Two-dimensional lattice Boltzmann model for magnetohydrodynamics.
Schaffenberger, Werner; Hanslmeier, Arnold
2002-10-01
We present a lattice Boltzmann model for the simulation of two-dimensional magnetohydro dynamic (MHD) flows. The model is an extension of a hydrodynamic lattice Boltzman model with 9 velocities on a square lattice resulting in a model with 17 velocities. Earlier lattice Boltzmann models for two-dimensional MHD used a bidirectional streaming rule. However, the use of such a bidirectional streaming rule is not necessary. In our model, the standard streaming rule is used, allowing smaller viscosities. To control the viscosity and the resistivity independently, a matrix collision operator is used. The model is then applied to the Hartmann flow, giving reasonable results.
Institute of Scientific and Technical Information of China (English)
Xu Quan; Tian Qiang
2009-01-01
This paper discusses the two-dimensional discrete monatomic Fermi-Pasta-Ulam lattice, by using the method of multiple-scale and the quasi-discreteness approach. By taking into account the interaction between the atoms in the lattice and their nearest neighbours, it obtains some classes of two-dimensional local models as follows: two-dimensional bright and dark discrete soliton trains, two-dimensional bright and dark line discrete breathers, and two-dimensional bright and dark discrete breather.
Critical phenomena in the majority voter model on two-dimensional regular lattices.
Acuña-Lara, Ana L; Sastre, Francisco; Vargas-Arriola, José Raúl
2014-05-01
In this work we studied the critical behavior of the critical point as a function of the number of nearest neighbors on two-dimensional regular lattices. We performed numerical simulations on triangular, hexagonal, and bilayer square lattices. Using standard finite-size scaling theory we found that all cases fall in the two-dimensional Ising model universality class, but that the critical point value for the bilayer lattice does not follow the regular tendency that the Ising model shows.
Costanza, E. F.; Costanza, G.
2016-10-01
Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to two-dimensional lattices is described in detail in the case of a rectangular lattice. This example shows the general features that possess the procedure and extensions are also suggested in order to provide a wider insight in the present approach.
Quantum search on the two-dimensional lattice using the staggered model with Hamiltonians
Portugal, R.; Fernandes, T. D.
2017-04-01
Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk models to provide efficient algorithms from the theoretical side and means to implement quantum walks in laboratories from the practical side. In this paper, we rigorously prove that the recent-proposed staggered quantum walk model provides an efficient quantum search on the two-dimensional lattice, if the reflection operators associated with the graph tessellations are used as Hamiltonians, which is an important theoretical result for validating the staggered model with Hamiltonians. Numerical results show that on the two-dimensional lattice staggered models without Hamiltonians are not as efficient as the one described in this paper and are, in fact, as slow as classical random-walk-based algorithms.
Tensor renormalization group approach to two-dimensional classical lattice models.
Levin, Michael; Nave, Cody P
2007-09-21
We describe a simple real space renormalization group technique for two-dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement. In this sense, the technique can be thought of as a classical analogue of the density matrix renormalization group method. We demonstrate the method - which we call the tensor renormalization group method - by computing the magnetization of the triangular lattice Ising model.
Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models
Directory of Open Access Journals (Sweden)
Xuemei Gao
2014-01-01
Full Text Available The aim of this paper is to extend the lattice method proposed by Ritchken and Trevor (1999 for pricing American options with one-dimensional stochastic volatility models to the two-dimensional cases with strangle payoff. This proposed method is compared with the least square Monte-Carlo method via numerical examples.
Quantum Monte Carlo simulation of a two-dimensional Majorana lattice model
Hayata, Tomoya; Yamamoto, Arata
2017-07-01
We study interacting Majorana fermions in two dimensions as a low-energy effective model of a vortex lattice in two-dimensional time-reversal-invariant topological superconductors. For that purpose, we implement ab initio quantum Monte Carlo simulation to the Majorana fermion system in which the path-integral measure is given by a semipositive Pfaffian. We discuss spontaneous breaking of time-reversal symmetry at finite temperatures.
Heteroepitaxial growth modes with dislocations in a two-dimensional elastic lattice model
Katsuno, Hiroyasu; Uwaha, Makio; Saito, Yukio
2008-11-01
We study equilibrium shapes of adsorbate crystals by allowing a possibility of dislocations on an elastic substrate in a two-dimensional lattice model. The ground state energy is calculated numerically with the use of an elastic lattice Green's function. From the equilibrium shapes determined for various coverages, we infer the growth mode. As the misfit parameter increases, the growth mode changes from the Frank-van der Merwe (FM) to the Stranski-Krastanov (SK), further to the FM with dislocations for a parameter range of ordinary semiconductor materials. Conceivable growth modes such as the SK with dislocations appear in a parameter range between the SK and the FM with dislocations.
Costanza, E. F.; Costanza, G.
2016-12-01
Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to two-dimensional lattices is described in detail in the case of a triangular lattice. This example shows the general features that possess the procedure and extensions are also suggested in order to provide a wider insight in the present approach.
Costanza, E. F.; Costanza, G.
2017-02-01
Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to two-dimensional lattices is described in detail in the case of a hexagonal lattice which has the particular feature that need four types of dynamical variables. This example shows additional features to the general procedure and some extensions are also suggested in order to provide a wider insight in the present approach.
Hamiltonian dynamics of the two-dimensional lattice {phi}{sup 4} model
Energy Technology Data Exchange (ETDEWEB)
Caiani, Lando [Scuola Internazionale Superiore di Studi Avanzati (SISSA/ISAS), Trieste (Italy); Casetti, Lapo [Istituto Nazionale di Fisica della Materia (INFM), Unita di Ricerca del Politecnico di Torino, Dipartimento di Fisica, Politecnico di Torino, Turin (Italy); Pettini, Marco [Osservatorio Astrofisico di Arcetri, Florence (Italy)
1998-04-17
The Hamiltonian dynamics of the classical {phi}{sup 4} model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the presence of the continuous phase transition at a finite energy density and are consistent both qualitatively and quantitatively with the predictions of equilibrium statistical mechanics. The Hamiltonian microscopic dynamics also exhibits critical slowing down close to the transition. Moreover, the relationship between chaos and the phase transition is considered, and interpreted in the light of a geometrization of dynamics. (author)
Dual geometric worm algorithm for two-dimensional discrete classical lattice models
Hitchcock, Peter; Sørensen, Erik S.; Alet, Fabien
2004-07-01
We present a dual geometrical worm algorithm for two-dimensional Ising models. The existence of such dual algorithms was first pointed out by Prokof’ev and Svistunov [N. Prokof’ev and B. Svistunov, Phys. Rev. Lett. 87, 160601 (2001)]. The algorithm is defined on the dual lattice and is formulated in terms of bond variables and can therefore be generalized to other two-dimensional models that can be formulated in terms of bond variables. We also discuss two related algorithms formulated on the direct lattice, applicable in any dimension. These latter algorithms turn out to be less efficient but of considerable intrinsic interest. We show how such algorithms quite generally can be “directed” by minimizing the probability for the worms to erase themselves. Explicit proofs of detailed balance are given for all the algorithms. In terms of computational efficiency the dual geometrical worm algorithm is comparable to well known cluster algorithms such as the Swendsen-Wang and Wolff algorithms, however, it is quite different in structure and allows for a very simple and efficient implementation. The dual algorithm also allows for a very elegant way of calculating the domain wall free energy.
Two-Dimensional Toda-Heisenberg Lattice
Directory of Open Access Journals (Sweden)
Vadim E. Vekslerchik
2013-06-01
Full Text Available We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which is closely related to the Ablowitz-Ladik hierarchy, and derive its N-soliton solutions.
Duality and Fisher zeros in the two-dimensional Potts model on a square lattice.
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.
Non-equilibrium relaxation in a two-dimensional stochastic lattice Lotka-Volterra model
Chen, Sheng; Täuber, Uwe C.
We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. There are stable states when the predators and prey coexist. If the local prey carrying capacity is finite, there emerges an extinction threshold for the predator population at a critical value of the predation rate. We investigate the non-equilibrium relaxation of the predator density in the vicinity of this critical point. The expected power law dependence between the relaxation time and predation rate is observed (critical slowing down). The numerically determined associated critical exponents are in accord with the directed percolation universality class. Following a sudden predation rate change to its critical value, one observes critical aging for the predator density autocorrelation function with a universal scaling exponent. This aging scaling signature of the absorbing state phase transition emerges at significantly earlier times than stationary critical power laws, and could thus serve as an advanced indicator of the population's proximity to its extinction threshold. This research is supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award DE-FG02-09ER46613.
Two-dimensional-lattice spin models with long-range antiferromagnetic interactions
Romano, S.
1991-10-01
We consider a classical system, consisting of m-component unit vectors (m=2,3), associated with a two-dimensional lattice \\{uk||k∈openZ2\\} and interacting via translationally and rotationally invariant antiferromagnetic pair potentials of the long-range form W=Wjk=ɛ||xj-xk||-puj.uk, p>2, where ɛ is a positive quantity, setting energy and temperature scales (i.e., T*=kBT/ɛ), and xk are the coordinates of the lattice sites. A spin-wave approach predicts orientational disorder (in the thermodynamic limit) at all finite temperatures and for all p>2 this agrees with available rigorous results for p>=4, whereas no such theorems are known in the literature when 22.
Institute of Scientific and Technical Information of China (English)
XU Quan; TIAN Qiang
2007-01-01
Two-dimensional compact-like discrete breathers in discrete two-dimensional monatomic square lattices are investigated by discussing a generafized discrete two-dimensional monatomic model.It is proven that the twodimensional compact-like discrete breathers exist not only in two-dimensional soft Ф4 potentials but also in hard two-dimensional Ф4 potentials and pure two-dimensional K4 lattices.The measurements of the two-dimensional compact-like discrete breather cores in soft and hard two-dimensional Ф4 potential are determined by coupling parameter K4,while those in pure two-dimensional K4 lattices have no coupling with parameter K4.The stabilities of the two-dimensional compact-like discrete breathers correlate closely to the coupling parameter K4 and the boundary condition of lattices.
Phase diagram of the two-dimensional O(3) model from dual lattice simulations
Bruckmann, Falk; Kloiber, Thomas; Sulejmanpasic, Tin
2016-01-01
We have simulated the asymptotically free two-dimensional O(3) model at nonzero chemical potential using the model's dual representation. We first demonstrate how the latter solves the sign (complex action) problem. The system displays a crossover at nonzero temperature, while at zero temperature it undergoes a quantum phase transition when mu reaches the particle mass (generated dynamically similar to QCD). The density follows a square root behavior universal for repulsive bosons in one spatial dimension. We have also measured the spin stiffness, known to be sensitive to the spatial correlation length, using different scaling trajectories to zero temperature and infinite size. It points to a dynamical critical exponent z=2. Comparisons to thermodynamic Bethe ansaetze are shown as well.
Two-dimensional subwavelength plasmonic lattice solitons
Ye, F; Hu, B; Panoiu, N C
2010-01-01
We present a theoretical study of plasmonic lattice solitons (PLSs) formed in two-dimensional (2D) arrays of metallic nanowires embedded into a nonlinear medium with Kerr nonlinearity. We analyze two classes of 2D PLSs families, namely, fundamental and vortical PLSs in both focusing and defocusing media. Their existence, stability, and subwavelength spatial confinement are studied in detai
Spatiotemporal dissipative solitons in two-dimensional photonic lattices.
Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S
2008-11-01
We analyze spatiotemporal dissipative solitons in two-dimensional photonic lattices in the presence of gain and loss. In the framework of the continuous-discrete cubic-quintic Ginzburg-Landau model, we demonstrate the existence of novel classes of two-dimensional spatiotemporal dissipative lattice solitons, which also include surface solitons located in the corners or at the edges of the truncated two-dimensional photonic lattice. We find the domains of existence and stability of such spatiotemporal dissipative solitons in the relevant parameter space, for both on-site and intersite lattice solitons. We show that the on-site solitons are stable in the whole domain of their existence, whereas most of the intersite solitons are unstable. We describe the scenarios of the instability-induced dynamics of dissipative solitons in two-dimensional lattices.
Directory of Open Access Journals (Sweden)
U. Löw
2009-01-01
Full Text Available The magnetic properties of the two-dimensional S=1/2 (quantum antiferromagnetic Heisenberg model on a honeycomb lattice with and without interlayer coupling are studied by means of a continuous Euclidean time Quantum Monte-Carlo algorithm. The internal energy, the magnetic susceptibility and the staggered magnetization are determined in the full temperature range. For the two-dimensional system the ground-state energy/bond is found to be E0hc=-0.36303(13, and the zero temperature staggered magnetization mst=0.2681(8. For coupled planes of honeycomb systems a phase transition from an ordered phase to a disordered phase is found at T/J=0.695(10.
Two-dimensional lattice Boltzmann model for compressible flows with high Mach number
Gan, Yanbiao; Xu, Aiguo; Zhang, Guangcai; Yu, Xijun; Li, Yingjun
2008-03-01
In this paper we present an improved lattice Boltzmann model for compressible Navier-Stokes system with high Mach number. The model is composed of three components: (i) the discrete-velocity-model by M. Watari and M. Tsutahara [Phys. Rev. E 67 (2003) 036306], (ii) a modified Lax-Wendroff finite difference scheme where reasonable dissipation and dispersion are naturally included, (iii) artificial viscosity. The improved model is convenient to compromise the high accuracy and stability. The included dispersion term can effectively reduce the numerical oscillation at discontinuity. The added artificial viscosity helps the scheme to satisfy the von Neumann stability condition. Shock tubes and shock reflections are used to validate the new scheme. In our numerical tests the Mach numbers are successfully increased up to 20 or higher. The flexibility of the new model makes it suitable for tracking shock waves with high accuracy and for investigating nonlinear nonequilibrium complex systems.
General model for a entanglement-enhanced composed quantum game on a two-dimensional lattice
Miszczak, Jarosław Adam; Sładkowski, Jan
2013-01-01
We introduce a method of analyzing entanglement enhanced quantum games on regular lattices of agents. Our method is valid for setups with periodic and non-periodic boundary conditions. To demonstrate our approach we study two different types games, namely the prisoner's dilemma game and a cooperative Parrondo's game. In both cases we obtain results showing, that entanglement is a crucial resource necessary for the agents to achieve positive capital gain.
Institute of Scientific and Technical Information of China (English)
LI Hua-Bing; JIN Li; QIU Bing
2008-01-01
To study two-dimensional red blood cells deforming in a shear flow with the membrane nonuniform on the rigidity and mass, the membrane is discretized into equilength segments. The fluid inside and outside the red blood cell is simulated by the D2Q9 lattice Boltzmann model and the hydrodynamic forces exerted on the membrane from the inner and outer of the red blood cell are calculated by a stress-integration method. Through the global deviation from the curvature of uniform-membrane, we find that when the membrane is nonuniform on the rigidity, the deviation first decreases with the time increases and implies that the terminal profile of the red blood cell is static. To a red blood cell with the mass nonuniform on the membrane, the deviation becomes more large, and the mass distribution affects the profile of the two sides of the flattened red blood cell in a shear flow.
Two Dimensional Lattice Boltzmann Method for Cavity Flow Simulation
Directory of Open Access Journals (Sweden)
Panjit MUSIK
2004-01-01
Full Text Available This paper presents a simulation of incompressible viscous flow within a two-dimensional square cavity. The objective is to develop a method originated from Lattice Gas (cellular Automata (LGA, which utilises discrete lattice as well as discrete time and can be parallelised easily. Lattice Boltzmann Method (LBM, known as discrete Lattice kinetics which provide an alternative for solving the Navier–Stokes equations and are generally used for fluid simulation, is chosen for the study. A specific two-dimensional nine-velocity square Lattice model (D2Q9 Model is used in the simulation with the velocity at the top of the cavity kept fixed. LBM is an efficient method for reproducing the dynamics of cavity flow and the results which are comparable to those of previous work.
Two-dimensional O(3) model at nonzero density: From dual lattice simulations to repulsive bosons
Bruckmann, Falk; Gattringer, Christof; Kloiber, Thomas; Sulejmanpasic, Tin
2016-12-01
We discuss the thermodynamics of the O(3) nonlinear sigma model in 1 +1 dimensions at nonzero chemical potential (equivalent to a magnetic field). In its conventional field theory representation the model suffers from a sign problem. By dualizing the model, we are able to fully access the nonzero density regime of an asymptotically free theory with dynamical mass gap at arbitrary chemical potential values. We find a quantum phase transition at zero temperature where as a function of the chemical potential the density assumes a nonzero value. Measuring the spin stiffness we present evidence for a corresponding dynamical critical exponent z close to 2. The low energy O(3) model is conjectured to be described by a massive boson triplet with repulsive interactions. We confirm the universal square-root behavior expected for such a system at low density (and temperature) and compare our data to the results of Bethe Ansatz solutions of the relativistic and nonrelativistic one-dimensional Bose gas. We also comment on a potential Berezinskii-Kosterlitz-Thouless transition at nonzero density.
Energy Technology Data Exchange (ETDEWEB)
Babaev, A. B., E-mail: b-albert78@mail.ru; Magomedov, M. A.; Murtazaev, A. K. [Russian Academy of Sciences, Amirkhanov Institute of Physics, Dagestan Scientific Center (Russian Federation); Kassan-Ogly, F. A.; Proshkin, A. I. [Russian Academy of Sciences, Institute of Metal Physics, Ural Branch (Russian Federation)
2016-02-15
Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J{sub 1} and J{sub 2}, respectively. PTs in these models are analyzed for the ratio r = J{sub 2}/J{sub 1} of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J{sub 1} < 0 and J{sub 2} < 0 exhibits a first-order PT in the range of 0 ⩽ r < 0.2, whereas, in the interval 0.2 ⩽ r ⩽ 1.0, frustrations arise in the system. At the same time, for J{sub 1} > 0 and J{sub 2} < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ⩽ |r| ⩽ 1/3, the model exhibits a second-order PT.
Dielectric-barrier discharges in two-dimensional lattice potentials
Sinclair, Josiah
2011-01-01
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 under-fill 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.
Spatiotemporal surface solitons in two-dimensional photonic lattices.
Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S
2007-11-01
We analyze spatiotemporal light localization in truncated two-dimensional photonic lattices and demonstrate the existence of two-dimensional surface light bullets localized in the lattice corners or the edges. We study the families of the spatiotemporal surface solitons and their properties such as bistability and compare them with the modes located deep inside the photonic lattice.
2008-01-01
The exact partition function of the two-dimensional nearest neighbour Ising model pertaining to square lattices is derived for N sites in the case of a non-vanishing magnetic field.When the magnetic field is zero,the partition functions estimated from the present analysis are identical with those arising from Onsager's exact solution.
Electronic Transmission Properties of Two-Dimensional Quasi-Lattice
Institute of Scientific and Technical Information of China (English)
侯志林; 傅秀军; 刘有延
2002-01-01
In the framework of the tight binding model, the electronic transmission properties of two-dimensional Penrose lattices with free boundary conditions are studied using the generalized eigenfunction method (Phys. Rev. B 60(1999)13444). The electronic transmission coefficients for Penrose lattices with different sizes and widths are calculated, and the result shows strong energy dependence because of the quasiperiodic structure and quantum coherent effect. Around the Fermi level E = 0, there is an energy region with zero transmission amplitudes,which suggests that the studied systems are insulating. The spatial distributions of several typical electronic states with different transmission coefficients are plotted to display the propagation process.
Stress Wave Propagation in Two-dimensional Buckyball Lattice
Xu, Jun; Zheng, Bowen
2016-11-01
Orderly arrayed granular crystals exhibit extraordinary capability to tune stress wave propagation. Granular system of higher dimension renders many more stress wave patterns, showing its great potential for physical and engineering applications. At nanoscale, one-dimensionally arranged buckyball (C60) system has shown the ability to support solitary wave. In this paper, stress wave behaviors of two-dimensional buckyball (C60) lattice are investigated based on square close packing and hexagonal close packing. We show that the square close packed system supports highly directional Nesterenko solitary waves along initially excited chains and hexagonal close packed system tends to distribute the impulse and dissipates impact exponentially. Results of numerical calculations based on a two-dimensional nonlinear spring model are in a good agreement with the results of molecular dynamics simulations. This work enhances the understanding of wave properties and allows manipulations of nanoscale lattice and novel design of shock mitigation and nanoscale energy harvesting devices.
