growth process and detailed physiochemical characterization such as XRD, FESEM image analysis photoluminescence property reveals the structure stability with non-covalent interactions, lattice dimensionality (3D-2D) correlations interweaving into the design of inorganic-organic hybrid materials.
Shahlaei, M.; Saghaie, L.
2014-01-01
A quantitative structure–activity relationship (QSAR) study is suggested for the prediction of biological activity (pIC50) of 3, 4-dihydropyrido [3,2-d] pyrimidone derivatives as p38 inhibitors. Modeling of the biological activities of compounds of interest as a function of molecular structures was established by means of principal component analysis (PCA) and least square support vector machine (LS-SVM) methods. The results showed that the pIC50 values calculated by LS-SVM are in good agreement with the experimental data, and the performance of the LS-SVM regression model is superior to the PCA-based model. The developed LS-SVM model was applied for the prediction of the biological activities of pyrimidone derivatives, which were not in the modeling procedure. The resulted model showed high prediction ability with root mean square error of prediction of 0.460 for LS-SVM. The study provided a novel and effective approach for predicting biological activities of 3, 4-dihydropyrido [3,2-d] pyrimidone derivatives as p38 inhibitors and disclosed that LS-SVM can be used as a powerful chemometrics tool for QSAR studies. PMID:26339262
NASA Astrophysics Data System (ADS)
Sato, Toshihiro; Tsunetsugu, Hirokazu
2016-08-01
We numerically study optical conductivity σ (ω ) near the "antiferromagnetic" phase transition in the square-lattice Hubbard model at half filling. We use a cluster dynamical mean field theory and calculate conductivity including vertex corrections and, to this end, we have reformulated the vertex corrections in the antiferromagnetic phase. We find that the vertex corrections change various important details in temperature and ω dependencies of conductivity in the square lattice, and this contrasts sharply the case of the Mott transition in the frustrated triangular lattice. Generally, the vertex corrections enhance variations in the ω dependence, and sharpen the Drude peak and a high-ω incoherent peak in the paramagnetic phase. They also enhance the dip in σ (ω ) at ω =0 in the antiferromagnetic phase. Therefore, the dc conductivity is enhanced in the paramagnetic phase and suppressed in the antiferromagnetic phase, but this change occurs slightly below the transition temperature. We also find a temperature region above the transition temperature in which the dc conductivity shows an insulating behavior but σ (ω ) retains the Drude peak, and this region is stabilized by the vertex corrections. We also investigate which fluctuations are important in the vertex corrections and analyze momentum dependence of the vertex function in detail.
Boyarinov, V. F. Kondrushin, A. E. Fomichenko, P. A.
2014-12-15
Two-dimensional time-dependent finite-difference equations of the surface harmonics method (SHM) for the description of the neutron transport are derived for square-lattice reactors. These equations are implemented in the SUHAM-TD code. Verification of the derived equations and the developed code are performed by the example of known test problems, and the potential and efficiency of the SHM as applied to the solution of the time-dependent neutron transport equation in the diffusion approximation in two-dimensional geometry are demonstrated. These results show the substantial advantage of SHM over direct finite-difference modeling in computational costs.
NASA Astrophysics Data System (ADS)
Boyarinov, V. F.; Kondrushin, A. E.; Fomichenko, P. A.
2014-12-01
Two-dimensional time-dependent finite-difference equations of the surface harmonics method (SHM) for the description of the neutron transport are derived for square-lattice reactors. These equations are implemented in the SUHAM-TD code. Verification of the derived equations and the developed code are performed by the example of known test problems, and the potential and efficiency of the SHM as applied to the solution of the time-dependent neutron transport equation in the diffusion approximation in two-dimensional geometry are demonstrated. These results show the substantial advantage of SHM over direct finite-difference modeling in computational costs.
Liu, Junjie; Goddard, Paul A; Singleton, John; Brambleby, Jamie; Foronda, Francesca; Möller, Johannes S; Kohama, Yoshimitsu; Ghannadzadeh, Saman; Ardavan, Arzhang; Blundell, Stephen J; Lancaster, Tom; Xiao, Fan; Williams, Robert C; Pratt, Francis L; Baker, Peter J; Wierschem, Keola; Lapidus, Saul H; Stone, Kevin H; Stephens, Peter W; Bendix, Jesper; Woods, Toby J; Carreiro, Kimberly E; Tran, Hope E; Villa, Cecelia J; Manson, Jamie L
2016-04-01
The crystal structures of NiX2(pyz)2 (X = Cl (1), Br (2), I (3), and NCS (4)) were determined by synchrotron X-ray powder diffraction. All four compounds consist of two-dimensional (2D) square arrays self-assembled from octahedral NiN4X2 units that are bridged by pyz ligands. The 2D layered motifs displayed by 1-4 are relevant to bifluoride-bridged [Ni(HF2)(pyz)2]EF6 (E = P, Sb), which also possess the same 2D layers. In contrast, terminal X ligands occupy axial positions in 1-4 and cause a staggered packing of adjacent layers. Long-range antiferromagnetic (AFM) order occurs below 1.5 (Cl), 1.9 (Br and NCS), and 2.5 K (I) as determined by heat capacity and muon-spin relaxation. The single-ion anisotropy and g factor of 2, 3, and 4 were measured by electron-spin resonance with no evidence for zero-field splitting (ZFS) being observed. The magnetism of 1-4 spans the spectrum from quasi-two-dimensional (2D) to three-dimensional (3D) antiferromagnetism. Nearly identical results and thermodynamic features were obtained for 2 and 4 as shown by pulsed-field magnetization, magnetic susceptibility, as well as their Néel temperatures. Magnetization curves for 2 and 4 calculated by quantum Monte Carlo simulation also show excellent agreement with the pulsed-field data. Compound 3 is characterized as a 3D AFM with the interlayer interaction (J⊥) being slightly stronger than the intralayer interaction along Ni-pyz-Ni segments (J(pyz)) within the two-dimensional [Ni(pyz)2](2+) square planes. Regardless of X, J(pyz) is similar for the four compounds and is roughly 1 K. PMID:27002487
NASA Astrophysics Data System (ADS)
Iskin, M.
2016-01-01
We consider a two-component Fermi gas with attractive interactions on a square optical lattice, and study the interplay of Zeeman field, spin-orbit coupling, and next-nearest-neighbor hopping on the ground-state phase diagrams in the entire BCS-BEC evolution. In particular, we first classify and distinguish all possible superfluid phases by the momentum-space topology of their zero-energy quasiparticle-quasihole excitations, and then numerically establish a plethora of quantum phase transitions in between. These transitions are further signaled and evidenced by the changes in the corresponding topological invariant of the system, i.e., its Chern number. Lastly, we find that the superfluid phase exhibits a reentrant structure, separated by a fingering normal phase, the origin of which is traced back to the changes in the single-particle density of states.
NASA Astrophysics Data System (ADS)
Liang, Ying; Guo, Huaiming
2012-09-01
The effect of dominant three-body interaction to the hard-core boson Hubbard model is studied on a two-dimensional square lattice. In terms of the quantum Monte Carlo method, a ρ = 2/3 solid phase is shown explicitly with the coexistence of a charge-density wave and a bond-order wave appearing due to the presence of the dominant three-body interaction. For the strong three-body interaction, the ρ = 2/3 solid phase appears between superfluid phases and shrinks as the strength of the three-body interaction decreases, forming a lobe structure in the phase diagram. For weak three-body interactions, the superfluid phase exists for the whole range of hard-core densities except the full filled case, where the system is a Mott insulator. Our results may be realized in cold-atom experiments.
NASA Astrophysics Data System (ADS)
Ling, Hong; Scaramaazza, Jasen; Kain, Ben
2015-05-01
We study superfluid pairings of two-component fermions interacting by exchanging virtual phonons of a dipolar condensate in an optical lattice that preserves the symmetry of D4. We construct, within the Hartree-Fock-Bogoliubov theory, the matrix representation of the linearized gap equation in the irreducible representations of D4. We find that each matrix element, which is a four-dimensional (4D) integral in momentum space, can be put in a separable form involving a 1D integral, which is only a function of temperature and the chemical potential, and a pairing-specific ``effective'' interaction, which is an analytical function of the parameters that characterize Fermi-Fermi interactions. We analyze the critical temperatures of various competing orders (superfluids with s-, dx2-y2-, dxy-, and g-wave symmetries and density waves) as functions of different system parameters in both the absence and presence of the dipolar interaction. We find that tuning a dipolar interaction can dramatically enhance various unconventional pairings. KITP, University of Santa Barbara; ITAMP, Harvard-Smithsonian Center for Astrophysics.
NASA Astrophysics Data System (ADS)
RačiÅ«nas, Mantas; Žlabys, Giedrius; Eckardt, André; Anisimovas, Egidijus
2016-04-01
We propose a simple scheme for the realization of a topological quasienergy band structure with ultracold atoms in a periodically driven optical square lattice. It is based on a circular lattice shaking in the presence of a superlattice that lowers the energy on every other site. The topological band gap, which separates the two bands with Chern numbers ±1 , is opened in a way characteristic of Floquet topological insulators, namely, by terms of the effective Hamiltonian that appear in subleading order of a high-frequency expansion. These terms correspond to processes where a particle tunnels several times during one driving period. The interplay of such processes with particle interactions also gives rise to new interaction terms of several distinct types. For bosonic atoms with on-site interactions, they include nearest-neighbor density-density interactions introduced at the cost of weakened on-site repulsion as well as density-assisted tunneling. Using exact diagonalization, we investigate the impact of the individual induced interaction terms on the stability of a bosonic fractional Chern insulator state at half filling of the lowest band.
NASA Astrophysics Data System (ADS)
Kundu, Joyjit; Rajesh, R.
2015-01-01
A system of hard rectangles of size m ×m k on a square lattice undergoes three entropy-driven phase transitions with increasing density for large-enough aspect ratio k : first from a low-density isotropic to an intermediate-density nematic phase, second from the nematic to a columnar phase, and third from the columnar to a high-density sublattice phase. In this paper we show, from extensive Monte Carlo simulations of systems with m =1 ,2 , and 3, that the transition density for the isotropic-nematic transition is ≈A1/k when k ≫1 , where A1 is independent of m . We estimate A1=4.80 ±0.05 . Within a Bethe approximation and virial expansion truncated at the second virial coefficient, we obtain A1=2 . The critical density for the nematic-columnar transition when m =2 is numerically shown to tend to a value less than the full packing density as k-1 when k →∞ . We find that the critical Binder cumulant for this transition is nonuniversal and decreases as k-1 for k ≫1 . However, the transition is shown to be in the Ising universality class.
Burgoyne, Thomas; Morris, Edward P.; Luther, Pradeep K.
2015-01-01
The Z-band in vertebrate striated muscle crosslinks actin filaments of opposite polarity from adjoining sarcomeres and transmits tension along myofibrils during muscular contraction. It is also the location of a number of proteins involved in signalling and myofibrillogenesis; mutations in these proteins lead to myopathies. Understanding the high-resolution structure of the Z-band will help us understand its role in muscle contraction and the role of these proteins in the function of muscle. The appearance of the Z-band in transverse-section electron micrographs typically resembles a small-square lattice or a basketweave appearance. In longitudinal sections, the Z-band width varies more with muscle type than species: slow skeletal and cardiac muscles have wider Z-bands than fast skeletal muscles. As the Z-band is periodic, Fourier methods have previously been used for three-dimensional structural analysis. To cope with variations in the periodic structure of the Z-band, we have used subtomogram averaging of tomograms of rat cardiac muscle in which subtomograms are extracted and compared and similar ones are averaged. We show that the Z-band comprises four to six layers of links, presumably α-actinin, linking antiparallel overlapping ends of the actin filaments from the adjoining sarcomeres. The reconstruction shows that the terminal 5–7 nm of the actin filaments within the Z-band is devoid of any α-actinin links and is likely to be the location of capping protein CapZ. PMID:26362007
Burgoyne, Thomas; Morris, Edward P; Luther, Pradeep K
2015-11-01
The Z-band in vertebrate striated muscle crosslinks actin filaments of opposite polarity from adjoining sarcomeres and transmits tension along myofibrils during muscular contraction. It is also the location of a number of proteins involved in signalling and myofibrillogenesis; mutations in these proteins lead to myopathies. Understanding the high-resolution structure of the Z-band will help us understand its role in muscle contraction and the role of these proteins in the function of muscle. The appearance of the Z-band in transverse-section electron micrographs typically resembles a small-square lattice or a basketweave appearance. In longitudinal sections, the Z-band width varies more with muscle type than species: slow skeletal and cardiac muscles have wider Z-bands than fast skeletal muscles. As the Z-band is periodic, Fourier methods have previously been used for three-dimensional structural analysis. To cope with variations in the periodic structure of the Z-band, we have used subtomogram averaging of tomograms of rat cardiac muscle in which subtomograms are extracted and compared and similar ones are averaged. We show that the Z-band comprises four to six layers of links, presumably α-actinin, linking antiparallel overlapping ends of the actin filaments from the adjoining sarcomeres. The reconstruction shows that the terminal 5-7nm of the actin filaments within the Z-band is devoid of any α-actinin links and is likely to be the location of capping protein CapZ. PMID:26362007
NASA Astrophysics Data System (ADS)
Doretto, R. L.
2014-03-01
We study the plaquette valence-bond solid phase of the spin-1/2J1-J2 antiferromagnet Heisenberg model on the square lattice within the bond-operator theory. We start by considering four S =1/2 spins on a single plaquette and determine the bond operator representation for the spin operators in terms of singlet, triplet, and quintet boson operators. The formalism is then applied to the J1-J2 model and an effective interacting boson model in terms of singlets and triplets is derived. The effective model is analyzed within the harmonic approximation and the previous results of Zhitomirsky and Ueda [Phys. Rev. B 54, 9007 (1996), 10.1103/PhysRevB.54.9007] are recovered. By perturbatively including cubic (triplet-triplet-triplet and singlet-triplet-triplet) and quartic interactions, we find that the plaquette valence-bond solid phase is stable within the parameter region 0.34
Singleton, John; Mc Donald, R; Sengupta, P; Cox, S; Manson, J; Southerland, H; Warter, M; Stone, K; Stephens, P; Lancaster, T; Steele, A; Blundell, S; Baker, P; Pratt, F; Lee, C; Whangbo, M
2009-01-01
X-ray powder diffraction and magnetic susceptibility measurements show that Ag(pyz){sub 2}(S{sub 2}O{sub 8}) consists of 2D square nets of Ag{sup 2+} ions resulting from the corner-sharing of axially elongated AgN{sub 4}O{sub 2} octahedra and exhibits characteristic 2D antiferromagnetism. Nevertheless, {mu}{sup +}Sr measurements indicate that Ag(pyz){sub 2}(S{sub 2}O{sub 8}) undergoes 3D magnetic ordering below 7.8(3) K.
NASA Astrophysics Data System (ADS)
Singh, Kevin; Geiger, Zachary; Senaratne, Ruwan; Rajagopal, Shankari; Fujiwara, Kurt; Weld, David; Weld Group Team
2015-05-01
Quasiperiodicity is intimately involved in quantum phenomena from localization to the quantum Hall effect. Recent experimental investigation of quasiperiodic quantum effects in photonic and electronic systems have revealed intriguing connections to topological phenomena. However, such experiments have been limited by the absence of techniques for creating tunable quasiperiodic structures. We propose a new type of quasiperiodic optical lattice, constructed by intersecting a Gaussian beam with a 2D square lattice at an angle with an irrational tangent. The resulting potential, a generalization of the Fibonacci lattice, is a physical realization of the mathematical ``cut-and-project'' construction which underlies all quasiperiodic structures. Calculation of the energies and wavefunctions of atoms loaded into the proposed quasiperiodic lattice demonstrate a fractal energy spectrum and the existence of edge states. We acknowledge support from the ONR (award N00014-14-1-0805), the ARO and the PECASE program (award W911NF-14-1-0154), the AFOSR (award FA9550-12-1-0305), and the Alfred P. Sloan foundation (grant BR2013-110).
Dielectric-barrier discharges in two-dimensional lattice potentials.
Sinclair, J; Walhout, M
2012-01-20
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
NASA Astrophysics Data System (ADS)
Horváth, Miklós; Markó, Zoltán
2016-05-01
Motivated by the known results for an ongoing problem, in this paper we define the partial Cauchy data set for the discrete Schrödinger operator on a finite subset of the grid, and we prove a reconstruction theorem for the potential. Our methods are applicable in some general situations; we give a potential reconstruction theorem in the case of the hexagonal lattice as an example.
Collective spin excitations in 2D paramagnet with dipole interaction
NASA Astrophysics Data System (ADS)
Tsiberkin, Kirill
2016-02-01
The collective spin excitations in the unbounded 2D paramagnetic system with dipole interactions are studied. The model Hamiltonian includes Zeeman energy and dipole interaction energy, while the exchange vanishes. The system is placed into a constant uniform magnetic field which is orthogonal to the lattice plane. It provides the equilibrium state with spin ordering along the field direction, and the saturation is reached at zero temperature. We consider the deviations of spin magnetic moments from its equilibrium position along the external field. The Holstein-Primakoff representation is applied to spin operators in low-temperature approximation. When the interaction between the spin waves is negligible and only two-magnon terms are taken into account, the Hamiltonian diagonalisation is possible. We obtain the dispersion relation for spin waves in the square and hexagonal honeycomb lattice. Bose-Einstein statistics determine the average number of spin deviations, and total system magnetization. The lattice structure does not influence on magnetization at the long-wavelength limit. The dependencies of the relative magnetization and longitudinal susceptibility on temperature and external field intensity are found. The internal energy and specific heat of the Bose gas of spin waves are calculated. The collective spin excitations play a significant role in the properties of the paramagnetic system at low temperature and strong external magnetic field.
Proctor, T.R.; Kouri, D.J.; Gerber, R.B.
1984-04-15
In this paper, we present the first formal and computational studies of ..delta..m/sub j/ transitions occurring in homonuclear molecule-corrugated surface collisions. The model potential is a pairwise additive one which correctly incorporates the fact that ..delta..m/sub j/ transitions occur only for corrugated surfaces (provided the quantization axis is chosen to be the average surface normal). The principal results are: (a) ..delta..m/sub j/ transitions are extremely sensitive to lattice symmetry; (b) strong selection rules obtain for specular scattering; (c) the magnitude of ..delta..m/sub j/ -transition probabilities are strongly sensitive to surface corrugation; (d) the ..delta..m/sub j/ transitions depend strongly on diffraction peak; (e) the ratio of molecular length to lattice dimension (r/a) has a strong influence on the magnitude of ..delta..m/sub j/ -transition probabilities (with the probabilities increasing as (r/a) increases); (f) ..delta..m/sub j/ rainbows are predicted to occur as a function of the (r/a) ratio increases; (g) ..delta..m/sub j/ transitions and the ..delta..m/sub j/ rainbow are expected to accompany ..delta..j-rotational rainbows; (h) such magnetic transition rainbows accompanying ..delta..j rainbows are suggested as an explanation of recent experimental observations of quenching of NO polarization for larger ..delta..j transitions in NO/Ag(111) scattering.
Takagawa, Yousuke; Ogawa, Shinpei; Kimata, Masafumi
2015-01-01
Wavelength-selective uncooled infrared (IR) sensors are highly promising for a wide range of applications, such as fire detection, gas analysis and biomedical analysis. We have recently developed wavelength-selective uncooled IR sensors using square lattice two-dimensional plasmonic absorbers (2-D PLAs). The PLAs consist of a periodic 2-D lattice of Au-based dimples, which allow photons to be manipulated using surface plasmon modes. In the present study, a detailed investigation into control of the detection wavelength was conducted by varying the PLA lattice structure. A comparison was made between wavelength-selective uncooled IR sensors with triangular and square PLA lattices that were fabricated using complementary metal oxide semiconductor and micromachining techniques. Selective enhancement of the responsivity could be achieved, and the detection wavelength for the triangular lattice was shorter than that for the square lattice. The results indicate that the detection wavelength is determined by the reciprocal-lattice vector for the PLAs. The ability to control the detection wavelength in this manner enables the application of such PLAs to many types of thermal IR sensors. The results obtained here represent an important step towards multi-color imaging in the IR region. PMID:26067198
NASA Astrophysics Data System (ADS)
Ciminelli, C.; Armenise, M. N.
2007-07-01
In this paper report on the design of a 2D PBG filter in polymeric material. The filter is a Fabry-Perot cavity having a self-sustained membrane configuration. A deep parametric analysis has been carried out for improving the performance, taking also into account the fabrication tolerances Best performance in terms of lateral confinement have been obtained in case of square lattice. As for materials, polystyrene shown best in terms of refractive index value, length of the photonic crystal structure and attenuation value in the band gap. The filter can be used either in sensing applications or in telecommunication field.
A lattice-Boltzmann scheme of the Navier-Stokes equations on a 3D cuboid lattice
NASA Astrophysics Data System (ADS)
Min, Haoda; Peng, Cheng; Wang, Lian-Ping
2015-11-01
The standard lattice-Boltzmann method (LBM) for fluid flow simulation is based on a square (in 2D) or cubic (in 3D) lattice grids. Recently, two new lattice Boltzmann schemes have been developed on a 2D rectangular grid using the MRT (multiple-relaxation-time) collision model, by adding a free parameter in the definition of moments or by extending the equilibrium moments. Here we developed a lattice Boltzmann model on 3D cuboid lattice, namely, a lattice grid with different grid lengths in different spatial directions. We designed our MRT-LBM model by matching the moment equations from the Chapman-Enskog expansion with the Navier-Stokes equations. The model guarantees correct hydrodynamics. A second-order term is added to the equilibrium moments in order to restore the isotropy of viscosity on a cuboid lattice. The form and the coefficients of the extended equilibrium moments are determined through an inverse design process. An additional benefit of the model is that the viscosity can be adjusted independent of the stress-moment relaxation parameter, thus improving the numerical stability of the model. The resulting cuboid MRT-LBM model is then validated through benchmark simulations using laminar channel flow, turbulent channel flow, and the 3D Taylor-Green vortex flow.
ERIC Educational Resources Information Center
Frederiksen, John G.
1969-01-01
A rational presentation of the so-called long division method for extracting the square root of a number. Diagrams are used to show relationship of this technique to the binomial theorem. Presentation exposes student to many facets of mathematics in addition to the mechanics of funding square root and cube root. Geometry, algebraic statements,…
Solids and Supersolids of Three-Body Interacting Polar Molecules on an Optical Lattice
Schmidt, Kai P.; Dorier, Julien; Laeuchli, Andreas M.
2008-10-10
We study the physics of cold polar molecules loaded into an optical lattice in the regime of strong three-body interactions, as put forward recently by Buechler et al.[Nature Phys. 3, 726 (2007)]. To this end, quantum Monte Carlo simulations, exact diagonalization, and a semiclassical approach are used to explore hard-core bosons on the 2D square lattice which interact solely by long-ranged three-body terms. The resulting phase diagram shows a sequence of solid and supersolid phases. Our findings are directly relevant for future experimental implementations and open a new route towards the discovery of a lattice supersolid phase in experiment.
Lattice architecture effect on the cooperativity of spin transition coordination polymers
NASA Astrophysics Data System (ADS)
Chiruta, Daniel; Jureschi, Catalin-Maricel; Linares, Jorge; Garcia, Yann; Rotaru, Aurelian
2014-02-01
We have investigated in the framework of the Ising-like model, by means of Monte Carlo Metropolis method with open boundary condition, the architecture effect on the cooperativity of spin transition coordination polymers. We have analyzed the influence of several physical parameters (size, pressure, and edge effects) on different lattice architectures which were in good agreement with reported experimental data. We show that the cooperativity of a spin crossover system, characterized by the same number of molecules and the same short- and long-range interaction parameters, is progressively enhanced when going from a 1D chain to a 1D ladder type lattice and to a 2D square lattice.
ERIC Educational Resources Information Center
DeTemple, Duane
2010-01-01
Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2]…
Vehicular motion in 2D city traffic network with signals controlled by phase shift
NASA Astrophysics Data System (ADS)
Komada, Kazuhito; Kojima, Kengo; Nagatani, Takashi
2011-03-01
We study the dynamic behavior of vehicular traffic through the series of traffic lights controlled by phase shift in two-dimensional (2D) city traffic network. The nonlinear-map model is presented for the vehicular traffic. The city traffic network is made of one-way perpendicular streets arranged in a square lattice with traffic signals where vertical streets are oriented upwards and horizontal streets are oriented rightwards. There are two traffic lights for the movement to north or that to east at each crossing. The traffic lights are controlled by the cycle time, split, and phase shift. The vehicle moves through the series of signals on a path selected by the driver. The city traffic with a heterogeneous density distribution is also studied. The dependence of the arrival time on cycle time, split, phase shift, selected path, and density is clarified for 2D city traffic. It is shown that the vehicular traffic is efficiently controlled by the phase shift.
ERIC Educational Resources Information Center
Hubbard, Guy
2003-01-01
Discusses the role of the square in art and explains that students can study modern art. Includes background information and artwork by four artists: (1) Richard Anuszkiewicz; (2) Victor Vasarely; (3) Frank Stella; and (4) Bridget Riley. (CMK)
2005-07-01
Aniso2d is a two-dimensional seismic forward modeling code. The earth is parameterized by an X-Z plane in which the seismic properties Can have monoclinic with x-z plane symmetry. The program uses a user define time-domain wavelet to produce synthetic seismograms anrwhere within the two-dimensional media.
ERIC Educational Resources Information Center
Holton, Derek; Knights, Carol
2008-01-01
Here, we investigate what loci are produced when a square of side-length one is allowed to rotate around a square of side-length n, where n is a whole number. We find that if i = 1, 2, 3 or 4 (mod 4), the loci obtained for n [congruent to] i (mod 4) all have the same symmetry and we show how the perimeter of each class can be determined. We also…
Sarkar, Anirban; Shivakiran Bhaktha, B N
2015-11-01
Angle-dependent emission from a dye infiltrated 2-D on-average periodic structured optofluidic random laser is studied. Distinct signatures of periodicity and randomness are observed in the angle-resolved emission spectra of the device. Emission patterns composed of concentric ellipses are observed on transverse excitation of the device, attributed to the in-plane diffraction of light by a 2-D square lattice. The effect of randomness on the emission spectra is demonstrated by a highly resolved angle-dependent spectral scan of a single diffraction fringe. Finally, we conclude that the randomness in the size of the scatterers resolves the random lasing modes angularly. PMID:26512491
Zaletel, Michael P; Bardarson, Jens H; Moore, Joel E
2011-07-01
Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut. PMID:21797582
NASA Astrophysics Data System (ADS)
Zaletel, Michael P.; Bardarson, Jens H.; Moore, Joel E.
2011-07-01
Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the “Shannon entropy” of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut.
Directional scaling symmetry of high-symmetry two-dimensional lattices.
Liao, Longguang; Cao, Zexian
2014-01-01
Two-dimensional lattices provide the arena for many physics problems of essential importance, a scale symmetry, which rarely exists as noticed by Galileo, in such lattices can help reveal the underlying physics. Here we report the discovery and proof of directional scaling symmetry for high symmetry 2D lattices, i.e., the square lattice, the equilateral triangular lattice and thus the honeycomb lattice, with aid of the function y = arcsin(sin(2πxn)), where the parameter x is either the platinum number μ = 2 - √3 or the silver number λ = √2 - 1, which are related to the 12-fold and 8-fold quasiperiodic structures, respectively. The directions and scale factors for the symmetric scaling transformation are determined. The revealed scale symmetry may have a bearing on various physical problems modeled on 2D lattices, and the function adopted here can be used to generate quasiperiodic lattices with enumeration of lattice points. Our result is expected to initiate the search of directional scaling symmetry in more complicated geometries. PMID:25156083
Directional Scaling Symmetry of High-symmetry Two-dimensional Lattices
Liao, Longguang; Cao, Zexian
2014-01-01
Two-dimensional lattices provide the arena for many physics problems of essential importance, a scale symmetry, which rarely exists as noticed by Galileo, in such lattices can help reveal the underlying physics. Here we report the discovery and proof of directional scaling symmetry for high symmetry 2D lattices, i.e., the square lattice, the equilateral triangular lattice and thus the honeycomb lattice, with aid of the function y = arcsin(sin(2πxn)), where the parameter x is either the platinum number or the silver number , which are related to the 12-fold and 8-fold quasiperiodic structures, respectively. The directions and scale factors for the symmetric scaling transformation are determined. The revealed scale symmetry may have a bearing on various physical problems modeled on 2D lattices, and the function adopted here can be used to generate quasiperiodic lattices with enumeration of lattice points. Our result is expected to initiate the search of directional scaling symmetry in more complicated geometries. PMID:25156083
Castro-Chavez, Fernando
2012-01-01
Background Three binary representations of the genetic code according to the ancient I Ching of Fu-Xi will be presented, depending on their defragging capabilities by pairing based on three biochemical properties of the nucleic acids: H-bonds, Purine/Pyrimidine rings, and the Keto-enol/Amino-imino tautomerism, yielding the last pair a 32/32 single-strand self-annealed genetic code and I Ching tables. Methods Our working tool is the ancient binary I Ching's resulting genetic code chromosomes defragged by vertical and by horizontal pairing, reverse engineered into non-binaries of 2D rotating 4×4×4 circles and 8×8 squares and into one 3D 100% symmetrical 16×4 tetrahedron coupled to a functional tetrahedron with apical signaling and central hydrophobicity (codon formula: 4[1(1)+1(3)+1(4)+4(2)]; 5:5, 6:6 in man) forming a stella octangula, and compared to Nirenberg's 16×4 codon table (1965) pairing the first two nucleotides of the 64 codons in axis y. Results One horizontal and one vertical defragging had the start Met at the center. Two, both horizontal and vertical pairings produced two pairs of 2×8×4 genetic code chromosomes naturally arranged (M and I), rearranged by semi-introversion of central purines or pyrimidines (M' and I') and by clustering hydrophobic amino acids; their quasi-identity was disrupted by amino acids with odd codons (Met and Tyr pairing to Ile and TGA Stop); in all instances, the 64-grid 90° rotational ability was restored. Conclusions We defragged three I Ching representations of the genetic code while emphasizing Nirenberg's historical finding. The synthetic genetic code chromosomes obtained reflect the protective strategy of enzymes with a similar function, having both humans and mammals a biased G-C dominance of three H-bonds in the third nucleotide of their most used codons per amino acid, as seen in one chromosome of the i, M and M' genetic codes, while a two H-bond A-T dominance was found in their complementary chromosome, as seen
Least-squares finite element methods for quantum chromodynamics
Ketelsen, Christian; Brannick, J; Manteuffel, T; Mccormick, S
2008-01-01
A significant amount of the computational time in large Monte Carlo simulations of lattice quantum chromodynamics (QCD) is spent inverting the discrete Dirac operator. Unfortunately, traditional covariant finite difference discretizations of the Dirac operator present serious challenges for standard iterative methods. For interesting physical parameters, the discretized operator is large and ill-conditioned, and has random coefficients. More recently, adaptive algebraic multigrid (AMG) methods have been shown to be effective preconditioners for Wilson's discretization of the Dirac equation. This paper presents an alternate discretization of the Dirac operator based on least-squares finite elements. The discretization is systematically developed and physical properties of the resulting matrix system are discussed. Finally, numerical experiments are presented that demonstrate the effectiveness of adaptive smoothed aggregation ({alpha}SA ) multigrid as a preconditioner for the discrete field equations resulting from applying the proposed least-squares FE formulation to a simplified test problem, the 2d Schwinger model of quantum electrodynamics.
Greg Flach, Frank Smith
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assignsmore » an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.« less
NASA Astrophysics Data System (ADS)
Lotsch, Bettina V.
2015-07-01
Graphene's legacy has become an integral part of today's condensed matter science and has equipped a whole generation of scientists with an armory of concepts and techniques that open up new perspectives for the postgraphene area. In particular, the judicious combination of 2D building blocks into vertical heterostructures has recently been identified as a promising route to rationally engineer complex multilayer systems and artificial solids with intriguing properties. The present review highlights recent developments in the rapidly emerging field of 2D nanoarchitectonics from a materials chemistry perspective, with a focus on the types of heterostructures available, their assembly strategies, and their emerging properties. This overview is intended to bridge the gap between two major—yet largely disjunct—developments in 2D heterostructures, which are firmly rooted in solid-state chemistry or physics. Although the underlying types of heterostructures differ with respect to their dimensions, layer alignment, and interfacial quality, there is common ground, and future synergies between the various assembly strategies are to be expected.
Edwards, A W F
2012-03-01
The origin and development of Punnett's Square for the enumeration and display of genotypes arising in a cross in Mendelian genetics is described. Due to R. C. Punnett, the idea evolved through the work of the 'Cambridge geneticists', including Punnett's colleagues William Bateson, E. R. Saunders and R. H. Lock, soon after the rediscovery of Mendel's paper in 1900. These geneticists were thoroughly familiar with Mendel's paper, which itself contained a similar square diagram. A previously-unpublished three-factor diagram by Sir Francis Galton existing in the Bateson correspondence in Cambridge University Library is then described. Finally the connection between Punnett's Square and Venn Diagrams is emphasized, and it is pointed out that Punnett, Lock and John Venn overlapped as Fellows of Gonville and Caius College, Cambridge. Copious illustrations are given. PMID:22326091
All-optical digital 4 × 2 encoder based on 2D photonic crystal ring resonators
NASA Astrophysics Data System (ADS)
Moniem, Tamer A.
2016-04-01
The photonic crystals draw significant attention to build all-optical logic devices and are considered one of the solutions for the opto-electronic bottleneck via speed and size. The paper presents a novel optical 4 × 2 encoder based on 2D square lattice photonic crystals of silicon rods. The main realization of optical encoder is based on the photonic crystal ring resonator NOR gates. The proposed structure has four logic input ports, two output ports, and two bias input port. The photonic crystal structure has a square lattice of silicon rods with a refractive index of 3.39 in air. The structure has lattice constant 'a' equal to 630 nm and bandgap range from 0.32 to 044. The total size of the proposed 4 × 2 encoder is equal to 35 μm × 35 μm. The simulation results using the dimensional finite difference time domain and Plane Wave Expansion methods confirm the operation and the feasibility of the proposed optical encoder for ultrafast optical digital circuits.
Incommensurate lattice modulations in Potassium Vanadate
NASA Astrophysics Data System (ADS)
Chakoumakos, Bryan; Banerjee, Arnab; Mark, Lumsden; Cao, Huibo; Kim, Jong-Woo; Hoffman, Christina; Wang, Xiaoping
Potassium Vanadate (K2V3O8) is an S = 1/2 2D square lattice antiferromagnet that shows spin reorientation indicating a strong coupling between the magnetism and its dielectric properties with a promise of rich physics that promises multiferroicity. These tangible physical properties are strongly tied through a spin-lattice coupling to the underlying lattice and superlattice behavior. It has a superlattice (SL) onsetting below Tc = 115 K with an approximate [3 x 3 x 2] modulation. Here we present our recent experiments at TOPAZ beamline at SNS which for the first time proves conclusively that the lattice modulations are incommensurate, with an in-plane Q of 0.315. We will also show our attempts to refine the data using JANA which requires a redefinition of the lattice, as well as the temperature and Q dependence of the superlattice modulation measured using neutrons at HFIR and synchrotron x-rays at APS. Our results are not only relevant for the ongoing search of multifunctional behavior in K2V3O8 but also generally for the superlattice modulations observed in a large family of fresnoites. Work performed at ORNL and ANL is supported by U.S. Dept. of Energy, Office of Basic Energy Sciences and Office of User Facilities Division.