Pseudo-two-dimensional random dimer lattices
Energy Technology Data Exchange (ETDEWEB)
Naether, U., E-mail: naether@unizar.es [Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC – Universidad de Zaragoza, 50009 Zaragoza (Spain); Mejía-Cortés, C.; Vicencio, R.A. [Departamento de Física and MSI – Nucleus for Advanced Optics, Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago (Chile)
2015-06-05
We study the long-time wave transport in correlated and uncorrelated disordered 2D arrays. When a separation of dimensions is applied to the model, we find that the previously predicted 1D random dimer phenomenology also appears in so-called pseudo-2D arrays. Therefore, a threshold behavior is observed in terms of the effective size for eigenmodes, as well as in long-time dynamics. A minimum system size is required to observe this threshold, which is very important when considering a possible experimental realization. For the long-time evolution, we find that for correlated lattices a super-diffusive long-range transport is observed. For completely uncorrelated disorder 2D transport becomes sub-diffusive within the localization length and for random binary pseudo-2D arrays localization is observed.
2007-01-01
An explicit expression for the partition function of two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived by a systematic enumeration of all the spin configurations pertaining to a square lattice of sixteen sites. The critical temperature is shown to be in excellent agreement with the reported values while the corresponding dimensionless magnetic field is obtained as 0.004.
Two dimensional axisymmetric smooth lattice Ricci flow
Brewin, Leo
2015-01-01
A lattice based method will be presented for numerical investigations of Ricci flow. The method will be applied to the particular case of 2-dimensional axially symmetric initial data on manifolds with S^2 topology. Results will be presented that show that the method works well and agrees with results obtained using contemporary finite difference methods.
Almarza, N G; Pȩkalski, J; Ciach, A
2014-04-28
The triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion, introduced by Pȩkalski, Ciach, and Almarza [J. Chem. Phys. 140, 114701 (2014)] is studied by Monte Carlo simulation. Introduction of appropriate order parameters allowed us to construct a phase diagram, where different phases with patterns made of clusters, bubbles or stripes are thermodynamically stable. We observe, in particular, two distinct lamellar phases-the less ordered one with global orientational order and the more ordered one with both orientational and translational order. Our results concern spontaneous pattern formation on solid surfaces, fluid interfaces or membranes that is driven by competing interactions between adsorbing particles or molecules.
Logarithmic divergent thermal conductivity in two-dimensional nonlinear lattices.
Wang, Lei; Hu, Bambi; Li, Baowen
2012-10-01
Heat conduction in three two-dimensional (2D) momentum-conserving nonlinear lattices are numerically calculated via both nonequilibrium heat-bath and equilibrium Green-Kubo algorithms. It is expected by mainstream theories that heat conduction in such 2D lattices is divergent and the thermal conductivity κ increases with lattice length N logarithmically. Our simulations for the purely quartic lattice firmly confirm it. However, very robust finite-size effects are observed in the calculations for the other two lattices, which well explain some existing studies and imply the extreme difficulties in observing their true asymptotic behaviors with affordable computation resources.
Institute of Scientific and Technical Information of China (English)
XU Quan; TIAN Qiang
2009-01-01
We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for twodimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry's linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete twodimensional monatomic β-FPU lattice.
Topological states in two-dimensional hexagon lattice bilayers
Zhang, Ming-Ming; Xu, Lei; Zhang, Jun
2016-10-01
We investigate the topological states of the two-dimensional hexagon lattice bilayer. The system exhibits a quantum valley Hall (QVH) state when the interlayer interaction t⊥ is smaller than the nearest neighbor hopping energy t, and then translates to a trivial band insulator state when t⊥ / t > 1. Interestingly, the system is found to be a single-edge QVH state with t⊥ / t = 1. The topological phase transition also can be presented via changing bias voltage and sublattice potential in the system. The QVH states have different edge modes carrying valley current but no net charge current. The bias voltage and external electric field can be tuned easily in experiments, so the present results will provide potential application in valleytronics based on the two-dimensional hexagon lattice.
Vibrational Properties of a Two-Dimensional Silica Kagome Lattice.
Björkman, Torbjörn; Skakalova, Viera; Kurasch, Simon; Kaiser, Ute; Meyer, Jannik C; Smet, Jurgen H; Krasheninnikov, Arkady V
2016-12-27
Kagome lattices are structures possessing fascinating magnetic and vibrational properties, but in spite of a large body of theoretical work, experimental realizations and investigations of their dynamics are scarce. Using a combination of Raman spectroscopy and density functional theory calculations, we study the vibrational properties of two-dimensional silica (2D-SiO2), which has a kagome lattice structure. We identify the signatures of crystalline and amorphous 2D-SiO2 structures in Raman spectra and show that, at finite temperatures, the stability of 2D-SiO2 lattice is strongly influenced by phonon-phonon interaction. Our results not only provide insights into the vibrational properties of 2D-SiO2 and kagome lattices in general but also suggest a quick nondestructive method to detect 2D-SiO2.
Negative Dispersion of Lattice Waves in a Two-Dimensional Yukawa System
Institute of Scientific and Technical Information of China (English)
刘艳红; 刘斌; 杨思泽; 王龙
2002-01-01
Collective motion modes existing in a two-dimensional Yukawa system are investigated by molecular dynamics simulation. The dispersion relations of transverse and longitudinal lattice waves obtained for hexagonal lattice are in agreement with the theoretical results. The negative dispersion of the parallel longitudinal wave is demonstrated by the simulation, and is explained by a physical model.
Two-dimensional chiral topological superconductivity in Shiba lattices
Li, Jian; Neupert, Titus; Wang, Zhijun; MacDonald, A. H.; Yazdani, A.; Bernevig, B. Andrei
2016-07-01
The chiral p-wave superconductor is the archetypal example of a state of matter that supports non-Abelian anyons, a highly desired type of exotic quasiparticle. With this, it is foundational for the distant goal of building a topological quantum computer. While some candidate materials for bulk chiral superconductors exist, they are subject of an ongoing debate about their actual paring state. Here we propose an alternative route to chiral superconductivity, consisting of the surface of an ordinary superconductor decorated with a two-dimensional lattice of magnetic impurities. We furthermore identify a promising experimental platform to realize this proposal.
The characters of nonlinear vibration in the two-dimensional discrete monoatomic lattice
Institute of Scientific and Technical Information of China (English)
XU Quan; TIAN Qiang
2005-01-01
The two-dimensional discrete monoatomic lattice is analyzed. Taking nearest-neighbor interaction into account, the characters of the nonlinear vibration in two-dimensional discrete monoatomic lattice are described by the two-dimensional cubic nonlinear Schrodinger equation. Considering the quartic nonlinear potential, the two-dimensional discrete-soliton trains and the solutions perturbed by the neck mode are presented.
Many body localization in two dimensional square and triangular lattices
Gonzalez-Garcia, L; Paredes, R
2016-01-01
Ultracold interacting Bose atoms placed in disordered two dimensional optical lattices with square and triangular symmetries are found to be localized above a certain disorder strength amplitude. From a Gross-Pitaevskii mean analysis we determine the localization length as a function of the disorder strength and investigate the energy spectrum in terms of the disorder magnitude. We found that the localization length is observed to decrease faster in triangular geometries than in square ones. In the presence of a harmonic confinement localization is observed at the center of the trap. The analysis of the energy spectrum reveals that discrete energy levels acquire a finite width that is always smaller than the distance among energy levels.
Compact triplexer in two-dimensional hexagonal lattice photonic crystals
Institute of Scientific and Technical Information of China (English)
Hongliang Ren; Jianping Ma; Hao Wen; Yali Qin; Zhefu Wu; Weisheng Hu; Chun Jiang; Yaohui Jin
2011-01-01
We design a contpact triplexer based on two-dimensional (2D) hexagonal lattice photonic crystals (PCs). A folded directional coupler (FDC) is introduced in the triplexer beside the point-defect micro-cavities and line-defect waveguides. Because of the reflection feedback of the FDC, high channel drop efficiency can be realized and a compact size with the order of micrometers can be maintained. The proposed device is analyzed using the plane wave expansion method, and its transmission characteristics are calculated using the finites-difference time-domain method. The footprint of the triplexer is about 12× 9 μm, and its extinction ratios are less than -20 dB for 1310 nm, approximately -20 dB for 1490 nm, and under -4O dB for 1550 nm, making it a potentially essential device ii future fiber-to-the-home networks.%@@ We design a compact triplexer based on two-dimensional (2D) hexagonal lattice photonic crystals (PCs).A folded directional coupler (FDC) is introduced in the triplexer beside the point-defect micro-cavities and line-defect waveguides.Because of the reflection feedback of the FDC, high channel drop efficiency can be realized and a compact size with the order of micrometers can be maintained.The proposed device is analyzed using the plane wave expansion method, and its transmission characteristics are calculated using the finite-difference time-domain method.The footprint of the triplexer is about 12×9 μm, and its extinction ratios are less than -20 dB for 1310 nm, approximately -20 dB for 1490 nm, and under -40 dB for 1550 nm, making it a potentially essential device in future fiber-to-the-home networks.
Thermal diode from two-dimensional asymmetrical Ising lattices.
Wang, Lei; Li, Baowen
2011-06-01
Two-dimensional asymmetrical Ising models consisting of two weakly coupled dissimilar segments, coupled to heat baths with different temperatures at the two ends, are studied by Monte Carlo simulations. The heat rectifying effect, namely asymmetric heat conduction, is clearly observed. The underlying mechanisms are the different temperature dependencies of thermal conductivity κ at two dissimilar segments and the match (mismatch) of flipping frequencies of the interface spins.
Lattice gas dynamics: application to driven vortices in two dimensional superconductors.
Gotcheva, Violeta; Wang, Albert T J; Teitel, S
2004-06-18
A continuous time Monte Carlo lattice gas dynamics is developed to model driven steady states of vortices in two dimensional superconducting networks. Dramatic differences are found when compared to a simpler Metropolis dynamics. Subtle finite size effects are found at low temperature, with a moving smectic that becomes unstable to an anisotropic liquid on sufficiently large length scales.
Quantum computing via defect states in two-dimensional antidot lattices.
Flindt, Christian; Mortensen, Niels Asger; Jauho, Antti-Pekka
2005-12-01
We propose a new structure suitable for quantum computing in a solid-state environment: designed defect states in antidot lattices superimposed on a two-dimensional electron gas at a semiconductor heterostructure. State manipulation can be obtained with gate control. Model calculations indicate that it is feasible to fabricate structures whose energy level structure is robust against thermal dephasing.
Two-dimensional discrete gap breathers in a two-dimensional discrete diatomic Klein-Gordon lattice
Institute of Scientific and Technical Information of China (English)
XU Quan; QIANG Tian
2009-01-01
We study the existence and stability of two-dimensional discrete breathers in a two-dimensional discrete diatomic Klein-Gordon lattice consisting of alternating light and heavy atoms, with nearest-neighbor harmonic coupling.Localized solutions to the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum, i.e. two-dimensional gap breathers, are investigated numerically. The numerical results of the corresponding algebraic equations demonstrate the possibility of the existence of two-dimensional gap breathers with three types of symmetries, i.e., symmetric, twin-antisymmetric and single-antisymmetric. Their stability depends on the nonlinear on-site potential (soft or hard), the interaction potential (attractive or repulsive)and the center of the two-dimensional gap breather (on a light or a heavy atom).
Hofstadter butterfly evolution in the space of two-dimensional Bravais lattices
Yılmaz, F.; Oktel, M. Ö.
2017-06-01
The self-similar energy spectrum of a particle in a periodic potential under a magnetic field, known as the Hofstadter butterfly, is determined by the lattice geometry as well as the external field. Recent realizations of artificial gauge fields and adjustable optical lattices in cold-atom experiments necessitate the consideration of these self-similar spectra for the most general two-dimensional lattice. In a previous work [F. Yılmaz et al., Phys. Rev. A 91, 063628 (2015), 10.1103/PhysRevA.91.063628], we investigated the evolution of the spectrum for an experimentally realized lattice which was tuned by changing the unit-cell structure but keeping the square Bravais lattice fixed. We now consider all possible Bravais lattices in two dimensions and investigate the structure of the Hofstadter butterfly as the lattice is deformed between lattices with different point-symmetry groups. We model the optical lattice with a sinusoidal real-space potential and obtain the tight-binding model for any lattice geometry by calculating the Wannier functions. We introduce the magnetic field via Peierls substitution and numerically calculate the energy spectrum. The transition between the two most symmetric lattices, i.e., the triangular and the square lattices, displays the importance of bipartite symmetry featuring deformation as well as closing of some of the major energy gaps. The transitions from the square to rectangular lattice and from the triangular to centered rectangular lattices are analyzed in terms of coupling of one-dimensional chains. We calculate the Chern numbers of the major gaps and Chern number transfer between bands during the transitions. We use gap Chern numbers to identify distinct topological regions in the space of Bravais lattices.
Tunable band topology reflected by fractional quantum Hall States in two-dimensional lattices.
Wang, Dong; Liu, Zhao; Cao, Junpeng; Fan, Heng
2013-11-01
Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from the Hofstadter model and demonstrate that the band topology transitions can be realized by simply introducing tunable longer-range hopping. The rich phase diagram of band Chern numbers is obtained for the simple rational flux density and a classification of phases is presented. In the presence of interactions, the existence of fractional quantum Hall states in both |C| = 1 and |C| > 1 bands is confirmed, which can reflect the band topologies in different phases. In contrast, when our model reduces to a one-dimensional lattice, the ground states are crucially different from fractional quantum Hall states. Our results may provide insights into the study of new fractional quantum Hall states and experimental realizations of various topological phases in optical lattices.
The mean field study of phase transitions in two dimensional Kagome lattice under local anisotropy
Directory of Open Access Journals (Sweden)
S. Mortezapour
2007-06-01
Full Text Available In this work we investigated the critical properties of the anti-ferromagnetic XY model on a two dimensional Kagome lattice under single-ion easy-axes anisotropy. Employing the mean field theory, we found that this model shows a second order phase transition from disordered to all-in all-out state for any value of anisotropy.
Energy Technology Data Exchange (ETDEWEB)
Rubin, P., E-mail: rubin@fi.tartu.ee; Sherman, A.
2014-11-07
The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest-neighbor and antiferromagnetic third-nearest-neighbor exchange interactions, J{sub 1}=−(1−p)J and J{sub 2}=pJ, J>0(0≤p≤1), is studied with the use of the SPINPACK code. This model is applicable for the description of the magnetic properties of NiGa{sub 2}S{sub 4}. The ground, low-lying excited state energies and spin-spin correlation functions have been found for lattices with N=16 and N=20 sites with the periodic boundary conditions. These results are in qualitative agreement with earlier authors' results obtained with Mori's projection operator technique. - Highlights: • The S=1J{sub 1}–J{sub 3} Heisenberg model on a triangular lattice is studied. • The ferromagnetic nearest and AF 3rd-nearest-neighbor couplings are considered. • The exact diagonalization study of finite lattices was done. • The SPINPACK code using Lanczos' method is used for calculations. • The obtained results are in agreement with those obtained by Mori's approach.
Two-dimensional Chern semimetals on the Lieb lattice
Palumbo, Giandomenico; Meichanetzidis, Konstantinos
2015-12-01
In this work we propose a simple model that supports Chern semimetals. These gapless topological phases share several properties with the Chern insulators like a well-defined Chern number associated with each band, topologically protected edge states and topological phase transitions that occur when the bands touch each, with linear dispersion around the contact points. The tight-binding model, defined on the Lieb lattice with intra-unit-cell and suitable nearest-neighbor hopping terms between three different species of spinless fermions, supports a single Dirac-like point. The dispersion relation around this point is fully relativistic and the 3 ×3 matrices in the corresponding effective Hamiltonian satisfy the Duffin-Kemmer-Petiau algebra. We show the robustness of the topologically protected edge states by employing the entanglement spectrum. Moreover, we prove that the Chern number of the lowest band is robust with respect to weak disorder. For its simplicity, our model can be naturally implemented in real physical systems like cold atoms in optical lattices.
Two-dimensional lattice gauge theories with superconducting quantum circuits
Energy Technology Data Exchange (ETDEWEB)
Marcos, D., E-mail: david.marcos@me.com [Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Widmer, P. [Albert Einstein Center, Institute for Theoretical Physics, Bern University, CH-3012, Bern (Switzerland); Rico, E. [IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg (France); Hafezi, M. [Joint Quantum Institute, NIST/University of Maryland, College Park 20742 (United States); Department of Electrical Engineering and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742 (United States); Rabl, P. [Institute of Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020 Wien (Austria); Wiese, U.-J. [Albert Einstein Center, Institute for Theoretical Physics, Bern University, CH-3012, Bern (Switzerland); Zoller, P. [Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria)
2014-12-15
A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.
Configurational entropy of a set of dipoles placed on a two-dimensional lattice
Dammig Quiña, P. L.; Irurzun, I. M.; Mola, E. E.
2017-01-01
In the present work we calculate the configurational entropy of an arbitrary number of dipoles placed on a square lattice. We use a quasi-two-dimensional (Q2D) space to capture the main features determining the occupation statistics of this system. We show that our result is in agreement with both, lattice-gas predictions at low coverages and the exact value derived in the close-packed limit as well. Therefore our equation provides a substantial improvement to the most recent calculations based on semiempirical models and Monte Carlo simulations.
Boundaries determine the formation energies of lattice defects in two-dimensional buckled materials
Jain, Sandeep K.; Juričić, Vladimir; Barkema, Gerard T.
2016-07-01
Lattice defects are inevitably present in two-dimensional materials, with direct implications on their physical and chemical properties. We show that the formation energy of a lattice defect in buckled two-dimensional crystals is not uniquely defined as it takes different values for different boundary conditions even in the thermodynamic limit, as opposed to their perfectly planar counterparts. Also, the approach to the thermodynamic limit follows a different scaling: inversely proportional to the logarithm of the system size for buckled materials, rather than the usual power-law approach. In graphene samples of ˜1000 atoms, different boundary conditions can cause differences exceeding 10 eV. Besides presenting numerical evidence in simulations, we show that the universal features in this behavior can be understood with simple bead-spring models. Fundamentally, our findings imply that it is necessary to specify the boundary conditions for the energy of the lattice defects in the buckled two-dimensional crystals to be uniquely defined, and this may explain the lack of agreement in the reported values of formation energies in graphene. We argue that boundary conditions may also have an impact on other physical observables such as the melting temperature.
Phase Transitions in Two-Dimensional Traffic Flow Models
Cuesta, J A; Molera, J M; Cuesta, José A; Martinez, Froilán C; Molera, Juan M
1993-01-01
Abstract: We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a jammed state, with a critical point. The jammed phase presents new transitions corresponding to structural transformations of the jam. We discuss their relevance in the infinite size limit.
Phase Transitions in Two-Dimensional Traffic Flow Models
Cuesta, José A; Molera, Juan M; Escuela, Angel Sánchez; 10.1103/PhysRevE.48.R4175
2009-01-01
We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a jammed state, with a critical point. The jammed phase presents new transitions corresponding to structural transformations of the jam. We discuss their relevance in the infinite size limit.
Two-Dimensional Lattice Gravity as a Spin System
Beirl, W; Riedler, J
1994-01-01
Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin system with higher couplings on a Kagome lattice. Various measures acting as external field are considered. Extensions to matter fields and higher dimensions are discussed.
Li, Shuai; Qiu, Wen-Xuan; Gao, Jin-Hua
2016-07-07
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.
Tie, B.; Tian, B. Y.; Aubry, D.
2013-12-01
The elastic wave propagation phenomena in two-dimensional periodic beam lattices are studied by using the Bloch wave transform. The numerical modeling is applied to the hexagonal and the rectangular beam lattices, in which, both the in-plane (with respect to the lattice plane) and out-of-plane waves are considered. The dispersion relations are obtained by calculating the Bloch eigenfrequencies and eigenmodes. The frequency bandgaps are observed and the influence of the elastic and geometric properties of the primitive cell on the bandgaps is studied. By analyzing the phase and the group velocities of the Bloch wave modes, the anisotropic behaviors and the dispersive characteristics of the hexagonal beam lattice with respect to the wave propagation are highlighted in high frequency domains. One important result presented herein is the comparison between the first Bloch wave modes to the membrane and bending/transverse shear wave modes of the classical equivalent homogenized orthotropic plate model of the hexagonal beam lattice. It is shown that, in low frequency ranges, the homogenized plate model can correctly represent both the in-plane and out-of-plane dynamic behaviors of the beam lattice, its frequency validity domain can be precisely evaluated thanks to the Bloch modal analysis. As another important and original result, we have highlighted the existence of the retropropagating Bloch wave modes with a negative group velocity, and of the corresponding "retro-propagating" frequency bands.
DEFF Research Database (Denmark)
Nielsen, Morten; Miao, Ling; Ipsen, John Hjorth;
1996-01-01
In this work we concentrate on phase equilibria in two-dimensional condensed systems of particles where both translational and internal degrees of freedom are present and coupled through microscopic interactions, with a focus on the manner of the macroscopic coupling between the two types...