Roy Chaudhuri, Partha
2014-01-01
In this work, a new design of ultraflat dispersion PCF based on square-lattice geometry with all uniform air holes towards broadband smooth SCG around the C-band of wavelength has been presented. The air hole of the inner ring was infiltrated with liquid of certain refractive indices. Numerical investigations establish a near zero ultraflattened dispersion of 0 ± 0.78 ps/nm/km in a wavelength range of 1496 nm to 2174 nm (678 nm bandwidth) covering most of the communications bands with the first zero dispersion wavelength around 1.54 μm. With the optimized ultraflattened fiber, we have achieved a broadband SC spectrum with FWHM of 350 nm with the central wavelength of 1550 nm with less than a meter long of the fiber by using a picosecond pulse laser. We have also analyzed the sensitivity of the optimized dispersion design by small variations from the optimum value of the geometrical structural parameters. Our investigations establish that for a negative change of PCF parameters, the profile retains the smooth and flat SCG spectra; however, for a positive change, the smooth and a flat spectrum is lost. The new design of the fiber will be capable of covering huge diverse field of DWDM sources, spectroscopy, meteorology, optical coherence tomography, and optical sensing. PMID:27355018
Maji, Partha Sona; Roy Chaudhuri, Partha
2014-01-01
In this work, a new design of ultraflat dispersion PCF based on square-lattice geometry with all uniform air holes towards broadband smooth SCG around the C-band of wavelength has been presented. The air hole of the inner ring was infiltrated with liquid of certain refractive indices. Numerical investigations establish a near zero ultraflattened dispersion of 0 ± 0.78 ps/nm/km in a wavelength range of 1496 nm to 2174 nm (678 nm bandwidth) covering most of the communications bands with the first zero dispersion wavelength around 1.54 μm. With the optimized ultraflattened fiber, we have achieved a broadband SC spectrum with FWHM of 350 nm with the central wavelength of 1550 nm with less than a meter long of the fiber by using a picosecond pulse laser. We have also analyzed the sensitivity of the optimized dispersion design by small variations from the optimum value of the geometrical structural parameters. Our investigations establish that for a negative change of PCF parameters, the profile retains the smooth and flat SCG spectra; however, for a positive change, the smooth and a flat spectrum is lost. The new design of the fiber will be capable of covering huge diverse field of DWDM sources, spectroscopy, meteorology, optical coherence tomography, and optical sensing. PMID:27355018
ERIC Educational Resources Information Center
Lyon, Betty Clayton
1990-01-01
One method of making magic squares using a prolongated square is illustrated. Discussed are third-order magic squares, fractional magic squares, fifth-order magic squares, decimal magic squares, and even magic squares. (CW)
Permanent magnetic lattices for ultracold atoms and quantum degenerate gases
NASA Astrophysics Data System (ADS)
Ghanbari, Saeed; Kieu, Tien D.; Sidorov, Andrei; Hannaford, Peter
2006-02-01
We propose the use of periodic arrays of permanent magnetic films for producing magnetic lattices of microtraps for confining, manipulating and controlling small clouds of ultracold atoms and quantum degenerate gases. Using analytical expressions and numerical calculations we show that periodic arrays of magnetic films can produce one-dimensional (1D) and two-dimensional (2D) magnetic lattices with non-zero potential minima, allowing ultracold atoms to be trapped without losses due to spin flips. In particular, we show that two crossed layers of periodic arrays of parallel rectangular magnets plus bias fields, or a single layer of periodic arrays of square-shaped magnets with three different thicknesses plus bias fields, can produce 2D magnetic lattices of microtraps having non-zero potential minima and controllable trap depth. For arrays with micron-scale periodicity, the magnetic microtraps can have very large trap depths (~0.5 mK for the realistic parameters chosen for the 2D lattice) and very tight confinement.
Han, Qiang
2010-01-27
In this paper, we present a method to construct the eigenspace of the tight-binding electrons moving on a 2D square lattice with nearest-neighbor hopping in the presence of a perpendicular uniform magnetic field which imposes (quasi-)periodic boundary conditions for the wavefunctions in the magnetic unit cell. Exact unitary transformations are put forward to correlate the discrete eigenvectors of the 2D electrons with those of the Harper equation. The cyclic tridiagonal matrix associated with the Harper equation is then tridiagonalized by another unitary transformation. The obtained truncated eigenbasis is utilized to expand the Bogoliubov-de Gennes equations for the superconducting vortex lattice state, which shows the merit of our method in studying large-sized systems. To test our method, we have applied our results to study the vortex lattice state of an s-wave superconductor. PMID:21386295
Phonons and elasticity in critically coordinated lattices
NASA Astrophysics Data System (ADS)
Lubensky, T. C.; Kane, C. L.; Mao, Xiaoming; Souslov, A.; Sun, Kai
2015-07-01
Much of our understanding of vibrational excitations and elasticity is based upon analysis of frames consisting of sites connected by bonds occupied by central-force springs, the stability of which depends on the average number of neighbors per site z. When z < zc ≈ 2d, where d is the spatial dimension, frames are unstable with respect to internal deformations. This pedagogical review focuses on the properties of frames with z at or near zc, which model systems like randomly packed spheres near jamming and network glasses. Using an index theorem, N0 -NS = dN -NB relating the number of sites, N, and number of bonds, NB, to the number, N0, of modes of zero energy and the number, NS, of states of self stress, in which springs can be under positive or negative tension while forces on sites remain zero, it explores the properties of periodic square, kagome, and related lattices for which z = zc and the relation between states of self stress and zero modes in periodic lattices to the surface zero modes of finite free lattices (with free boundary conditions). It shows how modifications to the periodic kagome lattice can eliminate all but trivial translational zero modes and create topologically distinct classes, analogous to those of topological insulators, with protected zero modes at free boundaries and at interfaces between different topological classes.
Optimized geometries for future generation optical lattice clocks
NASA Astrophysics Data System (ADS)
Krämer, S.; Ostermann, L.; Ritsch, H.
2016-04-01
Atoms deeply trapped in magic wavelength optical lattices provide a Doppler- and collision-free dense ensemble of quantum emitters ideal for high-precision spectroscopy and they are the basis of some of the best optical atomic clocks to date. However, despite their minute optical dipole moments the inherent long-range dipole-dipole interactions in such lattices still generate line shifts, dephasing and modified decay. We show that in a perfectly filled lattice line shifts and decay are resonantly enhanced depending on the lattice constant and geometry. Potentially, this yields clock shifts of many atomic linewidths and reduces the measurement by optimizing the lattice geometry. Such collective effects can be tailored to yield zero effective shifts and prolong dipole lifetimes beyond the single-atom decay. In particular, we identify dense 2D hexagonal or square lattices as the most promising configurations for an accuracy and precision well below the independent ensemble limit. This geometry should also be an ideal basis for related applications such as superradiant lasers, precision magnetometry or long-lived quantum memories.
Quantum phases of quadrupolar Fermi gases in optical lattices
NASA Astrophysics Data System (ADS)
Bhongale, Satyan; Mathey, Ludwig; Zhao, Erhai; Yellin, Susanne; Lemeshko, Mikhail
2013-05-01
We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moment but possessing a significant value of electric quadrupole moment. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.
Quantum Phases of Quadrupolar Fermi Gases in Optical Lattices
NASA Astrophysics Data System (ADS)
Bhongale, S. G.; Mathey, L.; Zhao, Erhai; Yelin, S. F.; Lemeshko, Mikhail
2013-04-01
We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moments but possessing a significant value of electric quadrupole moments. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create a topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.
NASA Astrophysics Data System (ADS)
Wang, Jin; Ma, Jianyong; Zhou, Changhe
2014-11-01
A 3×3 high divergent 2D-grating with period of 3.842μm at wavelength of 850nm under normal incidence is designed and fabricated in this paper. This high divergent 2D-grating is designed by the vector theory. The Rigorous Coupled Wave Analysis (RCWA) in association with the simulated annealing (SA) is adopted to calculate and optimize this 2D-grating.The properties of this grating are also investigated by the RCWA. The diffraction angles are more than 10 degrees in the whole wavelength band, which are bigger than the traditional 2D-grating. In addition, the small period of grating increases the difficulties of fabrication. So we fabricate the 2D-gratings by direct laser writing (DLW) instead of traditional manufacturing method. Then the method of ICP etching is used to obtain the high divergent 2D-grating.
Dual negative refraction in a two dimension square photonic crystal
NASA Astrophysics Data System (ADS)
Derbali, J.; AbdelMalek, F.
2015-09-01
Dual refraction effect based on the overlapping bands in a two dimensional (2D) photonic crystal (PhC) is demonstrated. The PhC consists of alumina rods with a dielectric constant ε=8.9, arranged in a square lattice in air. To disperse light which has special excitation frequency and a specific incident angle, by this PhC we optimize his structural parameters such as the radius of dielectric rods). It is shown that two focusing phenomena are formed in the PhC image plan; the degeneracy of modes can be applied to realize optical interference and wave front division. The simulation results are obtained by employing the PWM for analyzing bands structure and the finite-difference time-domain (FDTD) to predict the evolution of the electric fields.
2D ice from first principles: structures and phase transitions
NASA Astrophysics Data System (ADS)
Chen, Ji; Schusteritsch, Georg; Pickard, Chris J.; Salzmann, Christoph G.; Michaelides, Angelos
Despite relevance to disparate areas such as cloud microphysics and tribology, major gaps in the understanding of the structures and phase transitions of low-dimensional water ice remain. Here we report a first principles study of confined 2D ice as a function of pressure. We find that at ambient pressure hexagonal and pentagonal monolayer structures are the two lowest enthalpy phases identified. Upon mild compression the pentagonal structure becomes the most stable and persists up to ca. 2 GPa at which point square and rhombic phases are stable. The square phase agrees with recent experimental observations of square ice confined within graphene sheets. We also find a double layer AA stacked square ice phase, which clarifies the difference between experimental observations and earlier force field simulations. This work provides a fresh perspective on 2D confined ice, highlighting the sensitivity of the structures observed to both the confining pressure and width.
Matter-wave propagation in optical lattices: geometrical and flat-band effects
NASA Astrophysics Data System (ADS)
Metcalf, Mekena; Chern, Gia-Wei; Di Ventra, Massimiliano; Chien, Chih-Chun
2016-04-01
The geometry of optical lattices can be engineered, allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question feasible to atomic systems is related to the speed of matter-wave propagation as a function of the lattice geometry. To address this issue, we investigated, theoretically, the quantum transport of noninteracting and weakly-interacting ultracold fermionic atoms in several 2D optical lattice geometries. We find that the triangular lattice has a higher propagation velocity compared to the square lattice, and the cross-linked square lattice has an even faster propagation velocity. The increase results from the mixing of the momentum states which leads to different group velocities in quantum systems. Standard band theory provides an explanation and allows for a systematic way to search and design systems with controllable matter-wave propagation. Moreover, the presence of a flat band such as in a two-leg ladder geometry leads to a dynamical density discontinuity due to its localized atoms. Possible realizations of those dynamical phenomena are discussed.
2004-08-01
AnisWave2D is a 2D finite-difference code for a simulating seismic wave propagation in fully anisotropic materials. The code is implemented to run in parallel over multiple processors and is fully portable. A mesh refinement algorithm has been utilized to allow the grid-spacing to be tailored to the velocity model, avoiding the over-sampling of high-velocity materials that usually occurs in fixed-grid schemes.
Analysis of photonic logic gates based on single hexagonal-lattice photonic crystal ring resonator
NASA Astrophysics Data System (ADS)
Jiang, Junzhen; Qiang, Zexuan; Xu, Xiaofu; Chen, Xiyao
2011-01-01
We devised a new configuration of optical logic gates based on a single hexagonal-lattice photonic crystal ring resonator (PCRR) composed of two-dimensional (2D) cylindrical silicon rods in air. The modal behavior of the proposed logic gates was comprehensively analyzed with a topology optimization technique based on the principle of beam interference and perturbation theory. It was then numerically verified by using a 2D finite-difference time-domain technique. The predictions have a very good agreement with the numerical results. This new single PCRR can really function as NOT and NOR gates. And the logic ``0'' and ``1'' of the hexagonal ring can be defined as less than 8% and greater than 86%, respectively, much better than earlier reported square-lattice results.
Kasala, Kailash; Saravanamuttu, Kalaichelvi
2013-01-29
We report that incandescent beams patterned with amplitude depressions (dips) suffer instability in a photopolymerizable system and organize into lattices of black and bright self-trapped beams propagating respectively, through self-induced black and bright waveguides. Such optochemically organized lattices emerge when beams embedded with a hexagonal or square array of dips initiate free-radical polymerization and corresponding changes in refractive index (Δn) along their propagation paths. Under these nonlinear conditions, the dips evolve into a hexagonal or square lattice of black beams, while their bright interstitial regions become unstable and divide spontaneously into multiple filaments of light. These filaments have a characteristic diameter (d(f)) and organize into a variety of geometries, which are determined by the shape and dimensions of the bright interstices. At interstitial widths > 2d(f), filaments are randomly positioned in space, whereas at widths < 2d(f), the interstices are occupied by a single file of filaments encircling each dark channel. When the interstitial width ≈ d(f), the filaments organize into lattices with long-range hexagonal or square symmetry. By employing anisotropic interstices such as rectangles, filamentation can be selectively elicited along the long axis, leading to a lattice of filament doublets. This work demonstrates the versatility and significant potential of optochemical organization to generate complex, optically functional polymer lattices, which cannot be constructed through conventional lithography or self-assembly. Specifically, the study introduces a new generation of waveguide lattices, in which light propagation is co-operatively managed by black and bright waveguides; the former suppress local light propagation and, in this way, enhance light confinement and guidance in proximal bright waveguides. PMID:23252718
Shape-dependent designability studies of lattice proteins.
Peto, Myron; Kloczkowski, Andrzej; Jernigan, Robert L
2007-07-18
One important problem in computational structural biology is protein designability, that is, why protein sequences are not random strings of amino acids but instead show regular patterns that encode protein structures. Many previous studies that have attempted to solve the problem have relied upon reduced models of proteins. In particular, the 2D square and the 3D cubic lattices together with reduced amino acid alphabet models have been examined extensively and have lead to interesting results that shed some light on evolutionary relationship among proteins. Here we perform designability studies on the 2D square lattice and explore the effects of variable overall shapes on protein designability using a binary hydrophobic-polar (HP) amino acid alphabet. Because we rely on a simple energy function that counts the total number of H-H interactions between non-sequential residues, we restrict our studies to protein shapes that have the same number of residues and also a constant number of non-bonded contacts. We have found that there is a marked difference in the designability between various protein shapes, with some of them accounting for a significantly larger share of the total foldable sequences. PMID:18079979
A new inversion method for (T2, D) 2D NMR logging and fluid typing
NASA Astrophysics Data System (ADS)
Tan, Maojin; Zou, Youlong; Zhou, Cancan
2013-02-01
One-dimensional nuclear magnetic resonance (1D NMR) logging technology has some significant limitations in fluid typing. However, not only can two-dimensional nuclear magnetic resonance (2D NMR) provide some accurate porosity parameters, but it can also identify fluids more accurately than 1D NMR. In this paper, based on the relaxation mechanism of (T2, D) 2D NMR in a gradient magnetic field, a hybrid inversion method that combines least-squares-based QR decomposition (LSQR) and truncated singular value decomposition (TSVD) is examined in the 2D NMR inversion of various fluid models. The forward modeling and inversion tests are performed in detail with different acquisition parameters, such as magnetic field gradients (G) and echo spacing (TE) groups. The simulated results are discussed and described in detail, the influence of the above-mentioned observation parameters on the inversion accuracy is investigated and analyzed, and the observation parameters in multi-TE activation are optimized. Furthermore, the hybrid inversion can be applied to quantitatively determine the fluid saturation. To study the effects of noise level on the hybrid method and inversion results, the numerical simulation experiments are performed using different signal-to-noise-ratios (SNRs), and the effect of different SNRs on fluid typing using three fluid models are discussed and analyzed in detail.
All Square Chiliagonal Numbers
ERIC Educational Resources Information Center
A?iru, Muniru A.
2016-01-01
A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square…
Observation of 2D Ising criticality of liquid-gas transition by the flowgram method
NASA Astrophysics Data System (ADS)
Yarmolinsky, Max; Kuklov, Anatoly
We study the critical properties of the transition in 2D liquid-gas system with the square-well potential interaction by Monte Carlo simulations in the grand canonical ensemble. Due to lack of the underlying Ising symmetry, the analysis cannot be done reliably by the standard methods applicable to lattice systems. In contrast, the analysis based on the flowgram method allowed us to find the critical point to significantly higher (and controllable) accuracy than in previous studies by other authors. Simulations were performed in a progression of sizes L up to size L = 84 , with the particle numbers varying over 3 orders of magnitude and the subcritical behavior not extending beyond L = 10 - 15 . The finite size scaling analysis of the critical exponents and their ratio, μ and γ / ν , gives values consistent with the 2D Ising universality class within 1-2% of errors. Our result essentially closes proposals that the nature of the liquid-gas transition might be different from the Ising model in systems with short-range interactions. This work was supported by the NSF Grant PHY1314469.
Implications of lack-of-ergodicity in 2D Potts model
NASA Astrophysics Data System (ADS)
Ota, Smita
2015-03-01
Microcanonical Monte Carlo simulation is used to study two dimensional (2D) q state Potts model. We consider a 2D square lattice having NxN spins with periodic boundary condition and simulated the system with N =15 and q =10. The demon energy distribution is found to be exponential for high system energy and large system size. For smaller system size and above the first order transition the demon energy distribution is found to deviate from exp(- βED) and has the form exp(- βED + γ ED2). Here β = 1/kBT and kB is the Boltzmann constant. It is found that γ is finite at higher temperatures. As the system energy is reduced γ becomes zero near the first order transition. It is found that during cooling γ changes sign from negative to positive and then to negative again near the 1st order transition. Therefore the demon energy distribution becomes exp(- βED) (or ergodic) at two values of system energy near the 1st order transition. Further cooling or at still lower temperatures the system shows lack of ergodicity. However, difference in heating cooling curves are apparent in E vs γ. The system energies for which γ is zero during cooling can represent the 'ergodic' states. This can be related to the two-level systems observed in glasses at low temperatures.
NASA Astrophysics Data System (ADS)
Venderbos, J. W. F.
2016-03-01
In this work we introduce a symmetry classification for electronic density waves which break translational symmetry due to commensurate wave-vector modulations. The symmetry classification builds on the concept of extended point groups: symmetry groups which contain, in addition to the lattice point group, translations that do not map the enlarged unit cell of the density wave to itself, and become "nonsymmorphic"-like elements. Multidimensional representations of the extended point group are associated with degenerate wave vectors. Electronic properties such as (nodal) band degeneracies and topological character can be straightforwardly addressed, and often follow directly. To further flesh out the idea of symmetry, the classification is constructed so as to manifestly distinguish time-reversal invariant charge (i.e., site and bond) order, and time-reversal breaking flux order. For the purpose of this work, we particularize to spin-rotation invariant density waves. As a first example of the application of the classification we consider the density waves of a simple single- and two-orbital square lattice model. The main objective, however, is to apply the classification to two-dimensional (2D) hexagonal lattices, specifically the triangular and the honeycomb lattices. The multicomponent density waves corresponding to the commensurate M -point ordering vectors are worked out in detail. To show that our results generally apply to 2 D hexagonal lattices, we develop a general low-energy SU(3 ) theory of (spinless) saddle-point electrons.
Completeness of classical φ4 theory on two-dimensional lattices
NASA Astrophysics Data System (ADS)
Karimipour, Vahid; Zarei, Mohammad Hossein
2012-03-01
We formulate a quantum formalism for the statistical mechanical models of discretized field theories on lattices and then show that the discrete version of φ4 theory on 2D square lattice is complete in the sense that the partition function of any other discretized scalar field theory on an arbitrary lattice with arbitrary interactions can be realized as a special case of the partition function of this model. To achieve this, we extend the recently proposed quantum formalism for the Ising model [M. Van den Nest, W. Dur, and H. J. Briegel, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.98.117207 98, 117207 (2007)] and its completeness property [M. Van den Nest, W. Dur, and H. J. Briegel, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.100.110501 100, 110501 (2008)] to the continuous variable case.
Common features in phase-space networks of frustrated spin models and lattice-gas models
NASA Astrophysics Data System (ADS)
Wang, Feng; Peng, Yi; Han, Yilong
2012-02-01
We mapped the phase spaces of the following four models into networks: (1a) the Ising antiferromagnet on triangular lattice at the ground state and (1b) above the ground state, (2) the six-vertex model (i.e. square ice or spin ice), (3) 1D lattice gas and (4) 2D lattice gas. Their phase-space networks share some common features including the Gaussian degree distribution, the Gaussian spectral density, and the small-world properties. Models 1a, 2 and 3 with long-range correlations in real space exhibit fractal phase spaces, while models 1b and 4 with short-range correlations in real space exhibit non-fractal phase spaces. This result supports one of the untested assumptions in Tsallis's non-extensive statistics.
Probability of incipient spanning clusters in critical square bond percolation
Shchur, L.N.; Kosyakov, S.S.
1997-06-01
The probability of simultaneous occurrence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice with free boundaries at the bond percolation threshold p{sub c} = {1/2}. It is found that the probability of k and more Incipient Spanning Clusters (ISC) have the values P(k > 1) {approx} 0.00658(3) and P(k > 2) {approx} 0.00000148(21) provided that the limit of these probabilities for infinite lattice exists. The probability P(k > 3) of more than three ISC could be estimated to be of the order of 10{sup -11} and is beyond the possibility to compute such a value by nowadays computers. So, it is impossible to check in simulations the Aizenman law for the probabilities when k {much_gt} 1. We have detected a single sample with four ISC in a total number of about 10{sup 10} samples investigated. The probability of this single event is 1/10 for the number of samples. The influence of boundary conditions is discussed in the last section.
Thermodynamics of elementary excitations in artificial magnetic square ice
NASA Astrophysics Data System (ADS)
Silva, R. C.; Nascimento, F. S.; Mól, L. A. S.; Moura-Melo, W. A.; Pereira, A. R.
2012-01-01
We investigate the thermodynamics of artificial square spin ice systems assuming only dipolar interactions among the islands that compose the array. Emphasis is given to the effects of temperature on elementary excitations (magnetic monopoles and their strings). By using Monte Carlo techniques we calculate the specific heat, the density of poles and their average separation as functions of temperature. The specific heat and average separation between monopoles with opposite charges exhibit a sharp peak and a local maximum, respectively, at the same temperature, Tp ≈ 7.2D/kB (here, D is the strength of the dipolar interaction and kB the Boltzmann constant). When the lattice size is increased, the amplitude of these features also increases but very slowly. Really, the specific heat and the maximum of the average separation dmax between oppositely charged monopoles increase logarithmically with system size, indicating that completely isolated charges could be found only at the thermodynamic limit. In general, the results obtained here suggest that, for temperatures T ⩾ Tp, these systems may exhibit a phase with separated monopoles, although the quantity dmax should not be larger than a few lattice spacings for viable artificial materials.
NASA Astrophysics Data System (ADS)
Mayor, Louise
2016-05-01
Graphene might be the most famous example, but there are other 2D materials and compounds too. Louise Mayor explains how these atomically thin sheets can be layered together to create flexible “van der Waals heterostructures”, which could lead to a range of novel applications.
Thermal conductivity measurements in a 2D Yukawa system
NASA Astrophysics Data System (ADS)
Nosenko, V.; Ivlev, A.; Zhdanov, S.; Morfill, G.; Goree, J.; Piel, A.
2007-03-01
Thermal conductivity was measured for a 2D Yukawa system. First, we formed a monolayer suspension of microspheres in a plasma, i.e., a dusty plasma, which is like a colloidal suspension, but with an extremely low volume fraction and a partially-ionized rarefied gas instead of solvent. In the absence of manipulation, the suspension forms a 2D triangular lattice. To melt this lattice and form a liquid, we used a laser-heating method. Two focused laser beams were moved rapidly around in the monolayer. The kinetic temperature of the particles increased with the laser power applied, and above a threshold a melting transition occurred. We used digital video microscopy for direct imaging and particle tracking. The spatial profiles of the particle kinetic temperature were calculated. Using the heat transport equation with an additional term to account for the energy dissipation due to the gas drag, we analyzed the temperature distribution to derive the thermal conductivity.
EPR study of the onset of long-range order in the 2D organo-metallic magnet Cu(pyz)2(pyo)2(PF6)2
Mcdonald, Ross D; Ayala - Valenzuela, Oscar E; Singleton, John; Goddard, Paul A; Franke, I; Manson, J. L.
2011-01-14
The spin (S) 1/2 two-dimensional (2D) square-lattice quantum Heisenberg antiferromagnet system has long been interesting to theoretical physicists due to the variety of transitions that can arise. Moreover, the role of S = 1/2 fluctuations on a square lattice in the mechanism for cuprate superconductivity is hotly debated. Low dimensional metal-organic magnets, such as Cu(pyz){sub 2}(pyo){sub 2}(PF{sub 6}){sub 2}, offer the possibility to readily control the exchange parameters in a 20 system by changing chemical composition, thus creating spin architectures with desirable properties 'to order'. For a perfectly 20 system, long range magnetic order would not occur at finite temperature. However, in the metal-organic systems, interlayer coupling gives rise to a finite Neel temperature. For these quasi-2D systems the ordering temperature is dominated by the weakest (the interlayer) exchange interaction, whereas the saturation magnetic field is dominated by the strongest exchange interactions, thus providing a means of estimating the spatial exchange anisotropy in the system. It should be noted that the more 2D the system, the wider the temperature (T) range, T{sub N} < T < J/k{sub B}, over which magnetic fluctuations dominate. As evident by the ratio of magnetic saturation field, H{sub sat} {approx} 30 T, to the Neel temperature, T{sub N} = 1.72 K, Cu(pyz){sub 2}(pyo){sub 2}(PF{sub 6}){sub 2} is a good example of a 2D system with the anisotropy between inplane and interplane exchange interactions being of the order of 10{sup 3}.
Artificial Staggered Magnetic Field for Ultracold Atoms in Optical Lattices
NASA Astrophysics Data System (ADS)
Morais Smith, Cristiane
2011-03-01
Uniform magnetic fields are ubiquitous in nature, but this is not the case for staggered magnetic fields. In this talk, I will discuss an experimental set-up for cold atoms recently proposed by us, which allows for the realization of a ``staggered gauge field'' in a 2D square optical lattice. If the lattice is loaded with bosons, it may be described by an effective Bose-Hubbard Hamiltonian, with complex and anisotropic hopping coefficients. A very rich phase diagram emerges: besides the usual Mott-insulator and zero-momentum condensate, a new phase with a finite momentum condensate becomes the ground-state at strong gauge fields. By using the technique of Feshbach resonance, the dynamics of a coherent superposition of a vortex-carrying atomic condensate and a conventional zero-momentum molecular condensate can also be studied within the same scheme. On the other hand, if the lattice is loaded with fermions, a highly tunable, graphene-like band structure can be realized, without requiring the honeycomb lattice symmetry. When the system is loaded with a mixture of bosons and two-species fermions, several features of the high-Tc phase diagram can be reproduced. A dome-shaped unconventional superconducting region arises, surrounded by a non-Fermi liquid and a Fermi liquid at low and high doping, respectively. We acknowledge financial support from the Netherlands Organization for Scientific Research (NWO).
2001-01-31
This software reduces the data from two-dimensional kSA MOS program, k-Space Associates, Ann Arbor, MI. Initial MOS data is recorded without headers in 38 columns, with one row of data per acquisition per lase beam tracked. The final MOSS 2d data file is reduced, graphed, and saved in a tab-delimited column format with headers that can be plotted in any graphing software.
Metrology for graphene and 2D materials
NASA Astrophysics Data System (ADS)
Pollard, Andrew J.
2016-09-01
The application of graphene, a one atom-thick honeycomb lattice of carbon atoms with superlative properties, such as electrical conductivity, thermal conductivity and strength, has already shown that it can be used to benefit metrology itself as a new quantum standard for resistance. However, there are many application areas where graphene and other 2D materials, such as molybdenum disulphide (MoS2) and hexagonal boron nitride (h-BN), may be disruptive, areas such as flexible electronics, nanocomposites, sensing and energy storage. Applying metrology to the area of graphene is now critical to enable the new, emerging global graphene commercial world and bridge the gap between academia and industry. Measurement capabilities and expertise in a wide range of scientific areas are required to address this challenge. The combined and complementary approach of varied characterisation methods for structural, chemical, electrical and other properties, will allow the real-world issues of commercialising graphene and other 2D materials to be addressed. Here, examples of metrology challenges that have been overcome through a multi-technique or new approach are discussed. Firstly, the structural characterisation of defects in both graphene and MoS2 via Raman spectroscopy is described, and how nanoscale mapping of vacancy defects in graphene is also possible using tip-enhanced Raman spectroscopy (TERS). Furthermore, the chemical characterisation and removal of polymer residue on chemical vapour deposition (CVD) grown graphene via secondary ion mass spectrometry (SIMS) is detailed, as well as the chemical characterisation of iron films used to grow large domain single-layer h-BN through CVD growth, revealing how contamination of the substrate itself plays a role in the resulting h-BN layer. In addition, the role of international standardisation in this area is described, outlining the current work ongoing in both the International Organization of Standardization (ISO) and the
Nanoimprint lithography: 2D or not 2D? A review
NASA Astrophysics Data System (ADS)
Schift, Helmut
2015-11-01
Nanoimprint lithography (NIL) is more than a planar high-end technology for the patterning of wafer-like substrates. It is essentially a 3D process, because it replicates various stamp topographies by 3D displacement of material and takes advantage of the bending of stamps while the mold cavities are filled. But at the same time, it keeps all assets of a 2D technique being able to pattern thin masking layers like in photon- and electron-based traditional lithography. This review reports about 20 years of development of replication techniques at Paul Scherrer Institut, with a focus on 3D aspects of molding, which enable NIL to stay 2D, but at the same time enable 3D applications which are "more than Moore." As an example, the manufacturing of a demonstrator for backlighting applications based on thermally activated selective topography equilibration will be presented. This technique allows generating almost arbitrary sloped, convex and concave profiles in the same polymer film with dimensions in micro- and nanometer scale.
Mechanics of advanced fiber reinforced lattice composites
NASA Astrophysics Data System (ADS)
Fan, Hua-Lin; Zeng, Tao; Fang, Dai-Ning; Yang, Wei
2010-12-01
Fiber reinforced lattice composites are light-weight attractive due to their high specific strength and specific stiffness. In the past 10 years, researchers developed three-dimensional (3D) lattice trusses and two-dimensional (2D) lattice grids by various methods including interlacing, weaving, interlocking, filament winding and molding hot-press. The lattice composites have been applied in the fields of radar cross-section reduction, explosive absorption and heat-resistance. In this paper, topologies of the lattice composites, their manufacturing routes, as well as their mechanical and multifunctional applications, were surveyed.
Competing structures in two dimensions: Square-to-hexagonal transition
NASA Astrophysics Data System (ADS)
Gränz, Barbara; Korshunov, Sergey E.; Geshkenbein, Vadim B.; Blatter, Gianni
2016-08-01
We study a system of particles in two dimensions interacting via a dipolar long-range potential D /r3 and subject to a square-lattice substrate potential V (r ) with amplitude V and lattice constant b . The isotropic interaction favors a hexagonal arrangement of the particles with lattice constant a , which competes against the square symmetry of the underlying substrate lattice. We determine the minimal-energy states at fixed external pressure p generating the commensurate density n =1 /b2=(4/3 ) 1 /2/a2 in the absence of thermal and quantum fluctuations, using both analytical techniques based on the harmonic and continuum elastic approximations as well as numerical relaxation of particle configurations. At large substrate amplitude V >0.2 eD, with eD=D /b3 the dipolar energy scale, the particles reside in the substrate minima and hence arrange in a square lattice. Upon decreasing V , the square lattice turns unstable with respect to a zone-boundary shear mode and deforms into a period-doubled zigzag lattice. Analytic and numerical results show that this period-doubled phase in turn becomes unstable at V ≈0.074 eD towards a nonuniform phase developing an array of domain walls or solitons; as the density of solitons increases, the particle arrangement approaches that of a rhombic (or isosceles triangular) lattice. At a yet smaller substrate value estimated as V ≈0.046 eD, a further solitonic transition establishes a second nonuniform phase which smoothly approaches the hexagonal (or equilateral triangular) lattice phase with vanishing amplitude V . At small but finite amplitude V , the hexagonal phase is distorted and hexatically locked at an angle of φ ≈3 .8∘ with respect to the substrate lattice. The square-to-hexagonal transformation in this two-dimensional commensurate-incommensurate system thus involves a complex pathway with various nontrivial lattice- and modulated phases.
Harms, Gary A.
2015-09-01
The US Department of Energy (DOE) Nuclear Energy Research Initiative funded the design and construction of the Seven Percent Critical Experiment (7uPCX) at Sandia National Laboratories. The start-up of the experiment facility and the execution of the experiments described here were funded by the DOE Nuclear Criticality Safety Program. The 7uPCX is designed to investigate critical systems with fuel for light water reactors in the enrichment range above 5% ^{235}U. The 7uPCX assembly is a water-moderated and -reflected array of aluminum-clad square-pitched U(6.90%)O_{2} fuel rods.
Dipolar matter-wave solitons in two-dimensional anisotropic discrete lattices
NASA Astrophysics Data System (ADS)
Chen, Huaiyu; Liu, Yan; Zhang, Qiang; Shi, Yuhan; Pang, Wei; Li, Yongyao
2016-05-01
We numerically demonstrate two-dimensional (2D) matter-wave solitons in the disk-shaped dipolar Bose-Einstein condensates (BECs) trapped in strongly anisotropic optical lattices (OLs) in a disk's plane. The considered OLs are square lattices which can be formed by interfering two pairs of plane waves with different intensities. The hopping rates of the condensates between two adjacent lattices in the orthogonal directions are different, which gives rise to a linearly anisotropic system. We find that when the polarized orientation of the dipoles is parallel to disk's plane with the same direction, the combined effects of the linearly anisotropy and the nonlocal nonlinear anisotropy strongly influence the formations, as well as the dynamics of the lattice solitons. Particularly, the isotropy-pattern solitons (IPSs) are found when these combined effects reach a balance. Motion, collision, and rotation of the IPSs are also studied in detail by means of systematic simulations. We further find that these IPSs can move freely in the 2D anisotropic discrete system, hence giving rise to an anisotropic effective mass. Four types of collisions between the IPSs are identified. By rotating an external magnetic field up to a critical angular velocity, the IPSs can still remain localized and play as a breather. Finally, the influences from the combined effects between the linear and the nonlocal nonlinear anisotropy with consideration of the contact and/or local nonlinearity are discussed too.
ERIC Educational Resources Information Center
Watson, Gale A.
2003-01-01
Demonstrates the transformations that are possible to construct a variety of magic squares, including modifications to challenge students from elementary grades through algebra. Presents an example of using magic squares with students who have special needs. (YDS)
ERIC Educational Resources Information Center
Emanouilidis, Emanuel
2005-01-01
Latin squares have existed for hundreds of years but it wasn't until rather recently that Latin squares were used in other areas such as statistics, graph theory, coding theory and the generation of random numbers as well as in the design and analysis of experiments. This note describes Latin and diagonal Latin squares, a method of constructing…
Square ice in graphene nanocapillaries
NASA Astrophysics Data System (ADS)
Algara-Siller, G.; Lehtinen, O.; Wang, F. C.; Nair, R. R.; Kaiser, U.; Wu, H. A.; Geim, A. K.; Grigorieva, I. V.
2015-03-01
Bulk water exists in many forms, including liquid, vapour and numerous crystalline and amorphous phases of ice, with hexagonal ice being responsible for the fascinating variety of snowflakes. Much less noticeable but equally ubiquitous is water adsorbed at interfaces and confined in microscopic pores. Such low-dimensional water determines aspects of various phenomena in materials science, geology, biology, tribology and nanotechnology. Theory suggests many possible phases for adsorbed and confined water, but it has proved challenging to assess its crystal structure experimentally. Here we report high-resolution electron microscopy imaging of water locked between two graphene sheets, an archetypal example of hydrophobic confinement. The observations show that the nanoconfined water at room temperature forms `square ice'--a phase having symmetry qualitatively different from the conventional tetrahedral geometry of hydrogen bonding between water molecules. Square ice has a high packing density with a lattice constant of 2.83 Å and can assemble in bilayer and trilayer crystallites. Molecular dynamics simulations indicate that square ice should be present inside hydrophobic nanochannels independently of their exact atomic nature.
Square ice in graphene nanocapillaries.
Algara-Siller, G; Lehtinen, O; Wang, F C; Nair, R R; Kaiser, U; Wu, H A; Geim, A K; Grigorieva, I V
2015-03-26
Bulk water exists in many forms, including liquid, vapour and numerous crystalline and amorphous phases of ice, with hexagonal ice being responsible for the fascinating variety of snowflakes. Much less noticeable but equally ubiquitous is water adsorbed at interfaces and confined in microscopic pores. Such low-dimensional water determines aspects of various phenomena in materials science, geology, biology, tribology and nanotechnology. Theory suggests many possible phases for adsorbed and confined water, but it has proved challenging to assess its crystal structure experimentally. Here we report high-resolution electron microscopy imaging of water locked between two graphene sheets, an archetypal example of hydrophobic confinement. The observations show that the nanoconfined water at room temperature forms 'square ice'--a phase having symmetry qualitatively different from the conventional tetrahedral geometry of hydrogen bonding between water molecules. Square ice has a high packing density with a lattice constant of 2.83 Å and can assemble in bilayer and trilayer crystallites. Molecular dynamics simulations indicate that square ice should be present inside hydrophobic nanochannels independently of their exact atomic nature. PMID:25810206
Bornyakov, V.G.
2005-06-01
Possibilities that are provided by a lattice regularization of QCD for studying nonperturbative properties of QCD are discussed. A review of some recent results obtained from computer calculations in lattice QCD is given. In particular, the results for the QCD vacuum structure, the hadron mass spectrum, and the strong coupling constant are considered.
NASA Astrophysics Data System (ADS)
Medvedev, S. N.
2015-10-01
Stacking by CDP technique is inapplicable for processing of data from bottom seismic stations or acoustic sonobuoys. In addition, big amount of unknown velocity and structural parameters of the real layered medium do not allow these parameters to be defined by standard processing methods. Local sloped stacking is proposed for simultaneous obtaining the stacked tracks, travel time curve of a chosen wave, and the first derivative of this travel time curve. The additionally defined parameters are second derivative of this travel time curve and integrated average of squared travel time curve. These data are sufficient to reduce the amount of unknown parameters (down to one-two for each boundary) when layer-by-layer top-to-bottom processing. As a result, the stable estimates of velocity parameters of the layered (isotropic or anisotropic) medium can be obtained and stacked tracks obtained by local sloped staking can be transformed into boundaries in the time and depth sections.
Quantum phases of quadrupolar Fermi gases in optical lattices.
Bhongale, S G; Mathey, L; Zhao, Erhai; Yelin, S F; Lemeshko, Mikhail
2013-04-12
We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moments but possessing a significant value of electric quadrupole moments. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create a topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities. PMID:25167282
Lattice Green's functions in all dimensions
NASA Astrophysics Data System (ADS)
Guttmann, Anthony J.
2010-07-01
We give a systematic treatment of lattice Green's functions (LGF) on the d-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality d >= 2 for the first three lattices, and for 2 <= d <= 5 for the hyper-fcc lattice. We show that there is a close connection between the LGF of the d-dimensional hyper-cubic lattice and that of the (d - 1)-dimensional diamond lattice. We give constant-term formulations of LGFs for each of these lattices in all dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the sc, bcc and diamond LGFs and some Ramanujan-type formulae for 1/π.
Lattice kinetic simulation of nonisothermal magnetohydrodynamics.
Chatterjee, Dipankar; Amiroudine, Sakir
2010-06-01
In this paper, a lattice kinetic algorithm is presented to simulate nonisothermal magnetohydrodynamics in the low-Mach number incompressible limit. The flow and thermal fields are described by two separate distribution functions through respective scalar kinetic equations and the magnetic field is governed by a vector distribution function through a vector kinetic equation. The distribution functions are only coupled via the macroscopic density, momentum, magnetic field, and temperature computed at the lattice points. The novelty of the work is the computation of the thermal field in conjunction with the hydromagnetic fields in the lattice Boltzmann framework. A 9-bit two-dimensional (2D) lattice scheme is used for the numerical computation of the hydrodynamic and thermal fields, whereas the magnetic field is simulated in a 5-bit 2D lattice. Simulation of Hartmann flow in a channel provides excellent agreement with corresponding analytical results. PMID:20866540
Ti3CrCu4: A possible 2-D ferromagnetic spin fluctuating system
NASA Astrophysics Data System (ADS)
Dhar, S. K.; Provino, A.; Manfrinetti, P.; Kulkarni, R.; Goyal, Neeraj; Paudyal, D.
2016-05-01
Ti3CrCu4 is a new ternary compound which crystallizes in the tetragonal Ti3Pd5 structure type. The Cr atoms form square nets in the a-b plane (a = 3.124 Å) which are separated by an unusually large distance c = 11.228 Å along the tetragonal axis, thus forming a -2-D Cr-sublattice. The paramagnetic susceptibility is characterized by a low effective moment, μeff = 1.1 μB, a low paramagnetic Curie temperature θP (below 7 K) and a temperature independent χ0 = 6.7 x 10-4 emu/mol. The magnetization at 1.8 K increases rapidly with field nearly saturating to 0.2 μB/f.u. The zero field heat capacity C/T shows an upturn below 7 K (˜190 mJ/mol K2 at ˜0.1K) which is suppressed in applied magnetic fields and interpreted as suggesting the presence of spin fluctuations. The resistivity at low temperatures shows non-Fermi liquid behavior. Overall, the experimental data thus reveal an unusual magnetic state in Ti3CrCu4, which likely has its origin in the layered nature of the Cr sub-lattice and ferromagnetic spin fluctuations. Density functional theoretical calculations reveal a sharp Cr density of states peak just above the Fermi level, indicating the propensity of Ti3CrCu4 to become magnetic.
Stacked charge stripes in the quasi-2D trilayer nickelate La4Ni3O8.
Zhang, Junjie; Chen, Yu-Sheng; Phelan, D; Zheng, Hong; Norman, M R; Mitchell, J F
2016-08-01
The quasi-2D nickelate La4Ni3O8 (La-438), consisting of trilayer networks of square planar Ni ions, is a member of the so-called T' family, which is derived from the Ruddlesden-Popper (R-P) parent compound La4Ni3O10-x by removing two oxygen atoms and rearranging the rock salt layers to fluorite-type layers. Although previous studies on polycrystalline samples have identified a 105-K phase transition with a pronounced electronic and magnetic response but weak lattice character, no consensus on the origin of this transition has been reached. Here, we show using synchrotron X-ray diffraction on high-pO2 floating zone-grown single crystals that this transition is associated with a real space ordering of charge into a quasi-2D charge stripe ground state. The charge stripe superlattice propagation vector, q = (2/3, 0, 1), corresponds with that found in the related 1/3-hole doped single-layer R-P nickelate, La5/3Sr1/3NiO4 (LSNO-1/3; Ni(2.33+)), with orientation at 45° to the Ni-O bonds. The charge stripes in La-438 are weakly correlated along c to form a staggered ABAB stacking that reduces the Coulomb repulsion among the stripes. Surprisingly, however, we find that the charge stripes within each trilayer of La-438 are stacked in phase from one layer to the next, at odds with any simple Coulomb repulsion argument. PMID:27462109
ERIC Educational Resources Information Center
Parris, Richard
2011-01-01
Given a segment that joins two lattice points in R[superscript 3], when is it possible to form a lattice cube that uses this segment as one of its twelve edges? A necessary and sufficient condition is that the length of the segment be an integer. This paper presents an algorithm for finding such a cube when the prime factors of the length are…
ERIC Educational Resources Information Center
Wagon, Stan; Cox, Barry
2009-01-01
A technique discovered in 1939 can be used to build a device that is driven by standard circular motion (as in a drill press) and drills exact square holes. This device is quite different from the classic design by Watts, which uses a Reuleaux triangle and drills a hole that is almost, but not exactly, square. We describe the device in detail,…
ERIC Educational Resources Information Center
Misiurewicz, Michal
2013-01-01
If students are presented the standard proof of irrationality of [square root]2, can they generalize it to a proof of the irrationality of "[square root]p", "p" a prime if, instead of considering divisibility by "p", they cling to the notions of even and odd used in the standard proof?
ERIC Educational Resources Information Center
Adams, Deborah
2006-01-01
This article describes an approach to teaching square dance that is advantageous for both the teacher and students. Lessons in dance become more meaningful to students when the music and vocabulary is consistent with experiences in their own lives. When students create their own squaring to the rap, lessons become more student-centered,…
Leavitt, M.A.; Lutz, I.C.
1958-08-01
An amplifier circuit is described for amplifying sigmals having an alternating current component superimposed upon a direct current component, without loss of any segnnent of the alternating current component. The general circuit arrangement includes a vibrator, two square wave amplifiers, and recombination means. The amplifier input is connected to the vibrating element of the vibrator and is thereby alternately applied to the input of each square wave amplifier. The detailed circuitry of the recombination means constitutes the novelty of the annplifier and consists of a separate, dual triode amplifier coupled to the output of each square wave amplifier with a recombination connection from the plate of one amplifier section to a grid of one section of the other amplifier. The recombination circuit has provisions for correcting distortion caused by overlapping of the two square wave voltages from the square wave amplifiers.
NASA Astrophysics Data System (ADS)
Cabo Montes de Oca, A.; March, N. H.; Cabo-Bizet, A.
2014-12-01
Former results for a tight-binding (TB) model of CuO planes in La2CuO4 are reinterpreted here to underline their wider implications. It is noted that physical systems being appropriately described by the TB model can exhibit the main strongly correlated electron system (SCES) properties, when they are solved in the HF approximation, by also allowing crystal symmetry breaking effects and noncollinear spin orientations of the HF orbitals. It is argued how a simple 2D square lattice system of Coulomb interacting electrons can exhibit insulator gaps and pseudogap states, and quantum phase transitions as illustrated by the mentioned former works. A discussion is also presented here indicating the possibility of attaining room temperature superconductivity, by means of a surface coating with water molecules of cleaved planes of graphite, being orthogonal to its c-axis. The possibility that 2D arrays of quantum dots can give rise to the same effect is also proposed to consideration. The analysis also furnishes theoretical insight to solve the Mott-Slater debate, at least for the La2CuO4 and TMO band structures. The idea is to apply a properly noncollinear GW scheme to the electronic structure calculation of these materials. The fact is that the GW approach can be viewed as a HF procedure in which the screening polarization is also determined. This directly indicates the possibility of predicting the assumed dielectric constant in the previous works. Thus, the results seem to identify that the main correlation properties in these materials are determined by screening. Finally, the conclusions also seem to be of help for the description of the experimental observations of metal-insulator transitions and Mott properties in atoms trapped in planar photonic lattices.
NASA Astrophysics Data System (ADS)
Huang, Ran; Purushottam, D. Gujrati
2015-09-01
Two types of recursive lattices with the identical coordination number but different unit cells (2-D square and 3-D cube) are constructed and the antiferromagnetic Ising model is solved exactly on them to study the stable and metastable states. A multi-branched structure of the 2-D plaquette model, which we introduced in this work, makes it possible to be an analog to the cubic lattice. Two solutions of each model can be found to exhibit the crystallization of liquid, and the ideal glass transition of supercooled liquid respectively. Based on the solutions, the thermodynamics on both lattices, e.g. the free energy, energy density, and entropy of the supercooled liquid, crystal, and liquid state of the model are calculated and compared with each other. Interactions between particles farther away than the nearest neighbor distance and multi-spins interactions are taken into consideration, and their effects on the thermal behavior are examined. The two lattices show comparable properties on the thermodynamics, which proves that both of them are practical to describe the regular 3-D case, especially to locate the ideal glass transition, while the 2-D multi-branched plaquette model is less accurate with the advantage of simpler formulation and less computation time consumption. Supported by National Natural Science Foundation of China under Grant No. 11505110
NKG2D ligands as therapeutic targets
Spear, Paul; Wu, Ming-Ru; Sentman, Marie-Louise; Sentman, Charles L.
2013-01-01
The Natural Killer Group 2D (NKG2D) receptor plays an important role in protecting the host from infections and cancer. By recognizing ligands induced on infected or tumor cells, NKG2D modulates lymphocyte activation and promotes immunity to eliminate ligand-expressing cells. Because these ligands are not widely expressed on healthy adult tissue, NKG2D ligands may present a useful target for immunotherapeutic approaches in cancer. Novel therapies targeting NKG2D ligands for the treatment of cancer have shown preclinical success and are poised to enter into clinical trials. In this review, the NKG2D receptor and its ligands are discussed in the context of cancer, infection, and autoimmunity. In addition, therapies targeting NKG2D ligands in cancer are also reviewed. PMID:23833565
Subwavelength Lattice Optics by Evolutionary Design
2015-01-01
This paper describes a new class of structured optical materials—lattice opto-materials—that can manipulate the flow of visible light into a wide range of three-dimensional profiles using evolutionary design principles. Lattice opto-materials are based on the discretization of a surface into a two-dimensional (2D) subwavelength lattice whose individual lattice sites can be controlled to achieve a programmed optical response. To access a desired optical property, we designed a lattice evolutionary algorithm that includes and optimizes contributions from every element in the lattice. Lattice opto-materials can exhibit simple properties, such as on- and off-axis focusing, and can also concentrate light into multiple, discrete spots. We expanded the unit cell shapes of the lattice to achieve distinct, polarization-dependent optical responses from the same 2D patterned substrate. Finally, these lattice opto-materials can also be combined into architectures that resemble a new type of compound flat lens. PMID:25380062
Subwavelength lattice optics by evolutionary design.
Huntington, Mark D; Lauhon, Lincoln J; Odom, Teri W
2014-12-10
This paper describes a new class of structured optical materials--lattice opto-materials--that can manipulate the flow of visible light into a wide range of three-dimensional profiles using evolutionary design principles. Lattice opto-materials are based on the discretization of a surface into a two-dimensional (2D) subwavelength lattice whose individual lattice sites can be controlled to achieve a programmed optical response. To access a desired optical property, we designed a lattice evolutionary algorithm that includes and optimizes contributions from every element in the lattice. Lattice opto-materials can exhibit simple properties, such as on- and off-axis focusing, and can also concentrate light into multiple, discrete spots. We expanded the unit cell shapes of the lattice to achieve distinct, polarization-dependent optical responses from the same 2D patterned substrate. Finally, these lattice opto-materials can also be combined into architectures that resemble a new type of compound flat lens. PMID:25380062
Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
NASA Astrophysics Data System (ADS)
Shi, Qian-Qian; Wang, Hong-Lei; Li, Sheng-Hao; Cho, Sam Young; Batchelor, Murray T.; Zhou, Huan-Qiang
2016-06-01
Geometric entanglement (GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. In this paper we outline a systematic method to compute GE for two-dimensional (2D) quantum many-body lattice models based on the translational invariant structure of infinite projected entangled pair state (iPEPS) representations. By employing this method, the q -state quantum Potts model on the square lattice with q ∈{2 ,3 ,4 ,5 } is investigated as a prototypical example. Further, we have explored three 2D Heisenberg models: the antiferromagnetic spin-1/2 X X X and anisotropic X Y X models in an external magnetic field, and the antiferromagnetic spin-1 X X Z model. We find that continuous GE does not guarantee a continuous phase transition across a phase transition point. We observe and thus classify three different types of continuous GE across a phase transition point: (i) GE is continuous with maximum value at the transition point and the phase transition is continuous, (ii) GE is continuous with maximum value at the transition point but the phase transition is discontinuous, and (iii) GE is continuous with nonmaximum value at the transition point and the phase transition is continuous. For the models under consideration, we find that the second and the third types are related to a point of dual symmetry and a fully polarized phase, respectively.
NASA Astrophysics Data System (ADS)
Chhipa, Mayur Kumar; Dusad, Lalit Kumar
2016-05-01
In this paper, the design & performance of two dimensional (2-D) photonic crystal structure based channel drop filter is investigated using quad shaped photonic crystal ring resonator. In this paper, Photonic Crystal (PhC) based on square lattice periodic arrays of Gallium Indium Phosphide (GaInP) rods in air structure have been investigated using Finite Difference Time Domain (FDTD) method and photonic band gap is being calculated using Plane Wave Expansion (PWE) method. The PhC designs have been optimized for telecommunication wavelength λ= 1571 nm by varying the rods lattice constant. The number of rods in Z and X directions is 21 and 20, with lattice constant 0.540 nm it illustrates that the arrangement of Gallium Indium Phosphide (GaInP) rods in the structure which gives the overall size of the device around 11.4 µm × 10.8 µm. The designed filter gives good dropping efficiency using 3.298, refractive index. The designed structure is useful for CWDM systems. This device may serve as a key component in photonic integrated circuits. The device is ultra compact with the overall size around 123 µm2.
Square dielectric THz waveguides.
Aflakian, N; Yang, N; LaFave, T; Henderson, R M; O, K K; MacFarlane, D L
2016-06-27
A holey cladding dielectric waveguide with square cross section is designed, simulated, fabricated and characterized. The TOPAS waveguide is designed to be single mode across the broad frequency range of 180 GHz to 360 GHz as shown by finite-difference time domain simulation and to robustly support simultaneous TE and TM mode propagation. The square fiber geometry is realized by pulling through a heat distribution made square by appropriate furnace design. The transmitted mode profile is imaged using a vector network analyzer with a pinhole at the receiver module. Good agreement between the measured mode distribution and the calculated mode distribution is demonstrated. PMID:27410645
Parametric analysis of 2D guided-wave photonic band gap structures
NASA Astrophysics Data System (ADS)
Ciminelli, C.; Peluso, F.; Armenise, M. N.
2005-11-01
The parametric analysis of the electromagnetic properties of 2D guided wave photonic band gap structures is reported with the aim of providing a valid tool for the optimal design. The modelling approach is based on the Bloch-Floquet method. Different lattice configurations and geometrical parameters are considered. An optimum value for the ratio between the hole (or rod) radius and the lattice constant does exist and the calculation demonstrated that it is almost independent from the etching depth, only depending on the lattice type. The results are suitable for the design optimisation of photonic crystal reflectors to be used in integrated optical devices.
Parametric analysis of 2D guided-wave photonic band gap structures.
Ciminelli, C; Peluso, F; Armenise, M
2005-11-28
The parametric analysis of the electromagnetic properties of 2D guided wave photonic band gap structures is reported with the aim of providing a valid tool for the optimal design. The modelling approach is based on the Bloch-Floquet method. Different lattice configurations and geometrical parameters are considered. An optimum value for the ratio between the hole (or rod) radius and the lattice constant does exist and the calculation demonstrated that it is almost independent from the etching depth, only depending on the lattice type. The results are suitable for the design optimisation of photonic crystal reflectors to be used in integrated optical devices. PMID:19503180
ERIC Educational Resources Information Center
Parker, Dan
2001-01-01
Presents design features of the Dawson Elementary School (Corpus Chriti, Texas) where an atmosphere of an old town square and the feeling of community have been created. Photos and a floor plan are provided. (GR)
A unified viscous theory of lift and drag of 2-D thin airfoils and 3-D thin wings
NASA Technical Reports Server (NTRS)
Yates, John E.
1991-01-01
A unified viscous theory of 2-D thin airfoils and 3-D thin wings is developed with numerical examples. The viscous theory of the load distribution is unique and tends to the classical inviscid result with Kutta condition in the high Reynolds number limit. A new theory of 2-D section induced drag is introduced with specific applications to three cases of interest: (1) constant angle of attack; (2) parabolic camber; and (3) a flapped airfoil. The first case is also extended to a profiled leading edge foil. The well-known drag due to absence of leading edge suction is derived from the viscous theory. It is independent of Reynolds number for zero thickness and varies inversely with the square root of the Reynolds number based on the leading edge radius for profiled sections. The role of turbulence in the section induced drag problem is discussed. A theory of minimum section induced drag is derived and applied. For low Reynolds number the minimum drag load tends to the constant angle of attack solution and for high Reynolds number to an approximation of the parabolic camber solution. The parabolic camber section induced drag is about 4 percent greater than the ideal minimum at high Reynolds number. Two new concepts, the viscous induced drag angle and the viscous induced separation potential are introduced. The separation potential is calculated for three 2-D cases and for a 3-D rectangular wing. The potential is calculated with input from a standard doublet lattice wing code without recourse to any boundary layer calculations. Separation is indicated in regions where it is observed experimentally. The classical induced drag is recovered in the 3-D high Reynolds number limit with an additional contribution that is Reynold number dependent. The 3-D viscous theory of minimum induced drag yields an equation for the optimal spanwise and chordwise load distribution. The design of optimal wing tip planforms and camber distributions is possible with the viscous 3-D wing theory.
Perspectives for spintronics in 2D materials
NASA Astrophysics Data System (ADS)
Han, Wei
2016-03-01
The past decade has been especially creative for spintronics since the (re)discovery of various two dimensional (2D) materials. Due to the unusual physical characteristics, 2D materials have provided new platforms to probe the spin interaction with other degrees of freedom for electrons, as well as to be used for novel spintronics applications. This review briefly presents the most important recent and ongoing research for spintronics in 2D materials.
Highly anisotropic Dirac fermions in square graphynes
NASA Astrophysics Data System (ADS)
Zhang, Lizhi; Wang, Zhengfei; Rao, Jiansheng; Li, Ziheng; Huang, Wulin; Wang, Zhiming; Du, Shixuan; Gao, Hongjun; Liu, Feng
Recently, there have been intense search of new 2D materials, and one especially appealing class of 2D materials is the all-carbon allotropes of Dirac materials. Here, we predict a new family of 2D carbon allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac Fermions, using first-principle calculations within density functional theory. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 x 105 to 7.2 x 105 m/s along different k directions. Near the Fermi level, the Dirac crescent can be nicely expressed by an extended 2D Dirac model Hamiltonian. Furthermore, tight-binding band fitting reveals that the Dirac crescent originates from the next-nearest-neighbor interactions between C atoms. Our findings enrich the Dirac physics founded in other 2D Dirac systems, and offer a new design mechanism for creating Dirac band by tuning the interaction range. We envision that the highly anisotropic Dirac crescent may be exploited in all-carbon-based electronic devices for manipulating anisotropic electron propagation.
Highly anisotropic Dirac fermions in square graphynes
NASA Astrophysics Data System (ADS)
Zhang, Lizhi; Wang, Zhengfei; Rao, Jiansheng; Li, Ziheng; Huang, Wulin; Wang, Zhiming; Du, Shixuan; Gao, Hongjun; Liu, Feng
Recently, there have been intense search of new 2D materials, and one especially appealing class of 2D materials is the all-carbon allotropes of Dirac materials. Here, we predict a new family of 2D carbon allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac Fermions, using first-principle calculations within density functional theory. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 ×105 to 7.2 ×105 m/s along different k directions. Near the Fermi level, the Dirac crescent can be nicely expressed by an extended 2D Dirac model Hamiltonian. Furthermore, tight-binding band fitting reveals that the Dirac crescent originates from the next-nearest-neighbor interactions between C atoms. Our findings enrich the Dirac physics founded in other 2D Dirac systems, and offer a new design mechanism for creating Dirac band by tuning the interaction range. We envision that the highly anisotropic Dirac crescent may be exploited in all-carbon-based electronic devices for manipulating anisotropic electron propagation.
Transition under noise in the Sznajd model on square lattice
NASA Astrophysics Data System (ADS)
Lima, F. W. S.
2016-08-01
In order to describe the formation of a consensus in human opinion dynamics, in this paper, we study the Sznajd model with probabilistic noise in two dimensions. The time evolution of this system is performed via Monte Carlo simulations. This social behavior model with noise presents a well defined second-order phase transition. For small enough noise q < 0.33 most agents end up sharing the same opinion.
NASA Astrophysics Data System (ADS)
Li, Shuai; Qiu, Wen-Xuan; Gao, Jin-Hua
2016-06-01
Recently, a new kind of artificial two dimensional (2D) electron lattice on the nanoscale, i.e. molecular graphene, has drawn a lot of interest, where the metal surface electrons are transformed into a honeycomb lattice via absorbing a molecular lattice on the metal surface [Gomes et al., Nature, 2012, 438, 306; Wang et al., Phys. Rev. Lett., 2014, 113, 196803]. In this work, we theoretically demonstrate that this technique can be readily used to build other complex 2D electron lattices on a metal surface, which are of high interest in the field of condensed matter physics. The main challenge to build a complex 2D electron lattice is that this is a quantum antidot system, where the absorbed molecule normally exerts a repulsive potential on the surface electrons. Thus, there is no straightforward corresponding relation between the molecular lattice pattern and the desired 2D lattice of surface electrons. Here, we give an interesting example about the Kagome lattice, which has exotic correlated electronic states. We design a special molecular pattern and show that this molecular lattice can transform the surface electrons into a Kagome-like lattice. The numerical simulation is conducted using a Cu(111) surface and CO molecules. We first estimate the effective parameters of the Cu/CO system by fitting experimental data of the molecular graphene. Then, we calculate the corresponding energy bands and LDOS of the surface electrons in the presence of the proposed molecular lattice. Finally, we interpret the numerical results by the tight binding model of the Kagome lattice. We hope that our work can stimulate further theoretical and experimental interest in this novel artificial 2D electron lattice system.
Li, Shuai; Qiu, Wen-Xuan; Gao, Jin-Hua
2016-07-01
Recently, a new kind of artificial two dimensional (2D) electron lattice on the nanoscale, i.e. molecular graphene, has drawn a lot of interest, where the metal surface electrons are transformed into a honeycomb lattice via absorbing a molecular lattice on the metal surface [Gomes et al., Nature, 2012, 438, 306; Wang et al., Phys. Rev. Lett., 2014, 113, 196803]. In this work, we theoretically demonstrate that this technique can be readily used to build other complex 2D electron lattices on a metal surface, which are of high interest in the field of condensed matter physics. The main challenge to build a complex 2D electron lattice is that this is a quantum antidot system, where the absorbed molecule normally exerts a repulsive potential on the surface electrons. Thus, there is no straightforward corresponding relation between the molecular lattice pattern and the desired 2D lattice of surface electrons. Here, we give an interesting example about the Kagome lattice, which has exotic correlated electronic states. We design a special molecular pattern and show that this molecular lattice can transform the surface electrons into a Kagome-like lattice. The numerical simulation is conducted using a Cu(111) surface and CO molecules. We first estimate the effective parameters of the Cu/CO system by fitting experimental data of the molecular graphene. Then, we calculate the corresponding energy bands and LDOS of the surface electrons in the presence of the proposed molecular lattice. Finally, we interpret the numerical results by the tight binding model of the Kagome lattice. We hope that our work can stimulate further theoretical and experimental interest in this novel artificial 2D electron lattice system. PMID:27279292
Annotated Bibliography of EDGE2D Use
J.D. Strachan and G. Corrigan
2005-06-24
This annotated bibliography is intended to help EDGE2D users, and particularly new users, find existing published literature that has used EDGE2D. Our idea is that a person can find existing studies which may relate to his intended use, as well as gain ideas about other possible applications by scanning the attached tables.
Staring 2-D hadamard transform spectral imager
Gentry, Stephen M.; Wehlburg, Christine M.; Wehlburg, Joseph C.; Smith, Mark W.; Smith, Jody L.
2006-02-07
A staring imaging system inputs a 2D spatial image containing multi-frequency spectral information. This image is encoded in one dimension of the image with a cyclic Hadamarid S-matrix. The resulting image is detecting with a spatial 2D detector; and a computer applies a Hadamard transform to recover the encoded image.
NASA Astrophysics Data System (ADS)
Buchheim, Jakob; Wyss, Roman M.; Shorubalko, Ivan; Park, Hyung Gyu
2016-04-01
We report experimentally and theoretically the behavior of freestanding graphene subjected to bombardment of energetic ions, investigating the capability of large-scale patterning of freestanding graphene with nanometer sized features by focused ion beam technology. A precise control over the He+ and Ga+ irradiation offered by focused ion beam techniques enables investigating the interaction of the energetic particles and graphene suspended with no support and allows determining sputter yields of the 2D lattice. We found a strong dependency of the 2D sputter yield on the species and kinetic energy of the incident ion beams. Freestanding graphene shows material semi-transparency to He+ at high energies (10-30 keV) allowing the passage of >97% He+ particles without creating destructive lattice vacancy. Large Ga+ ions (5-30 keV), in contrast, collide far more often with the graphene lattice to impart a significantly higher sputter yield of ~50%. Binary collision theory applied to monolayer and few-layer graphene can successfully elucidate this collision mechanism, in great agreement with experiments. Raman spectroscopy analysis corroborates the passage of a large fraction of He+ ions across graphene without much damaging the lattice whereas several colliding ions create single vacancy defects. Physical understanding of the interaction between energetic particles and suspended graphene can practically lead to reproducible and efficient pattern generation of unprecedentedly small features on 2D materials by design, manifested by our perforation of sub-5 nm pore arrays. This capability of nanometer-scale precision patterning of freestanding 2D lattices shows the practical applicability of focused ion beam technology to 2D material processing for device fabrication and integration.We report experimentally and theoretically the behavior of freestanding graphene subjected to bombardment of energetic ions, investigating the capability of large-scale patterning of
Mirror effects and optical meta-surfaces in 2d atomic arrays
NASA Astrophysics Data System (ADS)
Shahmoon, Ephraim; Wild, Dominik; Lukin, Mikhail; Yelin, Susanne
2016-05-01
Strong optical response of natural and artificial (meta-) materials typically relies on the fact that the lattice constant that separates their constituent particles (atoms or electromagnetic resonators, respectively) is much smaller than the optical wavelength. Here we consider a single layer of a 2d atom array with a lattice constant on the order of an optical wavelength, which can be thought of as a highly dilute 2d metamaterial (meta-surface). Our theoretical analysis shows how strong scattering of resonant incoming light off the array can be controlled by choosing its lattice constant, e.g. allowing the array to operate as a perfect mirror or a retro-reflector for most incident angles of the incoming light. We discuss the prospects for quantum metasurfaces, i.e. the ability to shape the output quantum state of light by controlling the atomic states, and the possible generality of our results as a universal wave phenomena.
Buchheim, Jakob; Wyss, Roman M; Shorubalko, Ivan; Park, Hyung Gyu
2016-04-21
We report experimentally and theoretically the behavior of freestanding graphene subjected to bombardment of energetic ions, investigating the capability of large-scale patterning of freestanding graphene with nanometer sized features by focused ion beam technology. A precise control over the He(+) and Ga(+) irradiation offered by focused ion beam techniques enables investigating the interaction of the energetic particles and graphene suspended with no support and allows determining sputter yields of the 2D lattice. We found a strong dependency of the 2D sputter yield on the species and kinetic energy of the incident ion beams. Freestanding graphene shows material semi-transparency to He(+) at high energies (10-30 keV) allowing the passage of >97% He(+) particles without creating destructive lattice vacancy. Large Ga(+) ions (5-30 keV), in contrast, collide far more often with the graphene lattice to impart a significantly higher sputter yield of ∼50%. Binary collision theory applied to monolayer and few-layer graphene can successfully elucidate this collision mechanism, in great agreement with experiments. Raman spectroscopy analysis corroborates the passage of a large fraction of He(+) ions across graphene without much damaging the lattice whereas several colliding ions create single vacancy defects. Physical understanding of the interaction between energetic particles and suspended graphene can practically lead to reproducible and efficient pattern generation of unprecedentedly small features on 2D materials by design, manifested by our perforation of sub-5 nm pore arrays. This capability of nanometer-scale precision patterning of freestanding 2D lattices shows the practical applicability of focused ion beam technology to 2D material processing for device fabrication and integration. PMID:27043304
Cold atoms in a rotating optical lattice
NASA Astrophysics Data System (ADS)
Foot, Christopher J.
2009-05-01
We have demonstrated a novel experimental arrangement which can rotate a two-dimensional optical lattice at frequencies up to several kilohertz. Our arrangement also allows the periodicity of the optical lattice to be varied dynamically, producing a 2D ``accordion lattice'' [1]. The angles of the laser beams are controlled by acousto-optic deflectors and this allows smooth changes with little heating of the trapped cold (rubidium) atoms. We have loaded a BEC into lattices with periodicities ranging from 1.8μm to 18μm, observing the collapse and revival of the diffraction orders of the condensate over a large range of lattice parameters as recently reported by a group in NIST [2]. We have also imaged atoms in situ in a 2D lattice over a range of lattice periodicities. Ultracold atoms in a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields, i.e. the Hamiltonian of the atoms in the rotating frame resembles that of a charged particle in a strong magnetic field. In the future, we plan to use this to investigate a range of phenomena such as the analogue of the fractional quantum Hall effect. [4pt] [1] R. A. Williams, J. D. Pillet, S. Al-Assam, B. Fletcher, M. Shotter, and C. J. Foot, ``Dynamic optical lattices: two-dimensional rotating and accordion lattices for ultracold atoms,'' Opt. Express 16, 16977-16983 (2008) [0pt] [2] J. H. Huckans, I. B. Spielman, B. Laburthe Tolra, W. D. Phillips, and J. V. Porto, Quantum and Classical Dynamics of a BEC in a Large-Period Optical Lattice, arXiv:0901.1386v1
Numerical study on localized defect modes in two-dimensional lattices: a high Q-resonant cavity
NASA Astrophysics Data System (ADS)
Moussa, R.; Salomon, L.; de Fornel, F.; Aourag, H.
2003-10-01
The spectral widths and the quality factors of defect modes localized for different defects structures formed in a 2D photonic crystal composed of a square lattice of circular rods of indium antimonide (InSb) are theoretically investigated. It is first shown that some factors such as the lattice nature, the line defect orientation, the nature and the defect width have a significant influence on the optical properties of the studied structures and can improve the Q factor and defect peak transmission intensity. Particularly, the transmission spectra of the defects calculated by means the transfer-matrix-method for a particular structure of eight line defects introduced in its center showed a high-quality factor which exceeded 4×10 5. This is an important issue for the fabrication of photonic crystals with such desired properties.
Lattice Boltzmann Method for 3-D Flows with Curved Boundary
NASA Technical Reports Server (NTRS)
Mei, Renwei; Shyy, Wei; Yu, Dazhi; Luo, Li-Shi
2002-01-01
In this work, we investigate two issues that are important to computational efficiency and reliability in fluid dynamics applications of the lattice, Boltzmann equation (LBE): (1) Computational stability and accuracy of different lattice Boltzmann models and (2) the treatment of the boundary conditions on curved solid boundaries and their 3-D implementations. Three athermal 3-D LBE models (D3QI5, D3Ql9, and D3Q27) are studied and compared in terms of efficiency, accuracy, and robustness. The boundary treatment recently developed by Filippova and Hanel and Met et al. in 2-D is extended to and implemented for 3-D. The convergence, stability, and computational efficiency of the 3-D LBE models with the boundary treatment for curved boundaries were tested in simulations of four 3-D flows: (1) Fully developed flows in a square duct, (2) flow in a 3-D lid-driven cavity, (3) fully developed flows in a circular pipe, and (4) a uniform flow over a sphere. We found that while the fifteen-velocity 3-D (D3Ql5) model is more prone to numerical instability and the D3Q27 is more computationally intensive, the 63Q19 model provides a balance between computational reliability and efficiency. Through numerical simulations, we demonstrated that the boundary treatment for 3-D arbitrary curved geometry has second-order accuracy and possesses satisfactory stability characteristics.
Light field morphing using 2D features.
Wang, Lifeng; Lin, Stephen; Lee, Seungyong; Guo, Baining; Shum, Heung-Yeung
2005-01-01
We present a 2D feature-based technique for morphing 3D objects represented by light fields. Existing light field morphing methods require the user to specify corresponding 3D feature elements to guide morph computation. Since slight errors in 3D specification can lead to significant morphing artifacts, we propose a scheme based on 2D feature elements that is less sensitive to imprecise marking of features. First, 2D features are specified by the user in a number of key views in the source and target light fields. Then the two light fields are warped view by view as guided by the corresponding 2D features. Finally, the two warped light fields are blended together to yield the desired light field morph. Two key issues in light field morphing are feature specification and warping of light field rays. For feature specification, we introduce a user interface for delineating 2D features in key views of a light field, which are automatically interpolated to other views. For ray warping, we describe a 2D technique that accounts for visibility changes and present a comparison to the ideal morphing of light fields. Light field morphing based on 2D features makes it simple to incorporate previous image morphing techniques such as nonuniform blending, as well as to morph between an image and a light field. PMID:15631126
2D materials for nanophotonic devices
NASA Astrophysics Data System (ADS)
Xu, Renjing; Yang, Jiong; Zhang, Shuang; Pei, Jiajie; Lu, Yuerui
2015-12-01
Two-dimensional (2D) materials have become very important building blocks for electronic, photonic, and phononic devices. The 2D material family has four key members, including the metallic graphene, transition metal dichalcogenide (TMD) layered semiconductors, semiconducting black phosphorous, and the insulating h-BN. Owing to the strong quantum confinements and defect-free surfaces, these atomically thin layers have offered us perfect platforms to investigate the interactions among photons, electrons and phonons. The unique interactions in these 2D materials are very important for both scientific research and application engineering. In this talk, I would like to briefly summarize and highlight the key findings, opportunities and challenges in this field. Next, I will introduce/highlight our recent achievements. We demonstrated atomically thin micro-lens and gratings using 2D MoS2, which is the thinnest optical component around the world. These devices are based on our discovery that the elastic light-matter interactions in highindex 2D materials is very strong. Also, I would like to introduce a new two-dimensional material phosphorene. Phosphorene has strongly anisotropic optical response, which creates 1D excitons in a 2D system. The strong confinement in phosphorene also enables the ultra-high trion (charged exciton) binding energies, which have been successfully measured in our experiments. Finally, I will briefly talk about the potential applications of 2D materials in energy harvesting.
Inertial solvation in femtosecond 2D spectra
NASA Astrophysics Data System (ADS)
Hybl, John; Albrecht Ferro, Allison; Farrow, Darcie; Jonas, David
2001-03-01
We have used 2D Fourier transform spectroscopy to investigate polar solvation. 2D spectroscopy can reveal molecular lineshapes beneath ensemble averaged spectra and freeze molecular motions to give an undistorted picture of the microscopic dynamics of polar solvation. The transition from "inhomogeneous" to "homogeneous" 2D spectra is governed by both vibrational relaxation and solvent motion. Therefore, the time dependence of the 2D spectrum directly reflects the total response of the solvent-solute system. IR144, a cyanine dye with a dipole moment change upon electronic excitation, was used to probe inertial solvation in methanol and propylene carbonate. Since the static Stokes' shift of IR144 in each of these solvents is similar, differences in the 2D spectra result from solvation dynamics. Initial results indicate that the larger propylene carbonate responds more slowly than methanol, but appear to be inconsistent with rotational estimates of the inertial response. To disentangle intra-molecular vibrations from solvent motion, the 2D spectra of IR144 will be compared to the time-dependent 2D spectra of the structurally related nonpolar cyanine dye HDITCP.