Optical properties of two-dimensional magnetoelectric point scattering lattices
DEFF Research Database (Denmark)
Hansen, Per Lunnemann; Sersic, Ivana; Koenderink, A. Femius
2013-01-01
of split ring resonators and provide a quantitative comparison of measured and calculated transmission spectra at normal incidence as a function of lattice density, showing excellent agreement. We further show angle-dependent transmission calculations for circularly polarized light and compare...
Hydration of an apolar solute in a two-dimensional waterlike lattice fluid.
Buzano, C; De Stefanis, E; Pretti, M
2005-05-01
In a previous work, we investigated a two-dimensional lattice-fluid model, displaying some waterlike thermodynamic anomalies. The model, defined on a triangular lattice, is now extended to aqueous solutions with apolar species. Water molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three equivalent bonding arms. Bond formation depends both on orientation and local density. The insertion of inert molecules displays typical signatures of hydrophobic hydration: large positive transfer free energy, large negative transfer entropy (at low temperature), strong temperature dependence of the transfer enthalpy and entropy, i.e., large (positive) transfer heat capacity. Model properties are derived by a generalized first order approximation on a triangle cluster.
Montgomery, R. C.; Sundararajan, N.
1984-01-01
The basic theory of least square lattice filters and their use in identification of structural dynamics systems is summarized. Thereafter, this theory is applied to a two-dimensional grid structure made of overlapping bars. Previously, this theory has been applied to an integral beam. System identification results are presented for both simulated and experimental tests and they are compared with those predicted using finite element modelling. The lattice filtering approach works well for simulated data based on finite element modelling. However, considerable discrepancy exists between estimates obtained from experimental data and the finite element analysis. It is believed that this discrepancy is the result of inadequacies in the finite element modelling to represent the damped motion of the laboratory apparatus.
Elastic models of defects in two-dimensional crystals
Kolesnikova, A. L.; Orlova, T. S.; Hussainova, I.; Romanov, A. E.
2014-12-01
Elastic models of defects in two-dimensional (2D) crystals are presented in terms of continuum mechanics. The models are based on the classification of defects, which is founded on the dimensionality of the specification region of their self-distortions, i.e., lattice distortions associated with the formation of defects. The elastic field of an infinitesimal dislocation loop in a film is calculated for the first time. The fields of the center of dilatation, dislocation, disclination, and circular inclusion in planar 2D elastic media, namely, nanofilms and graphenes, are considered. Elastic fields of defects in 2D and 3D crystals are compared.
Chern, Li Ern; Hwang, Kyusung; Mizoguchi, Tomonari; Huh, Yejin; Kim, Yong Baek
2017-07-01
The Kagome-lattice-based material, volborthite, Cu3V2O7(OH) 2.2 H2O , has been considered as a promising platform for discovery of unusual quantum ground states due to the frustrated nature of spin interaction. We explore possible quantum spin liquid and magnetically ordered phases in a two-dimensional nonsymmorphic lattice, which is described by the plane group p 2 g g , consistent with the spatial anisotropy of the spin model derived from density functional theory (DFT) for volborthite. Using the projective symmetry group (PSG) analysis and Schwinger boson mean field theory, we classify possible spin liquid phases with bosonic spinons and investigate magnetically ordered phases connected to such states. It is shown, in general, that only translationally invariant mean field spin liquid ansatzes are allowed in two-dimensional nonsymmorphic lattices. We study the mean field phase diagram of the DFT-derived spin model and find that possible quantum spin liquid phases are connected to two types of magnetically ordered phases, a coplanar incommensurate (q ,0 ) spiral order as the ground state and a closely competing coplanar commensurate (π ,π ) spin density wave order. In addition, periodicity enhancement of the two-spinon continuum, a consequence of symmetry fractionalization, is found in the spin liquid state connected to the (π ,π ) spin density wave order. We discuss relevance of these results to recent and future experiments on volborthite.
Larkin-Ovchinnikov phases in two-dimensional square lattices
Baarsma, J. E.; Törmä, P.
2016-10-01
We consider a two-component gas of fermions in optical lattices in the presence of a population imbalance within a mean-field theory. We study phase transitions from a normal gas of unpaired fermions to a superfluid phase of Bose-condensed Cooper pairs. The possibility of Cooper pairs with a nonzero centre-of-mass momentum is included, which corresponds to a so-called Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state. We find that for population-imbalanced systems such states can form the ground state. The FF and LO state are compared and it is shown that actually the LO state is energetically more favourable. We complete the mean-field phase diagram for the LO phase and show that it is qualitatively in excellent agreement with recent diagrammatic Monte Carlo calculations. Subsequently, we calculate the atomic density modulations in the LO phase.
Vector meson masses in two-dimensional SU(NC) lattice gauge theory with massive quarks
Institute of Scientific and Technical Information of China (English)
JIANG Jun-Qin
2008-01-01
Using an improved lattice Hamiltonian with massive Wilson quarks a variational method is applied to study the dependence of the vector meson mass Mv on the quark mass m and the Wilson parameter r in in the scaling window 1 ≤ 1/g2 ≤ 2, Mv/g is approximately linear in m, but Mv/g obviously does not depend on r (this differs from the quark condensate). Particularly for m → 0 our numerical results agree very well with Bhattacharya's analytical strong coupling result in the continuum, and the value of ((e)Mv/(e)m) |mm=0 in two-dimensional SU(NC) lattice gauge theory is very close to that in Schwinger model.
Two-dimensional ion trap lattice on a microchip for quantum simulation
Sterling, R C; Weidt, S; Lake, K; Srinivasan, P; Webster, S C; Kraft, M; Hensinger, W K
2013-01-01
Using a controllable quantum system it is possible to simulate other highly complex quantum systems efficiently overcoming an in-principle limitation of classical computing. Trapped ions constitute such a highly controllable quantum system. So far, no dedicated architectures for the simulation of two-dimensional spin lattices using trapped ions in radio-frequency ion traps have been produced, limiting the possibility of carrying out such quantum simulations on a large scale. We report the operation of a two-dimensional ion trap lattice integrated in a microchip capable of implementing quantum simulations of two-dimensional spin lattices. Our device provides a scalable microfabricated architecture for trapping such ion lattices with coupling strengths between neighbouring ions sufficient to provide a powerful platform for the implementation of quantum simulations. In order to realize this device we developed a specialist fabrication process that allows for the application of very large voltages. We fabricated ...
Bloch oscillations and Zener tunneling in two-dimensional photonic lattices.
Trompeter, Henrike; Krolikowski, Wieslaw; Neshev, Dragomir N; Desyatnikov, Anton S; Sukhorukov, Andrey A; Kivshar, Yuri S; Pertsch, Thomas; Peschel, Ulf; Lederer, Falk
2006-02-10
We report on the first experimental observation of photonic Bloch oscillations and Zener tunneling in two-dimensional periodic systems. We study the propagation of an optical beam in a square lattice superimposed on a refractive index ramp. We observe oscillations of the beam inside the first Brilloin zone and tunneling of light from the first to the higher-order bands of the lattice band gap spectrum.
Batrouni, George
2011-03-01
I will discuss pairing in fermionic systems in one- and two-dimensional optical lattices with population imbalance. This will be done in the context of the attractive fermionic Hubbard model using the Stochastic Green Function algorithm in d=1 while for d=2 we use Determinant Quantum Monte Carlo. This is the first exact QMC study examining the effects of finite temperature which is very important in experiments on ultra-cold atoms. Our results show that, in the ground state, the dominant pairing mechanism is at nonzero center of mass momentum, i.e. FFLO. I will then discuss the effect of finite temperature in the uniform and confined systems and present finite temperature phase diagrams. The numerical results will be compared with experiments. With M. J. Wolak (CQT, National University of Singapore) and V. G. Rousseau (Department of Physics and Astronomy, Louisiana State University).
Equation of State of the Two-Dimensional Hubbard Model
Cocchi, Eugenio; Miller, Luke A.; Drewes, Jan H.; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael
2016-04-01
The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0 ≲U /t ≲20 and temperatures, down to kBT /t =0.63 (2 ) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.
Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices
Energy Technology Data Exchange (ETDEWEB)
Rojas-Rojas, Santiago, E-mail: srojas@cefop.cl [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Naether, Uta [Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, 50009 Zaragoza (Spain); Delgado, Aldo [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Vicencio, Rodrigo A. [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago (Chile)
2016-09-16
Highlights: • We study discrete two-dimensional breathers in dipolar Bose–Einstein Condensates. • Important differences in the properties of three fundamental modes are found. • Norm threshold for existence of 2D breathers varies with dipolar interaction. • The Effective Potential Method is implemented for stability analysis. • Uncommon mobility of 2D discrete solitons is observed. - Abstract: We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model.
Topological phase transitions driven by next-nearest-neighbor hopping in two-dimensional lattices
Beugeling, W.; Everts, J.C.; de Morais Smith, C.
2012-01-01
For two-dimensional lattices in a tight-binding description, the intrinsic spin-orbit coupling, acting as a complex next-nearest-neighbor hopping, opens gaps that exhibit the quantum spin Hall effect. In this paper, we study the effect of a real next-nearest-neighbor hopping term on the band structu
Dipolar fermions in a two-dimensional lattice at non-zero temperature
DEFF Research Database (Denmark)
Larsen, Anne-Louise G.; Bruun, Georg
2012-01-01
We examine density-ordered and superfluid phases of fermionic dipoles in a two-dimensional square lattice at nonzero temperature. The critical temperature of the density-ordered phases is determined and is shown to be proportional to the coupling strength for strong coupling. We calculate...
Two-dimensional Talbot self-imaging via Electromagnetically induced lattice
Wen, Feng; Wang, Wei; Ahmed, Irfan; Wang, Hongxing; Zhang, Yiqi; Zhang, Yanpeng; Mahesar, Abdul Rasheed; Xiao, Min
2017-02-01
We propose a lensless optical method for imaging two-dimensional ultra-cold atoms (or molecules) in which the image can be non-locally observed by coincidence recording of entangled photon pairs. In particular, we focus on the transverse and longitudinal resolutions of images under various scanning methods. In addition, the role of the induced nonmaterial lattice on the image contrast is investigated. Our work shows a non-destructive and lensless way to image ultra-cold atoms or molecules that can be further used for two-dimensional atomic super-resolution optical testing and sub-wavelength lithography.
Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice
Institute of Scientific and Technical Information of China (English)
Yize Wang; Fengming Li; Yuesheng Wang; Kikuo Kishimoto; Wenhu Huang
2009-01-01
In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The gener-alized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet the-orem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the plane-wave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectric-ity with the larger lattice constant ratios and the filling frac-tions.
Robustness and breakup of the spiral wave in a two-dimensional lattice network of neurons
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The robustness and breakup of spiral wave in a two-dimensional lattice networks of neurons are investigated. The effect of small- world type connection is often simplified with local regular connection and the long-range connection with certain probability. The network effect on the development of spiral wave can be better described by local regular connection and changeable long-range connection probability than fixed long-range connection probability because the long-range probability could be changeable in realistic biological system. The effect from the changeable probability for long-range connection is simplified by multiplicative noise. At first, a stable rotating spiral wave is developed by using appropriate initial values, parameters and no-flux boundary conditions, and then the effect of networks is investigated. Extensive numerical studies show that spiral wave keeps its alive and robust when the intensity of multiplicative noise is below a certain threshold, otherwise, the breakup of spiral wave occurs. A statistical factor of synchronization in two-dimensional array is defined to study the phase transition of spiral wave by checking the membrane potentials of all neurons corresponding to the critical parameters(the intensity of noise or forcing current)in the curve for factor of synchronization. The Hindmarsh-Rose model is investigated, the Hodgkin-Huxley neuron model in the presence of the channel noise is also studied to check the model independence of our conclusions. And it is found that breakup of spiral wave is easier to be induced by the multiplicative noise in presence of channel noise.
Institute of Scientific and Technical Information of China (English)
Xu Quan; Tian Qiang
2013-01-01
Using numerical method,we investigate whether periodic,quasiperiodic,and chaotic breathers are supported by the two-dimensional discrete Fermi-Pasta-Ulam (FPU) lattice with linear dispersion term.The spatial profile and time evolution of the two-dimensional discrete β-FPU lattice are segregated by the method of separation of variables,and the numerical simulations suggest that the discrete breathers (DBs) are supported by the system.By introducing a periodic interaction into the linear interaction between the atoms,we achieve the coupling of two incommensurate frequencies for a single DB,and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system,too.
Non-classical photon correlation in a two-dimensional photonic lattice
Gao, Jun; Lin, Xiao-Feng; Jiao, Zhi-Qiang; Feng, Zhen; Zhou, Zheng; Gao, Zhen-Wei; Xu, Xiao-Yun; Chen, Yuan; Tang, Hao; Jin, Xian-Min
2016-01-01
Quantum interference and quantum correlation, as two main features of quantum optics, play an essential role in quantum information applications, such as multi-particle quantum walk and boson sampling. While many experimental demonstrations have been done in one-dimensional waveguide arrays, it remains unexplored in higher dimensions due to tight requirement of manipulating and detecting photons in large-scale. Here, we experimentally observe non-classical correlation of two identical photons in a fully coupled two-dimensional structure, i.e. photonic lattice manufactured by three-dimensional femtosecond laser writing. Photon interference consists of 36 Hong-Ou-Mandel interference and 9 bunching. The overlap between measured and simulated distribution is up to $0.890\\pm0.001$. Clear photon correlation is observed in the two-dimensional photonic lattice. Combining with controllably engineered disorder, our results open new perspectives towards large-scale implementation of quantum simulation on integrated phot...
Two-Dimensional Photonic Band-Gap Defect Modes with Deformed Lattice
Institute of Scientific and Technical Information of China (English)
CAI Xiang-Hua; ZHENG Wan-Hua; MA Xiao-Tao; REN Gang; XIA Jian-Bai
2005-01-01
@@ A numerical study of the defect modes in two-dimensional photonic crystals with deformed triangular lattice is presented by using the supercell method and the finite-difference time-domain method We find the stretch or shrink of the lattice can bring the change not only on the frequencies of the defect modes but also on their magnetic field distributions. We obtain the separation of the doubly degenerate dipole modes with the change of the lattice and find that both the stretch and the shrink of the lattice can make the dipole modes separate large enough to realize the single-mode emission. These results may be advantageous to the manufacture of photonic crystal lasers and provide a new way to realize the single-mode operation in photonic crystal lasers.
Institute of Scientific and Technical Information of China (English)
HOU Jing-Min
2009-01-01
We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagome optical lattice under an effective magnetic field,which can be realized with laser beams.We derive the generalized Harper's equations from the Schr(o)dinger equation.The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper's equations.We analyze the properties of the Hofstadter's butterfly spectrum and discuss its observability.
Closed-form evaluation of two-dimensional static lattice sums
Yakubovich, S.; Drygas, P.; Mityushev, V.
2016-11-01
Closed-form formulae for the conditionally convergent two-dimensional (2D) static lattice sums S2 (for conductivity) and T2 (for elasticity) are deduced in terms of the complete elliptic integrals of the first and second kind. The obtained formulae yield asymptotic analytical formulae for the effective tensors of 2D composites with circular inclusions up to the third order in concentration. Exact relations between S2 and T2 for different lattices are established. In particular, the value S2=π for the square and hexagonal arrays is discussed and T2=π/2 for the hexagonal is deduced.
Evans, J. W.; Nord, R. S.
1985-02-01
An analytic treatment of competitive, irreversible (immobile) random one-, two-, three-, . . . point adsorption (or monomer, dimer, trimer, . . . filling) on infinite, uniform two-dimensional lattices is provided by applying previously developed truncation schemes to the hierarchial form of the appropriate master equations. The behavior of these processes for two competing species is displayed by plotting families of ``filling trajectories'' in the partial-coverage plane for various ratios of adsorption rates. The time or coverage dependence of various subconfiguration probabilities can also be analyzed. For processes where no one-point (monomer) adsorption occurs, the lattice cannot fill completely; accurate estimates of the total (and partial) saturation coverages can be obtained.
Fundamental and vortex solitons in a two-dimensional optical lattice
Yang, J; Yang, Jianke; Musslimani, Ziad
2003-01-01
Fundamental and vortex solitons in a two-dimensional optically induced waveguide array are reported. In the strong localization regime, the fundamental soliton is largely confined to one lattice site, while the vortex state comprises of four fundamental modes superimposed in a square configuration with a phase structure that is topologically equivalent to the conventional vortex. However, in the weak localization regime, both the fundamental and vortex solitons spread over many lattice sites. We further show that fundamental and vortex solitons are stable against small perturbations in the strong localization regime.
Chremmos, Ioannis; Giamalaki, Melpomeni; Yannopapas, Vassilios; Paspalakis, Emmanuel
2014-01-01
We present a formulation for deriving effective medium properties of infinitely periodic two-dimensional metamaterial lattice structures beyond the static and quasi-static limits. We utilize the multipole expansions, where the polarization currents associated with the supported Bloch modes are expressed via the electric dipole, magnetic dipole, and electric quadrupole moments per unit length. We then propose a method to calculate the Bloch modes based on the lattice geometry and individual unit element structure. The results revert to well-known formulas in the quasistatic limit and are useful for the homogenization of nanorod-type metamaterials which are frequently used in optical applications.
Extending models for two-dimensional constraints
DEFF Research Database (Denmark)
Forchhammer, Søren
2009-01-01
Random fields in two dimensions may be specified on 2 times 2 elements such that the probabilities of finite configurations and the entropy may be calculated explicitly. The Pickard random field is one example where probability of a new (non-boundary) element is conditioned on three previous...... elements. To extend the concept we consider extending such a field such that a vector or block of elements is conditioned on a larger set of previous elements. Given a stationary model defined on 2 times 2 elements, iterative scaling is used to define the extended model. The extended model may be used...
Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model
Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; Neupert, Titus; Maciejko, Joseph
2016-08-01
We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1 /2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d -density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state—protected by time-reversal and reflection symmetries—cannot be connected adiabatically to a free-fermion topological phase.
Peto, Myron; Sen, Taner Z.; Jernigan, Robert L.; Kloczkowski, Andrzej
2007-07-01
We enumerated all compact conformations within simple geometries on the two-dimensional (2D) triangular and three-dimensional (3D) face centered cubic (fcc) lattice. These compact conformations correspond mathematically to Hamiltonian paths and Hamiltonian circuits and are frequently used as simple models of proteins. The shapes that were studied for the 2D triangular lattice included m ×n parallelograms, regular equilateral triangles, and various hexagons. On the 3D fcc lattice we generated conformations for a limited class of skewed parallelepipeds. Symmetries of the shape were exploited to reduce the number of conformations. We compared surface to volume ratios against protein length for compact conformations on the 3D cubic lattice and for a selected set of real proteins. We also show preliminary work in extending the transfer matrix method, previously developed by us for the 2D square and the 3D cubic lattices, to the 2D triangular lattice. The transfer matrix method offers a superior way of generating all conformations within a given geometry on a lattice by completely avoiding attrition and reducing this highly complicated geometrical problem to a simple algebraic problem of matrix multiplication.
Peto, Myron; Sen, Taner Z; Jernigan, Robert L; Kloczkowski, Andrzej
2007-07-28
We enumerated all compact conformations within simple geometries on the two-dimensional (2D) triangular and three-dimensional (3D) face centered cubic (fcc) lattice. These compact conformations correspond mathematically to Hamiltonian paths and Hamiltonian circuits and are frequently used as simple models of proteins. The shapes that were studied for the 2D triangular lattice included mxn parallelograms, regular equilateral triangles, and various hexagons. On the 3D fcc lattice we generated conformations for a limited class of skewed parallelepipeds. Symmetries of the shape were exploited to reduce the number of conformations. We compared surface to volume ratios against protein length for compact conformations on the 3D cubic lattice and for a selected set of real proteins. We also show preliminary work in extending the transfer matrix method, previously developed by us for the 2D square and the 3D cubic lattices, to the 2D triangular lattice. The transfer matrix method offers a superior way of generating all conformations within a given geometry on a lattice by completely avoiding attrition and reducing this highly complicated geometrical problem to a simple algebraic problem of matrix multiplication.
DISCRETE MODELLING OF TWO-DIMENSIONAL LIQUID FOAMS
Institute of Scientific and Technical Information of China (English)
Qicheng Sun
2003-01-01
Liquid foam is a dense random packing of gas or liquid bubbles in a small amount of immiscible liquid containing surfactants. The liquid within the Plateau borders, although small in volume, causes considerable difficulties to the investigation of the spatial structure and physical properties of foams, and the situation becomes even more complicated as the fluid flows. To solve these problems, a discrete model of two-dimensional liquid foams on the bubble scale is proposed in this work. The bubble surface is represented with finite number of nodes, and the liquid within Plateau borders is discretized into lattice particles. The gas in bubbles is treated as ideal gas at constant temperatures. This model is tested by choosing an arbitrary shape bubble as the initial condition. This then automatically evolves into a circular shape, which indicates that the surface energy minimum routine is obeyed without calling external controlling conditions. Without inserting liquid particle among the bubble channels, periodic ordered and disordered dry foams are both simulated, and the fine foam structures are developed. Wet foams are also simulated by inserting fluid among bubble channels. The calculated coordination number, as a function of liquid fractions, agrees well with the standard values.
Quantum State Transfer in a Two-dimensional Regular Spin Lattice of Triangular Shape
Miki, Hiroshi; Vinet, Luc; Zhedanov, Alexei
2012-01-01
Quantum state transfer in a triangular domain of a two-dimensional, equally-spaced, spin lat- tice with non-homogeneous nearest-neighbor couplings is analyzed. An exact solution of the one- excitation dynamics is provided in terms of 2-variable Krawtchouk orthogonal polynomials that have been recently defined. The probability amplitude for an excitation to transit from one site to another is given. For some values of the parameters, perfect transfer is shown to take place from the apex of the lattice to the boundary hypotenuse.
Peng-Jen Chen; Horng-Tay Jeng
2016-01-01
A new semiconducting phase of two-dimensional phosphorous in the Kagome lattice is proposed from first-principles calculations. The band gaps of the monolayer (ML) and bulk Kagome phosphorous (Kagome-P) are 2.00 and 1.11 eV, respectively. The magnitude of the band gap is tunable by applying the in-plane strain and/or changing the number of stacking layers. High optical absorption coefficients at the visible light region are predicted for multilayer Kagome-P, indicating potential applications ...
Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice
Giguère, Eric
2015-01-01
We perform lattice simulations of two-dimensional supersymmetric Yang-Mills theory with sixteen supercharges with a lattice action which has two exact supercharges (Sugino lattice action). According to the gauge/gravity duality, the theory at finite temperature is expected to be well described by the corresponding black 1-branes, at low temperature in the large N limit. We aim to confirm the duality conjecture by comparing the lattice results with the theoretical predictions obtained in the gravity side. In this article, at the beginning of this study, we examine the supersymmetric Ward-Takahashi identity to test whether the lattice action reproduces the correct continuum theory. Numerical results of the SUSY WTI strongly suggest us that any cut-off effects, which break supersymmetry, disappear in the continuum limit. In addition, we study the issue of degenerate vacua and find that the admissiblilty condition or any other constraints of the link fields which guarantee the unique vacuum are not always needed.
Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice
Energy Technology Data Exchange (ETDEWEB)
Giguère, Eric [Department of Physics, University of Hokkaido,Sapporo, Hokkaido 060-0810 (Japan); Kadoh, Daisuke [KEK Theory Center, High Energy Accelerator Research Organization (KEK),Tsukuba, Ibaraki 305-0801 (Japan)
2015-05-18
We perform lattice simulations of two-dimensional supersymmetric Yang-Mills theory with sixteen supercharges with a lattice action which has two exact supercharges (Sugino lattice action). According to the gauge/gravity duality, the theory at finite temperature is expected to be well described by the corresponding black 1-branes, at low temperature in the large N limit. We aim to confirm the duality conjecture by comparing the lattice results with the theoretical predictions obtained in the gravity side. In this article, at the beginning of this study, we examine the supersymmetric Ward-Takahashi identity to test whether the lattice action reproduces the correct continuum theory. Numerical results of the SUSY WTI strongly suggest us that any cut-off effects, which break supersymmetry, disappear in the continuum limit. In addition, we study the issue of degenerate vacua and find that the admissiblilty condition or any other constraints of the link fields which guarantee the unique vacuum are not always needed.
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.
1998-01-01
The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either...
Entanglement entropy for a Maxwell field: Numerical calculation on a two dimensional lattice
Casini, Horacio
2014-01-01
We study entanglement entropy (EE) for a Maxwell field in 2+1 dimensions. We do numerical calculations in two dimensional lattices. This gives a concrete example of the general results of our recent work on entropy for lattice gauge fields using an algebraic approach. To evaluate the entropies we extend the standard calculation methods for the entropy of Gaussian states in canonical commutation algebras to the more general case of algebras with center and arbitrary numerical commutators. We find that while the entropy depends on the details of the algebra choice, mutual information has a well defined continuum limit. We study several universal terms for the entropy of the Maxwell field and compare with the case of a massless scalar field. We find some interesting new phenomena: An "evanescent" logarithmically divergent term in the entropy with topological coefficient which does not have any correspondence with ultraviolet entanglement in the universal quantities, and a non standard way in which strong subaddi...
Competitive irreversible random one-, two-, three-,. point adsorption on two-dimensional lattices
Energy Technology Data Exchange (ETDEWEB)
Evans, J.W.; Nord, R.S.
1985-02-15
An analytic treatment of competitive, irreversible (immobile) random one-, two-, three-, . . . point adsorption (or monomer, dimer, trimer, . . . filling) on infinite, uniform two-dimensional lattices is provided by applying previously developed truncation schemes to the hierarchial form of the appropriate master equations. The behavior of these processes for two competing species is displayed by plotting families of ''filling trajectories'' in the partial-coverage plane for various ratios of adsorption rates. The time or coverage dependence of various subconfiguration probabilities can also be analyzed. For processes where no one-point (monomer) adsorption occurs, the lattice cannot fill completely; accurate estimates of the total (and partial) saturation coverages can be obtained.
Spin superconductivity in the frustrated two-dimensional antiferromagnet in the square lattice
Lima, L. S.
2017-02-01
We use the SU(2) Schwinger boson formalism to study the spin transport in the two-dimensional S = 1 / 2 frustrated Heisenberg antiferromagnet in a square lattice, considering the second-neighbors interactions in the diagonal. We have obtained a spin superfluid behavior for the spin transport to this system similar to obtained recently to the triangular lattice. We consider an antiferromagnetic inter-chain coupling on the diagonal, J2 > 0 , and the nearest-neighbor coupling antiferromagnetic J1 > 0 . We also have in the critical temperature T0, where the correlation length ξ → 0 , that the system suffers a transition from an ordered ground state to a disordered ground state.
Michel, K. H.; ćakır, D.; Sevik, C.; Peeters, F. M.
2017-03-01
The elastic constant C11 and piezoelectric stress constant e1 ,11 of two-dimensional (2D) dielectric materials comprising h-BN, 2 H -MoS2 , and other transition-metal dichalcogenides and dioxides are calculated using lattice dynamical theory. The results are compared with corresponding quantities obtained with ab initio calculations. We identify the difference between clamped-ion and relaxed-ion contributions with the dependence on inner strains which are due to the relative displacements of the ions in the unit cell. Lattice dynamics allows us to express the inner-strain contributions in terms of microscopic quantities such as effective ionic charges and optoacoustical couplings, which allows us to clarify differences in the piezoelectric behavior between h-BN and MoS2. Trends in the different microscopic quantities as functions of atomic composition are discussed.
Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices.
Chong, C; Kevrekidis, P G; Ablowitz, M J; Ma, Yi-Ping
2016-01-01
Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. For weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. The transition between these two types of propagation is explored.
Chen, Yi-Chung; Yossifon, Gilad; Yang, Ya-Tang
2016-11-01
Photothermal convection has been a major obstacle for stable particle trapping in plasmonic optical tweezer at high optical power. Here, we demonstrate a strategy to suppress the plasmonic photothermal convection by using vanishingly small thermal expansion coefficient of water at low temperature. A simple square nanoplasmonic array is illuminated with a loosely Gaussian beam to produce a two dimensional optical lattice for trapping of micro particles. We observe stable particle trapping due to near-field optical gradient forces at elevated optical power at low temperature. In contrast, for the same optical power at room temperature, the particles are convected away from the center of the optical lattice without their accumulation. This technique will greatly increase usable optical power and enhance the trapping capability of plasmonic optical tweezer.
An improvement of the lattice theory of dislocation for a two-dimensional triangular crystal
Institute of Scientific and Technical Information of China (English)
Wang Shao-Feng
2005-01-01
The structure of dislocation in a two-dimensional triangular crystal has been studied theoretically on the basis of atomic interaction and lattice statics. The theory presented in this paper is an improvement to that published previously.Within a reasonable interaction approximation, a new dislocation equation is obtained, which remedies a fault existing in the lattice theory of dislocation. A better simplification of non-diagonal terms of the kernel is given. The solution of the new dislocation equation asymptotically becomes the same as that obtained in the elastic theory, and agrees with experimental data. It is found that the solution is formally identical with that proposed phenomenologically by Foreman et al, where the parameter can be chosen freely, but cannot uniquely determined from theory. Indeed, if the parameter in the expression of the solution is selected suitably, the expression can be well applied to describe the fine structure of the dislocation.
Cluster algorithm for two-dimensional U(1) lattice gauge theory
Sinclair, R.
1992-03-01
We use gauge fixing to rewrite the two-dimensional U(1) pure gauge model with Wilson action and periodic boundary conditions as a nonfrustrated XY model on a closed chain. The Wolff single-cluster algorithm is then applied, eliminating critical slowing down of topological modes and Polyakov loops.
Long-range ferrimagnetic order in a two-dimensional supramolecular Kondo lattice
Girovsky, Jan; Nowakowski, Jan; Ali, Md. Ehesan; Baljozovic, Milos; Rossmann, Harald R.; Nijs, Thomas; Aeby, Elise A.; Nowakowska, Sylwia; Siewert, Dorota; Srivastava, Gitika; Wäckerlin, Christian; Dreiser, Jan; Decurtins, Silvio; Liu, Shi-Xia; Oppeneer, Peter M.; Jung, Thomas A.; Ballav, Nirmalya
2017-05-01
Realization of long-range magnetic order in surface-supported two-dimensional systems has been challenging, mainly due to the competition between fundamental magnetic interactions as the short-range Kondo effect and spin-stabilizing magnetic exchange interactions. Spin-bearing molecules on conducting substrates represent a rich platform to investigate the interplay of these fundamental magnetic interactions. Here we demonstrate the direct observation of long-range ferrimagnetic order emerging in a two-dimensional supramolecular Kondo lattice. The lattice consists of paramagnetic hexadeca-fluorinated iron phthalocyanine (FeFPc) and manganese phthalocyanine (MnPc) molecules co-assembled into a checkerboard pattern on single-crystalline Au(111) substrates. Remarkably, the remanent magnetic moments are oriented in the out-of-plane direction with significant contribution from orbital moments. First-principles calculations reveal that the FeFPc-MnPc antiferromagnetic nearest-neighbour coupling is mediated by the Ruderman-Kittel-Kasuya-Yosida exchange interaction via the Au substrate electronic states. Our findings suggest the use of molecular frameworks to engineer novel low-dimensional magnetically ordered materials and their application in molecular quantum devices.
Long-range ferrimagnetic order in a two-dimensional supramolecular Kondo lattice.
Girovsky, Jan; Nowakowski, Jan; Ali, Md Ehesan; Baljozovic, Milos; Rossmann, Harald R; Nijs, Thomas; Aeby, Elise A; Nowakowska, Sylwia; Siewert, Dorota; Srivastava, Gitika; Wäckerlin, Christian; Dreiser, Jan; Decurtins, Silvio; Liu, Shi-Xia; Oppeneer, Peter M; Jung, Thomas A; Ballav, Nirmalya
2017-05-22
Realization of long-range magnetic order in surface-supported two-dimensional systems has been challenging, mainly due to the competition between fundamental magnetic interactions as the short-range Kondo effect and spin-stabilizing magnetic exchange interactions. Spin-bearing molecules on conducting substrates represent a rich platform to investigate the interplay of these fundamental magnetic interactions. Here we demonstrate the direct observation of long-range ferrimagnetic order emerging in a two-dimensional supramolecular Kondo lattice. The lattice consists of paramagnetic hexadeca-fluorinated iron phthalocyanine (FeFPc) and manganese phthalocyanine (MnPc) molecules co-assembled into a checkerboard pattern on single-crystalline Au(111) substrates. Remarkably, the remanent magnetic moments are oriented in the out-of-plane direction with significant contribution from orbital moments. First-principles calculations reveal that the FeFPc-MnPc antiferromagnetic nearest-neighbour coupling is mediated by the Ruderman-Kittel-Kasuya-Yosida exchange interaction via the Au substrate electronic states. Our findings suggest the use of molecular frameworks to engineer novel low-dimensional magnetically ordered materials and their application in molecular quantum devices.
Dipolar matter-wave solitons in two-dimensional anisotropic discrete lattices
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.
Bandgaps and directional properties of two-dimensional square beam-like zigzag lattices
Energy Technology Data Exchange (ETDEWEB)
Wang, Yan-Feng; Wang, Yue-Sheng, E-mail: yswang@bjtu.edu.cn [Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044 (China); Zhang, Chuanzeng [Department of Civil Engineering, University of Siegen, Siegen 57068 (Germany)
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.
Magnetic properties of two dimensional silicon carbide triangular nanoflakes-based kagome lattices
Energy Technology Data Exchange (ETDEWEB)
Li Xiaowei [Peking University, Center for Applied Physics and Technology, College of Engineering (China); Zhou Jian [Peking University, Department of Materials Science and Engineering (China); Wang Qian, E-mail: qianwang2@pku.edu.cn [Peking University, Center for Applied Physics and Technology, College of Engineering (China); Jena, Puru [Virginia Commonwealth University, Department of Physics (United States)
2012-08-15
Two-dimensional (2D) magnetic kagome lattices are constructed using silicon carbide triangular nanoflakes (SiC-TNFs). Two types of structures with alternating Si and C atoms are studied: the first one is constructed using the C-edged SiC-TNFs as the building blocks and C atoms as the linkers of kagome sites (TNF{sub N}-C-TNF{sub N}) while the second one is composed of the Si-edged SiC-TNFs with Si atoms as linkers (TNF{sub N}-Si-TNF{sub N}). Using density functional theory-based calculations, we show that the fully relaxed TNF{sub N}-C-TNF{sub N} retains the morphology of regular kagome lattice and is ferromagnetism. On the other hand, the TNF{sub N}-Si-TNF{sub N} structure is deformed and antiferromagnetic. However, the ground state of TNF{sub N}-Si-TNF{sub N} structure can be transformed from the antiferromagnetic to ferromagnetic state by applying tensile strain. Monte Carlo simulations indicate that the SiC-TNFs-based kagome lattices can be ferromagnetic at room temperature.
Dai, Jian; Song, Xing-Chang
2001-07-01
One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as `natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices.
Diaz-Valencia, B. F.; Calero, J. M.
2017-02-01
In this work, we use the plane wave expansion method to calculate photonic band structures in two-dimensional photonic crystals which consist of high-temperature superconducting hollow rods arranged in a triangular lattice. The variation of the photonic band structure with respect to both, the inner radius and the system temperature, is studied, taking into account temperatures below the critical temperature of the superconductor in the low frequencies regime and assuming E polarization of the incident light. Permittivity contrast and nontrivial geometry of the hollow rods lead to the appearance of new band gaps as compared with the case of solid cylinders. Such band gaps can be modulated by means of the inner radius and system temperature.
Two-dimensional novel optical lattices with multi-well traps for cold atoms or molecules
Institute of Scientific and Technical Information of China (English)
Junfa Lu; Xianming Ji; Jianping Yin
2006-01-01
We propose some new schemes to constitute two-dimensional (2D) array of multi-well optical dipole traps for cold atoms (or molecules) by using an optical system consisting of a binary π-phase grating and a 2D array of rectangle microlens. We calculate the intensity distribution of each optical well in 2D array of multi-well traps and its geometric parameters and so on. The proposed 2D array of multi-well traps can be used to form novel 2D optical lattices with cold atoms (or molecules), and form various novel optical crystals with cold atoms (or molecules), or to perform quantum computing and quantum information processing on an atom chip, even to realize an array of all-optical multi-well atomic (or molecular) BoseEinstein condensates (BECs) on an all-optical integrated atom (or molecule) chip.
Energy Technology Data Exchange (ETDEWEB)
Budantsev, M. V., E-mail: budants@isp.nsc.ru; Lavrov, R. A.; Pogosov, A. G.; Zhdanov, E. Yu.; Pokhabov, D. A. [Russian Academy of Sciences, Rzhanov Institute of Semiconductor Physics, Siberian Branch (Russian Federation)
2011-02-15
Extraordinary piecewise parabolic behavior of the magnetoresistance has been experimentally detected in the two-dimensional electron gas with a dense triangular lattice of antidots, where commensurability magnetoresistance oscillations are suppressed. The magnetic field range of 0-0.6 T can be divided into three wide regions, in each of which the magnetoresistance is described by parabolic dependences with high accuracy (comparable to the experimental accuracy) and the transition regions between adjacent regions are much narrower than the regions themselves. In the region corresponding to the weakest magnetic fields, the parabolic behavior becomes almost linear. The observed behavior is reproducible as the electron gas density changes, which results in a change in the resistance by more than an order of magnitude. Possible physical mechanisms responsible for the observed behavior, including so-called 'memory effects,' are discussed.
Dynamical phase transitions in the two-dimensional ANNNI model
Energy Technology Data Exchange (ETDEWEB)
Barber, M.N.; Derrida, B.
1988-06-01
We study the phase diagram of the two-dimensional anisotropic next-nearest neighbor Ising (ANNNI) model by comparing the time evolution of two distinct spin configurations submitted to the same thermal noise. We clearly se several dynamical transitions between ferromagnetic, paramagnetic, antiphase, and floating phases. These dynamical transitions seem to occur rather close to the transition lines determined previously in the literature.
Two-dimensional effects in nonlinear Kronig-Penney models
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Christiansen, Peter Leth; Rasmussen, Kim
1997-01-01
An analysis of two-dimensional (2D) effects in the nonlinear Kronig-Penney model is presented. We establish an effective one-dimensional description of the 2D effects, resulting in a set of pseudodifferential equations. The stationary states of the 2D system and their stability is studied...
Branes and integrable lattice models
Yagi, Junya
2016-01-01
This is a brief review of my work on the correspondence between four-dimensional $\\mathcal{N} = 1$ supersymmetric field theories realized by brane tilings and two-dimensional integrable lattice models. I explain how to construct integrable lattice models from extended operators in partially topological quantum field theories, and elucidate the correspondence as an application of this construction.
Universality class of the two-dimensional site-diluted Ising model.
Martins, P H L; Plascak, J A
2007-07-01
In this work, we evaluate the probability distribution function of the order parameter for the two-dimensional site-diluted Ising model. Extensive Monte Carlo simulations have been performed for different spin concentrations p (0.70universality class of the diluted Ising model seems to be independent of the amount of dilution. Logarithmic corrections of the finite-size critical temperature behavior of the model can also be inferred even for such small lattices.
Two-dimensional model of elastically coupled molecular motors
Institute of Scientific and Technical Information of China (English)
Zhang Hong-Wei; Wen Shu-Tang; Chen Gai-Rong; Li Yu-Xiao; Cao Zhong-Xing; Li Wei
2012-01-01
A flashing ratchet model of a two-headed molecular motor in a two-dimensional potential is proposed to simulate the hand-over-hand motion of kinesins.Extensive Langevin simulations of the model are performed.We discuss the dependences of motion and efficiency on the model parameters,including the external force and the temperature.A good qualitative agreement with the expected behavior is observed.
Towards a two dimensional model of surface piezoelectricity
Monge Víllora, Oscar
2016-01-01
We want to understand the behaviour of flexoelectricity and surface piezoelectricity and distinguish them in order to go deep into the controversies of the filed. This motivate the construction of a model of continuum flexoelectric theory. The model proposed is a two-dimensional model that integrates the electromechanical equations that include the elastic, dielectric, piezoelectric and flexoelectric effect on a rectangular sample. As the flexoelectric and the surface piezoelectric effects ap...
The exact interface model for wetting in the two-dimensional Ising model
Upton, P. J.
2002-01-01
We use exact methods to derive an interface model from an underlying microscopic model, i.e., the Ising model on a square lattice. At the wetting transition in the two-dimensional Ising model, the long Peierls contour (or interface) gets depinned from the substrate. Using exact transfer-matrix methods, we find that on sufficiently large length scales (i.e., length scales sufficiently larger than the bulk correlation length) the distribution of the long contour is given by a unique probability...
Creating tuneable microwave media from a two-dimensional lattice of re-entrant posts
Goryachev, Maxim; Tobar, Michael E.