Internal Photoemission Spectroscopy of 2-D Materials
NASA Astrophysics Data System (ADS)
Nguyen, Nhan; Li, Mingda; Vishwanath, Suresh; Yan, Rusen; Xiao, Shudong; Xing, Huili; Cheng, Guangjun; Hight Walker, Angela; Zhang, Qin
Recent research has shown the great benefits of using 2-D materials in the tunnel field-effect transistor (TFET), which is considered a promising candidate for the beyond-CMOS technology. The on-state current of TFET can be enhanced by engineering the band alignment of different 2D-2D or 2D-3D heterostructures. Here we present the internal photoemission spectroscopy (IPE) approach to determine the band alignments of various 2-D materials, in particular SnSe2 and WSe2, which have been proposed for new TFET designs. The metal-oxide-2-D semiconductor test structures are fabricated and characterized by IPE, where the band offsets from the 2-D semiconductor to the oxide conduction band minimum are determined by the threshold of the cube root of IPE yields as a function of photon energy. In particular, we find that SnSe2 has a larger electron affinity than most semiconductors and can be combined with other semiconductors to form near broken-gap heterojunctions with low barrier heights which can produce a higher on-state current. The details of data analysis of IPE and the results from Raman spectroscopy and spectroscopic ellipsometry measurements will also be presented and discussed.
ERIC Educational Resources Information Center
Schulman, Steven M.
2014-01-01
In this article the author describes a problem posed to his class, "How many squares are there on a checkerboard?" The problem is deliberately vague so that the teacher can get the students to begin asking questions. The first goal is to come to an agreement about what the problem means (Identify the problem). The second goal is to get…
ERIC Educational Resources Information Center
Smith, Scott G.
1993-01-01
A Reuleaux triangle is constructed by drawing an arc connecting each pair of vertices of an equilateral triangle with radius equal to the side of the triangle. Investigates the application of drilling a square hole using a drill bit in the shape of a Reuleaux triangle. (MDH)
NASA Astrophysics Data System (ADS)
Chang, Shu-Chiuan; Shrock, Robert
2001-07-01
The q-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width Ly and arbitrary length Lx has the form Z(G,q,v)=∑ j=1N Z,G,λ c Z,G,j(λ Z,G,j) L x, where v is a temperature-dependent variable. The special case of the zero-temperature antiferromagnet ( v=-1) is the chromatic polynomial P( G, q). Using coloring and transfer matrix methods, we give general formulas for C X,G=∑ j=1N X,G,λ c X,G,j for X= Z, P on cyclic and Möbius strip graphs of the square and triangular lattice. Combining these with a general expression for the (unique) coefficient cZ, G, j of degree d in q: c (d)=U 2d( q/2) , where Un( x) is the Chebyshev polynomial of the second kind, we determine the number of λZ, G, j's with coefficient c( d) in Z( G, q, v) for these cyclic strips of width Ly to be n Z(L y,d)=(2d+1)(L y+d+1) -1{2L y}/{L y-d } for 0⩽ d⩽ Ly and zero otherwise. For both cyclic and Möbius strips of these lattices, the total number of distinct eigenvalues λZ, G, j is calculated to be N Z,L y,λ = {2L y}/{L y}. Results are also presented for the analogous numbers nP( Ly, d) and NP, Ly, λ for P( G, q). We find that nP( Ly,0)= nP( Ly-1,1)= MLy-1 (Motzkin number), nZ( Ly,0)= CLy (the Catalan number), and give an exact expression for NP, Ly, λ. Our results for NZ, Ly, λ and NP, Ly, λ apply for both the cyclic and Möbius strips of both the square and triangular lattices; we also point out the interesting relations NZ, Ly, λ=2 NDA, tri, Ly and NP, Ly, λ=2 NDA, sq, Ly, where NDA, Λ, n denotes the number of directed lattice animals on the lattice Λ. We find the asymptotic growths NZ, Ly, λ∼ Ly-1/24 Ly and NP, Ly, λ∼ Ly-1/23 Ly as Ly→∞. Some general geometric identities for Potts model partition functions are also presented.
Madelung energy of Yukawa lattices.
Pereira, P C N; Apolinario, S W S
2012-10-01
We propose a method to obtain an approximate closed form expression for the Madelung energy (ME) of Yukawa lattices. Such a method is applied for lattices of different topologies and dimensions. The obtained Madelung energies have a satisfactory accuracy for all ranges of the screening parameter κ of the Yukawa potential, and it becomes exact in the asymptotic limits κ→0 and κ→+∞. For instance, for the triangular lattice, the maximum relative error of the ME given by the method is about 0.0047. Also, satisfactory results are obtained for the one-component plasma limit. The Madelung constants of the two-dimensional hexagonal BN and square NaCl and the three-dimensional cubic NaCl crystals are estimated with a relative error of 0.004, 0.006, and 0.03, respectively. Finally, different ways to improve the method are presented and discussed. PMID:23214705
Unusual dimensionality effects and surface charge density in 2D Mg(OH)2
NASA Astrophysics Data System (ADS)
Suslu, Aslihan; Wu, Kedi; Sahin, Hasan; Chen, Bin; Yang, Sijie; Cai, Hui; Aoki, Toshihiro; Horzum, Seyda; Kang, Jun; Peeters, Francois M.; Tongay, Sefaattin
2016-02-01
We present two-dimensional Mg(OH)2 sheets and their vertical heterojunctions with CVD-MoS2 for the first time as flexible 2D insulators with anomalous lattice vibration and chemical and physical properties. New hydrothermal crystal growth technique enabled isolation of environmentally stable monolayer Mg(OH)2 sheets. Raman spectroscopy and vibrational calculations reveal that the lattice vibrations of Mg(OH)2 have fundamentally different signature peaks and dimensionality effects compared to other 2D material systems known to date. Sub-wavelength electron energy-loss spectroscopy measurements and theoretical calculations show that Mg(OH)2 is a 6 eV direct-gap insulator in 2D, and its optical band gap displays strong band renormalization effects from monolayer to bulk, marking the first experimental confirmation of confinement effects in 2D insulators. Interestingly, 2D-Mg(OH)2 sheets possess rather strong surface polarization (charge) effects which is in contrast to electrically neutral h-BN materials. Using 2D-Mg(OH)2 sheets together with CVD-MoS2 in the vertical stacking shows that a strong change transfer occurs from n-doped CVD-MoS2 sheets to Mg(OH)2, naturally depleting the semiconductor, pushing towards intrinsic doping limit and enhancing overall optical performance of 2D semiconductors. Results not only establish unusual confinement effects in 2D-Mg(OH)2, but also offer novel 2D-insulating material with unique physical, vibrational, and chemical properties for potential applications in flexible optoelectronics.
Unusual dimensionality effects and surface charge density in 2D Mg(OH)2
Suslu, Aslihan; Wu, Kedi; Sahin, Hasan; Chen, Bin; Yang, Sijie; Cai, Hui; Aoki, Toshihiro; Horzum, Seyda; Kang, Jun; Peeters, Francois M.; Tongay, Sefaattin
2016-01-01
We present two-dimensional Mg(OH)2 sheets and their vertical heterojunctions with CVD-MoS2 for the first time as flexible 2D insulators with anomalous lattice vibration and chemical and physical properties. New hydrothermal crystal growth technique enabled isolation of environmentally stable monolayer Mg(OH)2 sheets. Raman spectroscopy and vibrational calculations reveal that the lattice vibrations of Mg(OH)2 have fundamentally different signature peaks and dimensionality effects compared to other 2D material systems known to date. Sub-wavelength electron energy-loss spectroscopy measurements and theoretical calculations show that Mg(OH)2 is a 6 eV direct-gap insulator in 2D, and its optical band gap displays strong band renormalization effects from monolayer to bulk, marking the first experimental confirmation of confinement effects in 2D insulators. Interestingly, 2D-Mg(OH)2 sheets possess rather strong surface polarization (charge) effects which is in contrast to electrically neutral h-BN materials. Using 2D-Mg(OH)2 sheets together with CVD-MoS2 in the vertical stacking shows that a strong change transfer occurs from n-doped CVD-MoS2 sheets to Mg(OH)2, naturally depleting the semiconductor, pushing towards intrinsic doping limit and enhancing overall optical performance of 2D semiconductors. Results not only establish unusual confinement effects in 2D-Mg(OH)2, but also offer novel 2D-insulating material with unique physical, vibrational, and chemical properties for potential applications in flexible optoelectronics. PMID:26846617
Unusual dimensionality effects and surface charge density in 2D Mg(OH)2.
Suslu, Aslihan; Wu, Kedi; Sahin, Hasan; Chen, Bin; Yang, Sijie; Cai, Hui; Aoki, Toshihiro; Horzum, Seyda; Kang, Jun; Peeters, Francois M; Tongay, Sefaattin
2016-01-01
We present two-dimensional Mg(OH)2 sheets and their vertical heterojunctions with CVD-MoS2 for the first time as flexible 2D insulators with anomalous lattice vibration and chemical and physical properties. New hydrothermal crystal growth technique enabled isolation of environmentally stable monolayer Mg(OH)2 sheets. Raman spectroscopy and vibrational calculations reveal that the lattice vibrations of Mg(OH)2 have fundamentally different signature peaks and dimensionality effects compared to other 2D material systems known to date. Sub-wavelength electron energy-loss spectroscopy measurements and theoretical calculations show that Mg(OH)2 is a 6 eV direct-gap insulator in 2D, and its optical band gap displays strong band renormalization effects from monolayer to bulk, marking the first experimental confirmation of confinement effects in 2D insulators. Interestingly, 2D-Mg(OH)2 sheets possess rather strong surface polarization (charge) effects which is in contrast to electrically neutral h-BN materials. Using 2D-Mg(OH)2 sheets together with CVD-MoS2 in the vertical stacking shows that a strong change transfer occurs from n-doped CVD-MoS2 sheets to Mg(OH)2, naturally depleting the semiconductor, pushing towards intrinsic doping limit and enhancing overall optical performance of 2D semiconductors. Results not only establish unusual confinement effects in 2D-Mg(OH)2, but also offer novel 2D-insulating material with unique physical, vibrational, and chemical properties for potential applications in flexible optoelectronics. PMID:26846617
Optimal design of 2D digital filters based on neural networks
NASA Astrophysics Data System (ADS)
Wang, Xiao-hua; He, Yi-gang; Zheng, Zhe-zhao; Zhang, Xu-hong
2005-02-01
Two-dimensional (2-D) digital filters are widely useful in image processing and other 2-D digital signal processing fields,but designing 2-D filters is much more difficult than designing one-dimensional (1-D) ones.In this paper, a new design approach for designing linear-phase 2-D digital filters is described,which is based on a new neural networks algorithm (NNA).By using the symmetry of the given 2-D magnitude specification,a compact express for the magnitude response of a linear-phase 2-D finite impulse response (FIR) filter is derived.Consequently,the optimal problem of designing linear-phase 2-D FIR digital filters is turned to approximate the desired 2-D magnitude response by using the compact express.To solve the problem,a new NNA is presented based on minimizing the mean-squared error,and the convergence theorem is presented and proved to ensure the designed 2-D filter stable.Three design examples are also given to illustrate the effectiveness of the NNA-based design approach.
GAUGE INVARIANCE IN A Z2 HAMILTONIAN LATTICE GUAGE THEORY.
SUGIHARA, T.
2005-07-25
We propose an efficient variational method for Z{sub 2} lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. On the ladder lattice, we identify gauge invariant low-lying states by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian. On the square lattice, the second order phase transition is well reproduced.
Unbiased sampling of lattice Hamilton path ensembles
NASA Astrophysics Data System (ADS)
Mansfield, Marc L.
2006-10-01
Hamilton paths, or Hamiltonian paths, are walks on a lattice which visit each site exactly once. They have been proposed as models of globular proteins and of compact polymers. A previously published algorithm [Mansfield, Macromolecules 27, 5924 (1994)] for sampling Hamilton paths on simple square and simple cubic lattices is tested for bias and for efficiency. Because the algorithm is a Metropolis Monte Carlo technique obviously satisfying detailed balance, we need only demonstrate ergodicity to ensure unbiased sampling. Two different tests for ergodicity (exact enumeration on small lattices, nonexhaustive enumeration on larger lattices) demonstrate ergodicity unequivocally for small lattices and provide strong support for ergodicity on larger lattices. Two other sampling algorithms [Ramakrishnan et al., J. Chem. Phys. 103, 7592 (1995); Lua et al., Polymer 45, 717 (2004)] are both known to produce biases on both 2×2×2 and 3×3×3 lattices, but it is shown here that the current algorithm gives unbiased sampling on these same lattices. Successive Hamilton paths are strongly correlated, so that many iterations are required between statistically independent samples. Rules for estimating the number of iterations needed to dissipate these correlations are given. However, the iteration time is so fast that the efficiency is still very good except on extremely large lattices. For example, even on lattices of total size 10×10×10 we are able to generate tens of thousands of uncorrelated Hamilton paths per hour of CPU time.
Brittle damage models in DYNA2D
Faux, D.R.
1997-09-01
DYNA2D is an explicit Lagrangian finite element code used to model dynamic events where stress wave interactions influence the overall response of the system. DYNA2D is often used to model penetration problems involving ductile-to-ductile impacts; however, with the advent of the use of ceramics in the armor-anti-armor community and the need to model damage to laser optics components, good brittle damage models are now needed in DYNA2D. This report will detail the implementation of four brittle damage models in DYNA2D, three scalar damage models and one tensor damage model. These new brittle damage models are then used to predict experimental results from three distinctly different glass damage problems.
Ginsparg, P.
1991-01-01
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Ginsparg, P.
1991-12-31
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
2D electronic materials for army applications
NASA Astrophysics Data System (ADS)
O'Regan, Terrance; Perconti, Philip
2015-05-01
The record electronic properties achieved in monolayer graphene and related 2D materials such as molybdenum disulfide and hexagonal boron nitride show promise for revolutionary high-speed and low-power electronic devices. Heterogeneous 2D-stacked materials may create enabling technology for future communication and computation applications to meet soldier requirements. For instance, transparent, flexible and even wearable systems may become feasible. With soldier and squad level electronic power demands increasing, the Army is committed to developing and harnessing graphene-like 2D materials for compact low size-weight-and-power-cost (SWAP-C) systems. This paper will review developments in 2D electronic materials at the Army Research Laboratory over the last five years and discuss directions for future army applications.
2-d Finite Element Code Postprocessor
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forcesmore » along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.« less
Chemical Approaches to 2D Materials.
Samorì, Paolo; Palermo, Vincenzo; Feng, Xinliang
2016-08-01
Chemistry plays an ever-increasing role in the production, functionalization, processing and applications of graphene and other 2D materials. This special issue highlights a selection of enlightening chemical approaches to 2D materials, which nicely reflect the breadth of the field and convey the excitement of the individuals involved in it, who are trying to translate graphene and related materials from the laboratory into a real, high-impact technology. PMID:27478083
Statistical analysis of quiet stance sway in 2-D
DiZio, Paul; Lackner, James R.
2014-01-01
Subjects exposed to a rotating environment that perturbs their postural sway show adaptive changes in their voluntary spatially directed postural motion to restore accurate movement paths but do not exhibit any obvious learning during passive stance. We have found, however, that a variable known to characterize the degree of stochasticity in quiet stance can also reveal subtle learning phenomena in passive stance. We extended Chow and Collins (Phys Rev E 52(1):909–912, 1995) one-dimensional pinned-polymer model (PPM) to two dimensions (2-D) and then evaluated the model’s ability to make analytical predictions for 2-D quiet stance. To test the model, we tracked center of mass and centers of foot pressures, and compared and contrasted stance sway for the anterior–posterior versus medio-lateral directions before, during, and after exposure to rotation at 10 rpm. Sway of the body during rotation generated Coriolis forces that acted perpendicular to the direction of sway. We found significant adaptive changes for three characteristic features of the mean square displacement (MSD) function: the exponent of the power law defined at short time scales, the proportionality constant of the power law, and the saturation plateau value defined at longer time scales. The exponent of the power law of MSD at a short time scale lies within the bounds predicted by the 2-D PPM. The change in MSD during exposure to rotation also had a power-law exponent in the range predicted by the theoretical model. We discuss the Coriolis force paradigm for studying postural and movement control and the applicability of the PPM model in 2-D for studying postural adaptation. PMID:24477760
Statistical analysis of quiet stance sway in 2-D.
Bakshi, Avijit; DiZio, Paul; Lackner, James R
2014-04-01
Subjects exposed to a rotating environment that perturbs their postural sway show adaptive changes in their voluntary spatially directed postural motion to restore accurate movement paths but do not exhibit any obvious learning during passive stance. We have found, however, that a variable known to characterize the degree of stochasticity in quiet stance can also reveal subtle learning phenomena in passive stance. We extended Chow and Collins (Phys Rev E 52(1):909-912, 1995) one-dimensional pinned-polymer model (PPM) to two dimensions (2-D) and then evaluated the model's ability to make analytical predictions for 2-D quiet stance. To test the model, we tracked center of mass and centers of foot pressures, and compared and contrasted stance sway for the anterior-posterior versus medio-lateral directions before, during, and after exposure to rotation at 10 rpm. Sway of the body during rotation generated Coriolis forces that acted perpendicular to the direction of sway. We found significant adaptive changes for three characteristic features of the mean square displacement (MSD) function: the exponent of the power law defined at short time scales, the proportionality constant of the power law, and the saturation plateau value defined at longer time scales. The exponent of the power law of MSD at a short time scale lies within the bounds predicted by the 2-D PPM. The change in MSD during exposure to rotation also had a power-law exponent in the range predicted by the theoretical model. We discuss the Coriolis force paradigm for studying postural and movement control and the applicability of the PPM model in 2-D for studying postural adaptation. PMID:24477760
Extended 2D generalized dilaton gravity theories
NASA Astrophysics Data System (ADS)
de Mello, R. O.
2008-09-01
We show that an anomaly-free description of matter in (1+1) dimensions requires a deformation of the 2D relativity principle, which introduces a non-trivial centre in the 2D Poincaré algebra. Then we work out the reduced phase space of the anomaly-free 2D relativistic particle, in order to show that it lives in a noncommutative 2D Minkowski space. Moreover, we build a Gaussian wave packet to show that a Planck length is well defined in two dimensions. In order to provide a gravitational interpretation for this noncommutativity, we propose to extend the usual 2D generalized dilaton gravity models by a specific Maxwell component, which guages the extra symmetry associated with the centre of the 2D Poincaré algebra. In addition, we show that this extension is a high energy correction to the unextended dilaton theories that can affect the topology of spacetime. Further, we couple a test particle to the general extended dilaton models with the purpose of showing that they predict a noncommutativity in curved spacetime, which is locally described by a Moyal star product in the low energy limit. We also conjecture a probable generalization of this result, which provides strong evidence that the noncommutativity is described by a certain star product which is not of the Moyal type at high energies. Finally, we prove that the extended dilaton theories can be formulated as Poisson Sigma models based on a nonlinear deformation of the extended Poincaré algebra.
NASA Astrophysics Data System (ADS)
Murdin, P.
2000-11-01
A conspicuous asterism of four bright stars forming a square of approximately 15° a side, notable for the absence of any but very faint stars within it. It is formed by the stars β, α and γ Pegasi (apparent magnitudes 2.44, 2.49 and 2.83 respectively) and α Andromedae (magnitude 2.07), and is prominent in the evening sky in autumn....
Vorticity Generation by Rough Walls in 2D Decaying Turbulence
NASA Astrophysics Data System (ADS)
Tóth, Gábor; Jánosi, Imre M.
2015-12-01
In this work we present Lattice Boltzmann simulations of a decaying vortex array in a 2D rectangular domain, which is bounded by a random rough wall from one side. In order to separate the effects of the collisions with the rough wall, the opposite (smooth) rigid wall is placed at a larger distance from the center of the vortex array. Periodic boundary condition is imposed in the perpendicular direction. Well defined random roughness is generated by the widely studied Wolf-Villain surface growth algorithm. The main finding is that collisions with a rough wall generate excess vorticity compared with a smooth boundary, while the kinetic energy decreases monotonously. A proper measure is the integrated excess enstrophy, which exhibits an apparent maximum at an "optimal" roughness range. Numerical values of the excess enstrophy are very sensitive to a particular configuration (wall shape and vortex lattice randomization), however the "optimal" roughness exhibits surface features of similar characteristic sizes than that of the decaying vortices.
Lattice Boltzmann modeling of phonon transport
NASA Astrophysics Data System (ADS)
Guo, Yangyu; Wang, Moran
2016-06-01
A novel lattice Boltzmann scheme is proposed for phonon transport based on the phonon Boltzmann equation. Through the Chapman-Enskog expansion, the phonon lattice Boltzmann equation under the gray relaxation time approximation recovers the classical Fourier's law in the diffusive limit. The numerical parameters in the lattice Boltzmann model are therefore rigorously correlated to the bulk material properties. The new scheme does not only eliminate the fictitious phonon speed in the diagonal direction of a square lattice system in the previous lattice Boltzmann models, but also displays very robust performances in predicting both temperature and heat flux distributions consistent with analytical solutions for diverse numerical cases, including steady-state and transient, macroscale and microscale, one-dimensional and multi-dimensional phonon heat transport. This method may provide a powerful numerical tool for deep studies of nonlinear and nonlocal heat transports in nanosystems.
Lattice gas and lattice Boltzmann computational physics
Chen, S.
1993-05-01
Recent developments of the lattice gas automata method and its extension to the lattice Boltzmann method have provided new computational schemes for solving a variety of partial differential equations and modeling different physics systems. The lattice gas method, regarded as the simplest microscopic and kinetic approach which generates meaningful macroscopic dynamics, is fully parallel and can be easily programmed on parallel machines. In this talk, the author will review basic principles of the lattice gas and lattice Boltzmann method, its mathematical foundation and its numerical implementation. A detailed comparison of the lattice Boltzmann method with the lattice gas technique and other traditional numerical schemes, including the finite-difference scheme and the pseudo-spectral method, for solving the Navier-Stokes hydrodynamic fluid flows, will be discussed. Recent achievements of the lattice gas and the the lattice Boltzmann method and their applications in surface phenomena, spinodal decomposition and pattern formation in chemical reaction-diffusion systems will be presented.
Duality analysis on random planar lattices.
Ohzeki, Masayuki; Fujii, Keisuke
2012-11-01
The conventional duality analysis is employed to identify a location of a critical point on a uniform lattice without any disorder in its structure. In the present study, we deal with the random planar lattice, which consists of the randomized structure based on the square lattice. We introduce the uniformly random modification by the bond dilution and contraction on a part of the unit square. The random planar lattice includes the triangular and hexagonal lattices in extreme cases of a parameter to control the structure. A modern duality analysis fashion with real-space renormalization is found to be available for estimating the location of the critical points with a wide range of the randomness parameter. As a simple test bed, we demonstrate that our method indeed gives several critical points for the cases of the Ising and Potts models and the bond-percolation thresholds on the random planar lattice. Our method leads to not only such an extension of the duality analyses on the classical statistical mechanics but also a fascinating result associated with optimal error thresholds for a class of quantum error correction code, the surface code on the random planar lattice, which is known as a skillful technique to protect the quantum state. PMID:23214752
Duality analysis on random planar lattices
NASA Astrophysics Data System (ADS)
Ohzeki, Masayuki; Fujii, Keisuke
2012-11-01
The conventional duality analysis is employed to identify a location of a critical point on a uniform lattice without any disorder in its structure. In the present study, we deal with the random planar lattice, which consists of the randomized structure based on the square lattice. We introduce the uniformly random modification by the bond dilution and contraction on a part of the unit square. The random planar lattice includes the triangular and hexagonal lattices in extreme cases of a parameter to control the structure. A modern duality analysis fashion with real-space renormalization is found to be available for estimating the location of the critical points with a wide range of the randomness parameter. As a simple test bed, we demonstrate that our method indeed gives several critical points for the cases of the Ising and Potts models and the bond-percolation thresholds on the random planar lattice. Our method leads to not only such an extension of the duality analyses on the classical statistical mechanics but also a fascinating result associated with optimal error thresholds for a class of quantum error correction code, the surface code on the random planar lattice, which is known as a skillful technique to protect the quantum state.
Bishop, R. F.; Li, P. H. Y.
2011-04-15
An approximation hierarchy, called the lattice-path-based subsystem (LPSUBm) approximation scheme, is described for the coupled-cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-(1/2) Heisenberg antiferromagnetic) spin-lattice models, namely, the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization, and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods, and the CCM using the alternative lattice-animal-based subsystem (LSUBm) and the distance-based subsystem (DSUBm) schemes. Each of the three CCM schemes (LSUBm, DSUBm, and LPSUBm) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications.
NASA Astrophysics Data System (ADS)
Bishop, R. F.; Li, P. H. Y.
2011-04-01
An approximation hierarchy, called the lattice-path-based subsystem (LPSUBm) approximation scheme, is described for the coupled-cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-(1)/(2) Heisenberg antiferromagnetic) spin-lattice models, namely, the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization, and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods, and the CCM using the alternative lattice-animal-based subsystem (LSUBm) and the distance-based subsystem (DSUBm) schemes. Each of the three CCM schemes (LSUBm, DSUBm, and LPSUBm) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications.
Beam-Plasma Interaction and Instabilities in a 2D Yukawa Plasma
NASA Astrophysics Data System (ADS)
Kyrkos, S.; Kalman, G.; Rosenberg, M.
2008-11-01
In a complex plasma, penetrating charged particle beams may lead to beam-plasma instabilities. When either the plasma, the beam, or both, are strongly interacting [1], the features of the instability are different from those in a weakly coupled plasma. We consider the case when a 2D dusty plasma forms a lattice, and the beam is moving in the lattice plane. Both the grains and the beam particles interact through a Yukawa potential; the beam particles are weakly coupled to each other and to the lattice. The system develops both a longitudinal and a transverse instability. Based on the phonon spectrum of a 2D hexagonal Yukawa lattice [2], we determine and compare the transverse and longitudinal growth rates. As a function of the wavenumber, the growth rates exhibit remarkable gaps, where no instability is excited. The gap locations are governed by the ratio of the lattice and the beam plasma frequencies. The behavior of the growth rates also depends on the direction of the beam and on the relationship between the beam speed and the longitudinal and transverse sound speeds. [1] GJ Kalman, M Rosenberg, JPA 36, 5963 (2003). [2] T Sullivan, GJ Kalman, S Kyrkos, P Bakshi, M Rosenberg, Z Donko, JPA 39, 4607 (2006).
Optical modulators with 2D layered materials
NASA Astrophysics Data System (ADS)
Sun, Zhipei; Martinez, Amos; Wang, Feng
2016-04-01
Light modulation is an essential operation in photonics and optoelectronics. With existing and emerging technologies increasingly demanding compact, efficient, fast and broadband optical modulators, high-performance light modulation solutions are becoming indispensable. The recent realization that 2D layered materials could modulate light with superior performance has prompted intense research and significant advances, paving the way for realistic applications. In this Review, we cover the state of the art of optical modulators based on 2D materials, including graphene, transition metal dichalcogenides and black phosphorus. We discuss recent advances employing hybrid structures, such as 2D heterostructures, plasmonic structures, and silicon and fibre integrated structures. We also take a look at the future perspectives and discuss the potential of yet relatively unexplored mechanisms, such as magneto-optic and acousto-optic modulation.
Large Area Synthesis of 2D Materials
NASA Astrophysics Data System (ADS)
Vogel, Eric
Transition metal dichalcogenides (TMDs) have generated significant interest for numerous applications including sensors, flexible electronics, heterostructures and optoelectronics due to their interesting, thickness-dependent properties. Despite recent progress, the synthesis of high-quality and highly uniform TMDs on a large scale is still a challenge. In this talk, synthesis routes for WSe2 and MoS2 that achieve monolayer thickness uniformity across large area substrates with electrical properties equivalent to geological crystals will be described. Controlled doping of 2D semiconductors is also critically required. However, methods established for conventional semiconductors, such as ion implantation, are not easily applicable to 2D materials because of their atomically thin structure. Redox-active molecular dopants will be demonstrated which provide large changes in carrier density and workfunction through the choice of dopant, treatment time, and the solution concentration. Finally, several applications of these large-area, uniform 2D materials will be described including heterostructures, biosensors and strain sensors.
2D microwave imaging reflectometer electronics
Spear, A. G.; Domier, C. W. Hu, X.; Muscatello, C. M.; Ren, X.; Luhmann, N. C.; Tobias, B. J.
2014-11-15
A 2D microwave imaging reflectometer system has been developed to visualize electron density fluctuations on the DIII-D tokamak. Simultaneously illuminated at four probe frequencies, large aperture optics image reflections from four density-dependent cutoff surfaces in the plasma over an extended region of the DIII-D plasma. Localized density fluctuations in the vicinity of the plasma cutoff surfaces modulate the plasma reflections, yielding a 2D image of electron density fluctuations. Details are presented of the receiver down conversion electronics that generate the in-phase (I) and quadrature (Q) reflectometer signals from which 2D density fluctuation data are obtained. Also presented are details on the control system and backplane used to manage the electronics as well as an introduction to the computer based control program.
2D microwave imaging reflectometer electronics
NASA Astrophysics Data System (ADS)
Spear, A. G.; Domier, C. W.; Hu, X.; Muscatello, C. M.; Ren, X.; Tobias, B. J.; Luhmann, N. C.
2014-11-01
A 2D microwave imaging reflectometer system has been developed to visualize electron density fluctuations on the DIII-D tokamak. Simultaneously illuminated at four probe frequencies, large aperture optics image reflections from four density-dependent cutoff surfaces in the plasma over an extended region of the DIII-D plasma. Localized density fluctuations in the vicinity of the plasma cutoff surfaces modulate the plasma reflections, yielding a 2D image of electron density fluctuations. Details are presented of the receiver down conversion electronics that generate the in-phase (I) and quadrature (Q) reflectometer signals from which 2D density fluctuation data are obtained. Also presented are details on the control system and backplane used to manage the electronics as well as an introduction to the computer based control program.
2D microwave imaging reflectometer electronics.
Spear, A G; Domier, C W; Hu, X; Muscatello, C M; Ren, X; Tobias, B J; Luhmann, N C
2014-11-01
A 2D microwave imaging reflectometer system has been developed to visualize electron density fluctuations on the DIII-D tokamak. Simultaneously illuminated at four probe frequencies, large aperture optics image reflections from four density-dependent cutoff surfaces in the plasma over an extended region of the DIII-D plasma. Localized density fluctuations in the vicinity of the plasma cutoff surfaces modulate the plasma reflections, yielding a 2D image of electron density fluctuations. Details are presented of the receiver down conversion electronics that generate the in-phase (I) and quadrature (Q) reflectometer signals from which 2D density fluctuation data are obtained. Also presented are details on the control system and backplane used to manage the electronics as well as an introduction to the computer based control program. PMID:25430247
2D-Crystal-Based Functional Inks.
Bonaccorso, Francesco; Bartolotta, Antonino; Coleman, Jonathan N; Backes, Claudia
2016-08-01
The possibility to produce and process graphene, related 2D crystals, and heterostructures in the liquid phase makes them promising materials for an ever-growing class of applications as composite materials, sensors, in flexible optoelectronics, and energy storage and conversion. In particular, the ability to formulate functional inks with on-demand rheological and morphological properties, i.e., lateral size and thickness of the dispersed 2D crystals, is a step forward toward the development of industrial-scale, reliable, inexpensive printing/coating processes, a boost for the full exploitation of such nanomaterials. Here, the exfoliation strategies of graphite and other layered crystals are reviewed, along with the advances in the sorting of lateral size and thickness of the exfoliated sheets together with the formulation of functional inks and the current development of printing/coating processes of interest for the realization of 2D-crystal-based devices. PMID:27273554
ERIC Educational Resources Information Center
Scott, Paul
2006-01-01
A lattice is a (rectangular) grid of points, usually pictured as occurring at the intersections of two orthogonal sets of parallel, equally spaced lines. Polygons that have lattice points as vertices are called lattice polygons. It is clear that lattice polygons come in various shapes and sizes. A very small lattice triangle may cover just 3…
Zuhail, K P; Dhara, Surajit
2016-08-10
We report experimental studies on 2D colloidal crystals of dimers stabilized by vortex-like defects in planar nematic and π/2 twisted nematic cells. The dimers are prepared and self-assembled using a laser tweezer. We study the effect of temperature and electric field on the lattice parameters of the colloidal crystals. The lattice parameters vary with the temperature in the nematic phase and a discontinuous structural change is observed at the nematic to smectic-A phase transition. In the nematic phase, we observed a large change in the lattice parameters (≃30%) by applying an external electric field perpendicular to the plane of the 2D crystals. The idea and the active control of the lattice parameters could be useful for designing tunable colloidal crystals. PMID:27445255
Glassy dislocation dynamics in 2D colloidal dimer crystals.
Gerbode, Sharon J; Agarwal, Umang; Ong, Desmond C; Liddell, Chekesha M; Escobedo, Fernando; Cohen, Itai
2010-08-13
Although glassy relaxation is typically associated with disorder, here we report on a new type of glassy dynamics relating to dislocations within 2D crystals of colloidal dimers. Previous studies have demonstrated that dislocation motion in dimer crystals is restricted by certain particle orientations. Here, we drag an optically trapped particle through such dimer crystals, creating dislocations. We find a two-stage relaxation response where initially dislocations glide until encountering particles that cage their motion. Subsequent relaxation occurs logarithmically slowly through a second process where dislocations hop between caged configurations. Finally, in simulations of sheared dimer crystals, the dislocation mean squared displacement displays a caging plateau typical of glassy dynamics. Together, these results reveal a novel glassy system within a colloidal crystal. PMID:20868079
Enhancement of biomixing by swimming cells in 2D films
NASA Astrophysics Data System (ADS)
Gollub, Jerry; Kurtuldu, Huseyin; Guasto, Jeffrey; Johnson, Karl
2011-11-01
Fluid mixing in active suspensions of microorganisms is important to ecological phenomena and shows surprising statistical behavior. We investigate the mixing produced by swimming unicellular algal cells (Chlamydomonas) in quasi-2D films by tracking the motions of cells and of microscopic passive tracer particles advected by the fluid. The reduced spatial dimension of the system leads to long-range flows and a surprisingly strong dependence of tracer transport on the swimmer concentration. The mean square displacements are well described by a stochastic Langevin model, with an effective diffusion coefficient D growing as the 3/2 power of the swimmer concentration, due to the interaction of tracer particles with multiple swimmers. We also discuss the anomalous probability distributions of tracer displacements, which become Gaussian at high concentration, but show strong power-law tails at low concentration. Supported by NSF Grant DMR-0803153.
The 2D lingual appliance system.
Cacciafesta, Vittorio
2013-09-01
The two-dimensional (2D) lingual bracket system represents a valuable treatment option for adult patients seeking a completely invisible orthodontic appliance. The ease of direct or simplified indirect bonding of 2D lingual brackets in combination with low friction mechanics makes it possible to achieve a good functional and aesthetic occlusion, even in the presence of a severe malocclusion. The use of a self-ligating bracket significantly reduces chair-side time for the orthodontist, and the low-profile bracket design greatly improves patient comfort. PMID:24005953
Inkjet printing of 2D layered materials.
Li, Jiantong; Lemme, Max C; Östling, Mikael
2014-11-10
Inkjet printing of 2D layered materials, such as graphene and MoS2, has attracted great interests for emerging electronics. However, incompatible rheology, low concentration, severe aggregation and toxicity of solvents constitute critical challenges which hamper the manufacturing efficiency and product quality. Here, we introduce a simple and general technology concept (distillation-assisted solvent exchange) to efficiently overcome these challenges. By implementing the concept, we have demonstrated excellent jetting performance, ideal printing patterns and a variety of promising applications for inkjet printing of 2D layered materials. PMID:25169938
Measurement of 2D birefringence distribution
NASA Astrophysics Data System (ADS)
Noguchi, Masato; Ishikawa, Tsuyoshi; Ohno, Masahiro; Tachihara, Satoru
1992-10-01
A new measuring method of 2-D birefringence distribution has been developed. It has not been an easy job to get a birefringence distribution in an optical element with conventional ellipsometry because of its lack of scanning means. Finding an analogy between the rotating analyzer method in ellipsometry and the phase-shifting method in recently developed digital interferometry, we have applied the phase-shifting algorithm to ellipsometry, and have developed a new method that makes the measurement of 2-D birefringence distribution easy and possible. The system contains few moving parts, assuring reliability, and measures a large area of a sample at one time, making the measuring time very short.
Knight shift and spin relaxation in the single band 2D Hubbard model
NASA Astrophysics Data System (ADS)
Leblanc, James; Chen, Xi; Gull, Emanuel
We study in detail the roles of spin and charge fluctuations in the single band 2D Hubbard model. Using dynamical mean field theory and cluster extensions such as the dynamical cluster approximation (DCA), we compute the full two particle susceptibilities in the spin and charge representations. By performing analytic continuations we obtain the temperature and doping dependence of the spin-lattice relaxation (T1- 1) and knight shift in the 2D Hubbard model relevant to NMR results on doped cuprates and connect these to RPA results in weak coupling limits.
Magnetic vortex crystal formation in the antidot complement of square artificial spin ice
Araujo, C. I. L. de Silva, R. C.; Ribeiro, I. R. B.; Nascimento, F. S.; Felix, J. F.; Ferreira, S. O.; Moura-Melo, W. A.; Pereira, A. R.; Mól, L. A. S.
2014-03-03
We have studied ferromagnetic nickel thin films patterned with square lattices of elongated antidots that are negative analogues of square artificial spin ice. Micromagnetic simulations and direct current magnetic moment measurements reveal in-plane anisotropy of the magnetic hysteresis loops, and the formation of a dense array of magnetic vortices with random polarization and chirality. These multiply-connected antidot arrays could be superior to lattices of disconnected nanodisks for investigations of vortex switching by applied electric current.
Magnetic vortex crystal formation in the antidot complement of square artificial spin ice
NASA Astrophysics Data System (ADS)
de Araujo, C. I. L.; Silva, R. C.; Ribeiro, I. R. B.; Nascimento, F. S.; Felix, J. F.; Ferreira, S. O.; Mól, L. A. S.; Moura-Melo, W. A.; Pereira, A. R.
2014-03-01
We have studied ferromagnetic nickel thin films patterned with square lattices of elongated antidots that are negative analogues of square artificial spin ice. Micromagnetic simulations and direct current magnetic moment measurements reveal in-plane anisotropy of the magnetic hysteresis loops, and the formation of a dense array of magnetic vortices with random polarization and chirality. These multiply-connected antidot arrays could be superior to lattices of disconnected nanodisks for investigations of vortex switching by applied electric current.
Critical behavior of the q = 3 , 4-Potts model on quasiperiodic decagonal lattices
NASA Astrophysics Data System (ADS)
Ferraz, Carlos Handrey Araujo
2015-12-01
In this study, we performed Monte Carlo simulations of the q = 3 , 4-Potts model on quasiperiodic decagonal lattices (QDL) to assess the critical behavior of these systems. Using the single histogram technique in conjunction with the finite-size scaling analysis, we estimate the infinite lattice critical temperatures and the leading critical exponents for q = 3 and q = 4 states. Our estimates for the critical exponents on QDL are in good agreement with the exact values on 2D periodic lattices, supporting the claim that both the q = 3 and q = 4 Potts model on quasiperiodic lattices belong to the same universality class as those on 2D periodic lattices.
E-2D Advanced Hawkeye: primary flight display
NASA Astrophysics Data System (ADS)
Paolillo, Paul W.; Saxena, Ragini; Garruba, Jonathan; Tripathi, Sanjay; Blanchard, Randy
2006-05-01
This paper is a response to the challenge of providing a large area avionics display for the E-2D AHE aircraft. The resulting display design provides a pilot with high-resolution visual information content covering an image area of almost three square feet (Active Area of Samsung display = 33.792cm x 27.0336 cm = 13.304" x 10.643" = 141.596 square inches = 0.983 sq. ft x 3 = 2.95 sq. ft). The avionics display application, design and performance being described is the Primary Flight Display for the E-2D Advanced Hawkeye aircraft. This cockpit display has a screen diagonal size of 17 inches. Three displays, with minimum bezel width, just fit within the available instrument panel area. The significant design constraints of supporting an upgrade installation have been addressed. These constraints include a display image size that is larger than the mounting opening in the instrument panel. This, therefore, requires that the Electromagnetic Interference (EMI) window, LCD panel and backlight all fit within the limited available bezel depth. High brightness and a wide dimming range are supported with a dual mode Cold Cathode Fluorescent Tube (CCFT) and LED backlight. Packaging constraints dictated the use of multiple U shaped fluorescent lamps in a direct view backlight design for a maximum display brightness of 300 foot-Lamberts. The low intensity backlight levels are provided by remote LEDs coupled through a fiber optic mesh. This architecture generates luminous uniformity within a minimum backlight depth. Cross-cockpit viewing is supported with ultra-wide field-of-view performance including contrast and the color stability of an advanced LCD cell design supports. Display system design tradeoffs directed a priority to high optical efficiency for minimum power and weight.
Stability of skyrmion lattices and symmetries of Dzyaloshinskii-Moriya magnets
NASA Astrophysics Data System (ADS)
Güngördü, Utkan; Nepal, Rabindra; Tretiakov, Oleg A.; Belashchenko, Kirill; Kovalev, Alexey A.
Recently, there has been substantial interest in realizations of skyrmions, in particular in 2D systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultra-dense magnetic memories. Here, we use the most general form of the 2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices with four-fold symmetry and in-plane spirals, in some instances even in the absence of an external magnetic field. Our results relate different hexagonal and square cell phases to the symmetries of materials used for realizations of skyrmions. This will give clear directions for experimental rea lizations of hexagonal and square cell phases, and will allow engineering of skyrmions with unusual properties. We also predict striking differences in gyro-dynamics induced by spin currents for isolated skyrmions and for crystals where spin currents can be induced by charge carriers or by thermal magnons. DOE Early Career Award DE-SC0014189, NSF Grants Nos. Phy-1415600, PHY11-25915, DMR-1420645, and DMR-1308751; Grants-in-Aid from MEXT and SpinNet (Nos. 25800184, 25247056, and 15H01009).
Stability of skyrmion lattices and symmetries of quasi-two-dimensional chiral magnets
Gungordu, Utkan; Nepal, Rabindra; Tretiakov, Oleg A.; Belashchenko, Kirill; Kovalev, Alexey A.
2016-02-24
Recently there has been substantial interest in realizations of skyrmions, in particular in quasi-two-dimensional (2D) systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultradense magnetic memories. Here we use the most general form of the quasi-2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that the skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices withmore » fourfold symmetry and in-plane spirals, in some instances even in the absence of an external magnetic field. Our results relate different hexagonal and square cell phases to the symmetries of materials used for realizations of skyrmions. This will give clear directions for experimental realizations of hexagonal and square cell phases, and will allow engineering of skyrmions with unusual properties. We also predict striking differences in gyrodynamics induced by spin currents for isolated skyrmions and for crystals where spin currents can be induced by charge carriers or by thermal magnons. As a result, we find that under certain conditions, isolated skyrmions can move along the current without a side motion which can have implications for realizations of magnetic memories.« less
Stability of skyrmion lattices and symmetries of quasi-two-dimensional chiral magnets
NASA Astrophysics Data System (ADS)
Güngördü, Utkan; Nepal, Rabindra; Tretiakov, Oleg A.; Belashchenko, Kirill; Kovalev, Alexey A.
2016-02-01
Recently there has been substantial interest in realizations of skyrmions, in particular in quasi-two-dimensional (2D) systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultradense magnetic memories. Here we use the most general form of the quasi-2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that the skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices with fourfold symmetry and in-plane spirals, in some instances even in the absence of an external magnetic field. Our results relate different hexagonal and square cell phases to the symmetries of materials used for realizations of skyrmions. This will give clear directions for experimental realizations of hexagonal and square cell phases, and will allow engineering of skyrmions with unusual properties. We also predict striking differences in gyrodynamics induced by spin currents for isolated skyrmions and for crystals where spin currents can be induced by charge carriers or by thermal magnons. We find that under certain conditions, isolated skyrmions can move along the current without a side motion which can have implications for realizations of magnetic memories.
X , Y , and Z waves: extended structures in nonlinear lattices.
Kevrekidis, P G; Gagnon, J; Frantzeskakis, D J; Malomed, B A
2007-01-01
We propose a new type of waveforms in two-dimensional (2D) and three-dimensional (3D) discrete media-multilegged extended nonlinear structures (ENSs), built as arrays of lattice solitons (tiles and stones, in the 2D and 3D cases, respectively). We study the stability of the tiles and stones analytically, and then extend them numerically to complete ENS forms for both 2D and 3D lattices, aiming to single out stable ENSs. The predicted patterns can be realized in Bose-Einstein condensates trapped in deep optical lattices, crystals built of microresonators, and 2D photonic crystals. In the latter case, the patterns provide for a technique for writing reconfigurable virtual partitions in multipurpose photonic devices. PMID:17358275
X , Y , and Z waves: Extended structures in nonlinear lattices
NASA Astrophysics Data System (ADS)
Kevrekidis, P. G.; Gagnon, J.; Frantzeskakis, D. J.; Malomed, B. A.
2007-01-01
We propose a new type of waveforms in two-dimensional (2D) and three-dimensional (3D) discrete media-multilegged extended nonlinear structures (ENSs), built as arrays of lattice solitons (tiles and stones, in the 2D and 3D cases, respectively). We study the stability of the tiles and stones analytically, and then extend them numerically to complete ENS forms for both 2D and 3D lattices, aiming to single out stable ENSs. The predicted patterns can be realized in Bose-Einstein condensates trapped in deep optical lattices, crystals built of microresonators, and 2D photonic crystals. In the latter case, the patterns provide for a technique for writing reconfigurable virtual partitions in multipurpose photonic devices.
Multilayer DNA origami packed on hexagonal and hybrid lattices.
Ke, Yonggang; Voigt, Niels V; Gothelf, Kurt V; Shih, William M
2012-01-25
"Scaffolded DNA origami" has been proven to be a powerful and efficient approach to construct two-dimensional or three-dimensional objects with great complexity. Multilayer DNA origami has been demonstrated with helices packing along either honeycomb-lattice geometry or square-lattice geometry. Here we report successful folding of multilayer DNA origami with helices arranged on a close-packed hexagonal lattice. This arrangement yields a higher density of helical packing and therefore higher resolution of spatial addressing than has been shown previously. We also demonstrate hybrid multilayer DNA origami with honeycomb-lattice, square-lattice, and hexagonal-lattice packing of helices all in one design. The availability of hexagonal close-packing of helices extends our ability to build complex structures using DNA nanotechnology. PMID:22187940
View of Corto Square Road from Corto Square. Buildings No. ...
View of Corto Square Road from Corto Square. Buildings No. 27 at left, Building No. 25 at rear, and Building No. 26 at right. Parking areas on left and right, looking north - Easter Hill Village, Bordered by South Twenty-sixth Street, South Twenty-eighth Street, Hinkley Avenue, Foothill Avenue & Corto Square, Richmond, Contra Costa County, CA
Microparticle manipulation in optical lattices
NASA Astrophysics Data System (ADS)
Mu, Weiqiang
With the interference of several coherent beams, a periodical potential is produced for the particles trapped inside. The theoretical calculations show that the optical force applied on the particle in such optical lattice is in sinusoidal form. The force amplitudes vary greatly depending on the ratio of the particle size to the spacing of the optical lattice. A setup is constructed to demonstrate this dependence with two different methods: equipartition theorem and hydrodynamic-drag method. Based on this size dependence we develop an approach that allows tunable, size-dependent force selection of a subset of particles from an ensemble containing mixed particles. Combining a universal constant force with the sinusoidal optical force, a tilted washboard potential can be formed for the trapped particle. The diffusion of a particle over the barrier in this tilted washboard potential is briefly discussed. When the washboard potential oscillates, some interesting phenomena will happen: at high oscillation frequency, the particle's movement depends only on the oscillating amplitude; at low frequency, there are some combinations of the oscillation frequency and amplitude that induce the enhanced movement of the particle. This enhancement is first experimentally demonstrated with our setup. By implanting a single laser tweezers into the interferometric optical tweezers, we succeed in dynamically assembling designer colloidal lattices on the background of the interferometric optical tweezers. This new technique provides a flexible tool to design 2-d colloidal lattices.
Parallel stitching of 2D materials
Ling, Xi; Wu, Lijun; Lin, Yuxuan; Ma, Qiong; Wang, Ziqiang; Song, Yi; Yu, Lili; Huang, Shengxi; Fang, Wenjing; Zhang, Xu; et al
2016-01-27
Diverse parallel stitched 2D heterostructures, including metal–semiconductor, semiconductor–semiconductor, and insulator–semiconductor, are synthesized directly through selective “sowing” of aromatic molecules as the seeds in the chemical vapor deposition (CVD) method. Lastly, the methodology enables the large-scale fabrication of lateral heterostructures, which offers tremendous potential for its application in integrated circuits.
Parallel Stitching of 2D Materials.
Ling, Xi; Lin, Yuxuan; Ma, Qiong; Wang, Ziqiang; Song, Yi; Yu, Lili; Huang, Shengxi; Fang, Wenjing; Zhang, Xu; Hsu, Allen L; Bie, Yaqing; Lee, Yi-Hsien; Zhu, Yimei; Wu, Lijun; Li, Ju; Jarillo-Herrero, Pablo; Dresselhaus, Mildred; Palacios, Tomás; Kong, Jing
2016-03-01
Diverse parallel stitched 2D heterostructures, including metal-semiconductor, semiconductor-semiconductor, and insulator-semiconductor, are synthesized directly through selective "sowing" of aromatic molecules as the seeds in the chemical vapor deposition (CVD) method. The methodology enables the large-scale fabrication of lateral heterostructures, which offers tremendous potential for its application in integrated circuits. PMID:26813882
Baby universes in 2d quantum gravity
NASA Astrophysics Data System (ADS)
Ambjørn, Jan; Jain, Sanjay; Thorleifsson, Gudmar
1993-06-01
We investigate the fractal structure of 2d quantum gravity, both for pure gravity and for gravity coupled to multiple gaussian fields and for gravity coupled to Ising spins. The roughness of the surfaces is described in terms of baby universes and using numerical simulations we measure their distribution which is related to the string susceptibility exponent γstring.
ELRIS2D: A MATLAB Package for the 2D Inversion of DC Resistivity/IP Data
NASA Astrophysics Data System (ADS)
Akca, Irfan
2016-04-01
ELRIS2D is an open source code written in MATLAB for the two-dimensional inversion of direct current resistivity (DCR) and time domain induced polarization (IP) data. The user interface of the program is designed for functionality and ease of use. All available settings of the program can be reached from the main window. The subsurface is discretized using a hybrid mesh generated by the combination of structured and unstructured meshes, which reduces the computational cost of the whole inversion procedure. The inversion routine is based on the smoothness constrained least squares method. In order to verify the program, responses of two test models and field data sets were inverted. The models inverted from the synthetic data sets are consistent with the original test models in both DC resistivity and IP cases. A field data set acquired in an archaeological site is also used for the verification of outcomes of the program in comparison with the excavation results.
NASA Astrophysics Data System (ADS)
Komura, Yukihiro; Okabe, Yutaka
2014-03-01
We present sample CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm. We deal with the classical spin models; the Ising model, the q-state Potts model, and the classical XY model. As for the lattice, both the 2D (square) lattice and the 3D (simple cubic) lattice are treated. We already reported the idea of the GPU implementation for 2D models (Komura and Okabe, 2012). We here explain the details of sample programs, and discuss the performance of the present GPU implementation for the 3D Ising and XY models. We also show the calculated results of the moment ratio for these models, and discuss phase transitions. Catalogue identifier: AERM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERM_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5632 No. of bytes in distributed program, including test data, etc.: 14688 Distribution format: tar.gz Programming language: C, CUDA. Computer: System with an NVIDIA CUDA enabled GPU. Operating system: System with an NVIDIA CUDA enabled GPU. Classification: 23. External routines: NVIDIA CUDA Toolkit 3.0 or newer Nature of problem: Monte Carlo simulation of classical spin systems. Ising, q-state Potts model, and the classical XY model are treated for both two-dimensional and three-dimensional lattices. Solution method: GPU-based Swendsen-Wang multi-cluster spin flip Monte Carlo method. The CUDA implementation for the cluster-labeling is based on the work by Hawick et al. [1] and that by Kalentev et al. [2]. Restrictions: The system size is limited depending on the memory of a GPU. Running time: For the parameters used in the sample programs, it takes about a minute for each program. Of course, it depends on the system size, the number of Monte Carlo steps, etc. References: [1] K
Bayesian least squares deconvolution
NASA Astrophysics Data System (ADS)
Asensio Ramos, A.; Petit, P.
2015-11-01
Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
Generalized conjugate gradient squared
Fokkema, D.R.; Sleijpen, G.L.G.
1994-12-31
In order to solve non-symmetric linear systems of equations, the Conjugate Gradient Squared (CGS) is a well-known and widely used iterative method. In practice the method converges fast, often twice as fast as the Bi-Conjugate Gradient method. This is what you may expect, since CGS uses the square of the BiCG polynomial. However, CGS may suffer from its erratic convergence behavior. The method may diverge or the approximate solution may be inaccurate. BiCGSTAB uses the BiCG polynomial and a product of linear factors in an attempt to smoothen the convergence. In many cases, this has proven to be very effective. Unfortunately, the convergence of BiCGSTAB may stall when a linear factor (nearly) degenerates. BiCGstab({ell}) is designed to overcome this degeneration of linear factors. It generalizes BiCGSTAB and uses both the BiCG polynomial and a product of higher order factors. Still, CGS may converge faster than BiCGSTAB or BiCGstab({ell}). So instead of using a product of linear or higher order factors, it may be worthwhile to look for other polynomials. Since the BiCG polynomial is based on a three term recursion, a natural choice would be a polynomial based on another three term recursion. Possibly, a suitable choice of recursion coefficients would result in method that converges faster or as fast as CGS, but less erratic. It turns out that an algorithm for such a method can easily be formulated. One particular choice for the recursion coefficients leads to CGS. Therefore one could call this algorithm generalized CGS. Another choice for the recursion coefficients leads to BiCGSTAB. It is therefore possible to mix linear factors and some polynomial based on a three term recursion. This way one may get the best of both worlds. The authors will report on their findings.
Where is the continuum in lattice quantum chromodynamics?
NASA Technical Reports Server (NTRS)
Kennedy, A. D.; Pendleton, B. J.; Kuti, J.; Meyer, S.
1985-01-01
A Monte Carlo calculation of the quark-liberating phase transition in lattice quantum chromodynamics is presented. The transition temperature as a function of the lattice coupling g does not scale according to the perturbative beta function for 6/g-squared less than 6.1. Finite-size scaling is used in analyzing the properties of the lattice system near the transition point.
Novel Quantum Phases of Dipolar Bose Gases in Optical Lattices
NASA Astrophysics Data System (ADS)
Yi, S.; Li, T.; Sun, C. P.
2007-06-01
We investigate the quantum phases of polarized dipolar bosons loaded into a two-dimensional square and three-dimensional cubic optical lattices. We show that the long-range and anisotropic nature of the dipole-dipole interaction induces a rich variety of quantum phases, including the supersolid and striped supersolid phases in two-dimensional lattices, and the layered supersolid phase in three-dimensional lattices.
NASA Astrophysics Data System (ADS)
Yu, Huidan; Zhang, Jinsuo; Li, Ning
2006-03-01
We investigate the enhancement of mass transfer in 2D thermally driven cavities using lattice Boltzmann equation (LBE) method. The computational technique integrates three coupled LBEs for solving velocity, temperature, and concentration fields simultaneously. Simulation is performed for oxygen transfer in lead/lead-bismuth eutectic with variations of temperature boundary, Schmidt number, and field aspect ratio to investigate the effects on enhancement of oxygen transfer. Interested characteristics include oxygen concentration, Sherwood number, and velocity profiles, etc. Our results clearly indicate that oxygen transfer is dominated by convection while diffusion also plays a role on it. Comparative studies demonstrate that side heating and top cooling device is more efficient to transfer oxygen than side heating and cooling device and oxygen transfers more rapidly in square cavity than in rectangular cavity. This work establishes a reliable thermal LBE model for thermally driven heat and mass transfer.
Application of 2D Non-Graphene Materials and 2D Oxide Nanostructures for Biosensing Technology
Shavanova, Kateryna; Bakakina, Yulia; Burkova, Inna; Shtepliuk, Ivan; Viter, Roman; Ubelis, Arnolds; Beni, Valerio; Starodub, Nickolaj; Yakimova, Rositsa; Khranovskyy, Volodymyr
2016-01-01
The discovery of graphene and its unique properties has inspired researchers to try to invent other two-dimensional (2D) materials. After considerable research effort, a distinct “beyond graphene” domain has been established, comprising the library of non-graphene 2D materials. It is significant that some 2D non-graphene materials possess solid advantages over their predecessor, such as having a direct band gap, and therefore are highly promising for a number of applications. These applications are not limited to nano- and opto-electronics, but have a strong potential in biosensing technologies, as one example. However, since most of the 2D non-graphene materials have been newly discovered, most of the research efforts are concentrated on material synthesis and the investigation of the properties of the material. Applications of 2D non-graphene materials are still at the embryonic stage, and the integration of 2D non-graphene materials into devices is scarcely reported. However, in recent years, numerous reports have blossomed about 2D material-based biosensors, evidencing the growing potential of 2D non-graphene materials for biosensing applications. This review highlights the recent progress in research on the potential of using 2D non-graphene materials and similar oxide nanostructures for different types of biosensors (optical and electrochemical). A wide range of biological targets, such as glucose, dopamine, cortisol, DNA, IgG, bisphenol, ascorbic acid, cytochrome and estradiol, has been reported to be successfully detected by biosensors with transducers made of 2D non-graphene materials. PMID:26861346
Application of 2D Non-Graphene Materials and 2D Oxide Nanostructures for Biosensing Technology.
Shavanova, Kateryna; Bakakina, Yulia; Burkova, Inna; Shtepliuk, Ivan; Viter, Roman; Ubelis, Arnolds; Beni, Valerio; Starodub, Nickolaj; Yakimova, Rositsa; Khranovskyy, Volodymyr
2016-01-01
The discovery of graphene and its unique properties has inspired researchers to try to invent other two-dimensional (2D) materials. After considerable research effort, a distinct "beyond graphene" domain has been established, comprising the library of non-graphene 2D materials. It is significant that some 2D non-graphene materials possess solid advantages over their predecessor, such as having a direct band gap, and therefore are highly promising for a number of applications. These applications are not limited to nano- and opto-electronics, but have a strong potential in biosensing technologies, as one example. However, since most of the 2D non-graphene materials have been newly discovered, most of the research efforts are concentrated on material synthesis and the investigation of the properties of the material. Applications of 2D non-graphene materials are still at the embryonic stage, and the integration of 2D non-graphene materials into devices is scarcely reported. However, in recent years, numerous reports have blossomed about 2D material-based biosensors, evidencing the growing potential of 2D non-graphene materials for biosensing applications. This review highlights the recent progress in research on the potential of using 2D non-graphene materials and similar oxide nanostructures for different types of biosensors (optical and electrochemical). A wide range of biological targets, such as glucose, dopamine, cortisol, DNA, IgG, bisphenol, ascorbic acid, cytochrome and estradiol, has been reported to be successfully detected by biosensors with transducers made of 2D non-graphene materials. PMID:26861346
2D to 3D transition of polymeric carbon nitride nanosheets
Chamorro-Posada, Pedro; Vázquez-Cabo, José; Martín-Ramos, Pablo; Martín-Gil, Jesús; Navas-Gracia, Luis M.; Dante, Roberto C.
2014-11-15
The transition from a prevalent turbostratic arrangement with low planar interactions (2D) to an array of polymeric carbon nitride nanosheets with stronger interplanar interactions (3D), occurring for samples treated above 650 °C, was detected by terahertz-time domain spectroscopy (THz-TDS). The simulated 3D material made of stacks of shifted quasi planar sheets composed of zigzagged polymer ribbons, delivered a XRD simulated pattern in relatively good agreement with the experimental one. The 2D to 3D transition was also supported by the simulation of THz-TDS spectra obtained from quantum chemistry calculations, in which the same broad bands around 2 THz and 1.5 THz were found for 2D and 3D arrays, respectively. This transition was also in accordance with the tightening of the interplanar distance probably due to an interplanar π bond contribution, as evidenced also by a broad absorption around 2.6 eV in the UV–vis spectrum, which appeared in the sample treated at 650 °C, and increased in the sample treated at 700 °C. The band gap was calculated for 1D and 2D cases. The value of 3.374 eV for the 2D case is, within the model accuracy and precision, in a relative good agreement with the value of 3.055 eV obtained from the experimental results. - Graphical abstract: 2D lattice mode vibrations and structural changes correlated with the so called “2D to 3D transition”. - Highlights: • A 2D to 3D transition has been detected for polymeric carbon nitride. • THz-TDS allowed us to discover and detect the 2D to 3D transition of polymeric carbon nitride. • We propose a structure for polymeric carbon nitride confirming it with THz-TDS.
NASA Astrophysics Data System (ADS)
Li, Jianbao; Wang, Yue-Sheng; Zhang, Chuanzeng
2010-05-01
In this paper, a finite element method based on the ABAQUS code and user subroutine is presented to evaluate the propagation of acoustic waves in the two-dimensional phononic crystals with Archimedean-like tilings. Two systems composed of cylinder scatters embedded in a host in Ladybug and Bathroom lattices are considered. Complete and accurate band structures and transmission spectra are obtained to identify the band gaps and eigenmodes. We found that Archimedean-like structures can have some advantages over the traditional square lattice regarding the completeness of the gap and its position and width. Also, due to the same square primitive unit cell and the first Brillouin zone, the two square-like lattices have similar acoustic response in lower bands. The results indicate that the finite element method is precise for the band structure computation of the complex phononic crystals with Archimedean tilings.
Lattice splitting under intermittent flows
NASA Astrophysics Data System (ADS)
Schläpfer, Markus; Trantopoulos, Konstantinos
2010-05-01
We study the splitting of regular square lattices subject to stochastic intermittent flows. Various flow patterns are produced by different groupings of the nodes, based on their random alternation between two possible states. The resulting flows on the lattices decrease with the number of groups according to a power law. By Monte Carlo simulations we reveal how the time span until the occurrence of a splitting depends on the flow patterns. Increasing the flow fluctuation frequency shortens this time span, which reaches a minimum before rising again due to inertia effects incorporated in the model. The size of the largest connected component after the splitting is rather independent of the flow fluctuation frequency but slightly decreases with the link capacities. Our findings carry important implications for real-world networks, such as electric power grids with a large share of renewable intermittent energy sources.
Lattice splitting under intermittent flows.
Schläpfer, Markus; Trantopoulos, Konstantinos
2010-05-01
We study the splitting of regular square lattices subject to stochastic intermittent flows. Various flow patterns are produced by different groupings of the nodes, based on their random alternation between two possible states. The resulting flows on the lattices decrease with the number of groups according to a power law. By Monte Carlo simulations we reveal how the time span until the occurrence of a splitting depends on the flow patterns. Increasing the flow fluctuation frequency shortens this time span, which reaches a minimum before rising again due to inertia effects incorporated in the model. The size of the largest connected component after the splitting is rather independent of the flow fluctuation frequency but slightly decreases with the link capacities. Our findings carry important implications for real-world networks, such as electric power grids with a large share of renewable intermittent energy sources. PMID:20866296
Static & Dynamic Response of 2D Solids
1996-07-15
NIKE2D is an implicit finite-element code for analyzing the finite deformation, static and dynamic response of two-dimensional, axisymmetric, plane strain, and plane stress solids. The code is fully vectorized and available on several computing platforms. A number of material models are incorporated to simulate a wide range of material behavior including elasto-placicity, anisotropy, creep, thermal effects, and rate dependence. Slideline algorithms model gaps and sliding along material interfaces, including interface friction, penetration and single surfacemore » contact. Interactive-graphics and rezoning is included for analyses with large mesh distortions. In addition to quasi-Newton and arc-length procedures, adaptive algorithms can be defined to solve the implicit equations using the solution language ISLAND. Each of these capabilities and more make NIKE2D a robust analysis tool.« less
Stochastic Inversion of 2D Magnetotelluric Data
2010-07-01
The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function ismore » explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, it provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows« less
Stochastic Inversion of 2D Magnetotelluric Data
Chen, Jinsong
2010-07-01
The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function is explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, it provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows
Explicit 2-D Hydrodynamic FEM Program
1996-08-07
DYNA2D* is a vectorized, explicit, two-dimensional, axisymmetric and plane strain finite element program for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. DYNA2D* contains 13 material models and 9 equations of state (EOS) to cover a wide range of material behavior. The material models implemented in all machine versions are: elastic, orthotropic elastic, kinematic/isotropic elastic plasticity, thermoelastoplastic, soil and crushable foam, linear viscoelastic, rubber, high explosive burn, isotropic elastic-plastic, temperature-dependent elastic-plastic. Themore » isotropic and temperature-dependent elastic-plastic models determine only the deviatoric stresses. Pressure is determined by one of 9 equations of state including linear polynomial, JWL high explosive, Sack Tuesday high explosive, Gruneisen, ratio of polynomials, linear polynomial with energy deposition, ignition and growth of reaction in HE, tabulated compaction, and tabulated.« less
Schottky diodes from 2D germanane
NASA Astrophysics Data System (ADS)
Sahoo, Nanda Gopal; Esteves, Richard J.; Punetha, Vinay Deep; Pestov, Dmitry; Arachchige, Indika U.; McLeskey, James T.
2016-07-01
We report on the fabrication and characterization of a Schottky diode made using 2D germanane (hydrogenated germanene). When compared to germanium, the 2D structure has higher electron mobility, an optimal band-gap, and exceptional stability making germanane an outstanding candidate for a variety of opto-electronic devices. One-atom-thick sheets of hydrogenated puckered germanium atoms have been synthesized from a CaGe2 framework via intercalation and characterized by XRD, Raman, and FTIR techniques. The material was then used to fabricate Schottky diodes by suspending the germanane in benzonitrile and drop-casting it onto interdigitated metal electrodes. The devices demonstrate significant rectifying behavior and the outstanding potential of this material.
Layer Engineering of 2D Semiconductor Junctions.
He, Yongmin; Sobhani, Ali; Lei, Sidong; Zhang, Zhuhua; Gong, Yongji; Jin, Zehua; Zhou, Wu; Yang, Yingchao; Zhang, Yuan; Wang, Xifan; Yakobson, Boris; Vajtai, Robert; Halas, Naomi J; Li, Bo; Xie, Erqing; Ajayan, Pulickel
2016-07-01
A new concept for junction fabrication by connecting multiple regions with varying layer thicknesses, based on the thickness dependence, is demonstrated. This type of junction is only possible in super-thin-layered 2D materials, and exhibits similar characteristics as p-n junctions. Rectification and photovoltaic effects are observed in chemically homogeneous MoSe2 junctions between domains of different thicknesses. PMID:27136275
NASA Astrophysics Data System (ADS)
Smith, Greg; Lankshear, Allan
1998-07-01
2dF is a multi-object instrument mounted at prime focus at the AAT capable of spectroscopic analysis of 400 objects in a single 2 degree field. It also prepares a second 2 degree 400 object field while the first field is being observed. At its heart is a high precision robotic positioner that places individual fiber end magnetic buttons on one of two field plates. The button gripper is carried on orthogonal gantries powered by linear synchronous motors and contains a TV camera which precisely locates backlit buttons to allow placement in user defined locations to 10 (mu) accuracy. Fiducial points on both plates can also be observed by the camera to allow repeated checks on positioning accuracy. Field plates rotate to follow apparent sky rotation. The spectrographs both analyze light from the 200 observing fibers each and back- illuminate the 400 fibers being re-positioned during the observing run. The 2dF fiber position and spectrograph system is a large and complex instrument located at the prime focus of the Anglo Australian Telescope. The mechanical design has departed somewhat from the earlier concepts of Gray et al, but still reflects the audacity of those first ideas. The positioner is capable of positioning 400 fibers on a field plate while another 400 fibers on another plate are observing at the focus of the telescope and feeding the twin spectrographs. When first proposed it must have seemed like ingenuity unfettered by caution. Yet now it works, and works wonderfully well. 2dF is a system which functions as the result of the combined and coordinated efforts of the astronomers, the mechanical designers and tradespeople, the electronic designers, the programmers, the support staff at the telescope, and the manufacturing subcontractors. The mechanical design of the 2dF positioner and spectrographs was carried out by the mechanical engineering staff of the AAO and the majority of the manufacture was carried out in the AAO workshops.
Realistic and efficient 2D crack simulation
NASA Astrophysics Data System (ADS)
Yadegar, Jacob; Liu, Xiaoqing; Singh, Abhishek
2010-04-01
Although numerical algorithms for 2D crack simulation have been studied in Modeling and Simulation (M&S) and computer graphics for decades, realism and computational efficiency are still major challenges. In this paper, we introduce a high-fidelity, scalable, adaptive and efficient/runtime 2D crack/fracture simulation system by applying the mathematically elegant Peano-Cesaro triangular meshing/remeshing technique to model the generation of shards/fragments. The recursive fractal sweep associated with the Peano-Cesaro triangulation provides efficient local multi-resolution refinement to any level-of-detail. The generated binary decomposition tree also provides efficient neighbor retrieval mechanism used for mesh element splitting and merging with minimal memory requirements essential for realistic 2D fragment formation. Upon load impact/contact/penetration, a number of factors including impact angle, impact energy, and material properties are all taken into account to produce the criteria of crack initialization, propagation, and termination leading to realistic fractal-like rubble/fragments formation. The aforementioned parameters are used as variables of probabilistic models of cracks/shards formation, making the proposed solution highly adaptive by allowing machine learning mechanisms learn the optimal values for the variables/parameters based on prior benchmark data generated by off-line physics based simulation solutions that produce accurate fractures/shards though at highly non-real time paste. Crack/fracture simulation has been conducted on various load impacts with different initial locations at various impulse scales. The simulation results demonstrate that the proposed system has the capability to realistically and efficiently simulate 2D crack phenomena (such as window shattering and shards generation) with diverse potentials in military and civil M&S applications such as training and mission planning.
Compact 2-D graphical representation of DNA
NASA Astrophysics Data System (ADS)
Randić, Milan; Vračko, Marjan; Zupan, Jure; Novič, Marjana
2003-05-01
We present a novel 2-D graphical representation for DNA sequences which has an important advantage over the existing graphical representations of DNA in being very compact. It is based on: (1) use of binary labels for the four nucleic acid bases, and (2) use of the 'worm' curve as template on which binary codes are placed. The approach is illustrated on DNA sequences of the first exon of human β-globin and gorilla β-globin.
2D materials: Graphene and others
NASA Astrophysics Data System (ADS)
Bansal, Suneev Anil; Singh, Amrinder Pal; Kumar, Suresh
2016-05-01
Present report reviews the recent advancements in new atomically thick 2D materials. Materials covered in this review are Graphene, Silicene, Germanene, Boron Nitride (BN) and Transition metal chalcogenides (TMC). These materials show extraordinary mechanical, electronic and optical properties which make them suitable candidates for future applications. Apart from unique properties, tune-ability of highly desirable properties of these materials is also an important area to be emphasized on.
Mason, W.E.
1983-03-01
A set of finite element codes for the solution of nonlinear, two-dimensional (TACO2D) and three-dimensional (TACO3D) heat transfer problems. Performs linear and nonlinear analyses of both transient and steady state heat transfer problems. Has the capability to handle time or temperature dependent material properties. Materials may be either isotropic or orthotropic. A variety of time and temperature dependent boundary conditions and loadings are available including temperature, flux, convection, radiation, and internal heat generation.
NASA Astrophysics Data System (ADS)
Jeromin, A.; Schaffarczyk, A. P.; Puczylowski, J.; Peinke, J.; Hölling, M.
2014-12-01
For the investigation of atmospheric turbulent flows on small scales a new anemometer was developed, the so-called 2d-Atmospheric Laser Cantilever Anemometer (2d-ALCA). It performs highly resolved measurements with a spatial resolution in millimeter range and temporal resolution in kHz range, thus detecting very small turbulent structures. The anemometer is a redesign of the successfully operating 2d-LCA for laboratory application. The new device was designed to withstand hostile operating environments (rain and saline, humid air). In February 2012, the 2d-ALCA was used for the first time in a test field. The device was mounted in about 53 m above ground level on a lattice tower near the German North Sea coast. Wind speed was measured by the 2d-ALCA at 10 kHz sampling rate and by cup anemometers at 1 Hz. The instantaneous wind speed ranged from 8 m/s to 19 m/s at an average turbulence level of about 7 %. Wind field characteristics were analyzed based on cup anemometer as well as 2d-ALCA. The combination of both devices allowed the study of atmospheric turbulence over several magnitudes in turbulent scales.
Tomosynthesis imaging with 2D scanning trajectories
NASA Astrophysics Data System (ADS)
Khare, Kedar; Claus, Bernhard E. H.; Eberhard, Jeffrey W.
2011-03-01
Tomosynthesis imaging in chest radiography provides volumetric information with the potential for improved diagnostic value when compared to the standard AP or LAT projections. In this paper we explore the image quality benefits of 2D scanning trajectories when coupled with advanced image reconstruction approaches. It is intuitively clear that 2D trajectories provide projection data that is more complete in terms of Radon space filling, when compared with conventional tomosynthesis using a linearly scanned source. Incorporating this additional information for obtaining improved image quality is, however, not a straightforward problem. The typical tomosynthesis reconstruction algorithms are based on direct inversion methods e.g. Filtered Backprojection (FBP) or iterative algorithms that are variants of the Algebraic Reconstruction Technique (ART). The FBP approach is fast and provides high frequency details in the image but at the same time introduces streaking artifacts degrading the image quality. The iterative methods can reduce the image artifacts by using image priors but suffer from a slow convergence rate, thereby producing images lacking high frequency details. In this paper we propose using a fast converging optimal gradient iterative scheme that has advantages of both the FBP and iterative methods in that it produces images with high frequency details while reducing the image artifacts. We show that using favorable 2D scanning trajectories along with the proposed reconstruction method has the advantage of providing improved depth information for structures such as the spine and potentially producing images with more isotropic resolution.