2015-11-01
The potential capabilities of resonators based on two dimensional arrays of re-entrant posts is demonstrated. Such posts may be regarded as magnetically coupled lumped element microwave harmonic oscillators, arranged in a 2D lattices structure, which is enclosed in a 3D cavity. By arranging these elements in certain 2D patterns, we demonstrate how to achieve certain requirements with respect to field localisation and device spectra. Special attention is paid to symmetries of the lattices, mechanical tuning, design of areas of high localisation of magnetic energy; this in turn creates unique discrete mode spectra. We demonstrate analogies between systems designed on the proposed platform and well known physical phenomena such as polarisation, frustration, and Whispering Gallery Modes. The mechanical tunability of the cavity with multiple posts is analysed, and its consequences to optomechanical applications is calculated. One particular application to quantum memory is demonstrated with a cavity design consisting of separate resonators analogous to discrete Fabry-Pérot resonators. Finally, we propose a generalised approach to a microwave system design based on the concept of Programmable Cavity Arrays.
Ground State and Collective Modes of Magnetic Dipoles Fixed on Two-Dimensional Lattice Sites
Feldmann, John; Kalman, Gabor; Hartmann, Peter; Rosenberg, Marlene
2006-10-01
In complex (dusty) plasmas the grains may be endowed with intrinsic dipole moments. We present here our results of theoretical calculations accompanied by and Molecular Dynamics simulation findings on the ground state configuration and on the collective modes mode spectrum of a system of magnetic dipoles, interacting via the magnetic dipole pair-dipole potential, fixed on two-dimensional (2D) lattice sites. In particular, we We study a family of lattices that can be characterized by two parameters: (parallelogram)---the aspect ratio, c/a, and the rhombic angle, phi. The The new collective modes of in the system associated with the dipole-dipole interaction are the angular oscillations (or wobbling) of the direction of the dipoles about their equilibrium configurations. We identify in-plane and out-of-plane modes and display their dispersions. Orders of magnitudes of the parameters of the system relevant to possible future experiments will be discussed. JD Feldmann, G J Kalman and M Rosenberg, J. Phys. A: Math. Gen. 39 (2006) 4549-4553
Creating tuneable microwave media from a two-dimensional lattice of re-entrant posts
Energy Technology Data Exchange (ETDEWEB)
Goryachev, Maxim; Tobar, Michael E. [ARC Centre of Excellence for Engineered Quantum Systems, University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009 (Australia)
2015-11-28
The potential capabilities of resonators based on two dimensional arrays of re-entrant posts is demonstrated. Such posts may be regarded as magnetically coupled lumped element microwave harmonic oscillators, arranged in a 2D lattices structure, which is enclosed in a 3D cavity. By arranging these elements in certain 2D patterns, we demonstrate how to achieve certain requirements with respect to field localisation and device spectra. Special attention is paid to symmetries of the lattices, mechanical tuning, design of areas of high localisation of magnetic energy; this in turn creates unique discrete mode spectra. We demonstrate analogies between systems designed on the proposed platform and well known physical phenomena such as polarisation, frustration, and Whispering Gallery Modes. The mechanical tunability of the cavity with multiple posts is analysed, and its consequences to optomechanical applications is calculated. One particular application to quantum memory is demonstrated with a cavity design consisting of separate resonators analogous to discrete Fabry–Pérot resonators. Finally, we propose a generalised approach to a microwave system design based on the concept of Programmable Cavity Arrays.
Minor magnetization loops in two-dimensional dipolar Ising model
Energy Technology Data Exchange (ETDEWEB)
Sarjala, M. [Aalto University, Department of Applied Physics, P.O. Box 14100, FI-00076 Aalto (Finland); Seppaelae, E.T., E-mail: eira.seppala@nokia.co [Nokia Research Center, Itaemerenkatu 11-13, FI-00180 Helsinki (Finland); Alava, M.J., E-mail: mikko.alava@tkk.f [Aalto University, Department of Applied Physics, P.O. Box 14100, FI-00076 Aalto (Finland)
2011-05-15
The two-dimensional dipolar Ising model is investigated for the relaxation and dynamics of minor magnetization loops. Monte Carlo simulations show that in a stripe phase an exponential decrease can be found for the magnetization maxima of the loops, M{approx}exp(-{alpha}N{sub l}) where N{sub l} is the number of loops. We discuss the limits of this behavior and its relation to the equilibrium phase diagram of the model.
Montgomery, R. C.; Sundararajan, N.
1984-01-01
It is doubtful whether the dynamics of large space structures (LSS) can be predicted well enough for control system design applications. Hence, dynamic modeling from on-orbit measurements followed by a modification of the control system is of interest, taking into account the utilization of adaptive control concepts. The present paper is concerned with the model determination phase of the adaptive control problem. Using spectral decoupling to determine mode shapes, mode frequency and damping data can be obtained with the aid of an equation error parameter identification method. This method employs a second-order auto-regressive moving average (ARMA) model to represent the natural mode amplitudes. The discussed procedure involves an extension of the application of the least square lattice filter in system identification to a nonintegral, two-dimensional grid structure made of overlapping bars.
A two-dimensional analytical model of petroleum vapor intrusion
Yao, Yijun; Verginelli, Iason; Suuberg, Eric M.
2016-02-01
In this study we present an analytical solution of a two-dimensional petroleum vapor intrusion model, which incorporates a steady-state diffusion-dominated vapor transport in a homogeneous soil and piecewise first-order aerobic biodegradation limited by oxygen availability. This new model can help practitioners to easily generate two-dimensional soil gas concentration profiles for both hydrocarbons and oxygen and estimate hydrocarbon indoor air concentrations as a function of site-specific conditions such as source strength and depth, reaction rate constant, soil characteristics and building features. The soil gas concentration profiles generated by this new model are shown in good agreement with three-dimensional numerical simulations and two-dimensional measured soil gas data from a field study. This implies that for cases involving diffusion dominated soil gas transport, steady state conditions and homogenous source and soil, this analytical model can be used as a fast and easy-to-use risk screening tool by replicating the results of 3-D numerical simulations but with much less computational effort.
Multiple Potts Models Coupled to Two-Dimensional Quantum Gravity
Baillie, C F
1992-01-01
We perform Monte Carlo simulations using the Wolff cluster algorithm of {\\it multiple} $q=2,3,4$ state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the $c>1$ region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for $c>1$. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for $c>1$.
Multiple Potts models coupled to two-dimensional quantum gravity
Baillie, C. F.; Johnston, D. A.
1992-07-01
We perform Monte Carlo simulations using the Wolff cluster algorithm of multiple q=2, 3, 4 state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the c>1 region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for c>1. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for c>1.
Institute of Scientific and Technical Information of China (English)
XU Quan; TIAN Qiang; LUO Jun
2009-01-01
@@ We study a two-dimensional lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the two-dimensional Klein-Gordon lattice with hard on-site potential. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the driver.
Modeling of the optical properties of a two-dimensional system of small conductive particles.
Kondikov, A. A.; Tonkaev, P. A.; Chaldyshev, V. V.; Vartanyan, T. A.
2016-08-01
Software was developed for quick numerical calculations and graphic display of the absorption, reflection and transmittance spectra of two-dimensional systems of small conductive particles. It allowed us to make instant comparison of calculation results and experimental data. A lattice model was used to simulate nearly distributed particles, and the coherent-potential approximation was applied to obtain a solution to the problem of interacting particles. The Delphi programming environment was used.
Spontaneous supersymmetry breaking in the two-dimensional N=1 Wess-Zumino model
Steinhauer, Kyle
2014-01-01
We study the phase diagram of the two-dimensional N=1 Wess-Zumino model on the lattice using Wilson fermions and the fermion loop formulation. We give a complete nonperturbative determination of the ground state structure in the continuum and infinite volume limit. We also present a determination of the particle spectrum in the supersymmetric phase, in the supersymmetry broken phase and across the supersymmetry breaking phase transition. In the supersymmetry broken phase we observe the emergence of the Goldstino particle.
Noise Threshold for a Fault-Tolerant Two-Dimensional Lattice Architecture
Svore, K M; Terhal, B M; Svore, Krysta M.; Vincenzo, David P. Di; Terhal, Barbara M.
2006-01-01
We consider a model of quantum computation in which the set of operations is limited to nearest-neighbor interactions on a 2D lattice. We model movement of qubits with noisy SWAP operations. For this architecture we design a fault-tolerant coding scheme using the concatenated [[7,1,3
The Mott metal-insulator transition in half-filled two-dimensional Hubbard models
Directory of Open Access Journals (Sweden)
Peyman Sahebsara
2008-06-01
Full Text Available We study the Mott transition in the two dimensional Hubbard model by using the variational cluster approximation. The transition potential obtained is roughly Uc ≈ 2 and 6 for square and triangular lattices, respectively. A comparison between results of this approximation and other quantum cluster methods is presented. Our zero-temperature calculation at strong coupling show that the transition on the triangular and square lattices occur at lower values of compared with other numerical techniques such as DMFT, CDMFT, and DCA. We also study the thermodynamic limit by an extrapolation to infinite size.
The XY model coupled to two-dimensional quantum gravity
Baillie, C. F.; Johnston, D. A.
1992-09-01
We perform Monte Carlo simulations using the Wolff cluster algorithm of the XY model on both fixed and dynamical phi-cubed graphs (i.e. without and with coupling to two-dimensional quantum gravity). We compare the numerical results with the theoretical expectation that the phase transition remains of KT type when the XY model is coupled to gravity. We also examine whether the universality we discovered in our earlier work on various Potts models with the same value of the central charge, c, carries over to the XY model, which has c=1.
The XY Model Coupled to Two-Dimensional Quantum Gravity
Baillie, C F; 10.1016/0370-2693(92)91037-A
2009-01-01
We perform Monte Carlo simulations using the Wolff cluster algorithm of the XY model on both fixed and dynamical phi-cubed graphs (i.e. without and with coupling to two-dimensional quantum gravity). We compare the numerical results with the theoretical expectation that the phase transition remains of KT type when the XY model is coupled to gravity. We also examine whether the universality we discovered in our earlier work on various Potts models with the same value of the central charge, $c$, carries over to the XY model, which has $c=1$.
Kumar, Manish
2016-01-01
We propose a simple and straightforward method to generate a spatially variant lattice structures by optical interference lithography method. Using this method, it is possible to independently vary the orientation and period of the two-dimensional lattice. The method consists of two steps which are: numerical synthesis of corresponding phase mask by employing a two-dimensional integrated gradient calculations and experimental implementation of synthesized phase mask by making use of a phase only spatial light modulator in an optical 4f Fourier filtering setup. As a working example, we provide the experimental fabrication of a spatially variant square lattice structure which has the possibility to guide a Gaussian beam through a 90{\\deg} bend by photonic crystal self-collimation phenomena. The method is digitally reconfigurable, is completely scalable and could be extended to other kind of lattices as well.
Energy Technology Data Exchange (ETDEWEB)
Kumar, Manish, E-mail: manishk@physics.iitd.ac.in; Joseph, Joby, E-mail: joby@physics.iitd.ac.in [Photonics Research Laboratory, Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016 (India)
2014-08-04
We propose a simple and straightforward method to generate spatially variant lattice structures by optical interference lithography method. Using this method, it is possible to independently vary the orientation and period of the two-dimensional lattice. The method consists of two steps which are: numerical synthesis of corresponding phase mask by employing a two-dimensional integrated gradient calculations and experimental implementation of synthesized phase mask by making use of a phase only spatial light modulator in an optical 4f Fourier filtering setup. As a working example, we provide the experimental fabrication of a spatially variant square lattice structure which has the possibility to guide a Gaussian beam through a 90° bend by photonic crystal self-collimation phenomena. The method is digitally reconfigurable, is completely scalable, and could be extended to other kind of lattices as well.
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.
The sequence d(CGGCGGCCGC) self-assembles into a two dimensional rhombic DNA lattice
Energy Technology Data Exchange (ETDEWEB)
Venkadesh, S.; Mandal, P.K. [CAS in Crystallography and Biophysics, University of Madras, Chennai 600 025 (India); Gautham, N., E-mail: n_gautham@hotmail.com [CAS in Crystallography and Biophysics, University of Madras, Chennai 600 025 (India)
2011-04-15
Highlights: {yields} This is the first crystal structure of a four-way junction with sticky ends. {yields} Four junction structures bind to each other and form a rhombic cavity. {yields} Each rhombus binds to others to form 'infinite' 2D tiles. {yields} This is an example of bottom-up fabrication of a DNA nano-lattice. -- Abstract: We report here the crystal structure of the partially self-complementary decameric sequence d(CGGCGGCCGC), which self assembles to form a four-way junction with sticky ends. Each junction binds to four others through Watson-Crick base pairing at the sticky ends to form a rhombic structure. The rhombuses bind to each other and form two dimensional tiles. The tiles stack to form the crystal. The crystal diffracted in the space group P1 to a resolution of 2.5 A. The junction has the anti-parallel stacked-X conformation like other junction structures, though the formation of the rhombic net noticeably alters the details of the junction geometry.
Chen, Peng-Jen; Jeng, Horng-Tay
2016-03-16
A new semiconducting phase of two-dimensional phosphorous in the Kagome lattice is proposed from first-principles calculations. The band gaps of the monolayer (ML) and bulk Kagome phosphorous (Kagome-P) are 2.00 and 1.11 eV, respectively. The magnitude of the band gap is tunable by applying the in-plane strain and/or changing the number of stacking layers. High optical absorption coefficients at the visible light region are predicted for multilayer Kagome-P, indicating potential applications for solar cell devices. The nearly dispersionless top valence band of the ML Kagome-P with high density of states at the Fermi level leads to superconductivity with Tc of ~9 K under the optimal hole doping concentration. We also propose that the Kagome-P can be fabricated through the manipulation of the substrate-induced strain during the process of the sample growth. Our work demonstrates the high applicability of the Kagome-P in the fields of electronics, photovoltaics, and superconductivity.
Corner wetting transition in the two-dimensional Ising model
Lipowski, Adam
1998-07-01
We study the interfacial behavior of the two-dimensional Ising model at the corner of weakened bonds. Monte Carlo simulations results show that the interface is pinned to the corner at a lower temperature than a certain temperature Tcw at which it undergoes a corner wetting transition. The temperature Tcw is substantially lower than the temperature of the ordinary wetting transition with a line of weakened bonds. A solid-on-solid-like model is proposed, which provides a supplementary description of the corner wetting transition.
AN APPROACH IN MODELING TWO-DIMENSIONAL PARTIALLY CAVITATING FLOW
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
An approach of modeling viscosity, unsteady partially cavitating flows around lifting bodies is presented. By employing an one-fluid Navier-Stokers solver, the algorithm is proved to be able to handle two-dimensional laminar cavitating flows at moderate Reynolds number. Based on the state equation of water-vapor mixture, the constructive relations of densities and pressures are established. To numerically simulate the cavity wall, different pseudo transition of density models are presumed. The finite-volume method is adopted and the algorithm can be extended to three-dimensional cavitating flows.
Boschker, Jos E.; Momand, Jamo; Bragaglia, Valeria; Wang, Ruining; Perumal, Karthick; Giussani, Alessandro; Kooi, Bart J.; Riechert, Henning; Calarco, Raffaella
2014-01-01
Sb2Te3 films are used for studying the epitaxial registry between two-dimensionally bonded (2D) materials and three-dimensional bonded (3D) substrates. In contrast to the growth of 3D materials, it is found that the formation of coincidence lattices between Sb2Te3 and Si(111) depends on the geometry
Fabrication of deep-profile Al-doped ZnO one- and two-dimensional lattices as plasmonic elements
DEFF Research Database (Denmark)
Jensen, Flemming; Shkondin, Evgeniy; Takayama, Osamu
2016-01-01
In this work, we report on fabrication of deep-profile one- and two-dimensional lattices made from Al-doped ZnO (AZO). AZO is considered as an alternative plasmonic material having the real part of the permittivity negative in the near infrared range. The exact position of the plasma frequency...
Approaches to verification of two-dimensional water quality models
Energy Technology Data Exchange (ETDEWEB)
Butkus, S.R. (Tennessee Valley Authority, Chattanooga, TN (USA). Water Quality Dept.)
1990-11-01
The verification of a water quality model is the one procedure most needed by decision making evaluating a model predictions, but is often not adequate or done at all. The results of a properly conducted verification provide the decision makers with an estimate of the uncertainty associated with model predictions. Several statistical tests are available for quantifying of the performance of a model. Six methods of verification were evaluated using an application of the BETTER two-dimensional water quality model for Chickamauga reservoir. Model predictions for ten state variables were compared to observed conditions from 1989. Spatial distributions of the verification measures showed the model predictions were generally adequate, except at a few specific locations in the reservoir. The most useful statistics were the mean standard error of the residuals. Quantifiable measures of model performance should be calculated during calibration and verification of future applications of the BETTER model. 25 refs., 5 figs., 7 tabs.
Analysis of Two-Layered Random Interfaces for Two Dimensional Widom-Rowlinson's Model
Directory of Open Access Journals (Sweden)
Jun Wang
2011-01-01
Full Text Available The statistical behaviors of two-layered random-phase interfaces in two-dimensional Widom-Rowlinson's model are investigated. The phase interfaces separate two coexisting phases of the lattice Widom-Rowlinson model; when the chemical potential μ of the model is large enough, the convergence of the probability distributions which describe the fluctuations of the phase interfaces is studied. In this paper, the backbones of interfaces are introduced in the model, and the corresponding polymer chains and cluster expansions are developed and analyzed for the polymer weights. And the existence of the free energy for two-layered random-phase interfaces of the two-dimensional Widom-Rowlinson model is given.
Ordering in Two-Dimensional Ising Models with Competing Interactions
2004-01-01
We study the 2D Ising model on a square lattice with additional non-equal diagonal next-nearest neighbor interactions. The cases of classical and quantum (transverse) models are considered. Possible phases and their locations in the space of three Ising couplings are analyzed. In particular, incommensurate phases occurring only at non-equal diagonal couplings, are predicted. We also analyze a spin-pseudospin model comprised of the quantum Ising model coupled to XY spin chains in a particular ...
Two dimensional hydrodynamic modeling of a high latitude braided river
Humphries, E.; Pavelsky, T.; Bates, P. D.
2014-12-01
Rivers are a fundamental resource to physical, ecologic and human systems, yet quantification of river flow in high-latitude environments remains limited due to the prevalence of complex morphologies, remote locations and sparse in situ monitoring equipment. Advances in hydrodynamic modeling and remote sensing technology allow us to address questions such as: How well can two-dimensional models simulate a flood wave in a highly 3-dimensional braided river environment, and how does the structure of such a flood wave differ from flow down a similar-sized single-channel river? Here, we use the raster-based hydrodynamic model LISFLOOD-FP to simulate flood waves, discharge, water surface height, and velocity measurements over a ~70 km reach of the Tanana River in Alaska. In order to use LISFLOOD-FP a digital elevation model (DEM) fused with detailed bathymetric data is required. During summer 2013, we surveyed 220,000 bathymetric points along the study reach using an echo sounder system connected to a high-precision GPS unit. The measurements are interpolated to a smooth bathymetric surface, using Topo to Raster interpolation, and combined with an existing five meter DEM (Alaska IfSAR) to create a seamless river terrain model. Flood waves are simulated using varying complexities in model solvers, then compared to gauge records and water logger data to assess major sources of model uncertainty. Velocity and flow direction maps are also assessed and quantified for detailed analysis of braided channel flow. The most accurate model output occurs with using the full two-dimensional model structure, and major inaccuracies appear to be related to DEM quality and roughness values. Future work will intercompare model outputs with extensive ground measurements and new data from AirSWOT, an airborne analog for the Surface Water and Ocean Topography (SWOT) mission, which aims to provide high-resolution measurements of terrestrial and ocean water surface elevations globally.
Yang, Bo; Li, Xiao-Teng; Chen, Wei; Liu, Jian; Chen, Xiao-Song
2016-10-01
Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents v, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model. Supported by the National Natural Science Foundation of China under Grant Nos. 11121403 and 11504384
Surface Ship Shock Modeling and Simulation: Two-Dimensional Analysis
Directory of Open Access Journals (Sweden)
Young S. Shin
1998-01-01
Full Text Available The modeling and simulation of the response of a surface ship system to underwater explosion requires an understanding of many different subject areas. These include the process of underwater explosion events, shock wave propagation, explosion gas bubble behavior and bubble-pulse loading, bulk and local cavitation, free surface effect, fluid-structure interaction, and structural dynamics. This paper investigates the effects of fluid-structure interaction and cavitation on the response of a surface ship using USA-NASTRAN-CFA code. First, the one-dimensional Bleich-Sandler model is used to validate the approach, and second, the underwater shock response of a two-dimensional mid-section model of a surface ship is predicted with a surrounding fluid model using a constitutive equation of a bilinear fluid which does not allow transmission of negative pressures.
Two-dimensional Numerical Modeling Research on Continent Subduction Dynamics
Institute of Scientific and Technical Information of China (English)
WANG Zhimin; XU Bei; ZHOU Yaoqi; XU Hehua; HUANG Shaoying
2004-01-01
Continent subduction is one of the hot research problems in geoscience. New models presented here have been set up and two-dimensional numerical modeling research on the possibility of continental subduction has been made with the finite element software, ANSYS, based on documentary evidence and reasonable assumptions that the subduction of oceanic crust has occurred, the subduction of continental crust can take place and the process can be simplified to a discontinuous plane strain theory model. The modeling results show that it is completely possible for continental crust to be subducted to a depth of 120 km under certain circumstances and conditions. At the same time, the simulations of continental subduction under a single dynamical factor have also been made, including the pull force of the subducted oceanic lithosphere, the drag force connected with mantle convection and the push force of the mid-ocean ridge. These experiments show that the drag force connected with mantle convection is critical for continent subduction.
Xu, Cenke
Several examples of quantum spin systems and pseudo spin systems have been studied, and unconventional states of matters and phase transitions have been realized in all these systems under consideration. In the p +/- ip superconductor Josephson lattice and the p--band cold atomic system trapped in optical lattices, novel phases which behave similarly to 1+1 dimensional systems are realized, despite the fact that the real physical systems are in two or three dimensional spaces. For instance, by employing a spin-wave analysis together with a new duality transformation, we establish the existence and stability of a novel gapless "critical phase", which we refer to as a "bond algebraic liquid". This novel critical phase is analogous to the 1+1 dimensional algebraic boson liquid phase. The reason for the novel physics is that there is a quasilocal gauge symmetry in the effective low energy Hamiltonian. In a spin-1 system on the kagome lattice, and a hard-core boson system on the honeycomb lattice, the low energy physics is controlled by two components of compact U(1) gauge symmetries that emerge at low energy. Making use of the confinement nature of the 2+1 dimensional compact gauge theories and the powerful duality between gauge theories and height field theories, the crystalline phase diagrams are studied for both systems, and the transitions to other phases are also considered. These phase diagrams might be accessible in strongly correlated materials, or atomic systems in optical lattices. A novel quantum ground state of matter is realized in a bosonic model on three dimensional fcc lattice with emergent low energy excitations. The novel phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the
Two-Dimensional Wang-Landau Sampling of AN Asymmetric Ising Model
Tsai, Shan-Ho; Wang, Fugao; Landau, D. P.
We study the critical endpoint behavior of an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. We use a two-dimensional Wang-Landau sampling method to determine the density of states for this model. An accurate density of states allowed us to map out the phase diagram accurately and observe a clear divergence of the curvature of the spectator phase boundary and of the derivative of the magnetization coexistence diameter near the critical endpoint, in agreement with previous theoretical predictions.
Photonic band structures of two-dimensional photonic crystals with deformed lattices
Institute of Scientific and Technical Information of China (English)
Cai Xiang-Hua; Zheng Wan-Hua; Ma Xiao-Tao; Ren Gang; Xia Jian-Bai
2005-01-01
Using the plane-wave expansion method, we have calculated and analysed the changes of photonic band structures arising from two kinds of deformed lattices, including the stretching and shrinking of lattices. The square lattice with square air holes and the triangular lattice with circular air holes are both studied. Calculated results show that the change of lattice size in some special ranges can enlarge the band gap, which depends strongly on the filling factor of air holes in photonic crystals; and besides, the asymmetric band edges will appear with the broken symmetry of lattices.
A two-dimensional mathematical model of percutaneous drug absorption
Directory of Open Access Journals (Sweden)
Kubota K
2004-06-01
Full Text Available Abstract Background When a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, r. The values of r depend on the amount of diffusion and the normalized skin-capillary clearence. It is defined as the ratio of the steady-state drug concentration at the skin-capillary boundary to that at the skin-surface in one-dimensional models. The present paper studies the effect of the parameter values, when the region of contact of the skin with the drug, is a line segment on the skin surface. Methods Though a simple one-dimensional model is often useful to describe percutaneous drug absorption, it may be better represented by multi-dimensional models. A two-dimensional mathematical model is developed for percutaneous absorption of a drug, which may be used when the diffusion of the drug in the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. This model consists of a linear second-order parabolic equation with appropriate initial conditions and boundary conditions. These boundary conditions are of Dirichlet type, Neumann type or Robin type. A finite-difference method which maintains second-order accuracy in space along the boundary, is developed to solve the parabolic equation. Extrapolation in time is applied to improve the accuracy in time. Solution of the parabolic equation gives the concentration of the drug in the skin at a given time. Results Simulation of the numerical methods described is carried out with various values of the parameter r. The illustrations are given in the form of figures. Conclusion Based on the values of r, conclusions are drawn about (1 the flow rate of the drug, (2 the flux and the cumulative amount of drug eliminated into the receptor cell, (3 the steady-state value of the flux, (4 the time to reach the steady
Coherent two-dimensional spectroscopy of a Fano model
Poulsen, Felipe; Pullerits, Tõnu; Hansen, Thorsten
2016-01-01
The Fano lineshape arises from the interference of two excitation pathways to reach a continuum. Its generality has resulted in a tremendous success in explaining the lineshapes of many one-dimensional spectroscopies - absorption, emission, scattering, conductance, photofragmentation - applied to very varied systems - atoms, molecules, semiconductors and metals. Unravelling a spectroscopy into a second dimension reveals the relationship between states in addition to decongesting the spectra. Femtosecond-resolved two-dimensional electronic spectroscopy (2DES) is a four-wave mixing technique that measures the time-evolution of the populations, and coherences of excited states. It has been applied extensively to the dynamics of photosynthetic units, and more recently to materials with extended band-structures. In this letter, we solve the full time-dependent third-order response, measured in 2DES, of a Fano model and give the new system parameters that become accessible.
Current fluctuations in a two dimensional model of heat conduction
Pérez-Espigares, Carlos; Garrido, Pedro L.; Hurtado, Pablo I.
2011-03-01
In this work we study numerically and analytically current fluctuations in the two-dimensional Kipnis-Marchioro-Presutti (KMP) model of heat conduction. For that purpose, we use a recently introduced algorithm which allows the direct evaluation of large deviations functions. We compare our results with predictions based on the Hydrodynamic Fluctuation Theory (HFT) of Bertini and coworkers, finding very good agreement in a wide interval of current fluctuations. We also verify the existence of a well-defined temperature profile associated to a given current fluctuation which depends exclusively on the magnitude of the current vector, not on its orientation. This confirms the recently introduced Isometric Fluctuation Relation (IFR), which results from the time-reversibility of the dynamics, and includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by timereversibility on the statistics of nonequilibrium fluctuations.
Ochiai, Tetsuyuki
2017-02-01
We study the effects of a synthetic gauge field and pseudospin-orbit interaction in a stacked two-dimensional ring-network model. The model was introduced to simulate light propagation in the corresponding ring-resonator lattice, and is thus completely bosonic. Without these two items, the model exhibits Floquet-Weyl and Floquet-topological-insulator phases with topologically gapless and gapped band structures, respectively. The synthetic magnetic field implemented in the model results in a three-dimensional Hofstadter-butterfly-type spectrum in a photonic platform. The resulting gaps are characterized by the winding number of relevant S-matrices together with the Chern number of the bulk bands. The pseudospin-orbit interaction is defined as the mixing term between two pseudospin degrees of freedom in the rings, namely, the clockwise and counter-clockwise modes. It destroys the Floquet-topological-insulator phases, while the Floquet-Weyl phase with multiple Weyl points can be preserved by breaking the space-inversion symmetry. Implementing both the synthetic gauge field and pseudospin-orbit interaction requires a certain nonreciprocity.
Mathematical modeling of the neuron morphology using two dimensional images.
Rajković, Katarina; Marić, Dušica L; Milošević, Nebojša T; Jeremic, Sanja; Arsenijević, Valentina Arsić; Rajković, Nemanja
2016-02-01
In this study mathematical analyses such as the analysis of area and length, fractal analysis and modified Sholl analysis were applied on two dimensional (2D) images of neurons from adult human dentate nucleus (DN). Using mathematical analyses main morphological properties were obtained including the size of neuron and soma, the length of all dendrites, the density of dendritic arborization, the position of the maximum density and the irregularity of dendrites. Response surface methodology (RSM) was used for modeling the size of neurons and the length of all dendrites. However, the RSM model based on the second-order polynomial equation was only possible to apply to correlate changes in the size of the neuron with other properties of its morphology. Modeling data provided evidence that the size of DN neurons statistically depended on the size of the soma, the density of dendritic arborization and the irregularity of dendrites. The low value of mean relative percent deviation (MRPD) between the experimental data and the predicted neuron size obtained by RSM model showed that model was suitable for modeling the size of DN neurons. Therefore, RSM can be generally used for modeling neuron size from 2D images.
Directory of Open Access Journals (Sweden)
O. Ye. Hentosh
2016-01-01
Full Text Available The possibility of applying the method of reducing upon finite-dimensional invariant subspaces, generated by the eigenvalues of the associated spectral problem, to some two-dimensional generalization of the relativistic Toda lattice with the triple matrix Lax type linearization is investigated. The Hamiltonian property and Lax-Liouville integrability of the vector fields, given by this system, on the invariant subspace related with the Bargmann type reduction are found out.
Institute of Scientific and Technical Information of China (English)
罗孟波; 陈庆虎; 许祝安; 焦正宽
2001-01-01
The second-order phase transition in the two-dimensional (2D) classical Coulomb gas of half-integer charges on a square lattice is investigated by using Monte Carlo simulations. Based on the finite-size scaling analysis,we estimate the second-order phase transition temperature Tc and the static critical exponents β and v with a new numerical analysis method. More precise critical temperature Tc = 0.1311(2) and critical exponents β/ν = 0.1152(12) and ν = 0.857(15) are obtained. The estimated value of ν indicates that the charge lattice melting transition is different from the pure 2D Ising transition.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Absolute band gaps of a two-dimensional triangular-lattice photonic crystal are calculated with the finite-difference time-domain method in this paper.Through calculating the photonic band structures of the triangular-lattice photonic crystal consisting of Ge rods immersed in air with different shapes,it is found that a large absolute band gap of 0.098 (2c/a) can be obtained for the structures with hollow triangular Ge rods immersed in air,corresponding to 19.8% of the middle frequency.The influence of the different factors on the width of the absolute band gaps is also discussed.
From Discreteness to Continuity: Dislocation Equation for Two-Dimensional Triangular Lattice
Institute of Scientific and Technical Information of China (English)
WANG Shao-Feng
2007-01-01
@@ A systematic method from the discreteness to the continuity is presented for the dislocation equation of the triangular lattice. A modification of the Peierls equation has been derived strictly. The modified equation includes the higher order corrections of the discrete effect which are important for the core structure of dislocation. It is observed that the modified equation possesses a universal form which is model-independent except the factors.The factors, which depend on the detail of the model, are related to the derivatives of the kernel at its zero point in the wave-vector space. The results open a way to deal with the complicated models because what one needs to do is to investigate the behaviour near the zero point of the kernel in the wave-vector space instead of calculating the kernel completely.
Two-dimensional model for circulating fluidized-bed reactors
Energy Technology Data Exchange (ETDEWEB)
Schoenfelder, H.; Kruse, M.; Werther, J. [Technical Univ. Hamburg-Harburg, Hamburg (Germany). Dept. of Chemical Engineering
1996-07-01
Circulating fluidized bed reactors are widely used for the combustion of coal in power stations as well as for the cracking of heavy oil in the petroleum industry. A two-dimensional reactor model for circulating fluidized beds (CFB) was studied based on the assumption that at every location within the riser, a descending dense phase and a rising lean phase coexist. Fluid mechanical variables may be calculated from one measured radial solids flux profile (upward and downward). The internal mass-transfer behavior is described on the basis of tracer gas experiments. The CFB reactor model was tested against data from ozone decomposition experiments in a CFB cold flow model (15.6-m height, 0.4-m ID) operated in the ranges 2.5--4.5 m/s and 9--45 kg/(m{sup 2}{center_dot}s) of superficial gas velocity and solids mass flux, respectively. Based on effective reaction rate constants determined from the ozone exit concentration, the model was used to predict the spatial reactant distribution within the reactor. Model predictions agreed well with measurements.
p-wave superconductivity in a two-dimensional generalized Hubbard model
Energy Technology Data Exchange (ETDEWEB)
Millan, J. Samuel [Instituto de Investigaciones en Materiales, Universidad Nacional Autonoma de Mexico (UNAM), Apartado Postal 70-360, 04510, Mexico D.F. (Mexico); Facultad de Ingenieria, UNACAR, 24180, Cd. de Carmen, Campeche (Mexico); Perez, Luis A. [Instituto de Fisica, UNAM, Apartado Postal 20-364, 01000, Mexico D.F. (Mexico); Wang Chumin [Instituto de Investigaciones en Materiales, Universidad Nacional Autonoma de Mexico (UNAM), Apartado Postal 70-360, 04510, Mexico D.F. (Mexico)]. E-mail: chumin@servidor.unam.mx
2005-02-21
In this Letter, we consider a two-dimensional Hubbard model that includes a second-neighbor correlated hopping interaction, and we find a triplet p-wave superconducting ground state within the BCS formalism. A small distortion of the square-lattice right angles is introduced in order to break the degeneracy of kx+/-ky oriented p-wave pairing states. For the strong coupling limit, analytical results are obtained. An analysis of the superconducting critical temperature reveals the existence of an optimal electron density and the gap ratio exhibits a non-BCS behavior. Finally, the particular case of strontium ruthenate is examined.
Scaling and universality in the two-dimensional Ising model with a magnetic field.
Mangazeev, Vladimir V; Dudalev, Michael Yu; Bazhanov, Vladimir V; Batchelor, Murray T
2010-06-01
The scaling function of the two-dimensional Ising model on the square and triangular lattices is obtained numerically via Baxter's variational corner transfer-matrix approach. The use of Aharony-Fisher nonlinear scaling variables allowed us to perform calculations sufficiently away from the critical point and to confirm all predictions of the scaling and universality hypotheses. Our results are in excellent agreement with quantum field theory calculations of Fonseca and Zamolodchikov as well as with many previously known exact and numerical calculations, including susceptibility results by Barouch, McCoy, Tracy, and Wu.
Institute of Scientific and Technical Information of China (English)
ZHANG Yan; SHI Jun-Jie
2008-01-01
A two-dimensional photonic crystal model with a periodic square dielectric background is proposed.The photonic band modulation effects due to the two-dimensional periodic background are investigated jn detail.It is found that periodic modulation of the dielectric background greatly alters photonic band structures,especially for the Epolarization modes.The number,width and position of the photonic band gaps sensitively depend on the dielectric constants of the two-dimensional periodic background.Complete band gaps are found,and the dependence of the widths of these gaps on the structural and material parameters of the two alternating rods/holes is studied.
A two-dimensional CA model for traffic flow with car origin and destination
In-nami, Junji; Toyoki, Hiroyasu
2007-05-01
Dynamic phase transitions in a two-dimensional traffic flow model defined on a decorated square-lattice are studied numerically. The square-lattice point and the decorated site denote intersections and roads, respectively. In the present model, a car has a finite deterministic path between the origin and the destination, which is assigned to the car from the beginning. In this new model, we found a new phase between the free-flow phase and the frozen-jam phase that is absent from previous models. The new model is characterized by the persistence of a macroscopic cluster. Furthermore, the behavior in this macroscopic cluster phase is classified into three regions characterized by the shape of the cluster. The boundary of the three regions is phenomenologically estimated. When the trip length is short and the car density is high, both ends of the belt-like cluster connect to each other through the periodic boundary with some probability. This type of cluster is classified topologically as a string on a two-dimensional torus.
Dispersion of guided modes in two-dimensional split ring lattices
Lunnemann, Per
2014-01-01
We present a semi-analytical point-dipole method that uses Ewald lattice summation to find the dispersion relation of guided plasmonic and bianisotropic modes in metasurfaces composed of 2D periodic lattices of arbitrarily strongly scattering magneto-electric dipole scatterers. This method takes into account all retarded electrodynamic interactions as well as radiation damping selfconsistently. As illustration we analyze the dispersion of plasmon nanorod lattices, and of 2D split ring resonator lattices. Plasmon nanorod lattices support transverse and longitudinal in-plane electric modes. Scatterers that have an in-plane electric and out-of-plane magnetic polarizability, but without intrinsic magnetoelectric coupling, result in two bands that are mixtures of the bands of electric-only and magnetic-only lattices. Thereby bianisotropy through mutual coupling, in absence of building-block bianisotropy, is evident. Once strong bi-anisotropy is included in each building block, the Bloch modes become even more stro...
Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow: Two-Dimensional Case
Gan, Yan-Biao; Xu, Ai-Guo; Zhang, Guang-Cai; Zhang, Ping; Zhang, Lei; Li, Ying-Jun
2008-07-01
Lattice Boltzmann (LB) modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 (2007) 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests: shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.
A two-dimensional hydrodynamic model of a tidal estuary
Walters, Roy A.; Cheng, Ralph T.
1979-01-01
A finite element model is described which is used in the computation of tidal currents in an estuary. This numerical model is patterned after an existing algorithm and has been carefully tested in rectangular and curve-sided channels with constant and variable depth. One of the common uncertainties in this class of two-dimensional hydrodynamic models is the treatment of the lateral boundary conditions. Special attention is paid specifically to addressing this problem. To maintain continuity within the domain of interest, ‘smooth’ curve-sided elements must be used at all shoreline boundaries. The present model uses triangular, isoparametric elements with quadratic basis functions for the two velocity components and a linear basis function for water surface elevation. An implicit time integration is used and the model is unconditionally stable. The resultant governing equations are nonlinear owing to the advective and the bottom friction terms and are solved iteratively at each time step by the Newton-Raphson method. Model test runs have been made in the southern portion of San Francisco Bay, California (South Bay) as well as in the Bay west of Carquinez Strait. Owing to the complex bathymetry, the hydrodynamic characteristics of the Bay system are dictated by the generally shallow basins which contain deep, relict river channels. Great care must be exercised to ensure that the conservation equations remain locally as well as globally accurate. Simulations have been made over several representative tidal cycles using this finite element model, and the results compare favourably with existing data. In particular, the standing wave in South Bay and the progressive wave in the northern reach are well represented.
Development of two-dimensional hot pool model
Energy Technology Data Exchange (ETDEWEB)
Lee, Yong Bum; Hahn, H. D
2000-05-01
During a normal reactor scram, the heat generation is reduced almost instantaneously while the coolant flow rate follows the pump coast-down. This mismatch between power and flow results in a situation where the core flow entering the hot pool is at a lower temperature than the temperature of the bulk pool sodium. This temperature difference leads to thermal stratification. Thermal stratification can occur in the hot pool region if the entering coolant is colder than the existing hot pool coolant and the flow momentum is not large enough to overcome the negative buoyancy force. Since the fluid of hot pool enters IHX{sub s}, the temperature distribution of hot pool can alter the overall system response. Hence, it is necessary to predict the pool coolant temperature distribution with sufficient accuracy to determine the inlet temperature conditions for the IHX{sub s} and its contribution to the net buoyancy head. Therefore, in this study two-dimensional hot pool model is developed instead of existing one-dimensional model to predict the hot pool coolant temperature and velocity distribution more accurately and is applied to the SSC-K code.
Chen, Mingji; Pei, Yongmao; Fang, Daining
2012-07-01
Microwave absorbing structures (MASs) reinforced by two dimensional (2D) composite lattice elements have been designed and fabricated. The density of these MASs is lower than 0.5 g/cm3. Experimental measurements show that the sandwich structure with glass fiber reinforced composite (GFRC) lattice core can serve as a broadband MAS with its reflectivity below -10 dB over the frequency range of 4-18 GHz. The low permittivity GFRC is indicated to be the proper material for both the structural element of the core and the transparent face sheet. Calculations by the periodic moment method (PMM) demonstrate that the 2D Kagome lattice performs better for microwave absorbing than the square one at relatively low frequencies. The volume fraction and cell size of the structural element are also revealed to be key factors for microwave absorbing performance.