MAGNUM-2D computer code: user's guide
England, R.L.; Kline, N.W.; Ekblad, K.J.; Baca, R.G.
1985-01-01
Information relevant to the general use of the MAGNUM-2D computer code is presented. This computer code was developed for the purpose of modeling (i.e., simulating) the thermal and hydraulic conditions in the vicinity of a waste package emplaced in a deep geologic repository. The MAGNUM-2D computer computes (1) the temperature field surrounding the waste package as a function of the heat generation rate of the nuclear waste and thermal properties of the basalt and (2) the hydraulic head distribution and associated groundwater flow fields as a function of the temperature gradients and hydraulic properties of the basalt. MAGNUM-2D is a two-dimensional numerical model for transient or steady-state analysis of coupled heat transfer and groundwater flow in a fractured porous medium. The governing equations consist of a set of coupled, quasi-linear partial differential equations that are solved using a Galerkin finite-element technique. A Newton-Raphson algorithm is embedded in the Galerkin functional to formulate the problem in terms of the incremental changes in the dependent variables. Both triangular and quadrilateral finite elements are used to represent the continuum portions of the spatial domain. Line elements may be used to represent discrete conduits. 18 refs., 4 figs., 1 tab.
Engineering light outcoupling in 2D materials.
Lien, Der-Hsien; Kang, Jeong Seuk; Amani, Matin; Chen, Kevin; Tosun, Mahmut; Wang, Hsin-Ping; Roy, Tania; Eggleston, Michael S; Wu, Ming C; Dubey, Madan; Lee, Si-Chen; He, Jr-Hau; Javey, Ali
2015-02-11
When light is incident on 2D transition metal dichalcogenides (TMDCs), it engages in multiple reflections within underlying substrates, producing interferences that lead to enhancement or attenuation of the incoming and outgoing strength of light. Here, we report a simple method to engineer the light outcoupling in semiconducting TMDCs by modulating their dielectric surroundings. We show that by modulating the thicknesses of underlying substrates and capping layers, the interference caused by substrate can significantly enhance the light absorption and emission of WSe2, resulting in a ∼11 times increase in Raman signal and a ∼30 times increase in the photoluminescence (PL) intensity of WSe2. On the basis of the interference model, we also propose a strategy to control the photonic and optoelectronic properties of thin-layer WSe2. This work demonstrates the utilization of outcoupling engineering in 2D materials and offers a new route toward the realization of novel optoelectronic devices, such as 2D LEDs and solar cells. PMID:25602462
Sine-square deformation and supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Okunishi, Kouichi; Katsura, Hosho
2015-11-01
We investigate the sine-square deformation (SSD) of free fermions in one-dimensional continuous space. On the basis of supersymmetric quantum mechanics, we prove the correspondence between the many-body ground state of the system with SSD and that of the uniform system with periodic boundary conditions. We also discuss the connection between the SSD in the continuous space and its lattice version, where the geometric correction due to the real-space deformation plays an important role in relating the eigenstates of the lattice SSD with those of the continuous SSD.
Reconfigurable wave band structure of an artificial square ice
NASA Astrophysics Data System (ADS)
Iacocca, Ezio; Gliga, Sebastian; Stamps, Robert L.; Heinonen, Olle
2016-04-01
Artificial square ices are structures composed of magnetic nanoelements arranged on the sites of a two-dimensional square lattice, such that there are four interacting magnetic elements at each vertex, leading to geometrical frustration. Using a semianalytical approach, we show that square ices exhibit a rich spin-wave band structure that is tunable both by external magnetic fields and the magnetization configuration of individual elements. Internal degrees of freedom can give rise to equilibrium states with bent magnetization at the element edges leading to characteristic excitations; in the presence of magnetostatic interactions these form separate bands analogous to impurity bands in semiconductors. Full-scale micromagnetic simulations corroborate our semianalytical approach. Our results show that artificial square ices can be viewed as reconfigurable and tunable magnonic crystals that can be used as metamaterials for spin-wave-based applications at the nanoscale.
Strain-displacement relations for strain engineering in single-layer 2d materials
NASA Astrophysics Data System (ADS)
Midtvedt, Daniel; Lewenkopf, Caio H.; Croy, Alexander
2016-03-01
We investigate the electromechanical coupling in single-layer 2d materials. For non-Bravais lattices, we find important corrections to the standard macroscopic strain-microscopic atomic-displacement theory. We put forward a general and systematic approach to calculate strain-displacement relations for several classes of 2d materials. We apply our findings to graphene as a study case, by combining a tight binding and a valence force-field model to calculate electronic and mechanical properties of graphene nanoribbons under strain. The results show good agreement with the predictions of the Dirac equation coupled to continuum mechanics. For this long wave-limit effective theory, we find that the strain-displacement relations lead to a renormalization correction to the strain-induced pseudo-magnetic fields. A similar renormalization is found for the strain-induced band-gap of black phosphorous. Implications for nanomechanical properties and electromechanical coupling in 2d materials are discussed.
Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition
NASA Astrophysics Data System (ADS)
Chuang, Chern; Lee, Chee Kong; Moix, Jeremy M.; Knoester, Jasper; Cao, Jianshu
2016-05-01
The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D limits. It is found that the scaling relation is universal and independent of the temperature, disorder, and noise parameters, and the essential order parameter is the ratio between the localization length in 2D and the circumference of the tube. Phenomenological and quantitative expressions for transport properties as functions of disorder and noise are obtained and applied to real systems: In the natural chlorosomes found in light-harvesting bacteria the exciton transfer dynamics is predicted to be in the 2D limit, whereas a family of synthetic molecular aggregates is found to be in the homogeneous limit and is independent of dimensionality.
Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition.
Chuang, Chern; Lee, Chee Kong; Moix, Jeremy M; Knoester, Jasper; Cao, Jianshu
2016-05-13
The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D limits. It is found that the scaling relation is universal and independent of the temperature, disorder, and noise parameters, and the essential order parameter is the ratio between the localization length in 2D and the circumference of the tube. Phenomenological and quantitative expressions for transport properties as functions of disorder and noise are obtained and applied to real systems: In the natural chlorosomes found in light-harvesting bacteria the exciton transfer dynamics is predicted to be in the 2D limit, whereas a family of synthetic molecular aggregates is found to be in the homogeneous limit and is independent of dimensionality. PMID:27232033
Dual Element Intercalation into 2D Layered Bi₂Se₃ Nanoribbons.
Chen, Karen P; Chung, Frank R; Wang, Mengjing; Koski, Kristie J
2015-04-29
We demonstrate the intercalation of multiple zero-valent atomic species into two-dimensional (2D) layered Bi2Se3 nanoribbons. Intercalation is performed chemically through a stepwise combination of disproportionation redox reactions, hydrazine reduction, or carbonyl decomposition. Traditional intercalation is electrochemical thus limiting intercalant guests to a single atomic species. We show that multiple zero-valent atoms can be intercalated through this chemical route into the host lattice of a 2D crystal. Intermetallic species exhibit unique structural ordering demonstrated in a variety of superlattice diffraction patterns. We believe this method is general and can be used to achieve a wide variety of new 2D materials previously inaccessible. PMID:25851420
2D superconductivity by ionic gating
NASA Astrophysics Data System (ADS)
Iwasa, Yoshi
2D superconductivity is attracting a renewed interest due to the discoveries of new highly crystalline 2D superconductors in the past decade. Superconductivity at the oxide interfaces triggered by LaAlO3/SrTiO3 has become one of the promising routes for creation of new 2D superconductors. Also, the MBE grown metallic monolayers including FeSe are also offering a new platform of 2D superconductors. In the last two years, there appear a variety of monolayer/bilayer superconductors fabricated by CVD or mechanical exfoliation. Among these, electric field induced superconductivity by electric double layer transistor (EDLT) is a unique platform of 2D superconductivity, because of its ability of high density charge accumulation, and also because of the versatility in terms of materials, stemming from oxides to organics and layered chalcogenides. In this presentation, the following issues of electric filed induced superconductivity will be addressed; (1) Tunable carrier density, (2) Weak pinning, (3) Absence of inversion symmetry. (1) Since the sheet carrier density is quasi-continuously tunable from 0 to the order of 1014 cm-2, one is able to establish an electronic phase diagram of superconductivity, which will be compared with that of bulk superconductors. (2) The thickness of superconductivity can be estimated as 2 - 10 nm, dependent on materials, and is much smaller than the in-plane coherence length. Such a thin but low resistance at normal state results in extremely weak pinning beyond the dirty Boson model in the amorphous metallic films. (3) Due to the electric filed, the inversion symmetry is inherently broken in EDLT. This feature appears in the enhancement of Pauli limit of the upper critical field for the in-plane magnetic fields. In transition metal dichalcogenide with a substantial spin-orbit interactions, we were able to confirm the stabilization of Cooper pair due to its spin-valley locking. This work has been supported by Grant-in-Aid for Specially
Proust, Julien; Fehrembach, Anne-Laure; Bedu, Frédéric; Ozerov, Igor; Bonod, Nicolas
2016-01-01
Light reflection occuring at the surface of silicon wafers is drastically diminished by etching square pillars of height 110 nm and width 140 nm separated by a 100 nm gap distance in a square lattice. The design of the nanostructure is optimized to widen the spectral tolerance of the antireflective coatings over the visible spectrum for both fundamental polarizations. Angle and polarized resolved optical measurements report a light reflection remaining under 5% when averaged in the visible spectrum for both polarizations in a wide angular range. Light reflection remains almost insensitive to the light polarization even in oblique incidence. PMID:27109643
Proust, Julien; Fehrembach, Anne-Laure; Bedu, Frédéric; Ozerov, Igor; Bonod, Nicolas
2016-01-01
Light reflection occuring at the surface of silicon wafers is drastically diminished by etching square pillars of height 110 nm and width 140 nm separated by a 100 nm gap distance in a square lattice. The design of the nanostructure is optimized to widen the spectral tolerance of the antireflective coatings over the visible spectrum for both fundamental polarizations. Angle and polarized resolved optical measurements report a light reflection remaining under 5% when averaged in the visible spectrum for both polarizations in a wide angular range. Light reflection remains almost insensitive to the light polarization even in oblique incidence. PMID:27109643
Stress concentrations around a square cutout in a composite plate
NASA Astrophysics Data System (ADS)
Cannon, Colin P.
Composite structure in the aircraft industry has been in development for well over half a century and yet the understanding of the effects of a square cutout is generally limited to quasi-isotropic laminates. Currently, the closed-form solution to calculate the stresses around a cutout is limited to symmetric anisotropic laminates with limitations on the cutout shapes. Finite Element Analysis, using MSC PATRAN and NASTRAN, was performed on 2D composite laminates containing square cutouts with rounded corners. The laminate stacking sequence was varied from symmetrical and balanced to unsymmetrical and unbalanced and the square cutouts each had different radii at the corners. The stress concentration factors from a uniaxial load were identified at the laminate and the lamina level. The effects of the stacking sequence and the varying radii were identified to better understand the physics of a square cutout in a composite plate.
Statistical Transmutation in Floquet Driven Optical Lattices
NASA Astrophysics Data System (ADS)
Sedrakyan, Tigran A.; Galitski, Victor M.; Kamenev, Alex
2015-11-01
We show that interacting bosons in a periodically driven two dimensional (2D) optical lattice may effectively exhibit fermionic statistics. The phenomenon is similar to the celebrated Tonks-Girardeau regime in 1D. The Floquet band of a driven lattice develops the moat shape, i.e., a minimum along a closed contour in the Brillouin zone. Such degeneracy of the kinetic energy favors fermionic quasiparticles. The statistical transmutation is achieved by the Chern-Simons flux attachment similar to the fractional quantum Hall case. We show that the velocity distribution of the released bosons is a sensitive probe of the fermionic nature of their stationary Floquet state.
Statistical Transmutation in Floquet Driven Optical Lattices.
Sedrakyan, Tigran A; Galitski, Victor M; Kamenev, Alex
2015-11-01
We show that interacting bosons in a periodically driven two dimensional (2D) optical lattice may effectively exhibit fermionic statistics. The phenomenon is similar to the celebrated Tonks-Girardeau regime in 1D. The Floquet band of a driven lattice develops the moat shape, i.e., a minimum along a closed contour in the Brillouin zone. Such degeneracy of the kinetic energy favors fermionic quasiparticles. The statistical transmutation is achieved by the Chern-Simons flux attachment similar to the fractional quantum Hall case. We show that the velocity distribution of the released bosons is a sensitive probe of the fermionic nature of their stationary Floquet state. PMID:26588392
GBL-2D Version 1.0: a 2D geometry boolean library.
McBride, Cory L. (Elemental Technologies, American Fort, UT); Schmidt, Rodney Cannon; Yarberry, Victor R.; Meyers, Ray J.
2006-11-01
This report describes version 1.0 of GBL-2D, a geometric Boolean library for 2D objects. The library is written in C++ and consists of a set of classes and routines. The classes primarily represent geometric data and relationships. Classes are provided for 2D points, lines, arcs, edge uses, loops, surfaces and mask sets. The routines contain algorithms for geometric Boolean operations and utility functions. Routines are provided that incorporate the Boolean operations: Union(OR), XOR, Intersection and Difference. A variety of additional analytical geometry routines and routines for importing and exporting the data in various file formats are also provided. The GBL-2D library was originally developed as a geometric modeling engine for use with a separate software tool, called SummitView [1], that manipulates the 2D mask sets created by designers of Micro-Electro-Mechanical Systems (MEMS). However, many other practical applications for this type of software can be envisioned because the need to perform 2D Boolean operations can arise in many contexts.
NASA Astrophysics Data System (ADS)
Aso, N.; Ohta, K.; Ide, S.
2014-12-01
Deformation in a small volume of earth interior is expressed by a symmetric moment tensor located on a point source. The tensor contains information of characteristic directions, source amplitude, and source types such as isotropic, double-couple, or compensated-linear-vector-dipole (CLVD). Although we often assume a double couple as the source type of an earthquake, significant non-double-couple component including isotropic component is often reported for induced earthquakes and volcanic earthquakes. For discussions on source types including double-couple and non-double-couple components, it is helpful to display them using some visual diagrams. Since the information of source type has two degrees of freedom, it can be displayed onto a two-dimensional flat plane. Although the diagram developed by Hudson et al. [1989] is popular, the trace corresponding to the mechanism combined by two mechanisms is not always a smooth line. To overcome this problem, Chapman and Leaney [2012] developed a new diagram. This diagram has an advantage that a straight line passing through the center corresponds to the mechanism obtained by a combination of an arbitrary mechanism and a double-couple [Tape and Tape, 2012], but this diagram has some difficulties in use. First, it is slightly difficult to produce the diagram because of its curved shape. Second, it is also difficult to read out the ratios among isotropic, double-couple, and CLVD components, which we want to obtain from the estimated moment tensors, because they do not appear directly on the horizontal or vertical axes. In the present study, we developed another new square diagram that overcomes the difficulties of previous diagrams. This diagram is an orthogonal system of isotropic and deviatoric axes, so it is easy to get the ratios among isotropic, double-couple, and CLVD components. Our diagram has another advantage that the probability density is obtained simply from the area within the diagram if the probability density
Interparticle Attraction in 2D Complex Plasmas
NASA Astrophysics Data System (ADS)
Kompaneets, Roman; Morfill, Gregor E.; Ivlev, Alexei V.
2016-03-01
Complex (dusty) plasmas allow experimental studies of various physical processes occurring in classical liquids and solids by directly observing individual microparticles. A major problem is that the interaction between microparticles is generally not molecularlike. In this Letter, we propose how to achieve a molecularlike interaction potential in laboratory 2D complex plasmas. We argue that this principal aim can be achieved by using relatively small microparticles and properly adjusting discharge parameters. If experimentally confirmed, this will make it possible to employ complex plasmas as a model system with an interaction potential resembling that of conventional liquids.
Periodically sheared 2D Yukawa systems
Kovács, Anikó Zsuzsa; Hartmann, Peter; Donkó, Zoltán
2015-10-15
We present non-equilibrium molecular dynamics simulation studies on the dynamic (complex) shear viscosity of a 2D Yukawa system. We have identified a non-monotonic frequency dependence of the viscosity at high frequencies and shear rates, an energy absorption maximum (local resonance) at the Einstein frequency of the system at medium shear rates, an enhanced collective wave activity, when the excitation is near the plateau frequency of the longitudinal wave dispersion, and the emergence of significant configurational anisotropy at small frequencies and high shear rates.
ENERGY LANDSCAPE OF 2D FLUID FORMS
Y. JIANG; ET AL
2000-04-01
The equilibrium states of 2D non-coarsening fluid foams, which consist of bubbles with fixed areas, correspond to local minima of the total perimeter. (1) The authors find an approximate value of the global minimum, and determine directly from an image how far a foam is from its ground state. (2) For (small) area disorder, small bubbles tend to sort inwards and large bubbles outwards. (3) Topological charges of the same sign repel while charges of opposite sign attract. (4) They discuss boundary conditions and the uniqueness of the pattern for fixed topology.
A scalable 2-D parallel sparse solver
Kothari, S.C.; Mitra, S.
1995-12-01
Scalability beyond a small number of processors, typically 32 or less, is known to be a problem for existing parallel general sparse (PGS) direct solvers. This paper presents a parallel general sparse PGS direct solver for general sparse linear systems on distributed memory machines. The algorithm is based on the well-known sequential sparse algorithm Y12M. To achieve efficient parallelization, a 2-D scattered decomposition of the sparse matrix is used. The proposed algorithm is more scalable than existing parallel sparse direct solvers. Its scalability is evaluated on a 256 processor nCUBE2s machine using Boeing/Harwell benchmark matrices.
2D stepping drive for hyperspectral systems
NASA Astrophysics Data System (ADS)
Endrödy, Csaba; Mehner, Hannes; Grewe, Adrian; Sinzinger, Stefan; Hoffmann, Martin
2015-07-01
We present the design, fabrication and characterization of a compact 2D stepping microdrive for pinhole array positioning. The miniaturized solution enables a highly integrated compact hyperspectral imaging system. Based on the geometry of the pinhole array, an inch-worm drive with electrostatic actuators was designed resulting in a compact (1 cm2) positioning system featuring a step size of about 15 µm in a 170 µm displacement range. The high payload (20 mg) as required for the pinhole array and the compact system design exceed the known electrostatic inch-worm-based microdrives.
Orbital optical lattices with bosons
NASA Astrophysics Data System (ADS)
Kock, T.; Hippler, C.; Ewerbeck, A.; Hemmerich, A.
2016-02-01
This article provides a synopsis of our recent experimental work exploring Bose-Einstein condensation in metastable higher Bloch bands of optical lattices. Bipartite lattice geometries have allowed us to implement appropriate band structures, which meet three basic requirements: the existence of metastable excited states sufficiently protected from collisional band relaxation, a mechanism to excite the atoms initially prepared in the lowest band with moderate entropy increase, and the possibility of cross-dimensional tunneling dynamics, necessary to establish coherence along all lattice axes. A variety of bands can be selectively populated and a subsequent thermalization process leads to the formation of a condensate in the lowest energy state of the chosen band. As examples the 2nd, 4th and 7th bands in a bipartite square lattice are discussed. The geometry of the 2nd and 7th bands can be tuned such that two inequivalent energetically degenerate energy minima arise at the X ±-points at the edge of the 1st Brillouin zone. In this case even a small interaction energy is sufficient to lock the phase between the two condensation points such that a complex-valued chiral superfluid order parameter can emerge, which breaks time reversal symmetry. In the 4th band a condensate can be formed at the Γ-point in the center of the 1st Brillouin zone, which can be used to explore topologically protected band touching points. The new techniques to access orbital degrees of freedom in higher bands greatly extend the class of many-body scenarios that can be explored with bosons in optical lattices.
Weighted Least Squares Fitting Using Ordinary Least Squares Algorithms.
ERIC Educational Resources Information Center
Kiers, Henk A. L.
1997-01-01
A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. The approach consists of iteratively performing steps of existing algorithms for ordinary least squares fitting of the same model and is based on maximizing a function that majorizes WLS loss function. (Author/SLD)
NASA Astrophysics Data System (ADS)
Sommer, W.
2013-03-01
The basic experimental setup of a Fabry-Perot etalon between a collimating and a focusing lens is modified by introducing 2D rectangular lattices between the etalon and the collimating lens. Consequently, the irradiance of the interference fringes on a screen in the focal plane of the focusing lens changes and is modified by the diffraction pattern of the 2D lattice. The constructive interference directions resulting from both the etalon and the diffraction by the 2D lattice have to correlate in order to obtain maximum irradiance. Considering this experiment in a didactical context and analysing how a 2D rectangular lattice is seen through the etalon, the investigation provides us with the concept of an optical space containing a row of virtual 2D lattices. Due to the partially reflecting plane surfaces of the etalon, different virtual images of the 2D lattice form a 3D lattice with a tetragonal or orthorhombic structure. As an optical interface, the simple setup with a 2D lattice and an etalon models a 3D lattice. Using a laser, the diffraction pattern of a 2D lattice and etalon can be used to optically simulate 3D x-ray diffraction. The experiments can be included wherever undergraduate or graduate students have to follow up Laue's formulation of x-ray diffraction.
Titanium-silicon carbide composite lattice structures
NASA Astrophysics Data System (ADS)
Moongkhamklang, Pimsiree
Sandwich panel structures with stiff, strong face sheets and lightweight cellular cores are widely used for weight sensitive, bending dominated loading applications. The flexural stiffness and strength of a sandwich panel is determined by the stiffness, strength, thickness, and separation of the face sheets, and by the compressive and shear stiffness and strength of the cellular core. Panel performance can be therefore optimized using cores with high specific stiffness and strength. The specific stiffness and strength of all cellular materials depends upon the specific elastic modulus and strength of the material used to make the structure. The stiffest and strongest cores for ambient temperature applications utilize carbon fiber reinforced polymer (CFRP) honeycombs and lattice structures. Few options exist for lightweight sandwich panels intended for high temperature uses. High temperature alloys such as Ti-6A1-4V can be applied to SiC monofilaments to create very high specific modulus and strength fibers. These are interesting candidates for the cores of elevated temperature sandwich structures such as the skins of hypersonic vehicles. This dissertation explores the potential of sandwich panel concepts that utilize millimeter scale titanium matrix composite (TMC) lattice structures. A method has been developed for fabricating millimeter cell size cellular lattice structures with the square or diamond collinear truss topologies from 240 mum diameter Ti-6A1-4V coated SiC monofilaments (TMC monofilaments). Lattices with relative densities in the range 10% to 20% were manufactured and tested in compression and shear. Given the very high compressive strength of the TMC monofilaments, the compressive strengths of both the square and diamond lattices were dominated by elastic buckling of the constituent struts. However, under shear loading, some of the constituent struts of the lattices are subjected to tensile stresses and failure is then set by tensile failure of the
Superfluid density through 2D superconductor junctions
NASA Astrophysics Data System (ADS)
Nam, Hyoungdo; Shih, Chih-Kang
As S. Qin et al. reported, two monolayer (2 ML) lead film on a silicon (111) substrate has one of two different atomic structures on the silicon substrate: the unstrained 1x1 and the psedumorphically strained √3x √3 (i.e. the same lattice constant as the Si √3x √3 lattice). Most interestingly, although these two different regions show the same quantum well state features, they have different Tc's (5 K and 4 K). These two different regions of 2 ML film naturally form superconductor-superconductor (SS or SS') junctions along silicon step edges. Physical connection of the junction is only 1 ML thickness because of the step height difference of substrate. We will present this study of SS (or SS') junction system using scanning tunneling microscopy/spectroscopy and in-situ double-coil mutual inductance measurement. The transition of superconducting gaps across either SS or SS' junctions should show how to locally affect each other. Double coil measurement show a global Tc close to the lower Tc region with sizable superfluid density. We will discuss the phase rigidity and its relationship to the superfluid density in this ultra-thin Pb film that is only 2 ML thick.
Cooperative dynamics in ultrasoft 2D crystals
NASA Astrophysics Data System (ADS)
Sprakel, Joris; van der Meer, Berend; Dijkstra, Marjolein; van der Gucht, Jasper
2015-03-01
The creation, annihilation, and diffusion of defects in crystal lattices play an important role during crystal melting and deformation. Although it is well understood how defects form and react when crystals are subjected to external stresses, it remains unclear how crystals cope with internal stresses. We report a study in which we create a highly localized internal stress, by means of optical tweezing, in a crystal formed from micrometer-sized colloidal spheres and directly observe how the solid reacts using microscopy. We find that, even though the excitation is highly localized, a collective dance of colloidal particles results; these collective modes take the form of closed rings or open-ended strings, depending on the sequence of events which nucleate the rearrangements. Surprisingly, we find from Brownian Dynamics simulations that these cooperative dynamics are thermally-activated modes inherent to the crystal, and can even occur through a single, sufficiently large thermal fluctuation, resulting in the irreversible displacement of 100s of particles from their lattice sites.
Duality Between Spin Networks and the 2D Ising Model
NASA Astrophysics Data System (ADS)
Bonzom, Valentin; Costantino, Francesco; Livine, Etera R.
2016-06-01
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.
Quantum Simulation with 2D Arrays of Trapped Ions
NASA Astrophysics Data System (ADS)
Richerme, Philip
2016-05-01
The computational difficulty of solving fully quantum many-body spin problems is a significant obstacle to understanding the behavior of strongly correlated quantum matter. This work proposes the design and construction of a 2D quantum spin simulator to investigate the physics of frustrated materials, highly entangled states, mechanisms potentially underpinning high-temperature superconductivity, and other topics inaccessible to current 1D systems. The effective quantum spins will be encoded within the well-isolated electronic levels of trapped ions, confined in a two-dimensional planar geometry, and made to interact using phonon-mediated optical dipole forces. The system will be scalable to 100+ quantum particles, far beyond the realm of classical intractability, while maintaining individual-ion control, long quantum coherence times, and site-resolved projective spin measurements. Once constructed, the two-dimensional quantum simulator will implement a broad range of spin models on a variety of reconfigurable lattices and characterize their behavior through measurements of spin-spin correlations and entanglement. This versatile tool will serve as an important experimental resource for exploring difficult quantum many-body problems in a regime where classical methods fail.
Quiver gauge theories and integrable lattice models
NASA Astrophysics Data System (ADS)
Yagi, Junya
2015-10-01
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d N=1 theories known as brane box and brane tilling models, 3d N=2 and 2d N=(2,2) theories obtained from them by compactification, and 2d N=(0,2) theories closely related to these theories. We argue that their supersymmetric indices carry structures of TQFTs equipped with line operators, and as a consequence, are equal to the partition functions of lattice models. The integrability of these models follows from the existence of extra dimension in the TQFTs, which emerges after the theories are embedded in M-theory. The Yang-Baxter equation expresses the invariance of supersymmetric indices under Seiberg duality and its lower-dimensional analogs.
WFR-2D: an analytical model for PWAS-generated 2D ultrasonic guided wave propagation
NASA Astrophysics Data System (ADS)
Shen, Yanfeng; Giurgiutiu, Victor
2014-03-01
This paper presents WaveFormRevealer 2-D (WFR-2D), an analytical predictive tool for the simulation of 2-D ultrasonic guided wave propagation and interaction with damage. The design of structural health monitoring (SHM) systems and self-aware smart structures requires the exploration of a wide range of parameters to achieve best detection and quantification of certain types of damage. Such need for parameter exploration on sensor dimension, location, guided wave characteristics (mode type, frequency, wavelength, etc.) can be best satisfied with analytical models which are fast and efficient. The analytical model was constructed based on the exact 2-D Lamb wave solution using Bessel and Hankel functions. Damage effects were inserted in the model by considering the damage as a secondary wave source with complex-valued directivity scattering coefficients containing both amplitude and phase information from wave-damage interaction. The analytical procedure was coded with MATLAB, and a predictive simulation tool called WaveFormRevealer 2-D was developed. The wave-damage interaction coefficients (WDICs) were extracted from harmonic analysis of local finite element model (FEM) with artificial non-reflective boundaries (NRB). The WFR-2D analytical simulation results were compared and verified with full scale multiphysics finite element models and experiments with scanning laser vibrometer. First, Lamb wave propagation in a pristine aluminum plate was simulated with WFR-2D, compared with finite element results, and verified by experiments. Then, an inhomogeneity was machined into the plate to represent damage. Analytical modeling was carried out, and verified by finite element simulation and experiments. This paper finishes with conclusions and suggestions for future work.
Phase diagram of quantum square ice
NASA Astrophysics Data System (ADS)
Henry, Louis-Paul; Holdsworth, Peter; Mila, Frederic; Roscilde, Tommaso
2013-03-01
We have investigated the ground-state and finite-temperature phase diagram of quantum square ice - realized by the transverse-field Ising model on a checkerboard lattice - using both linear spin-wave (LSW) theory and quantum Monte Carlo (QMC). We generalize the model with different couplings between nearest (J1) and next-to-nearest (J2) neighbors on the checkerboard lattice. Our QMC approach generalizes the loop algorithm - very efficient in the study of constrained classical systems - to a ``brane algorithm'' for quantum systems. At the LSW level the vast degeneracy of the ground-state for J1 =J2 and J2 >J1 remains intact; moreover LSW theory breaks down in extended regions of the phase diagram, pointing at non-classical states. Our QMC study goes beyond perturbative schemes and addresses directly the nature of the low-temperature phases. We have critically examined the possibility of a resonating-plaquette state for J1 =J2 , suggested by degenerate perturbation theory on the ice-rule manifold for weak fields. Our QMC results for finite fields confirm the absence of Néel or collinear order, but they do not confirm the presence of resonating-plaquette order, pointing at a possibly more complex non-classical state.
Microwave Assisted 2D Materials Exfoliation
NASA Astrophysics Data System (ADS)
Wang, Yanbin
Two-dimensional materials have emerged as extremely important materials with applications ranging from energy and environmental science to electronics and biology. Here we report our discovery of a universal, ultrafast, green, solvo-thermal technology for producing excellent-quality, few-layered nanosheets in liquid phase from well-known 2D materials such as such hexagonal boron nitride (h-BN), graphite, and MoS2. We start by mixing the uniform bulk-layered material with a common organic solvent that matches its surface energy to reduce the van der Waals attractive interactions between the layers; next, the solutions are heated in a commercial microwave oven to overcome the energy barrier between bulk and few-layers states. We discovered the minutes-long rapid exfoliation process is highly temperature dependent, which requires precise thermal management to obtain high-quality inks. We hypothesize a possible mechanism of this proposed solvo-thermal process; our theory confirms the basis of this novel technique for exfoliation of high-quality, layered 2D materials by using an as yet unknown role of the solvent.
Photocurrent spectroscopy of 2D materials
NASA Astrophysics Data System (ADS)
Cobden, David
Confocal photocurrent measurements provide a powerful means of studying many aspects of the optoelectronic and electrical properties of a 2D device or material. At a diffraction-limited point they can provide a detailed absorption spectrum, and they can probe local symmetry, ultrafast relaxation rates and processes, electron-electron interaction strengths, and transport coefficients. We illustrate this with several examples, once being the photo-Nernst effect. In gapless 2D materials, such as graphene, in a perpendicular magnetic field a photocurrent antisymmetric in the field is generated near to the free edges, with opposite sign at opposite edges. Its origin is the transverse thermoelectric current associated with the laser-induced electron temperature gradient. This effect provides an unambiguous demonstration of the Shockley-Ramo nature of long-range photocurrent generation in gapless materials. It also provides a means of investigating quasiparticle properties. For example, in the case of graphene on hBN, it can be used to probe the Lifshitz transition that occurs due to the minibands formed by the Moire superlattice. We also observe and discuss photocurrent generated in other semimetallic (WTe2) and semiconducting (WSe2) monolayers. Work supported by DoE BES and NSF EFRI grants.
Multienzyme Inkjet Printed 2D Arrays.
Gdor, Efrat; Shemesh, Shay; Magdassi, Shlomo; Mandler, Daniel
2015-08-19
The use of printing to produce 2D arrays is well established, and should be relatively facile to adapt for the purpose of printing biomaterials; however, very few studies have been published using enzyme solutions as inks. Among the printing technologies, inkjet printing is highly suitable for printing biomaterials and specifically enzymes, as it offers many advantages. Formulation of the inkjet inks is relatively simple and can be adjusted to a variety of biomaterials, while providing nonharmful environment to the enzymes. Here we demonstrate the applicability of inkjet printing for patterning multiple enzymes in a predefined array in a very straightforward, noncontact method. Specifically, various arrays of the enzymes glucose oxidase (GOx), invertase (INV) and horseradish peroxidase (HP) were printed on aminated glass surfaces, followed by immobilization using glutardialdehyde after printing. Scanning electrochemical microscopy (SECM) was used for imaging the printed patterns and to ascertain the enzyme activity. The successful formation of 2D arrays consisting of enzymes was explored as a means of developing the first surface confined enzyme based logic gates. Principally, XOR and AND gates, each consisting of two enzymes as the Boolean operators, were assembled, and their operation was studied by SECM. PMID:26214072
Numerical study on the fluid flow pass a square cylinder: The temperature-viscosity dependence
NASA Astrophysics Data System (ADS)
Lu, Jianhua; Li, Sheng; Guo, Zhaoli; Shi, Baochang
2014-10-01
In this paper, the 2D fluid flow pass a heated/cooled square cylinder exposed to a constant free-stream upward velocity is simulated via a multiple relaxation time (MRT) lattice-Boltzmann (LB) method. The buoyancy effect on the drag and lift coefficients as well as Nusselt number related is compared with the results in the existing literatures to validate the code used. The effect of temperature-viscosity dependence is then investigated to test whether the effect can be neglected or not for the mixed convection case. It is shown that the effect cannot be ignored when |Ri| > 0.15. Fortunately, the effect can be captured by using an effective temperature formula [J. M. Shi, D. Ferlach, M. Breuer, G. Biswas and F. Durst, Phys. Fluids16, 4331 (2004)] in a rather large range of Ri. All the numerical results, from another angle, also demonstrate that the MRT method is an efficient tool in simulating the problems such as the present one.
NASA Astrophysics Data System (ADS)
Biciuşcă, Tonino; Horga, Adrian; Sofonea, Victor
2015-10-01
We use a two-dimensional Lattice Boltzmann model to investigate the liquid-vapour phase separation in an isothermal van der Waals fluid. The model is based on the expansion of the distribution function up to the third order in terms of Hermite polynomials. In two dimensions, this model is an off-lattice one and has 16 velocities. The Corner Transport Upwind Scheme is used to evolve the corresponding distribution functions on a square lattice. The resulting code allows one to follow the liquid-vapour phase separation on lattices up to 4096 × 4096 nodes using a Tesla M2090 Graphics Processing Unit.
2-D or not 2-D, that is the question: A Northern California test
Mayeda, K; Malagnini, L; Phillips, W S; Walter, W R; Dreger, D
2005-06-06
Reliable estimates of the seismic source spectrum are necessary for accurate magnitude, yield, and energy estimation. In particular, how seismic radiated energy scales with increasing earthquake size has been the focus of recent debate within the community and has direct implications on earthquake source physics studies as well as hazard mitigation. The 1-D coda methodology of Mayeda et al. has provided the lowest variance estimate of the source spectrum when compared against traditional approaches that use direct S-waves, thus making it ideal for networks that have sparse station distribution. The 1-D coda methodology has been mostly confined to regions of approximately uniform complexity. For larger, more geophysically complicated regions, 2-D path corrections may be required. The complicated tectonics of the northern California region coupled with high quality broadband seismic data provides for an ideal ''apples-to-apples'' test of 1-D and 2-D path assumptions on direct waves and their coda. Using the same station and event distribution, we compared 1-D and 2-D path corrections and observed the following results: (1) 1-D coda results reduced the amplitude variance relative to direct S-waves by roughly a factor of 8 (800%); (2) Applying a 2-D correction to the coda resulted in up to 40% variance reduction from the 1-D coda results; (3) 2-D direct S-wave results, though better than 1-D direct waves, were significantly worse than the 1-D coda. We found that coda-based moment-rate source spectra derived from the 2-D approach were essentially identical to those from the 1-D approach for frequencies less than {approx}0.7-Hz, however for the high frequencies (0.7{le} f {le} 8.0-Hz), the 2-D approach resulted in inter-station scatter that was generally 10-30% smaller. For complex regions where data are plentiful, a 2-D approach can significantly improve upon the simple 1-D assumption. In regions where only 1-D coda correction is available it is still preferable over 2
NASA Technical Reports Server (NTRS)
Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.
1983-01-01
The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.
ERIC Educational Resources Information Center
Emanouilidis, Emanuel
2008-01-01
Latin squares were first introduced and studied by the famous mathematician Leonhard Euler in the 1700s. Through the years, Latin squares have been used in areas such as statistics, graph theory, coding theory, the generation of random numbers as well as in the design and analysis of experiments. Recently, with the international popularity of…
Algebraic Squares: Complete and Incomplete.
ERIC Educational Resources Information Center
Gardella, Francis J.