Analysis of two-dimensional photonic band gap structure with a rhombus lattice
Institute of Scientific and Technical Information of China (English)
Limei Qi; Ziqiang Yang; Xi Gao; Zheng Liang
2008-01-01
@@ The relative band gap for a rhombus lattice photonic crystal is studied by plane wave expansion method and high frequency structure simulator (HFSS) simulation. General wave vectors in the first Briliouin zone are derived. The relative band gap as a function of air-filling factor and background material is investigated, respectively, and the nature of photonic band gap for different lattice angles is analyzed by the distribution of electric energy. These results would provide theoretical instruction for designing optical integrated devices using photonic crystal with a rhombus lattice.
Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
Ehlers, G.; White, S. R.; Noack, R. M.
2017-03-01
The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid-real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at n =0.875 filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both U /t =4.0 and 8.0 . We find that the strength of the charge ordering depends on U /t and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.
Two-Dimensional Anharmonic Crystal Lattices: Solitons, Solectrons, and Electric Conduction
Velarde, Manuel G.; Ebeling, Werner; Chetverikov, Alexander P.
2011-01-01
Reported here are salient features of soliton-mediated electron transport in anharmonic crystal lattices.After recalling how an electron-soliton bound state (solectron) can be formed we comment on consequences like electron surfing on a sound wave and balistic transport, possible percolation in 2d lattices, and a novel form of electron pairing with strongly correlated electrons both in real space and momentum space.
Percolation in spatial evolutionary prisoner's dilemma game on two-dimensional lattices
Choi, Woosik; Yook, Soon-Hyung; Kim, Yup
2015-11-01
We study the spatial evolutionary prisoner's dilemma game with updates of imitation max on triangular, hexagonal, and square lattices. We use the weak prisoner's dilemma game with a single parameter b . Due to the competition between the temptation value b and the coordination number z of the base lattice, a greater variety of percolation properties is expected to occur on the lattice with the larger z . From the numerical analysis, we find six different regimes on the triangular lattice (z =6 ). Regardless of the initial densities of cooperators and defectors, cooperators always percolate in the steady state in two regimes for small b . In these two regimes, defectors do not percolate. In two regimes for the intermediate value of b , both cooperators and defectors undergo percolation transitions. The defector always percolates in two regimes for large b . On the hexagonal lattice (z =3 ), there exist two distinctive regimes. For small b , both the cooperators and the defectors undergo percolation transitions while only defectors always percolate for large b . On the square lattice (z =4 ), there exist three regimes. Combining with the finite-size scaling analyses, we show that all the observed percolation transitions belong to the universality class of the random percolation. We also show how the detailed growth mechanism of cooperator and defector clusters decides each regime.
Energy Technology Data Exchange (ETDEWEB)
Mandal, R.; Barman, S.; Saha, S.; Barman, A., E-mail: abarman@bose.res.in [Department of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700 098 (India); Otani, Y. [CEMS-RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581 (Japan)
2015-08-07
Ferromagnetic antidot lattices are important systems for magnetic data storage and magnonic devices, and understanding their magnetization dynamics by varying their structural parameters is an important problems in magnetism. Here, we investigate the variation in spin wave spectrum in two-dimensional nanoscale Ni{sub 80}Fe{sub 20} antidot lattices with lattice symmetry. By varying the bias magnetic field values in a broadband ferromagnetic resonance spectrometer, we observed a stark variation in the spin wave spectrum with the variation of lattice symmetry. The simulated mode profiles showed further difference in the spatial nature of the modes between different lattices. While for square and rectangular lattices extended modes are observed in addition to standing spin wave modes, all modes in the hexagonal, honeycomb, and octagonal lattices are either localized or standing waves. In addition, the honeycomb and octagonal lattices showed two different types of modes confined within the honeycomb (octagonal) units and between two such consecutive units. Simulated internal magnetic fields confirm the origin of such a wide variation in the frequency and spatial nature of the spin wave modes. The tunability of spin waves with the variation of lattice symmetry is important for the design of future magnetic data storage and magnonic devices.
Two-Dimensional Electronic Spectroscopy of a Model Dimer System
Directory of Open Access Journals (Sweden)
Prokhorenko V.I.
2013-03-01
Full Text Available Two-dimensional spectra of a dimer were measured to determine the timescale for electronic decoherence at room temperature. Anti-correlated beats in the crosspeaks were observed only during the period corresponding to the measured homogeneous lifetime.
Naether, Uta; Johansson, Magnus
2010-01-01
We address the problem of directional mobility of discrete solitons in two-dimensional rectangular lattices, in the framework of a discrete nonlinear Schr\\"odinger model with saturable on-site nonlinearity. A numerical constrained Newton-Raphson method is used to calculate two-dimensional Peierls-Nabarro energy surfaces, which describe a pseudopotential landscape for the slow mobility of coherent localized excitations, corresponding to continuous phase-space trajectories passing close to stationary modes. Investigating the two-parameter space of the model through independent variations of the nonlinearity constant and the power, we show how parameter regimes and directions of good mobility are connected to existence of smooth surfaces connecting the stationary states. In particular, directions where solutions can move with minimum radiation can be predicted from flatter parts of the surfaces. For such mobile solutions, slight perturbations in the transverse direction yield additional transverse oscillations w...
Directory of Open Access Journals (Sweden)
F Bakhshi Garmi
2016-02-01
Full Text Available In this paper we studied the focusing effect of electromagnetic wave in the two-dimensional graded photonic crystal consisting of Silicon rods in the air background with gradually varying lattice constant. The results showed that graded photonic crystal can focus wide beams on a narrow area at frequencies near the lower edge of the band gap, where equal frequency contours are not concave. For calculation of photonic band structure and equal frequency contours, we have used plane wave expansion method and revised plane wave expansion method, respectively. The calculation of the electric and magnetic fields was performed by finite difference time domain method.
Bloch waves in an arbitrary two-dimensional lattice of subwavelength Dirichlet scatterers
Schnitzer, Ory
2016-01-01
We study waves governed by the planar Helmholtz equation, propagating in an infinite lattice of subwavelength Dirichlet scatterers, the periodicity being comparable to the wavelength. Applying the method of matched asymptotic expansions, the scatterers are effectively replaced by asymptotic point constraints. The resulting coarse-grained Bloch-wave dispersion problem is solved by a generalised Fourier series, whose singular asymptotics in the vicinities of scatterers yield the dispersion relation governing modes that are strongly perturbed from plane-wave solutions existing in the absence of the scatterers; there are also empty-lattice waves that are only weakly perturbed. Characterising the latter is useful in interpreting and potentially designing the dispersion diagrams of such lattices. The method presented, that simplifies and expands on Krynkin & McIver [Waves Random Complex, 19 347 2009], could be applied in the future to study more sophisticated designs entailing resonant subwavelength elements di...
Auxetic two-dimensional lattice with Poisson's Ratio arbitrarily close to -1
Cabras, L
2014-01-01
In this paper we propose a new lattice structure having macroscopic Poisson's ratio arbitrarily close to the stability limit -1. We tested experimentally the effective Poisson's ratio of the micro-structured medium; the uniaxial test has been performed on a thermoplastic lattice produced with a 3d printing technology. A theoretical analysis of the effective properties has been performed and the expression of the macroscopic constitutive properties is given in full analytical form as a function of the constitutive properties of the elements of the lattice and on the geometry of the microstructure. The analysis has been performed on three micro-geometry leading to an isotropic behaviour for the cases of three-fold and six-fold symmetry and to a cubic behaviour for the case of four-fold symmetry.
Average site perimeter of directed animals on the two-dimensional lattices
Bacher, Axel
2009-01-01
We introduce new combinatorial (bijective) methods that enable us to compute the average value of three parameters of directed animals of a given area, including the site perimeter. Our results cover directed animals of any one-line source on the square lattice and its bounded variants, and we give counterparts for most of them in the triangular lattices. We thus prove conjectures by Conway and Le Borgne. The techniques used are based on Viennot's correspondence between directed animals and heaps of pieces (or elements of a partially commutative monoid).
de Forges de Parny, L.; Rousseau, V. G.
2017-01-01
We study the ground state and the thermal phase diagram of a two-species Bose-Hubbard model, with U(1 ) ×Z2 symmetry, describing atoms and molecules on a two-dimensional optical lattice interacting via a Feshbach resonance. Using quantum Monte Carlo simulations and mean-field theory, we show that the conversion between the two species, coherently coupling the atomic and molecular states, has a crucial impact on the Mott-superfluid transition and stabilizes an insulating phase with a gap controlled by the conversion term—the Feshbach insulator—instead of a standard Mott-insulating phase. Depending on the detuning between atoms and molecules, this model exhibits three phases: the Feshbach insulator, a molecular condensate coexisting with noncondensed atoms, and a mixed atomic-molecular condensate. Employing finite-size scaling analysis, we observe three-dimensional (3D) X Y (3D Ising) transition when U(1 ) (Z2) symmetry is broken, whereas the transition is first order when both U(1 ) and Z2 symmetries are spontaneously broken. The finite-temperature phase diagram is also discussed. The thermal disappearance of the molecular superfluid leads to a Berezinskii-Kosterlitz-Thouless transition with unusual universal jump in the superfluid density. The loss of the quasi-long-range coherence of the mixed atomic and molecular superfluid is more subtle since only atoms exhibit conventional Berezinskii-Kosterlitz-Thouless criticality. We also observe a signal compatible with a classical first-order transition between the mixed superfluid and the normal Bose liquid at low temperature.
Wenzel, Sandro; Bogacz, Leszek; Janke, Wolfhard
2008-09-19
The two-dimensional J-J' dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio alpha=J'/J. The critical point of the order-disorder quantum phase transition in the J-J' model is determined as alpha_c=2.5196(2) by finite-size scaling for up to approximately 10 000 quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the J-J' model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.
Zhou Yun Song; Wang Fu He
2003-01-01
We investigate the properties of guide modes localized at the interfaces of photonic crystal (PC) heterostructures which are composed of two semi-infinite two-dimensional PCs consisting of non-circular air cylinders with different rotating angles embedded in a homogeneous host dielectric. Photonic band gap structures are calculated with the use of the plane-wave expansion method in combination with a supercell technique. We consider various configurations, for instance, rectangular (square) lattice-rectangular (square) air cylinders, and different rotating angles of the cylinders in the lattices on either side of the interface of a heterostructure. We find that the absolute gap width and the number of guide modes strongly depend on geometric and physical parameters of the heterostructures. It is anticipated that the guide modes in such heterostructures can be engineered by adjusting parameters.
Giberti, Claudio; Vernia, Cecilia
1994-12-01
We consider diffusively coupled logistic maps in one- and two-dimensional lattices. We investigate periodic behaviors as the coupling parameter varies, i.e., existence and bifurcations of some periodic orbits with the largest domain of attraction. Similarity and differences between the two lattices are shown. For small coupling the periodic behavior appears to be characterized by a number of periodic orbits structured in such a way to give rise to distinct, reverse period-doubling sequences. For intermediate values of the coupling a prominent role in the dynamics is played by the presence of normally attracting manifolds that contain periodic orbits. The dynamics on these manifolds is very weakly hyperbolic, which implies long transients. A detailed investigation allows the understanding of the mechanism of their formation. A complex bifurcation is found which causes an attracting manifold to become unstable.
Institute of Scientific and Technical Information of China (English)
Xu Quan; Tian Qiang
2009-01-01
We study a two-dimensional (2D) diatomic lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers (DBs) can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein-Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers (QDBs) and chaotic discrete breathers (CDBs) by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom.
Wang, Pengfei; Gaitanaros, Stavros; Lee, Seungwoo; Bathe, Mark; Shih, William M; Ke, Yonggang
2016-06-22
Scaffolded DNA origami has proven to be a versatile method for generating functional nanostructures with prescribed sub-100 nm shapes. Programming DNA-origami tiles to form large-scale 2D lattices that span hundreds of nanometers to the micrometer scale could provide an enabling platform for diverse applications ranging from metamaterials to surface-based biophysical assays. Toward this end, here we design a family of hexagonal DNA-origami tiles using computer-aided design and demonstrate successful self-assembly of micrometer-scale 2D honeycomb lattices and tubes by controlling their geometric and mechanical properties including their interconnecting strands. Our results offer insight into programmed self-assembly of low-defect supra-molecular DNA-origami 2D lattices and tubes. In addition, we demonstrate that these DNA-origami hexagon tiles and honeycomb lattices are versatile platforms for assembling optical metamaterials via programmable spatial arrangement of gold nanoparticles (AuNPs) into cluster and superlattice geometries.
Institute of Scientific and Technical Information of China (English)
Kyu; Hwan; Hwang; G.; Hugh; Song; Chanmook; Lim; Soan; Kim; Kyung-Won; Chun; Mahn; Yong; Park
2003-01-01
A channel-drop filter has been designed based on the two-dimensional triangular-lattice hole photonic-crystal structure, which consists of two line defects and two point defects, by a two-dimensional finite-difference time-domain simulation.
Two-dimensional lattice solitons in polariton condensates with spin-orbit coupling
Kartashov, Yaroslav V
2016-01-01
We study two-dimensional fundamental and vortex solitons in polariton condensates with spin-orbit coupling and Zeeman splitting evolving in square arrays of microcavity pillars. Due to repulsive excitonic nonlinearity such states are encountered in finite gaps in the spectrum of the periodic array. Spin-orbit coupling between two polarization components stemming from TE-TM energy splitting of the cavity photons acting together with Zeeman splitting lifts the degeneracy between vortex solitons with opposite topological charges and makes their density profiles different for a fixed energy. This results in formation of four distinct families of vortex solitons with topological charges m=+-1, all of which can be stable. At the same time, only two stable families of fundamental gap solitons characterized by domination of different polarization components are encountered.
Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension
Lin, Qian; Xiao, Meng; Yuan, Luqi; Fan, Shanhui
2016-12-01
Weyl points, as a signature of 3D topological states, have been extensively studied in condensed matter systems. Recently, the physics of Weyl points has also been explored in electromagnetic structures such as photonic crystals and metamaterials. These structures typically have complex three-dimensional geometries, which limits the potential for exploring Weyl point physics in on-chip integrated systems. Here we show that Weyl point physics emerges in a system of two-dimensional arrays of resonators undergoing dynamic modulation of refractive index. In addition, the phase of modulation can be controlled to explore Weyl points under different symmetries. Furthermore, unlike static structures, in this system the non-trivial topology of the Weyl point manifests in terms of surface state arcs in the synthetic space that exhibit one-way frequency conversion. Our system therefore provides a versatile platform to explore and exploit Weyl point physics on chip.
Fabrication of deep-profile Al-doped ZnO one- and two-dimensional lattices as plasmonic elements
Jensen, Flemming; Shkondin, Evgeniy; Takayama, Osamu; Larsen, Pernille V.; Mar, Mikkel D.; Malureanu, Radu; Lavrinenko, Andrei V.
2016-09-01
In this work, we report on fabrication of deep-profile one- and two-dimensional lattices made from Al-doped ZnO (AZO). AZO is considered as an alternative plasmonic material having the real part of the permittivity negative in the near infrared range. The exact position of the plasma frequency of AZO is doping concentration dependent, allowing for tuning possibilities. In addition, the thickness of the AZO film also affects its material properties. Physical vapor deposition techniques typically applied for AZO coating do not enable deep profiling of a plasmonic structure. Using the atomic layer deposition technique, a highly conformal deposition method, allows us to fabricate high-aspect ratio structures such as one-dimensional lattices with a period of 400 nm and size of the lamina of 200 nm in width and 3 μm in depth. Thus, our structures have an aspect ratio of 1:15 and are homogeneous on areas of 2×2 cm2 and more. We also produce two-dimensional arrays of circular nanopillars with similar dimensions. Instead of nanopillars hollow tubes with a wall thickness on demand from 20 nm up to a complete fill can be fabricated.
Three-dimensional vortex solitons in quasi-two-dimensional lattices.
Leblond, Hervé; Malomed, Boris A; Mihalache, Dumitru
2007-08-01
We consider the three-dimensional (3D) Gross-Pitaevskii or nonlinear Schrödinger equation with a quasi-2D square-lattice potential (which corresponds to the optical lattice trapping a self-attractive Bose-Einstein condensate, or, in some approximation, to a photonic-crystal fiber, in terms of nonlinear optics). Stable 3D solitons, with embedded vorticity S=1 and 2, are found by means of the variational approximation and in a numerical form. They are built, basically, as sets of four fundamental solitons forming a rhombus, with phase shifts piS2 between adjacent sites, and an empty site in the middle. The results demonstrate two species of stable 3D solitons, which were not studied before, viz., localized vortices ("spinning light bullets," in terms of optics) with S>1 , and vortex solitons (with any S not equal 0 ) supported by a lattice in the 3D space. Typical scenarios of instability development (collapse or decay) of unstable localized vortices are identified too.
Staggered Flux State in Two-Dimensional Hubbard Models
Yokoyama, Hisatoshi; Tamura, Shun; Ogata, Masao
2016-12-01
The stability and other properties of a staggered flux (SF) state or a correlated d-density wave state are studied for the Hubbard (t-t'-U) model on extended square lattices, as a low-lying state that competes with the dx2 - y2-wave superconductivity (d-SC) and possibly causes the pseudogap phenomena in underdoped high-Tc cuprates and organic κ-BEDT-TTF salts. In calculations, a variational Monte Carlo method is used. In the trial wave function, a configuration-dependent phase factor, which is vital to treat a current-carrying state for a large U/t, is introduced in addition to ordinary correlation factors. Varying U/t, t'/t, and the doping rate (δ) systematically, we show that the SF state becomes more stable than the normal state (projected Fermi sea) for a strongly correlated (U/t ≳ 5) and underdoped (δ ≲ 0.16) area. The decrease in energy is sizable, particularly in the area where Mott physics prevails and the circular current (order parameter) is strongly suppressed. These features are consistent with those for the t-J model. The effect of the frustration t'/t plays a crucial role in preserving charge homogeneity and appropriately describing the behavior of hole- and electron-doped cuprates and κ-BEDT-TTF salts. We argue that the SF state does not coexist with d-SC and is not a "normal state" from which d-SC arises. We also show that a spin current (flux or nematic) state is never stabilized in the same regime.
Interfacial adsorption in two-dimensional pure and random-bond Potts models
Fytas, Nikolaos G.; Theodorakis, Panagiotis E.; Malakis, Anastasios
2017-03-01
We use Monte Carlo simulations to study the finite-size scaling behavior of the interfacial adsorption of the two-dimensional square-lattice q -states Potts model. We consider the pure and random-bond versions of the Potts model for q =3 ,4 ,5 ,8 , and 10, thus probing the interfacial properties at the originally continuous, weak, and strong first-order phase transitions. For the pure systems our results support the early scaling predictions for the size dependence of the interfacial adsorption at both first- and second-order phase transitions. For the disordered systems, the interfacial adsorption at the (disordered induced) continuous transitions is discussed, applying standard scaling arguments and invoking findings for bulk critical properties. The self-averaging properties of the interfacial adsorption are also analyzed by studying the infinite limit-size extrapolation of properly defined signal-to-noise ratios.
Dispersion of guided modes in two-dimensional split ring lattices
DEFF Research Database (Denmark)
Hansen, Per Lunnemann; Koenderink, A. Femius
2014-01-01
-plane electric modes. Scatterers that have an in-plane electric and out-of-plane magnetic polarizability, but without intrinsic magnetoelectric coupling, result in two bands that are mixtures of the bands of electric-only and magnetic-only lattices. Thereby, bianisotropy through mutual coupling, in absence...... of building-block bianisotropy, is evident. Once strong bianisotropy is included in each building block, the Bloch modes become even more strongly magnetoelectric. Our results are important to understand spatial dispersion and bianisotropy of metasurface and metamaterial designs....
Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities
El-Jallal, Said; Oudich, Mourad; Pennec, Yan; Djafari-Rouhani, Bahram; Laude, Vincent; Beugnot, Jean-Charles; Martínez, Alejandro; Escalante, José María; Makhoute, Abdelkader
2013-11-01
We theoretically investigate phonon-photon interaction in cavities created in a phoxonic crystal slab constituted by a two-dimensional (2D) square array of holes in a silicon membrane. The structure without defects provides 2D band gaps for both electromagnetic and elastic waves. We consider two types of cavities, namely, an L3 cavity (a row of three holes is removed) and a cross-shape cavity, which both possess highly confined phononic and photonic localized modes suitable for enhancing their interaction. In our theoretical study, we take into account two mechanisms that contribute to optomechanical interaction, namely, the photoelastic and the interface motion effects. We show that, depending on the considered pair of photonic and phononic modes, the two mechanisms can have similar or very different magnitudes, and their contributions can be either in or out of phase. We find out that only acoustic modes with a specific symmetry are allowed to couple with photonic cavity modes. The coupling strength is quantified by two different methods. In the first method, we compute a direct estimation of coupling rates by overlap integrals, while in the second one, we analyze the temporal modulation of the resonant photonic frequency by the phonon-induced acoustic vibrational motion during one acoustic period. Interestingly, we obtain high optomechanical interaction, with the coupling rate reaching more than 2.4 MHz for some specific phonon-photon pairs.