2000-01-01
Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)
From Square Dance to Mathematics
ERIC Educational Resources Information Center
Bremer, Zoe
2010-01-01
In this article, the author suggests a cross-curricular idea that can link with PE, dance, music and history. Teacher David Schmitz, a maths teacher in Illinois who was also a square dance caller, had developed a maths course that used the standard square dance syllabus to teach mathematical principles. He presents an intensive, two-week course…
Numerical Simulations of a Circulating Fluidized Bed with a Square Cross-Section
Li, Tingwen
2011-01-01
In this study, both 2D and 3D numerical simulations of a well-documented circulating fluidized bed with a square cross-section were conducted. With some assumptions, a series of 2D simulations was first carried out to study the influence of grid resolution, initial flow field, and boundary condition on the flow hydrodynamics. It was found that 2D simulations under-predicted the solids inventory even with the finest grid (10-particle-diameter grid size). On the other hand, a 3D simulation with relatively coarse grid was found in better agreement with the experimental data. Differences between 2D and 3D simulations were briefly discussed.
Numerical Evaluation of 2D Ground States
NASA Astrophysics Data System (ADS)
Kolkovska, Natalia
2016-02-01
A ground state is defined as the positive radial solution of the multidimensional nonlinear problem
Canard configured aircraft with 2-D nozzle
NASA Technical Reports Server (NTRS)
Child, R. D.; Henderson, W. P.
1978-01-01
A closely-coupled canard fighter with vectorable two-dimensional nozzle was designed for enhanced transonic maneuvering. The HiMAT maneuver goal of a sustained 8g turn at a free-stream Mach number of 0.9 and 30,000 feet was the primary design consideration. The aerodynamic design process was initiated with a linear theory optimization minimizing the zero percent suction drag including jet effects and refined with three-dimensional nonlinear potential flow techniques. Allowances were made for mutual interference and viscous effects. The design process to arrive at the resultant configuration is described, and the design of a powered 2-D nozzle model to be tested in the LRC 16-foot Propulsion Wind Tunnel is shown.
2D Electrostatic Actuation of Microshutter Arrays
NASA Technical Reports Server (NTRS)
Burns, Devin E.; Oh, Lance H.; Li, Mary J.; Jones, Justin S.; Kelly, Daniel P.; Zheng, Yun; Kutyrev, Alexander S.; Moseley, Samuel H.
2015-01-01
An electrostatically actuated microshutter array consisting of rotational microshutters (shutters that rotate about a torsion bar) were designed and fabricated through the use of models and experiments. Design iterations focused on minimizing the torsional stiffness of the microshutters, while maintaining their structural integrity. Mechanical and electromechanical test systems were constructed to measure the static and dynamic behavior of the microshutters. The torsional stiffness was reduced by a factor of four over initial designs without sacrificing durability. Analysis of the resonant behavior of the microshutter arrays demonstrates that the first resonant mode is a torsional mode occurring around 3000 Hz. At low vacuum pressures, this resonant mode can be used to significantly reduce the drive voltage necessary for actuation requiring as little as 25V. 2D electrostatic latching and addressing was demonstrated using both a resonant and pulsed addressing scheme.
2D Electrostatic Actuation of Microshutter Arrays
NASA Technical Reports Server (NTRS)
Burns, Devin E.; Oh, Lance H.; Li, Mary J.; Kelly, Daniel P.; Kutyrev, Alexander S.; Moseley, Samuel H.
2015-01-01
Electrostatically actuated microshutter arrays consisting of rotational microshutters (shutters that rotate about a torsion bar) were designed and fabricated through the use of models and experiments. Design iterations focused on minimizing the torsional stiffness of the microshutters, while maintaining their structural integrity. Mechanical and electromechanical test systems were constructed to measure the static and dynamic behavior of the microshutters. The torsional stiffness was reduced by a factor of four over initial designs without sacrificing durability. Analysis of the resonant behavior of the microshutters demonstrates that the first resonant mode is a torsional mode occurring around 3000 Hz. At low vacuum pressures, this resonant mode can be used to significantly reduce the drive voltage necessary for actuation requiring as little as 25V. 2D electrostatic latching and addressing was demonstrated using both a resonant and pulsed addressing scheme.
Graphene suspensions for 2D printing
NASA Astrophysics Data System (ADS)
Soots, R. A.; Yakimchuk, E. A.; Nebogatikova, N. A.; Kotin, I. A.; Antonova, I. V.
2016-04-01
It is shown that, by processing a graphite suspension in ethanol or water by ultrasound and centrifuging, it is possible to obtain particles with thicknesses within 1-6 nm and, in the most interesting cases, 1-1.5 nm. Analogous treatment of a graphite suspension in organic solvent yields eventually thicker particles (up to 6-10 nm thick) even upon long-term treatment. Using the proposed ink based on graphene and aqueous ethanol with ethylcellulose and terpineol additives for 2D printing, thin (~5 nm thick) films with sheet resistance upon annealing ~30 MΩ/□ were obtained. With the ink based on aqueous graphene suspension, the sheet resistance was ~5-12 kΩ/□ for 6- to 15-nm-thick layers with a carrier mobility of ~30-50 cm2/(V s).
Hirobe, Tomohisa; Ito, Shosuke; Wakamatsu, Kazumasa
2013-09-01
The novel mutation named ru2(d) /Hps5(ru2-d) , characterized by light-colored coats and ruby-eyes, prohibits differentiation of melanocytes by inhibiting tyrosinase (Tyr) activity, expression of Tyr, Tyr-related protein 1 (Tyrp1), Tyrp2, and Kit. However, it is not known whether the ru2(d) allele affects pheomelanin synthesis in recessive yellow (e/Mc1r(e) ) or in pheomelanic stage in agouti (A) mice. In this study, effects of the ru2(d) allele on pheomelanin synthesis were investigated by chemical analysis of melanin present in dorsal hairs of 5-week-old mice from F2 generation between C57BL/10JHir (B10)-co-isogenic ruby-eye 2(d) and B10-congenic recessive yellow or agouti. Eumelanin content was decreased in ruby-eye 2(d) and ruby-eye 2(d) agouti mice, whereas pheomelanin content in ruby-eye 2(d) recessive yellow and ruby-eye 2(d) agouti mice did not differ from the corresponding Ru2(d) /- mice, suggesting that the ru2(d) allele inhibits eumelanin but not pheomelanin synthesis. PMID:23672590
Mechanical properties of lattice grid composites
NASA Astrophysics Data System (ADS)
Fan, Hualin; Fang, Daining; Jin, Fengnian
2008-08-01
An equivalent continuum method only considering the stretching deformation of struts was used to study the in-plane stiffness and strength of planar lattice grid composite materials. The initial yield equations of lattices were deduced. Initial yield surfaces were depicted separately in different 3D and 2D stress spaces. The failure envelope is a polyhedron in 3D spaces and a polygon in 2D spaces. Each plane or line of the failure envelope is corresponding to the yield or buckling of a typical bar row. For lattices with more than three bar rows, subsequent yield of the other bar row after initial yield made the lattice achieve greater limit strength. The importance of the buckling strength of the grids was strengthened while the grids were relative sparse. The integration model of the method was used to study the nonlinear mechanical properties of strain hardening grids. It was shown that the integration equation could accurately model the complete stress-strain curves of the grids within small deformations.
Image Appraisal for 2D and 3D Electromagnetic Inversion
Alumbaugh, D.L.; Newman, G.A.
1999-01-28
Linearized methods are presented for appraising image resolution and parameter accuracy in images generated with two and three dimensional non-linear electromagnetic inversion schemes. When direct matrix inversion is employed, the model resolution and posterior model covariance matrices can be directly calculated. A method to examine how the horizontal and vertical resolution varies spatially within the electromagnetic property image is developed by examining the columns of the model resolution matrix. Plotting the square root of the diagonal of the model covariance matrix yields an estimate of how errors in the inversion process such as data noise and incorrect a priori assumptions about the imaged model map into parameter error. This type of image is shown to be useful in analyzing spatial variations in the image sensitivity to the data. A method is analyzed for statistically estimating the model covariance matrix when the conjugate gradient method is employed rather than a direct inversion technique (for example in 3D inversion). A method for calculating individual columns of the model resolution matrix using the conjugate gradient method is also developed. Examples of the image analysis techniques are provided on 2D and 3D synthetic cross well EM data sets, as well as a field data set collected at the Lost Hills Oil Field in Central California.
Application of Bessel beams to 2D microfabrication
NASA Astrophysics Data System (ADS)
Li, X.-F.; Winfield, R. J.; O'Brien, S.; Crean, G. M.
2009-03-01
Fs laser-based two-photon polymerisation (2PP) has been widely reported as a means of directly writing three-dimensional nanoscale structures. Usually the voxel of a high numerical aperture microscope objective is scanned through the resin to build up the required model. In the case of high aspect ratio two-dimensional structures, such as cell scaffolds, repeated scanning is required to build up the height. The voxel shape can be substantially elongated by the inclusion of an axicon lens in the laser beam line. In this report we describe the use of a Bessel beam produced in the region beyond the focus of an objective lens when the beam has been modified in this way. A Ti:sapphire laser was used to write a range of 2D square cell structures in a Zr-loaded sol-gel system. The process was characterised, in terms of the dimensions of the polymerised Bessel region, for different processing conditions. Examples of the structures are also described.
Chaves Filho, V L; Lima, R P A; Lyra, M L
2015-06-01
We investigate the modulational instability of uniform wavepackets governed by the discrete nonlinear Schrodinger equation in finite linear chains and square lattices. We show that, while the critical nonlinear coupling χMI above which modulational instability occurs remains finite in square lattices, it decays as 1/L in linear chains. In square lattices, there is a direct transition between the regime of stable uniform wavefunctions and the regime of asymptotically localized solutions with stationary probability distributions. On the other hand, there is an intermediate regime in linear chains for which the wavefunction dynamics develops complex breathing patterns. We analytically compute the critical nonlinear strengths for modulational instability in both lattices, as well as the characteristic time τ governing the exponential increase of perturbations in the vicinity of the transition. We unveil that the interplay between modulational instability and self-trapping phenomena is responsible for the distinct wavefunction dynamics in linear and square lattices. PMID:26117095
Formation and Dynamics of Antiferromagnetic Correlations in Tunable Optical Lattices.
Greif, Daniel; Jotzu, Gregor; Messer, Michael; Desbuquois, Rémi; Esslinger, Tilman
2015-12-31
We report on the observation of antiferromagnetic correlations of ultracold fermions in a variety of optical lattice geometries that are well described by the Hubbard model, including dimers, 1D chains, ladders, isolated and coupled honeycomb planes, as well as square and cubic lattices. The dependence of the strength of spin correlations on the specific geometry is experimentally studied by measuring the correlations along different lattice tunneling links, where a redistribution of correlations between the different lattice links is observed. By measuring the correlations in a crossover between distinct geometries, we demonstrate an effective reduction of the dimensionality for our atom numbers and temperatures. We also investigate the formation and redistribution time of spin correlations by dynamically changing the lattice geometry and studying the time evolution of the system. Time scales ranging from a sudden quench of the lattice geometry to an adiabatic evolution are probed. PMID:26764974
Palmer, R.B.
1987-05-01
This paper looks at, and compares three types of damping ring lattices: conventional, wiggler lattice with finite ..cap alpha.., wiggler lattice with ..cap alpha.. = 0, and observes the attainable equilibrium emittances for the three cases assuming a constraint on the attainable longitudinal impedance of 0.2 ohms. The emittance obtained are roughly in the ratio 4:2:1 for these cases.
Entropic crystal–crystal transitions of Brownian squares
Zhao, Kun; Bruinsma, Robijn; Mason, Thomas G.
2011-01-01
When a monolayer of hard microscale square platelets, produced lithographically, is osmotically concentrated in a flat plane to raise the particle area fraction ϕA, an order–order transition occurs between a hexagonal rotator crystal and a rhombic crystal. Strikingly, phases having fourfold symmetry are not observed at any ϕA. The rhombic lattice angle α increases continuously with ϕA, as the system maximizes its total rotational and translational entropy. A cage model, based on packing rotationally swept squares, or “squaroids,” reasonably predicts the measured α(ϕA), indicating that rotational entropy and the square particle shape combine to produce the rhombic unit cell. PMID:21282614
Two-dimensional B-C-O alloys: a promising class of 2D materials for electronic devices.
Zhou, Si; Zhao, Jijun
2016-04-21
Graphene, a superior 2D material with high carrier mobility, has limited application in electronic devices due to zero band gap. In this regard, boron and nitrogen atoms have been integrated into the graphene lattice to fabricate 2D semiconducting heterostructures. It is an intriguing question whether oxygen can, as a replacement of nitrogen, enter the sp(2) honeycomb lattice and form stable B-C-O monolayer structures. Here we explore the atomic structures, energetic and thermodynamic stability, and electronic properties of various 2D B-C-O alloys using first-principles calculations. Our results show that oxygen can be stably incorporated into the graphene lattice by bonding with boron. The B and O species favor forming alternate patterns into the chain- or ring-like structures embedded in the pristine graphene regions. These B-C-O hybrid sheets can be either metals or semiconductors depending on the B : O ratio. The semiconducting (B2O)nCm and (B6O3)nCm phases exist under the B- and O-rich conditions, and possess a tunable band gap of 1.0-3.8 eV and high carrier mobility, retaining ∼1000 cm(2) V(-1) s(-1) even for half coverage of B and O atoms. These B-C-O alloys form a new class of 2D materials that are promising candidates for high-speed electronic devices. PMID:27072060
Counting Triangles to Sum Squares
ERIC Educational Resources Information Center
DeMaio, Joe
2012-01-01
Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.
NASA Astrophysics Data System (ADS)
Cheng, Chingyun; Kangara, Jayampathi; Arakelyan, Ilya; Thomas, John
2016-05-01
We tune the dimensionality of a strongly interacting degenerate 6 Li Fermi gas from 2D to quasi-2D, by adjusting the radial confinement of pancake-shaped clouds to control the radial chemical potential. In the 2D regime with weak radial confinement, the measured pair binding energies are in agreement with 2D-BCS mean field theory, which predicts dimer pairing energies in the many-body regime. In the qausi-2D regime obtained with increased radial confinement, the measured pairing energy deviates significantly from 2D-BCS theory. In contrast to the pairing energy, the measured radii of the cloud profiles are not fit by 2D-BCS theory in either the 2D or quasi-2D regimes, but are fit in both regimes by a beyond mean field polaron-model of the free energy. Supported by DOE, ARO, NSF, and AFOSR.
AKLSQF - LEAST SQUARES CURVE FITTING
NASA Technical Reports Server (NTRS)
Kantak, A. V.
1994-01-01
The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The data may be supplied to the routine either by direct keyboard entry or via a file. AKLSQF produces the least squares polynomial in two steps. First, the data points are least squares fitted using the orthogonal factorial polynomials. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. At every step the polynomial as well as the least squares fitting error is printed to the screen. In general, the program can produce a curve fitting up to a 100 degree polynomial. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. It has been implemented under DOS 3.2.1 using 23K of RAM. AKLSQF was developed in 1989.
Competing coexisting phases in 2D water
Zanotti, Jean-Marc; Judeinstein, Patrick; Dalla-Bernardina, Simona; Creff, Gaëlle; Brubach, Jean-Blaise; Roy, Pascale; Bonetti, Marco; Ollivier, Jacques; Sakellariou, Dimitrios; Bellissent-Funel, Marie-Claire
2016-01-01
The properties of bulk water come from a delicate balance of interactions on length scales encompassing several orders of magnitudes: i) the Hydrogen Bond (HBond) at the molecular scale and ii) the extension of this HBond network up to the macroscopic level. Here, we address the physics of water when the three dimensional extension of the HBond network is frustrated, so that the water molecules are forced to organize in only two dimensions. We account for the large scale fluctuating HBond network by an analytical mean-field percolation model. This approach provides a coherent interpretation of the different events experimentally (calorimetry, neutron, NMR, near and far infra-red spectroscopies) detected in interfacial water at 160, 220 and 250 K. Starting from an amorphous state of water at low temperature, these transitions are respectively interpreted as the onset of creation of transient low density patches of 4-HBonded molecules at 160 K, the percolation of these domains at 220 K and finally the total invasion of the surface by them at 250 K. The source of this surprising behaviour in 2D is the frustration of the natural bulk tetrahedral local geometry and the underlying very significant increase in entropy of the interfacial water molecules. PMID:27185018
2D Radiative Processes Near Cloud Edges
NASA Technical Reports Server (NTRS)
Varnai, T.
2012-01-01
Because of the importance and complexity of dynamical, microphysical, and radiative processes taking place near cloud edges, the transition zone between clouds and cloud free air has been the subject of intense research both in the ASR program and in the wider community. One challenge in this research is that the one-dimensional (1D) radiative models widely used in both remote sensing and dynamical simulations become less accurate near cloud edges: The large horizontal gradients in particle concentrations imply that accurate radiative calculations need to consider multi-dimensional radiative interactions among areas that have widely different optical properties. This study examines the way the importance of multidimensional shortwave radiative interactions changes as we approach cloud edges. For this, the study relies on radiative simulations performed for a multiyear dataset of clouds observed over the NSA, SGP, and TWP sites. This dataset is based on Microbase cloud profiles as well as wind measurements and ARM cloud classification products. The study analyzes the way the difference between 1D and 2D simulation results increases near cloud edges. It considers both monochromatic radiances and broadband radiative heating, and it also examines the influence of factors such as cloud type and height, and solar elevation. The results provide insights into the workings of radiative processes and may help better interpret radiance measurements and better estimate the radiative impacts of this critical region.
Simulation of Yeast Cooperation in 2D.
Wang, M; Huang, Y; Wu, Z
2016-03-01
Evolution of cooperation has been an active research area in evolutionary biology in decades. An important type of cooperation is developed from group selection, when individuals form spatial groups to prevent them from foreign invasions. In this paper, we study the evolution of cooperation in a mixed population of cooperating and cheating yeast strains in 2D with the interactions among the yeast cells restricted to their small neighborhoods. We conduct a computer simulation based on a game theoretic model and show that cooperation is increased when the interactions are spatially restricted, whether the game is of a prisoner's dilemma, snow drifting, or mutual benefit type. We study the evolution of homogeneous groups of cooperators or cheaters and describe the conditions for them to sustain or expand in an opponent population. We show that under certain spatial restrictions, cooperator groups are able to sustain and expand as group sizes become large, while cheater groups fail to expand and keep them from collapse. PMID:26988702
Phase Engineering of 2D Tin Sulfides.
Mutlu, Zafer; Wu, Ryan J; Wickramaratne, Darshana; Shahrezaei, Sina; Liu, Chueh; Temiz, Selcuk; Patalano, Andrew; Ozkan, Mihrimah; Lake, Roger K; Mkhoyan, K A; Ozkan, Cengiz S
2016-06-01
Tin sulfides can exist in a variety of phases and polytypes due to the different oxidation states of Sn. A subset of these phases and polytypes take the form of layered 2D structures that give rise to a wide host of electronic and optical properties. Hence, achieving control over the phase, polytype, and thickness of tin sulfides is necessary to utilize this wide range of properties exhibited by the compound. This study reports on phase-selective growth of both hexagonal tin (IV) sulfide SnS2 and orthorhombic tin (II) sulfide SnS crystals with diameters of over tens of microns on SiO2 substrates through atmospheric pressure vapor-phase method in a conventional horizontal quartz tube furnace with SnO2 and S powders as the source materials. Detailed characterization of each phase of tin sulfide crystals is performed using various microscopy and spectroscopy methods, and the results are corroborated by ab initio density functional theory calculations. PMID:27099950
Ion Transport in 2-D Graphene Nanochannels
NASA Astrophysics Data System (ADS)
Xie, Quan; Foo, Elbert; Duan, Chuanhua
2015-11-01
Graphene membranes have recently attracted wide attention due to its great potential in water desalination and selective molecular sieving. Further developments of these membranes, including enhancing their mass transport rate and/or molecular selectivity, rely on the understanding of fundamental transport mechanisms through graphene membranes, which has not been studied experimentally before due to fabrication and measurement difficulties. Herein we report the fabrication of the basic constituent of graphene membranes, i.e. 2-D single graphene nanochannels (GNCs) and the study of ion transport in these channels. A modified bonding technique was developed to form GNCs with well-defined geometry and uniform channel height. Ion transport in such GNCs was studied using DC conductance measurement. Our preliminary results showed that the ion transport in GNCs is still governed by surface charge at low concentrations (10-6M to 10-4M). However, GNCs exhibits much higher ionic conductances than silica nanochannels with the same geometries in the surface-charge-governed regime. This conductance enhancement can be attributed to the pre-accumulation of charges on graphene surfaces. The work is supported by the Faculty Startup Fund (Boston University, USA).
Parallel map analysis on 2-D grids
Berry, M.; Comiskey, J.; Minser, K.
1993-12-31
In landscape ecology, computer modeling is used to assess habitat fragmentation and its ecological iMPLications. Specifically, maps (2-D grids) of habitat clusters must be analyzed to determine number, sizes and geometry of clusters. Models prior to this study relied upon sequential Fortran-77 programs which limited the sizes of maps and densities of clusters which could be analyzed. In this paper, we present more efficient computer models which can exploit recursion or parallelism. Significant improvements over the original Fortran-77 programs have been achieved using both recursive and nonrecursive C implementations on a variety of workstations such as the Sun Sparc 2, IBM RS/6000-350, and HP 9000-750. Parallel implementations on a 4096-processor MasPar MP-1 and a 32-processor CM-5 are also studied. Preliminary experiments suggest that speed improvements for the parallel model on the MasPar MP-1 (written in MPL) and on the CM-5 (written in C using CMMD) can be as much as 39 and 34 times faster, respectively, than the most efficient sequential C program on a Sun Sparc 2 for a 512 map. An important goal in this research effort is to produce a scalable map analysis algorithm for the identification and characterization of clusters for relatively large maps on massively-parallel computers.
2D Turbulence with Complicated Boundaries
NASA Astrophysics Data System (ADS)
Roullet, G.; McWilliams, J. C.
2014-12-01
We examine the consequences of lateral viscous boundary layers on the 2D turbulence that arises in domains with complicated boundaries (headlands, bays etc). The study is carried out numerically with LES. The numerics are carefully designed to ensure all global conservation laws, proper boundary conditions and a minimal range of dissipation scales. The turbulence dramatically differs from the classical bi-periodic case. Boundary layer separations lead to creation of many small vortices and act as a continuing energy source exciting the inverse cascade of energy throughout the domain. The detachments are very intermittent in time. In free decay, the final state depends on the effective numerical resolution: laminar with a single dominant vortex for low Re and turbulent with many vortices for large enough Re. After very long time, the turbulent end-state exhibits a striking tendency for the emergence of shielded vortices which then interact almost elastically. In the forced case, the boundary layers allow the turbulence to reach a statistical steady state without any artificial hypo-viscosity or other large-scale dissipation. Implications are discussed for the oceanic mesoscale and submesoscale turbulence.
Competing coexisting phases in 2D water
NASA Astrophysics Data System (ADS)
Zanotti, Jean-Marc; Judeinstein, Patrick; Dalla-Bernardina, Simona; Creff, Gaëlle; Brubach, Jean-Blaise; Roy, Pascale; Bonetti, Marco; Ollivier, Jacques; Sakellariou, Dimitrios; Bellissent-Funel, Marie-Claire
2016-05-01
The properties of bulk water come from a delicate balance of interactions on length scales encompassing several orders of magnitudes: i) the Hydrogen Bond (HBond) at the molecular scale and ii) the extension of this HBond network up to the macroscopic level. Here, we address the physics of water when the three dimensional extension of the HBond network is frustrated, so that the water molecules are forced to organize in only two dimensions. We account for the large scale fluctuating HBond network by an analytical mean-field percolation model. This approach provides a coherent interpretation of the different events experimentally (calorimetry, neutron, NMR, near and far infra-red spectroscopies) detected in interfacial water at 160, 220 and 250 K. Starting from an amorphous state of water at low temperature, these transitions are respectively interpreted as the onset of creation of transient low density patches of 4-HBonded molecules at 160 K, the percolation of these domains at 220 K and finally the total invasion of the surface by them at 250 K. The source of this surprising behaviour in 2D is the frustration of the natural bulk tetrahedral local geometry and the underlying very significant increase in entropy of the interfacial water molecules.
Competing coexisting phases in 2D water.
Zanotti, Jean-Marc; Judeinstein, Patrick; Dalla-Bernardina, Simona; Creff, Gaëlle; Brubach, Jean-Blaise; Roy, Pascale; Bonetti, Marco; Ollivier, Jacques; Sakellariou, Dimitrios; Bellissent-Funel, Marie-Claire
2016-01-01
The properties of bulk water come from a delicate balance of interactions on length scales encompassing several orders of magnitudes: i) the Hydrogen Bond (HBond) at the molecular scale and ii) the extension of this HBond network up to the macroscopic level. Here, we address the physics of water when the three dimensional extension of the HBond network is frustrated, so that the water molecules are forced to organize in only two dimensions. We account for the large scale fluctuating HBond network by an analytical mean-field percolation model. This approach provides a coherent interpretation of the different events experimentally (calorimetry, neutron, NMR, near and far infra-red spectroscopies) detected in interfacial water at 160, 220 and 250 K. Starting from an amorphous state of water at low temperature, these transitions are respectively interpreted as the onset of creation of transient low density patches of 4-HBonded molecules at 160 K, the percolation of these domains at 220 K and finally the total invasion of the surface by them at 250 K. The source of this surprising behaviour in 2D is the frustration of the natural bulk tetrahedral local geometry and the underlying very significant increase in entropy of the interfacial water molecules. PMID:27185018
2-D wavelet with position controlled resolution
NASA Astrophysics Data System (ADS)
Walczak, Andrzej; Puzio, Leszek
2005-09-01
Wavelet transformation localizes all irregularities in the scene. It is most effective in the case when intensities in the scene have no sharp details. It is the case often present in a medical imaging. To identify the shape one has to extract it from the scene as typical irregularity. When the scene does not contain sharp changes then common differential filters are not efficient tool for a shape extraction. The new 2-D wavelet for such task has been proposed. Described wavelet transform is axially symmetric and has varied scale in dependence on the distance from the centre of the wavelet symmetry. The analytical form of the wavelet has been presented as well as its application for details extraction in the scene. Most important feature of the wavelet transform is that it gives a multi-scale transformation, and if zoom is on the wavelet selectivity varies proportionally to the zoom step. As a result, the extracted shape does not change during zoom operation. What is more the wavelet selectivity can be fit to the local intensity gradient properly to obtain best extraction of the irregularities.
Some properties of correlations of quantum lattice systems in thermal equilibrium
Fröhlich, Jürg; Ueltschi, Daniel
2015-05-15
Simple proofs of uniqueness of the thermodynamic limit of KMS states and of the decay of equilibrium correlations are presented for a large class of quantum lattice systems at high temperatures. New quantum correlation inequalities for general Heisenberg models are described. Finally, a simplified derivation of a general result on power-law decay of correlations in 2D quantum lattice systems with continuous symmetries is given, extending results of McBryan and Spencer for the 2D classical XY model.
Wang, An; Stout, C. David; Zhang, Qinghai; Johnson, Eric F.
2015-01-01
P450 2D6 contributes significantly to the metabolism of >15% of the 200 most marketed drugs. Open and closed crystal structures of P450 2D6 thioridazine complexes were obtained using different crystallization conditions. The protonated piperidine moiety of thioridazine forms a charge-stabilized hydrogen bond with Asp-301 in the active sites of both complexes. The more open conformation exhibits a second molecule of thioridazine bound in an expanded substrate access channel antechamber with its piperidine moiety forming a charge-stabilized hydrogen bond with Glu-222. Incubation of the crystalline open thioridazine complex with alternative ligands, prinomastat, quinidine, quinine, or ajmalicine, displaced both thioridazines. Quinine and ajmalicine formed charge-stabilized hydrogen bonds with Glu-216, whereas the protonated nitrogen of quinidine is equidistant from Asp-301 and Glu-216 with protonated nitrogen H-bonded to a water molecule in the access channel. Prinomastat is not ionized. Adaptations of active site side-chain rotamers and polypeptide conformations were evident between the complexes, with the binding of ajmalicine eliciting a closure of the open structure reflecting in part the inward movement of Glu-216 to form a hydrogen bond with ajmalicine as well as sparse lattice restraints that would hinder adaptations. These results indicate that P450 2D6 exhibits sufficient elasticity within the crystal lattice to allow the passage of compounds between the active site and bulk solvent and to adopt a more closed form that adapts for binding alternative ligands with different degrees of closure. These crystals provide a means to characterize substrate and inhibitor binding to the enzyme after replacement of thioridazine with alternative compounds. PMID:25555909
Mechanical Weyl Modes in Topological Maxwell Lattices
NASA Astrophysics Data System (ADS)
Rocklin, D. Zeb; Chen, Bryan Gin-ge; Falk, Martin; Vitelli, Vincenzo; Lubensky, T. C.
2016-04-01
We show that two-dimensional mechanical lattices can generically display topologically protected bulk zero-energy phonon modes at isolated points in the Brillouin zone, analogs of massless fermion modes of Weyl semimetals. We focus on deformed square lattices as the simplest Maxwell lattices, characterized by equal numbers of constraints and degrees of freedom, with this property. The Weyl points appear at the origin of the Brillouin zone along directions with vanishing sound speed and move away to the zone edge (or return to the origin) where they annihilate. Our results suggest a design strategy for topological metamaterials with bulk low-frequency acoustic modes and elastic instabilities at a particular, tunable finite wave vector.
Arbitrary lattice symmetries via block copolymer nanomeshes
Majewski, Pawel W.; Rahman, Atikur; Black, Charles T.; Yager, Kevin G.
2015-01-01
Self-assembly of block copolymers is a powerful motif for spontaneously forming well-defined nanostructures over macroscopic areas. Yet, the inherent energy minimization criteria of self-assembly give rise to a limited library of structures; diblock copolymers naturally form spheres on a cubic lattice, hexagonally packed cylinders and alternating lamellae. Here, we demonstrate multicomponent nanomeshes with any desired lattice symmetry. We exploit photothermal annealing to rapidly order and align block copolymer phases over macroscopic areas, combined with conversion of the self-assembled organic phase into inorganic replicas. Repeated photothermal processing independently aligns successive layers, providing full control of the size, symmetry and composition of the nanoscale unit cell. We construct a variety of symmetries, most of which are not natively formed by block copolymers, including squares, rhombuses, rectangles and triangles. In fact, we demonstrate all possible two-dimensional Bravais lattices. Finally, we elucidate the influence of nanostructure on the electrical and optical properties of nanomeshes. PMID:26100566
Pattern Recognition of Adsorbing HP Lattice Proteins
NASA Astrophysics Data System (ADS)
Wilson, Matthew S.; Shi, Guangjie; Wüst, Thomas; Landau, David P.; Schmid, Friederike
2015-03-01
Protein adsorption is relevant in fields ranging from medicine to industry, and the qualitative behavior exhibited by course-grained models could shed insight for further research in such fields. Our study on the selective adsorption of lattice proteins utilizes the Wang-Landau algorithm to simulate the Hydrophobic-Polar (H-P) model with an efficient set of Monte Carlo moves. Each substrate is modeled as a square pattern of 9 lattice sites which attract either H or P monomers, and are located on an otherwise neutral surface. The fully enumerated set of 102 unique surfaces is simulated with each protein sequence. A collection of 27-monomer sequences is used- each of which is non-degenerate and protein-like. Thermodynamic quantities such as the specific heat and free energy are calculated from the density of states, and are used to investigate the adsorption of lattice proteins on patterned substrates. Research supported by NSF.
Mechanical Weyl Modes in Topological Maxwell Lattices.
Rocklin, D Zeb; Chen, Bryan Gin-Ge; Falk, Martin; Vitelli, Vincenzo; Lubensky, T C
2016-04-01
We show that two-dimensional mechanical lattices can generically display topologically protected bulk zero-energy phonon modes at isolated points in the Brillouin zone, analogs of massless fermion modes of Weyl semimetals. We focus on deformed square lattices as the simplest Maxwell lattices, characterized by equal numbers of constraints and degrees of freedom, with this property. The Weyl points appear at the origin of the Brillouin zone along directions with vanishing sound speed and move away to the zone edge (or return to the origin) where they annihilate. Our results suggest a design strategy for topological metamaterials with bulk low-frequency acoustic modes and elastic instabilities at a particular, tunable finite wave vector. PMID:27081989
2-D Animation's Not Just for Mickey Mouse.
ERIC Educational Resources Information Center
Weinman, Lynda
1995-01-01
Discusses characteristics of two-dimensional (2-D) animation; highlights include character animation, painting issues, and motion graphics. Sidebars present Silicon Graphics animations tools and 2-D animation programs for the desktop computer. (DGM)
Holographic method for site-resolved detection of a 2D array of ultracold atoms
NASA Astrophysics Data System (ADS)
Hoffmann, Daniel Kai; Deissler, Benjamin; Limmer, Wolfgang; Hecker Denschlag, Johannes
2016-08-01
We propose a novel approach to site-resolved detection of a 2D gas of ultracold atoms in an optical lattice. A near-resonant laser beam is coherently scattered by the atomic array, and after passing a lens its interference pattern is holographically recorded by superimposing it with a reference laser beam on a CCD chip. Fourier transformation of the recorded intensity pattern reconstructs the atomic distribution in the lattice with single-site resolution. The holographic detection method requires only about two hundred scattered photons per atom in order to achieve a high reconstruction fidelity of 99.9 %. Therefore, additional cooling during detection might not be necessary even for light atomic elements such as lithium. Furthermore, first investigations suggest that small aberrations of the lens can be post-corrected in imaging processing.
Simulation of surface tension in 2D and 3D with smoothed particle hydrodynamics method
NASA Astrophysics Data System (ADS)
Zhang, Mingyu
2010-09-01
The methods for simulating surface tension with smoothed particle hydrodynamics (SPH) method in two dimensions and three dimensions are developed. In 2D surface tension model, the SPH particle on the boundary in 2D is detected dynamically according to the algorithm developed by Dilts [G.A. Dilts, Moving least-squares particle hydrodynamics II: conservation and boundaries, International Journal for Numerical Methods in Engineering 48 (2000) 1503-1524]. The boundary curve in 2D is reconstructed locally with Lagrangian interpolation polynomial. In 3D surface tension model, the SPH particle on the boundary in 3D is detected dynamically according to the algorithm developed by Haque and Dilts [A. Haque, G.A. Dilts, Three-dimensional boundary detection for particle methods, Journal of Computational Physics 226 (2007) 1710-1730]. The boundary surface in 3D is reconstructed locally with moving least squares (MLS) method. By transforming the coordinate system, it is guaranteed that the interface function is one-valued in the local coordinate system. The normal vector and curvature of the boundary surface are calculated according to the reconstructed boundary surface and then surface tension force can be calculated. Surface tension force acts only on the boundary particle. Density correction is applied to the boundary particle in order to remove the boundary inconsistency. The surface tension models in 2D and 3D have been applied to benchmark tests for surface tension. The ability of the current method applying to the simulation of surface tension in 2D and 3D is proved.
Stability analysis of lattice Boltzmann methods
Sterling, J.D.; Chen, Shiyi
1996-01-01
The lattice Boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered. Although the equation is a derivative of lattice gas automata, it may be interpreted as a Lagrangian finite-difference method for the numerical simulation of the discrete-velocity Boltzmann equation that makes use of a BGK collision operator. As a result, it is not surprising that numericaI instability of lattice Boltzmann methods have been frequently encountered by researchers. We present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constant-density uniform mean flow. The linear stability depends on the following parameters: the distribution of the mass at a site between the different discrete speeds, the BGK relaxation time, the mean velocity, and the wave-number of the perturbations. This parameter space is too large to compute the complete stability characteristics. We report some stability results for a subset of the parameter space for a 7-velocity hexagonal lattice, a 9-velocity square lattice, and a 15-velocity cubic lattice. Results common to all three lattices are (1) the BGK relaxation time {tau} must be greater than 1/2 corresponding to positive shear viscosity, (2) there exists a maximum stable mean velocity for fixed values of theother parameters, and (3) as {tau} is increased from 1/2 the maximum stable velocity increases monotonically until some fixed velocity is reached which does not change for larger {tau}.
Finite-lattice form factors in free-fermion models
NASA Astrophysics Data System (ADS)
Iorgov, N.; Lisovyy, O.
2011-04-01
We consider the general {Z}_2 -symmetric free-fermion model on the finite periodic lattice, which includes as special cases the Ising model on the square and triangular lattices and the {Z}_n -symmetric BBS τ(2)-model with n = 2. Translating Kaufman's fermionic approach to diagonalization of Ising-like transfer matrices into the language of Grassmann integrals, we determine the transfer matrix eigenvectors and observe that they coincide with the eigenvectors of a square lattice Ising transfer matrix. This allows us to find exact finite-lattice form factors of spin operators for the statistical model and the associated finite-length quantum chains, of which the most general is equivalent to the XY chain in a transverse field.
MAZE96. Generates 2D Input for DYNA NIKE & TOPAZ
Sanford, L.; Hallquist, J.O.
1992-02-24
MAZE is an interactive program that serves as an input and two-dimensional mesh generator for DYNA2D, NIKE2D, TOPAZ2D, and CHEMICAL TOPAZ2D. MAZE also generates a basic template for ISLAND input. MAZE has been applied to the generation of input data to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.
On 2D graphical representation of DNA sequence of nondegeneracy
NASA Astrophysics Data System (ADS)
Zhang, Yusen; Liao, Bo; Ding, Kequan
2005-08-01
Some two-dimensional (2D) graphical representations of DNA sequences have been given by Gates, Nandy, Leong and Mogenthaler, Randić, and Liao et al., which give visual characterizations of DNA sequences. In this Letter, we introduce a nondegeneracy 2D graphical representation of DNA sequence, which is different from Randić's novel 2D representation and Liao's 2D representation. We also present the nondegeneracy forms corresponding to the representations of Gates, Nandy, Leong and Mogenthaler.
Generates 2D Input for DYNA NIKE & TOPAZ
1996-07-15
MAZE is an interactive program that serves as an input and two-dimensional mesh generator for DYNA2D, NIKE2D, TOPAZ2D, and CHEMICAL TOPAZ2D. MAZE also generates a basic template for ISLAND input. MAZE has been applied to the generation of input data to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.
Evolution of the Hofstadter butterfly in a tunable optical lattice
NASA Astrophysics Data System (ADS)
Yılmaz, F.; Ünal, F. Nur; Oktel, M. Ã.-.
2015-06-01
Recent advances in realizing artificial gauge fields on optical lattices promise experimental detection of topologically nontrivial energy spectra. Self-similar fractal energy structures generally known as Hofstadter butterflies depend sensitively on the geometry of the underlying lattice, as well as the applied magnetic field. The recent demonstration of an adjustable lattice geometry [L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, Nature (London) 483, 302 (2012), 10.1038/nature10871] presents a unique opportunity to study this dependence. In this paper, we calculate the Hofstadter butterflies that can be obtained in such an adjustable lattice and find three qualitatively different regimes. We show that the existence of Dirac points at zero magnetic field does not imply the topological equivalence of spectra at finite field. As the real-space structure evolves from the checkerboard lattice to the honeycomb lattice, two square-lattice Hofstadter butterflies merge to form a honeycomb lattice butterfly. This merging is topologically nontrivial, as it is accomplished by sequential closings of gaps. Ensuing Chern number transfer between the bands can be probed with the adjustable lattice experiments. We also calculate the Chern numbers of the gaps for qualitatively different spectra and discuss the evolution of topological properties with underlying lattice geometry.
Self-Assembly of Shaped Nanoparticles into Free-Standing 2D and 3D Superlattices.
Li, Weikun; Wang, Ke; Zhang, Peng; He, Jie; Xu, Shaoyi; Liao, Yonggui; Zhu, Jintao; Xie, Xiaolin; Nie, Zhihong
2016-01-27
This article describes a novel supramolecular assembly-mediated strategy for the organization of Au nanoparticles (NPs) with different shapes (e.g., spheres, rods, and cubes) into large-area, free-standing 2D and 3D superlattices. This robust approach involves two major steps: (i) the organization of polymer-tethered NPs within the assemblies of supramolecular comblike block copolymers (CBCPs), and (ii) the disassembly of the assembled CBCP structures to produce free-standing NP superlattices. It is demonstrated that the crystal structures and lattice constants of the superlattices can be readily tailored by varying the molecular weight of tethered polymers, the volume fraction of NPs, and the matrix of CBCPs. This template-free approach may open a new avenue for the assembly of NPs into 2D and 3D structures with a wide range of potential applications. PMID:26649814
Electrochemical fabrication of 2D and 3D nickel nanowires using porous anodic alumina templates
NASA Astrophysics Data System (ADS)
Mebed, A. M.; Abd-Elnaiem, Alaa M.; Al-Hosiny, Najm M.
2016-06-01
Mechanically stable nickel (Ni) nanowires array and nanowires network were synthesized by pulse electrochemical deposition using 2D and 3D porous anodic alumina (PAA) templates. The structures and morphologies of as-prepared films were characterized by X-ray diffraction and scanning electron microscopy, respectively. The grown Ni nanowire using 3D PAA revealed more strength and larger surface area than has grown Ni use 2D PAA template. The prepared nanowires have a face-centered cubic crystal structure with average grain size 15 nm, and the preferred orientation of the nucleation of the nanowires is (111). The diameter of the nanowires is about 50-70 nm with length 3 µm. The resulting 3D Ni nanowire lattice, which provides enhanced mechanical stability and an increased surface area, benefits energy storage and many other applications which utilize the large surface area.
2d PDE Linear Symmetric Matrix Solver
1983-10-01
ICCG2 (Incomplete Cholesky factorized Conjugate Gradient algorithm for 2d symmetric problems) was developed to solve a linear symmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as resistive MHD, spatial diffusive transport, and phase space transport (Fokker-Planck equation) problems. These problems share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized withmore » finite-difference or finite-element methods,the resulting matrix system is frequently of block-tridiagonal form. To use ICCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. The incomplete Cholesky conjugate gradient algorithm is used to solve the linear symmetric matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For matrices lacking symmetry, ILUCG2 should be used. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less
2d PDE Linear Asymmetric Matrix Solver
1983-10-01
ILUCG2 (Incomplete LU factorized Conjugate Gradient algorithm for 2d problems) was developed to solve a linear asymmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as plasma diffusion, equilibria, and phase space transport (Fokker-Planck equation) problems. These equations share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized with finite-difference or finite-elementmore » methods, the resulting matrix system is frequently of block-tridiagonal form. To use ILUCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. A generalization of the incomplete Cholesky conjugate gradient algorithm is used to solve the matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For problems having a symmetric matrix ICCG2 should be used since it runs up to four times faster and uses approximately 30% less storage. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source, containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less
Ultrasonic 2D matrix PVDF transducer
NASA Astrophysics Data System (ADS)
Ptchelintsev, A.; Maev, R. Gr.
2000-05-01
During the past decade a substantial amount of work has been done in the area of ultrasonic imaging technology using 2D arrays. The main problems arising for the two-dimensional matrix transducers at megahertz frequencies are small size and huge count of the elements, high electrical impedance, low sensitivity, bad SNR and slower data acquisition rate. The major technological difficulty remains the high density of the interconnect. To solve these problems numerous approaches have been suggested. In the present work, a 24×24 elements (24 transmit+24 receive) matrix and a switching board were developed. The transducer consists of two 52 μm PVDF layers each representing a linear array of 24 elements placed one on the top of the other. Electrodes in these two layers are perpendicular and form the grid of 0.5×0.5 mm pitch. The layers are bonded together with the ground electrode being monolithic and located between the layers. The matrix is backed from the rear surface with an epoxy composition. During the emission, a linear element from the emitting layer generates a longitudinal wave pulse propagating inside the test object. Reflected pulses are picked-up by the receiving layer. During one transmit-receive cycle one transmit element and one receive element are selected by corresponding multiplexers. These crossed elements emulate a small element formed by their intersection. The present design presents the following advantages: minimizes number of active channels and density of the interconnect; reduces the electrical impedance of the element improving electrical matching; enables the transmit-receive mode; due to the efficient backing provides bandwidth and good time resolution; and, significantly reduces the electronics complexity. The matrix can not be used for the beam steering and focusing. Owing to this impossibility of focusing, the penetration depth is limited as well by the diffraction phenomena.
Canonical vs. micro-canonical sampling methods in a 2D Ising model
Kepner, J.
1990-12-01
Canonical and micro-canonical Monte Carlo algorithms were implemented on a 2D Ising model. Expressions for the internal energy, U, inverse temperature, Z, and specific heat, C, are given. These quantities were calculated over a range of temperature, lattice sizes, and time steps. Both algorithms accurately simulate the Ising model. To obtain greater than three decimal accuracy from the micro-canonical method requires that the more complicated expression for Z be used. The overall difference between the algorithms is small. The physics of the problem under study should be the deciding factor in determining which algorithm to use. 13 refs., 6 figs., 2 tabs.
Zhang, Zi-Xuan; Ding, Ni-Ni; Zhang, Wen-Hua; Chen, Jin-Xiang; Young, David J; Hor, T S Andy
2014-04-25
A 2D coordination polymer prepared with bulky diethylformamide solvates exhibits channels which allow dipyridyl bridging ligands to diffuse into the crystal lattice. The absorbed dipyridyls thread through the pores of one layer and substitute the surface diethylformamide molecules on the neighboring layers to stitch alternate layers to form flexible interpenetrated metal-orgaic frameworks. The threading process also results in exchange of the bulky diethylformamide solvates for aqua to minimize congestion and, more strikingly, forces the slippage of two-dimensional layers, while still maintaining crystallinity. PMID:24692130
Electrostatic 2D assembly of bionanoparticles on a cationic lipid monolayer.
NASA Astrophysics Data System (ADS)
Kewalramani, Sumit; Wang, Suntao; Fukuto, Masafumi; Yang, Lin; Niu, Zhongwei; Nguyen, Giang; Wang, Qian
2010-03-01
We present a grazing-incidence small-angle X-ray scattering (GISAXS) study on 2D assembly of cowpea mosaic virus (CPMV) under a mixed cationic-zwitterionic (DMTAP^+-DMPC) lipid monolayer at the air-water interface. The inter-particle and particle-lipid electrostatic interactions were varied by controlling the subphase pH and the membrane charge density. GISAXS data show that 2D crystals of CPMV are formed above a threshold membrane charge density and only in a narrow pH range just above CPMV's isoelectric point, where the charge on CPMV is expected to be weakly negative. The particle density for the 2D crystals is similar to that for the densest lattice plane in the 3D crystals of CPMV. The results show that the 2D crystallization is achieved in the part of the phase space where the electrostatic interactions are expected to maximize the adsorption of CPMV onto the lipid membrane. This electrostatics-based strategy for controlling interfacial nanoscale assembly should be generally applicable to other nanoparticles.
A Planar Quantum Transistor Based on 2D-2D Tunneling in Double Quantum Well Heterostructures
Baca, W.E.; Blount, M.A.; Hafich, M.J.; Lyo, S.K.; Moon, J.S.; Reno, J.L.; Simmons, J.A.; Wendt, J.R.
1998-12-14
We report on our work on the double electron layer tunneling transistor (DELTT), based on the gate-control of two-dimensional -- two-dimensional (2D-2D) tunneling in a double quantum well heterostructure. While previous quantum transistors have typically required tiny laterally-defined features, by contrast the DELTT is entirely planar and can be reliably fabricated in large numbers. We use a novel epoxy-bond-and-stop-etch (EBASE) flip-chip process, whereby submicron gating on opposite sides of semiconductor epitaxial layers as thin as 0.24 microns can be achieved. Because both electron layers in the DELTT are 2D, the resonant tunneling features are unusually sharp, and can be easily modulated with one or more surface gates. We demonstrate DELTTs with peak-to-valley ratios in the source-drain I-V curve of order 20:1 below 1 K. Both the height and position of the resonant current peak can be controlled by gate voltage over a wide range. DELTTs with larger subband energy offsets ({approximately} 21 meV) exhibit characteristics that are nearly as good at 77 K, in good agreement with our theoretical calculations. Using these devices, we also demonstrate bistable memories operating at 77 K. Finally, we briefly discuss the prospects for room temperature operation, increases in gain, and high-speed.
Dibrov, Sergey M.; McLean, Jaime; Parsons, Jerod; Hermann, Thomas
2011-12-22
The three-dimensional structures of noncoding RNA molecules reveal recurring architectural motifs that have been exploited for the design of artificial RNA nanomaterials. Programmed assembly of RNA nanoobjects from autonomously folding tetraloop-receptor complexes as well as junction motifs has been achieved previously through sequence-directed hybridization of complex sets of long oligonucleotides. Due to size and complexity, structural characterization of artificial RNA nanoobjects has been limited to low-resolution microscopy studies. Here we present the design, construction, and crystal structure determination at 2.2 {angstrom} of the smallest yet square-shaped nanoobject made entirely of double-stranded RNA. The RNA square is comprised of 100 residues and self-assembles from four copies each of two oligonucleotides of 10 and 15 bases length. Despite the high symmetry on the level of secondary structure, the three-dimensional architecture of the square is asymmetric, with all four corners adopting distinct folding patterns. We demonstrate the programmed self-assembly of RNA squares from complex mixtures of corner units and establish a concept to exploit the RNA square as a combinatorial nanoscale platform.
Correlated Electron Phenomena in 2D Materials
NASA Astrophysics Data System (ADS)
Lambert, Joseph G.
In this thesis, I present experimental results on coherent electron phenomena in layered two-dimensional materials: single layer graphene and van der Waals coupled 2D TiSe2. Graphene is a two-dimensional single-atom thick sheet of carbon atoms first derived from bulk graphite by the mechanical exfoliation technique in 2004. Low-energy charge carriers in graphene behave like massless Dirac fermions, and their density can be easily tuned between electron-rich and hole-rich quasiparticles with electrostatic gating techniques. The sharp interfaces between regions of different carrier densities form barriers with selective transmission, making them behave as partially reflecting mirrors. When two of these interfaces are set at a separation distance within the phase coherence length of the carriers, they form an electronic version of a Fabry-Perot cavity. I present measurements and analysis of multiple Fabry-Perot modes in graphene with parallel electrodes spaced a few hundred nanometers apart. Transition metal dichalcogenide (TMD) TiSe2 is part of the family of materials that coined the term "materials beyond graphene". It contains van der Waals coupled trilayer stacks of Se-Ti-Se. Many TMD materials exhibit a host of interesting correlated electronic phases. In particular, TiSe2 exhibits chiral charge density waves (CDW) below TCDW ˜ 200 K. Upon doping with copper, the CDW state gets suppressed with Cu concentration, and CuxTiSe2 becomes superconducting with critical temperature of T c = 4.15 K. There is still much debate over the mechanisms governing the coexistence of the two correlated electronic phases---CDW and superconductivity. I will present some of the first conductance spectroscopy measurements of proximity coupled superconductor-CDW systems. Measurements reveal a proximity-induced critical current at the Nb-TiSe2 interfaces, suggesting pair correlations in the pure TiSe2. The results indicate that superconducting order is present concurrently with CDW in
A Solution to Weighted Sums of Squares as a Square
ERIC Educational Resources Information Center
Withers, Christopher S.; Nadarajah, Saralees
2012-01-01
For n = 1, 2, ... , we give a solution (x[subscript 1], ... , x[subscript n], N) to the Diophantine integer equation [image omitted]. Our solution has N of the form n!, in contrast to other solutions in the literature that are extensions of Euler's solution for N, a sum of squares. More generally, for given n and given integer weights m[subscript…
Janse Van Rensburg, E.J.
1996-12-31
The geometry of polygonal knots in the cubic lattice may be used to define some knot invariants. One such invariant is the minimal edge number, which is the minimum number of edges necessary (and sufficient) to construct a lattice knot of given type. In addition, one may also define the minimal (unfolded) surface number, and the minimal (unfolded) boundary number; these are the minimum number of 2-cells necessary to construct an unfolded lattice Seifert surface of a given knot type in the lattice, and the minimum number of edges necessary in a lattice knot to guarantee the existence of an unfolded lattice Seifert surface. In addition, I derive some relations amongst these invariants. 8 refs., 5 figs., 2 tabs.
Self-leveling 2D DPN probe arrays
NASA Astrophysics Data System (ADS)
Haaheim, Jason R.; Val, Vadim; Solheim, Ed; Bussan, John; Fragala, J.; Nelson, Mike
2010-02-01
Dip Pen Nanolithography® (DPN®) is a direct write scanning probe-based technique which operates under ambient conditions, making it suitable to deposit a wide range of biological and inorganic materials. Precision nanoscale deposition is a fundamental requirement to advance nanoscale technology in commercial applications, and tailoring chemical composition and surface structure on the sub-100 nm scale benefits researchers in areas ranging from cell adhesion to cell-signaling and biomimetic membranes. These capabilities naturally suggest a "Desktop Nanofab" concept - a turnkey system that allows a non-expert user to rapidly create high resolution, scalable nanostructures drawing upon well-characterized ink and substrate pairings. In turn, this system is fundamentally supported by a portfolio of MEMS devices tailored for microfluidic ink delivery, directed placement of nanoscale materials, and cm2 tip arrays for high-throughput nanofabrication. Massively parallel two-dimensional nanopatterning is now commercially available via NanoInk's 2D nano PrintArray™, making DPN a high-throughput (>3×107 μm2 per hour), flexible and versatile method for precision nanoscale pattern formation. However, cm2 arrays of nanoscopic tips introduce the nontrivial problem of getting them all evenly touching the surface to ensure homogeneous deposition; this requires extremely precise leveling of the array. Herein, we describe how we have made the process simple by way of a selfleveling gimbal attachment, coupled with semi-automated software leveling routines which bring the cm^2 chip to within 0.002 degrees of co-planarity. This excellent co-planarity yields highly homogeneous features across a square centimeter, with <6% feature size standard deviation. We have engineered the devices to be easy to use, wire-free, and fully integrated with both of our patterning tools: the DPN 5000, and the NLP 2000.
Geometrical Correlation and Matching of 2d Image Shapes
NASA Astrophysics Data System (ADS)
Vizilter, Y. V.; Zheltov, S. Y.
2012-07-01
The problem of image correspondence measure selection for image comparison and matching is addressed. Many practical applications require image matching "just by shape" with no dependence on the concrete intensity or color values. Most popular technique for image shape comparison utilizes the mutual information measure based on probabilistic reasoning and information theory background. Another approach was proposed by Pytiev (so called "Pytiev morphology") based on geometrical and algebraic reasoning. In this framework images are considered as piecewise-constant 2D functions, tessellation of image frame by the set of non-intersected connected regions determines the "shape" of image and the projection of image onto the shape of other image is determined. Morphological image comparison is performed using the normalized morphological correlation coefficients. These coefficients estimate the closeness of one image to the shape of other image. Such image analysis technique can be characterized as an ""ntensity-to-geometry" matching. This paper generalizes the Pytiev morphological approach for obtaining the pure "geometry-to-geometry" matching techniques. The generalized intensity-geometrical correlation coefficient is proposed including the linear correlation coefficient and the square of Pytiev correlation coefficient as its partial cases. The morphological shape correlation coefficient is proposed based on the statistical averaging of images with the same shape. Centered morphological correlation coefficient is obtained under the condition of intensity centering of averaged images. Two types of symmetric geometrical normalized correlation coefficients are proposed for comparison of shape-tessellations. The technique for correlation and matching of shapes with ordered intensities is proposed with correlation measures invariant to monotonous intensity transformations. The quality of proposed geometrical correlation measures is experimentally estimated in the task of
CYP2D7 Sequence Variation Interferes with TaqMan CYP2D6*15 and *35 Genotyping
Riffel, Amanda K.; Dehghani, Mehdi; Hartshorne, Toinette; Floyd, Kristen C.; Leeder, J. Steven; Rosenblatt, Kevin P.; Gaedigk, Andrea
2016-01-01
TaqMan™ genotyping assays are widely used to genotype CYP2D6, which encodes a major drug metabolizing enzyme. Assay design for CYP2D6 can be challenging owing to the presence of two pseudogenes, CYP2D7 and CYP2D8, structural and copy number variation and numerous single nucleotide polymorphisms (SNPs) some of which reflect the wild-type sequence of the CYP2D7 pseudogene. The aim of this study was to identify the mechanism causing false-positive CYP2D6*15 calls and remediate those by redesigning and validating alternative TaqMan genotype assays. Among 13,866 DNA samples genotyped by the CompanionDx® lab on the OpenArray platform, 70 samples were identified as heterozygotes for 137Tins, the key SNP of CYP2D6*15. However, only 15 samples were confirmed when tested with the Luminex xTAG CYP2D6 Kit and sequencing of CYP2D6-specific long range (XL)-PCR products. Genotype and gene resequencing of CYP2D6 and CYP2D7-specific XL-PCR products revealed a CC>GT dinucleotide SNP in exon 1 of CYP2D7 that reverts the sequence to CYP2D6 and allows a TaqMan assay PCR primer to bind. Because CYP2D7 also carries a Tins, a false-positive mutation signal is generated. This CYP2D7 SNP was also responsible for generating false-positive signals for rs769258 (CYP2D6*35) which is also located in exon 1. Although alternative CYP2D6*15 and *35 assays resolved the issue, we discovered a novel CYP2D6*15 subvariant in one sample that carries additional SNPs preventing detection with the alternate assay. The frequency of CYP2D6*15 was 0.1% in this ethnically diverse U.S. population sample. In addition, we also discovered linkage between the CYP2D7 CC>GT dinucleotide SNP and the 77G>A (rs28371696) SNP of CYP2D6*43. The frequency of this tentatively functional allele was 0.2%. Taken together, these findings emphasize that regardless of how careful genotyping assays are designed and evaluated before being commercially marketed, rare or unknown SNPs underneath primer and/or probe regions can impact
CYP2D7 Sequence Variation Interferes with TaqMan CYP2D6 (*) 15 and (*) 35 Genotyping.
Riffel, Amanda K; Dehghani, Mehdi; Hartshorne, Toinette; Floyd, Kristen C; Leeder, J Steven; Rosenblatt, Kevin P; Gaedigk, Andrea
2015-01-01
TaqMan™ genotyping assays are widely used to genotype CYP2D6, which encodes a major drug metabolizing enzyme. Assay design for CYP2D6 can be challenging owing to the presence of two pseudogenes, CYP2D7 and CYP2D8, structural and copy number variation and numerous single nucleotide polymorphisms (SNPs) some of which reflect the wild-type sequence of the CYP2D7 pseudogene. The aim of this study was to identify the mechanism causing false-positive CYP2D6 (*) 15 calls and remediate those by redesigning and validating alternative TaqMan genotype assays. Among 13,866 DNA samples genotyped by the CompanionDx® lab on the OpenArray platform, 70 samples were identified as heterozygotes for 137Tins, the key SNP of CYP2D6 (*) 15. However, only 15 samples were confirmed when tested with the Luminex xTAG CYP2D6 Kit and sequencing of CYP2D6-specific long range (XL)-PCR products. Genotype and gene resequencing of CYP2D6 and CYP2D7-specific XL-PCR products revealed a CC>GT dinucleotide SNP in exon 1 of CYP2D7 that reverts the sequence to CYP2D6 and allows a TaqMan assay PCR primer to bind. Because CYP2D7 also carries a Tins, a false-positive mutation signal is generated. This CYP2D7 SNP was also responsible for generating false-positive signals for rs769258 (CYP2D6 (*) 35) which is also located in exon 1. Although alternative CYP2D6 (*) 15 and (*) 35 assays resolved the issue, we discovered a novel CYP2D6 (*) 15 subvariant in one sample that carries additional SNPs preventing detection with the alternate assay. The frequency of CYP2D6 (*) 15 was 0.1% in this ethnically diverse U.S. population sample. In addition, we also discovered linkage between the CYP2D7 CC>GT dinucleotide SNP and the 77G>A (rs28371696) SNP of CYP2D6 (*) 43. The frequency of this tentatively functional allele was 0.2%. Taken together, these findings emphasize that regardless of how careful genotyping assays are designed and evaluated before being commercially marketed, rare or unknown SNPs underneath primer
Columnar order and Ashkin-Teller criticality in mixtures of hard squares and dimers.
Ramola, Kabir; Damle, Kedar; Dhar, Deepak
2015-05-15
We show that critical exponents of the transition to columnar order in a mixture of 2×1 dimers and 2×2 hard squares on the square lattice depends on the composition of the mixture in exactly the manner predicted by the theory of Ashkin-Teller criticality, including in the hard-square limit. This result settles the question regarding the nature of the transition in the hard-square lattice gas. It also provides the first example of a polydisperse system whose critical properties depend on composition. Our ideas also lead to some interesting predictions for a class of frustrated quantum magnets that exhibit columnar ordering of the bond energies at low temperature. PMID:26024157
Loading an Rb-87 MOT directly into a variable-period accordion lattice
NASA Astrophysics Data System (ADS)
Huckans, John
2015-05-01
We report on our progress toward loading an Rb-87 three-dimensional magneto-optical trap (3D MOT) directly into a two-dimensional variable-period optical lattice (2D accordion lattice). Preliminary calculations suggest the feasibility of achieving an approximate 102 increase in phase space density by combining gray-molasses-type cooling techniques with spatial density compression of a 3D MOT with an accordion lattice.
Topological phases of shaken quantum Ising lattices
NASA Astrophysics Data System (ADS)
Fernández-Lorenzo, Samuel; José García-Ripoll, Juan; Porras, Diego
2016-02-01
The quantum compass model consists of a two-dimensional square spin lattice where the orientation of the spin-spin interactions depends on the spatial direction of the bonds. It has remarkable symmetry properties and the ground state shows topological degeneracy. The implementation of the quantum compass model in quantum simulation setups like ultracold atoms and trapped ions is far from trivial, since spin interactions in those systems typically are independent of the spatial direction. Ising spin interactions, on the contrary, can be induced and controlled in atomic setups with state-of-the art experimental techniques. In this work, we show how the quantum compass model on a rectangular lattice can be simulated by the use of the photon-assisted tunneling induced by periodic drivings on a quantum Ising spin model. We describe a procedure to adiabatically prepare one of the doubly degenerate ground states of this model by adiabatically ramping down a transverse magnetic field, with surprising differences depending on the parity of the lattice size. Exact diagonalizations confirm the validity of this approach for small lattices. Specific implementations of this scheme are presented with ultracold atoms in optical lattices in the Mott insulator regime, as well as with Rydberg atoms.
Clifford algebra approach to the coincidence problem for planar lattices.
Rodríguez, M A; Aragón, J L; Verde-Star, L
2005-03-01
The problem of coincidences of planar lattices is analyzed using Clifford algebra. It is shown that an arbitrary coincidence isometry can be decomposed as a product of coincidence reflections and this allows planar coincidence lattices to be characterized algebraically. The cases of square, rectangular and rhombic lattices are worked out in detail. One of the aims of this work is to show the potential usefulness of Clifford algebra in crystallography. The power of Clifford algebra for expressing geometric ideas is exploited here and the procedure presented can be generalized to higher dimensions. PMID:15724067
C[squared] = Creative Coordinates
ERIC Educational Resources Information Center
McHugh, Shelley R.
2007-01-01
"C[squared] = Creative Coordinates" is an engaging group of tasks that fosters the integration of mathematics and art to create meaningful understanding. The project lets students illustrate of find an image, then plot points to map their design on a grid. The project usually takes about a week to complete. When it is finished, students who are…
Numerical simulation of ( T 2, T 1) 2D NMR and fluid responses
NASA Astrophysics Data System (ADS)
Tan, Mao-Jin; Zou, You-Long; Zhang, Jin-Yan; Zhao, Xin
2012-12-01
One-dimensional nuclear magnetic resonance (1D NMR) logging technology is limited for fluid typing, while two-dimensional nuclear magnetic resonance (2D NMR) logging can provide more parameters including longitudinal relaxation time ( T 1) and transverse relaxation time ( T 2) relative to fluid types in porous media. Based on the 2D NMR relaxation mechanism in a gradient magnetic field, echo train simulation and 2D NMR inversion are discussed in detail. For 2D NMR inversion, a hybrid inversion method is proposed based on the damping least squares method (LSQR) and an improved truncated singular value decomposition (TSVD) algorithm. A series of spin echoes are first simulated with multiple waiting times ( T W s) in a gradient magnetic field for given fluid models and these synthesized echo trains are inverted by the hybrid method. The inversion results are consistent with given models. Moreover, the numerical simulation of various fluid models such as the gas-water, light oil-water, and vicious oil-water models were carried out with different echo spacings ( T E s) and T W s by this hybrid method. Finally, the influences of different signal-to-noise ratios (SNRs) on inversion results in various fluid models are studied. The numerical simulations show that the hybrid method and optimized observation parameters are applicable to fluid typing of gas-water and oil-water models.
Rupture dynamics and ground motions from earthquakes in 2-D heterogeneous media
NASA Astrophysics Data System (ADS)
Bydlon, Samuel A.; Dunham, Eric M.
2015-03-01
We perform 2-D simulations of earthquakes on rough faults in media with random heterogeneities (with von Karman distribution) to study the effects of geometric and material heterogeneity on the rupture process and resulting high-frequency ground motions in the near-fault region (out to ˜20 km). Variations in slip and rupture velocity can arise from material heterogeneity alone but are dominantly controlled by fault roughness. Scattering effects become appreciable beyond ˜3 km from the fault. Near-fault scattering extends the duration of incoherent, high-frequency ground motions and, at least in our 2-D simulations, elevates root-mean-square accelerations (i.e., Arias intensity) with negligible reduction in peak velocities. We also demonstrate that near-fault scattering typically occurs in the power law tail of the power spectral density function, quantified by the Hurst exponent and another parameter combining standard deviation and correlation length.
Probing transverse coherence of x-ray beam with 2-D phase grating interferometer
Marathe, Shashidhara; Shi, Xianbo; Wojcik, Michael J.; Kujala, Naresh G.; Divan, Ralu; Mancini, Derrick C.; Macrander, Albert T.; Assoufid, Lahsen
2014-01-01
Transverse coherence of the x-ray beam from a bending magnet source was studied along multiple directions using a 2-D π/2 phase grating by measuring interferogram visibilities at different distances behind the grating. These measurements suggest that the preferred measuring orientation of a 2-D checkerboard grating is along the diagonal directions of the square blocks, where the interferograms have higher visibility and are not sensitive to the deviation of the duty cycle of the grating period. These observations are verified by thorough wavefront propagation simulations. The accuracy of the measured coherence values was also validated by the simulation and analytical results obtained from the source parameters. In addition, capability of the technique in probing spatially resolved local transverse coherence is demonstrated. PMID:24977503
Probing transverse coherence of x-ray beam with 2-D phase grating interferometer.
Marathe, Shashidhara; Shi, Xianbo; Wojcik, Michael J; Kujala, Naresh G; Divan, Ralu; Mancini, Derrick C; Macrander, Albert T; Assoufid, Lahsen
2014-06-16
Transverse coherence of the x-ray beam from a bending magnet source was studied along multiple directions using a 2-D π/2 phase grating by measuring interferogram visibilities at different distances behind the grating. These measurements suggest that the preferred measuring orientation of a 2-D checkerboard grating is along the diagonal directions of the square blocks, where the interferograms have higher visibility and are not sensitive to the deviation of the duty cycle of the grating period. These observations are verified by thorough wavefront propagation simulations. The accuracy of the measured coherence values was also validated by the simulation and analytical results obtained from the source parameters. In addition, capability of the technique in probing spatially resolved local transverse coherence is demonstrated. PMID:24977503
Evolution of the Hofstadter butterfly in a tunable optical lattice
NASA Astrophysics Data System (ADS)
Oktel, Mehmet O.; Unal, Nur; Yilmaz, Firat
Advances in realizing artificial gauge fields on optical lattices promise experimental detection of topologically non-trivial energy spectra. Self-similar fractal energy structures, known as Hofstadter butterflies, depend sensitively on the geometry of the lattice, as well as the applied magnetic field. The recent demonstration of an adjustable lattice geometry [L. Tarruell et al., Nature 483, 302 (2012)] presents a unique opportunity to study this dependence. We calculate the Hofstadter butterflies that can be obtained in such an adjustable lattice and find three qualitatively different regimes. We show that the existence of Dirac points at zero magnetic field does not imply the topological equivalence of spectra at finite field. As the real-space structure evolves from the checkerboard to the honeycomb lattice, two square lattice Hofstadter butterflies merge to form a honeycomb lattice butterfly in a topologically non-trivial way, as it is accomplished by sequential closing of infinitely many gaps. We discuss the evolution of topological properties with underlying lattice geometry by calculating the Chern numbers and comment on the validity of simulating graphene in such an adjustable lattice
Differential CYP 2D6 Metabolism Alters Primaquine Pharmacokinetics
Potter, Brittney M. J.; Xie, Lisa H.; Vuong, Chau; Zhang, Jing; Zhang, Ping; Duan, Dehui; Luong, Thu-Lan T.; Bandara Herath, H. M. T.; Dhammika Nanayakkara, N. P.; Tekwani, Babu L.; Walker, Larry A.; Nolan, Christina K.; Sciotti, Richard J.; Zottig, Victor E.; Smith, Philip L.; Paris, Robert M.; Read, Lisa T.; Li, Qigui; Pybus, Brandon S.; Sousa, Jason C.; Reichard, Gregory A.
2015-01-01
Primaquine (PQ) metabolism by the cytochrome P450 (CYP) 2D family of enzymes is required for antimalarial activity in both humans (2D6) and mice (2D). Human CYP 2D6 is highly polymorphic, and decreased CYP 2D6 enzyme activity has been linked to decreased PQ antimalarial activity. Despite the importance of CYP 2D metabolism in PQ efficacy, the exact role that these enzymes play in PQ metabolism and pharmacokinetics has not been extensively studied in vivo. In this study, a series of PQ pharmacokinetic experiments were conducted in mice with differential CYP 2D metabolism characteristics, including wild-type (WT), CYP 2D knockout (KO), and humanized CYP 2D6 (KO/knock-in [KO/KI]) mice. Plasma and liver pharmacokinetic profiles from a single PQ dose (20 mg/kg of body weight) differed significantly among the strains for PQ and carboxy-PQ. Additionally, due to the suspected role of phenolic metabolites in PQ efficacy, these were probed using reference standards. Levels of phenolic metabolites were highest in mice capable of metabolizing CYP 2D6 substrates (WT and KO/KI 2D6 mice). PQ phenolic metabolites were present in different quantities in the two strains, illustrating species-specific differences in PQ metabolism between the human and mouse enzymes. Taking the data together, this report furthers understanding of PQ pharmacokinetics in the context of differential CYP 2D metabolism and has important implications for PQ administration in humans with different levels of CYP 2D6 enzyme activity. PMID:25645856
Dynamic response of an artificial square spin ice
NASA Astrophysics Data System (ADS)
Jungfleisch, M. B.; Zhang, W.; Iacocca, E.; Sklenar, J.; Ding, J.; Jiang, W.; Zhang, S.; Pearson, J. E.; Novosad, V.; Ketterson, J. B.; Heinonen, O.; Hoffmann, A.
2016-03-01
Magnetization dynamics in an artificial square spin-ice lattice made of Ni80Fe20 with magnetic field applied in the lattice plane is investigated by broadband ferromagnetic resonance spectroscopy. The experimentally observed dispersion shows a rich spectrum of modes corresponding to different magnetization states. These magnetization states are determined by exchange and dipolar interaction between individual islands, as is confirmed by a semianalytical model. In the low field regime below 400 Oe a hysteretic behavior in the mode spectrum is found. Micromagnetic simulations reveal that the origin of the observed spectra is due to the initialization of different magnetization states of individual nanomagnets. Our results indicate that it might be possible to determine the spin-ice state by resonance experiments and are a first step towards the understanding of artificial geometrically frustrated magnetic systems in the high-frequency regime.
2D to 3D to 2D Dimensionality Crossovers in Thin BSCCO Films
NASA Astrophysics Data System (ADS)
Williams, Gary A.
2003-03-01
With increasing temperature the superfluid fraction in very thin BSCCO films undergoes a series of dimensionality crossovers. At low temperatures the strong anisotropy causes the thermal excitations to be 2D pancake-antipancake pairs in uncoupled layers. At higher temperatures where the c-axis correlation length becomes larger than a layer there is a crossover to 3D vortex loops. These are initially elliptical, but as the 3D Tc is approached they become more circular as the anisotropy scales away, as modeled by Shenoy and Chattopadhyay [1]. Close to Tc when the correlation length becomes comparable to the film thickness there is a further crossover to a 2D Kosterlitz-Thouless transition, with a drop of the superfluid fraction to zero at T_KT which can be of the order of 1 K below T_c. Good agreement with this model is found for experiments on thin BSCCO 2212 films [2]. 1. S. R. Shenoy and B. Chattopadhyay, Phys. Rev. B 51, 9129 (1995). 2. K. Osborn et al., cond-mat/0204417.
Mechanical characterization of 2D, 2D stitched, and 3D braided/RTM materials
NASA Technical Reports Server (NTRS)
Deaton, Jerry W.; Kullerd, Susan M.; Portanova, Marc A.
1993-01-01
Braided composite materials have potential for application in aircraft structures. Fuselage frames, floor beams, wing spars, and stiffeners are examples where braided composites could find application if cost effective processing and damage tolerance requirements are met. Another important consideration for braided composites relates to their mechanical properties and how they compare to the properties of composites produced by other textile composite processes being proposed for these applications. Unfortunately, mechanical property data for braided composites do not appear extensively in the literature. Data are presented in this paper on the mechanical characterization of 2D triaxial braid, 2D triaxial braid plus stitching, and 3D (through-the-thickness) braid composite materials. The braided preforms all had the same graphite tow size and the same nominal braid architectures, (+/- 30 deg/0 deg), and were resin transfer molded (RTM) using the same mold for each of two different resin systems. Static data are presented for notched and unnotched tension, notched and unnotched compression, and compression after impact strengths at room temperature. In addition, some static results, after environmental conditioning, are included. Baseline tension and compression fatigue results are also presented, but only for the 3D braided composite material with one of the resin systems.