First-order phase transitions in repulsive rigid k-mers on two-dimensional lattices
Pasinetti, P. M.; Romá, F.; Ramirez-Pastor, A. J.
2012-02-01
In a previous paper [F. Romá, A. J. Ramirez-Pastor, and J. L. Riccardo, Phys. Rev. B 72, 035444 (2005)], the critical behavior of repulsive rigid rods of length k (k-mers) on a square lattice at half coverage has been studied by using Monte Carlo (MC) simulations. The obtained results indicated that (1) the phase transition occurring in the system is a second-order phase transition for all adsorbate sizes k; and (2) the universality class of the transition changes from 2D Ising-type for monomers (k = 1) to an unknown universality class for k ≥ 2. In the present work, we revisit our previous results together with further numerical evidences, resulting from new extensive MC simulations based on an efficient exchange algorithm and using high-performance computational capabilities. In contrast to our previous conclusions (1) and (2), the new numerical calculations clearly support the occurrence of a first-order phase transition for k ≥ 2. In addition, a similar scenario was found for k-mers adsorbed on the triangular lattice at coverage k/(2k+1).
Spectroscopy of Dipolar Fermions in Layered Two-Dimensional and Three-Dimensional Lattices
2011-09-06
term. We approximate Vαβ(j,ρ) by Vαβ(j,ρ) ≈ γαβU(j,ρ) (8) and Vsf by Vsf(j,ρ) ≈ ηU(j,ρ), (9) with U(j,ρ) = δ0j 1 ρ3 + A + (1 − δ0j ) 1 − 3( ( jdl )2 ρ2... jdl )2 ) [ρ2 + ( jdl )2]3/2 , (10) where γαβ = dααdββ/(4π 0), η = | ∫ dzw∗1(z)w2(z)|2d212/(4π 0), and dl is the lattice spacing, where A ∼ 3, with...3( ( jdl )2 ρ2+( jdl )2 ) [ρ2 + ( jdl )2]3/2 ] = 2π3/2 √ m β n (γ12 − γ11 + η) (thermal), (28) 033608-5 HAZZARD, GORSHKOV, AND REY PHYSICAL REVIEW A 84
Subtlety in the Critical Behavior of the Two Dimensional XY Model
Kim, Jae-Kwon
1996-03-01
We study the two dimensional classical XY model using the single cluster Monte Carlo algorithm^1. We present extensive high -temperature -phase bulk data that are extracted based on a novel finite- size- scaling Monte Carlo technique^2. The largest value of the estimated bulk correlation length is 1390 in lattice units. Our data reveal that η=1/4 sets in near criticality. The standard finite-size-scaling analysis of the data close to criticality, however, seems to indicate that η=1/4 is compatible only for a critical temperature (T_c) over the range 0.900 Wolff, Phys. Rev. Lett. 62, 361 (1989) ^2 J.-K. Kim, Euro. Phys. Lett. 28, 211 (1994) Research supported in part by the NSF
Hobrecht, Hendrik
2016-01-01
We present a systematic method to calculate the scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function $Z$ on an $L\\times M$ square lattice, wrapped around a torus with aspect ratio $\\rho=L/M$. By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a $2\\times2$ transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films $\\rho\\to 0$. Additionally, for the cylinder at criticality our result confirms the predictions...
Po, Hoi Chun; Zhou, Qi
2015-08-13
Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems.
Yamada, Masahiko G.; Soejima, Tomohiro; Tsuji, Naoto; Hirai, Daisuke; Dincǎ, Mircea; Aoki, Hideo
2016-08-01
We design from first principles a type of two-dimensional metal-organic framework (MOF) using phenalenyl-based ligands to exhibit a half-filled flat band of the kagome lattice, which is one of a family of lattices that show Lieb-Mielke-Tasaki's flat-band ferromagnetism. Among various MOFs, we find that trans-Au-THTAP (THTAP=trihydroxytriaminophenalenyl) has such an ideal band structure, where the Fermi energy is adjusted right at the flat band due to unpaired electrons of radical phenalenyl. The spin-orbit coupling opens a band gap giving a nonzero Chern number to the nearly flat band, as confirmed by the presence of the edge states in first-principles calculations and by fitting to the tight-binding model. This is a novel and realistic example of a system in which a nearly flat band is both ferromagnetic and topologically nontrivial.
Ma, Yandong; Kou, Liangzhi; Li, Xiao; Dai, Ying; Heine, Thomas
2016-01-01
So far, several transition metal dichalcogenide (TMDC)-based two-dimensional (2D) topological insulators (TIs) have been discovered, all of them based on a tetragonal lattice. However, in 2D crystals, the hexagonal rather than the tetragonal symmetry is the most common motif. Here, based on first principles calculations, we propose a class of stable 2D TMDCs of composition MX2(M =Mo ,W ;X =S ,Se ,Te ) with a hexagonal lattice. They are all in the same stability range as other 2D TMDC allotropes that have been demonstrated experimentally, and they are identified to be practical 2D TIs with large band gaps ranging from 41 to 198 meV, making them suitable for applications at room temperature. Besides, in contrast to tetragonal 2D TMDCs, their hexagonal lattice will greatly facilitate the integration of theses novel TI state van der Waals crystals with other hexagonal or honeycomb materials and thus provide a route for 2D material-based devices for wider nanoelectronic and spintronic applications. The nontrivial band gaps of both WS e2 and WT e2 2D crystals are 198 meV, which are larger than that in any previously reported TMDC-based TIs. These large band gaps entirely stem from the strong spin orbit coupling strength within the d orbitals of Mo/W atoms near the Fermi level. Our findings broaden the scientific and technological impact of both 2D TIs and TMDCs.
Nam, Keekwon; Kim, Bongsoo; Jong Lee, Sung
2014-08-01
We investigate the nonequilibrium relaxation dynamics of an interacting monomer-dimer model with nearest neighbor repulsion on a square lattice, which possesses two symmetric absorbing states. The model is known to exhibit two nearby continuous transitions: the Z2 symmetry-breaking order-disorder transition and the absorbing transition with directed percolation criticality. We performed a more detailed analysis of our extensive simulations on bigger lattice systems which reaffirms that the symmetry-breaking transition exhibits a non-Ising critical behavior with β ≃ 0.149(2) and η ≃ 0.30(1) that are distinct from those values of a pure two dimensional Ising model. Finite size scaling of dimer density near the symmetry breaking transition gives logarithmic scaling (α = 0.0) which is consistent with the hyperscaling relation but the corresponding exponent of νB ≃ 1.37(2) exhibits a conspicuous deviation from the pure Ising value of 1. The value of dynamic critical exponent z, however, is found to be close to that of the kinetic Ising model as 1/z ≃ 0.466(5) from the relaxation of staggered magnetization (and also similar but slightly smaller values from coarsening).
Transfer matrix computation of critical polynomials for two-dimensional Potts models
Lykke Jacobsen, Jesper; Scullard, Christian R.
2013-02-01
In our previous work [1] we have shown that critical manifolds of the q-state Potts model can be studied by means of a graph polynomial PB(q, v), henceforth referred to as the critical polynomial. This polynomial may be defined on any periodic two-dimensional lattice. It depends on a finite subgraph B, called the basis, and the manner in which B is tiled to construct the lattice. The real roots v = eK - 1 of PB(q, v) either give the exact critical points for the lattice, or provide approximations that, in principle, can be made arbitrarily accurate by increasing the size of B in an appropriate way. In earlier work, PB(q, v) was defined by a contraction-deletion identity, similar to that satisfied by the Tutte polynomial. Here, we give a probabilistic definition of PB(q, v), which facilitates its computation, using the transfer matrix, on much larger B than was previously possible. We present results for the critical polynomial on the (4, 82), kagome, and (3, 122) lattices for bases of up to respectively 96, 162, and 243 edges, compared to the limit of 36 edges with contraction-deletion. We discuss in detail the role of the symmetries and the embedding of B. The critical temperatures vc obtained for ferromagnetic (v > 0) Potts models are at least as precise as the best available results from Monte Carlo simulations or series expansions. For instance, with q = 3 we obtain vc(4, 82) = 3.742 489 (4), vc(kagome) = 1.876 459 7 (2), and vc(3, 122) = 5.033 078 49 (4), the precision being comparable or superior to the best simulation results. More generally, we trace the critical manifolds in the real (q, v) plane and discuss the intricate structure of the phase diagram in the antiferromagnetic (v < 0) region.
Energy Technology Data Exchange (ETDEWEB)
Dai Jian [Theory Group, Department of Physics, Peking University, Beijing (China)]. E-mail: jdai@mail.phy.pku.edu.cn; Song Xingchang [Theory Group, Department of Physics, Peking University, Beijing (China)]. E-mail: songxc@ibm320h.phy.pku.edu.cn
2001-07-13
One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as 'natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices. (author)
Oh, Joosung; Le, Manh Duc; Jeong, Jaehong; Lee, Jung-hyun; Woo, Hyungje; Song, Wan-Young; Perring, T. G.; Buyers, W. J. L.; Cheong, S.-W.; Park, Je-Geun
2013-12-01
The breakdown of magnons, the quasiparticles of magnetic systems, has rarely been seen. By using an inelastic neutron scattering technique, we report the observation of spontaneous magnon decay in multiferroic LuMnO3, a simple two dimensional Heisenberg triangular lattice antiferromagnet, with large spin S=2. The origin of this rare phenomenon lies in the nonvanishing cubic interaction between magnons in the spin Hamiltonian arising from the noncollinear 120° spin structure. We observed all three key features of the nonlinear effects as theoretically predicted: a rotonlike minimum, a flat mode, and a linewidth broadening, in our inelastic neutron scattering measurements of single crystal LuMnO3. Our results show that quasiparticles in a system hitherto thought of as “classical” can indeed break down.
Oh, Joosung; Le, Manh Duc; Jeong, Jaehong; Lee, Jung-hyun; Woo, Hyungje; Song, Wan-Young; Perring, T G; Buyers, W J L; Cheong, S-W; Park, Je-Geun
2013-12-20
The breakdown of magnons, the quasiparticles of magnetic systems, has rarely been seen. By using an inelastic neutron scattering technique, we report the observation of spontaneous magnon decay in multiferroic LuMnO3, a simple two dimensional Heisenberg triangular lattice antiferromagnet, with large spin S=2. The origin of this rare phenomenon lies in the nonvanishing cubic interaction between magnons in the spin Hamiltonian arising from the noncollinear 120° spin structure. We observed all three key features of the nonlinear effects as theoretically predicted: a rotonlike minimum, a flat mode, and a linewidth broadening, in our inelastic neutron scattering measurements of single crystal LuMnO3. Our results show that quasiparticles in a system hitherto thought of as "classical" can indeed break down.
Ochiai, Tetsuyuki
2016-01-01
We show the presence of Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice. The Weyl points in the three-dimensional Brillouin zone and Fermi-arc surface states are clearly demonstrated in the quasienergy spectrum of the system in the Weyl phase. In addition, chiral surface states coexist in this phase. The Floquet-topological-insulator phase is characterized by the winding number of two in the reflection matrices of the semi-infinite system and resulting two gapless surface states in the quasienergy g ap of the bulk. The phase diagram of the system is derived in the two-parameter space of hopping S-matrices among the rings. We also discuss a possible optical realization of the system together with the introduction of synthetic gauge fields.
Energy Technology Data Exchange (ETDEWEB)
Xi, Kui-Tian, E-mail: kuitianxi@gmail.com; Li, Jinbin, E-mail: jinbin@nuaa.edu.cn; Shi, Da-Ning, E-mail: shi@nuaa.edu.cn
2014-03-01
We consider a weakly interacting two-component Bose–Einstein condensate (BEC) in a two-dimensional (2D) quasi-periodic bichromatic optical lattice (BOL). The problem is studied by means of split-step Crank–Nicolson method. The effects of weak intra- and inter-component interactions on localization of a two-component BEC are investigated. It is shown that in the quasi-2D regime, due to the enhanced disorder, there is no symmetry breaking like that in the one-dimensional (1D) case under a sine-typed potential, while configurations of density profiles are also quite different from that in the 1D case. By modulating interactions, the interplay of disorder and weak repulsive or attractive interactions is studied in detail. The cases with sine- and cosine-typed potentials acting on components 1 and 2 respectively are also discussed.
Ochiai, Tetsuyuki
2016-10-01
We show the presence of Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice. The Weyl points in the three-dimensional Brillouin zone and Fermi-arc surface states are clearly demonstrated in the quasienergy spectrum of the system in the Floquet-Weyl phase. In addition, chiral surface states coexist in this phase. The Floquet-topological-insulator phase is characterized by the winding number of two in the reflection matrices of the semi-infinite system and resulting two gapless surface states in the quasienergy gap of the bulk. The phase diagram of the system is derived in the two-parameter space of hopping S-matrices among the rings. We also discuss a possible optical realization of the system together with the introduction of synthetic gauge fields.
A novel two-dimensional MgB6 crystal: metal-layer stabilized boron kagome lattice.
Xie, Sheng-Yi; Li, Xian-Bin; Tian, Wei Quan; Chen, Nian-Ke; Wang, Yeliang; Zhang, Shengbai; Sun, Hong-Bo
2015-01-14
Based on first-principles calculations, we designed for the first time a boron-kagome-based two-dimensional MgB6 crystal, in which two boron kagome layers sandwich a triangular magnesium layer. The two-dimensional lattice is metallic with several bands across the Fermi level, and among them a Dirac point appears at the K point of the first Brillouin zone. This metal-stabilized boron kagome system displays electron-phonon coupling, with a superconductivity critical transition temperature of 4.7 K, and thus it is another possible superconducting Mg-B compound besides MgB2. Furthermore, the proposed 2D MgB6 can also be used for hydrogen storage after decoration with Ca. Up to five H2 molecules can be attracted by one Ca with an average binding energy of 0.225 eV. The unique properties of 2D MgB6 will spur broad interest in nanoscience and technology.
The two-dimensional Godunov scheme and what it means for macroscopic pedestrian flow models
Van Wageningen-Kessels, F.L.M.; Daamen, W.; Hoogendoorn, S.P.
2015-01-01
An efficient simulation method for two-dimensional continuum pedestrian flow models is introduced. It is a two-dimensional and multi-class extension of the Go-dunov scheme for one-dimensional road traffic flow models introduced in the mid 1990’s. The method can be applied to continuum pedestrian flo
Lattice Boltzmann Model for Compressible Fluid on a Square Lattice
Institute of Scientific and Technical Information of China (English)
SUN Cheng-Hai
2000-01-01
A two-level four-direction lattice Boltzmann model is formulated on a square lattice to simulate compressible flows with a high Mach number. The particle velocities are adaptive to the mean velocity and internal energy. Therefore, the mean flow can have a high Mach number. Due to the simple form of the equilibrium distribution, the 4th order velocity tensors are not involved in the calculations. Unlike the standard lattice Boltzmann model, o special treatment is need for the homogeneity of 4th order velocity tensors on square lattices. The Navier-Stokes equations were derived by the Chapman-Enskog method from the BGK Boltzmann equation. The model can be easily extended to three-dimensional cubic lattices. Two-dimensional shock-wave propagation was simulated
Zeng, Jianhua
2013-01-01
It is commonly known that stable bright solitons in periodic potentials, which represent gratings in photonics/plasmonics, or optical lattices in quantum gases, exist either in the spectral semi-infinite gap (SIG) or in finite bandgaps. Using numerical methods, we demonstrate that, under the action of the cubic self-focusing nonlinearity, defects in the form of "holes" in two-dimensional (2D) lattices support continuous families of 2D solitons \\textit{embedded} into the first two Bloch bands of the respective linear spectrum, where solitons normally do not exist. The two families of the \\textit{embedded defect solitons} (EDSs) are found to be continuously linked by the branch of \\textit{gap defect solitons} (GDSs) populating the first finite bandgap. Further, the EDS branch traversing the first band links the GDS family with the branch of regular defect-supported solitons populating the SIG. Thus, we construct a continuous chain of regular, embedded, and gap-mode solitons ("superfamily") threading the entire ...
Fluctuations in an ordered c (2×2) two-dimensional lattice-gas system with repulsive interactions
Argyrakis, P.; Chumak, A. A.; Maragakis, M.
2005-06-01
Fluctuations of the particle density in an ordered c(2×2) two-dimensional lattice-gas system are studied both analytically and by means of Monte Carlo simulations. The ordering is caused by a strong interparticle repulsive interaction resulting in the second order phase transition. The lattice of adsorption sites is divided into two sublattices (almost filled and almost empty sublattices) each of which contains a small number of structural “defects,” i.e., vacancies and excess particles. The relaxation of the correlation function of fluctuations turns out to be governed by two different functions. This peculiarity is to be contrasted with the traditional fluctuation theory which predicts the existence of a single damping constant, determined by the collective diffusion coefficient. A specific thesis of the proposed approach is that transport phenomena in ordered systems may be described in terms of both displacements and generation-recombination of structural defects. Accordingly, the correlation function of fluctuations depends on diffusion coefficients of two defect species as well as on the generation-recombination frequency. Our theory reduces to the usual one when fluctuations occur under local equilibrium conditions, i.e., for a sufficiently large size of probe areas and not too great values of interaction parameter. The analytical results agree well with those obtained in the Monte Carlo framework.
Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.
2016-05-01
Progress in describing thermodynamic phase transitions in quantum systems is obtained by noticing that the Gibbs operator e-β H for a two-dimensional (2D) lattice system with a Hamiltonian H can be represented by a three-dimensional tensor network, the third dimension being the imaginary time (inverse temperature) β . Coarse graining the network along β results in a 2D projected entangled-pair operator (PEPO) with a finite bond dimension D . The coarse graining is performed by a tree tensor network of isometries. The isometries are optimized variationally, taking into account full tensor environment, to maximize the accuracy of the PEPO. The algorithm is applied to the isotropic quantum compass model on an infinite square lattice near a symmetry-breaking phase transition at finite temperature. From the linear susceptibility in the symmetric phase and the order parameter in the symmetry-broken phase, the critical temperature is estimated at Tc=0.0606 (4 ) J , where J is the isotropic coupling constant between S =1/2 pseudospins.
Analytical two-dimensional model of solar cell current-voltage characteristics
Energy Technology Data Exchange (ETDEWEB)
Caldararu, F.; Caldararu, M.; Nan, S.; Nicolaescu, D.; Vasile, S. (ICCE, Bucharest (RO). R and D Center for Electron Devices)
1991-06-01
This paper describes an analytical two-dimensional model for pn junction solar cell I-V characteristic. In order to solve the two-dimensional equations for the minority carrier concentration the Laplace transformation method is used. The model eliminates Hovel's assumptions concerning a one-dimensional model and provides an I-V characteristic that is simpler than those derived from the one-dimensional model. The method can be extended to any other device with two-dimensional symmetry. (author).
E and S hysteresis model for two-dimensional magnetic properties
Soda, N
2000-01-01
We define an effective hysteresis model of two-dimensional magnetic properties for the magnetic field analysis. Our hysteresis model is applicable to both alternating and rotating flux conditions. Moreover, we compare the calculated results with the measured ones, and verify the accuracy of this model. We can calculate iron losses in the magnetic materials exactly. As a result, it is shown that the hysteresis model is generally applicable to two-dimensional magnetic properties of some kinds of magnetic materials.
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.
Energy Technology Data Exchange (ETDEWEB)
Mahato, Bipul Kumar; Rana, Bivas; Kumar, Dheeraj; Barman, Saswati; Barman, Anjan, E-mail: abarman@bose.res.in [Thematic Unit of Excellence on Nanodevice Technology, Department of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098 (India); Sugimoto, Satoshi [Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581 (Japan); Otani, YoshiChika [Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581 (Japan); CEMS-RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan)
2014-07-07
We demonstrate tunable spin wave spectrum in two-dimensional Ni{sub 80}Fe{sub 20} nanodot lattices by varying dot shape. A single collective mode in elliptical dot lattices transforms into three distinct modes for the half-elliptical, rectangular, and diamond dot lattices, albeit with different peak frequencies and intensities. A drastic change is observed for the triangular dots, where eight modes covering a broad band are observed. Using micromagnetic simulations, we characterized the modes as different localized, extended, and quantized modes, whose frequencies and spatial profiles are determined by a combination of internal field profiles within the nanodots and the stray magnetic field within the lattice.
Two-dimensional MHD model of the Jovian magnetodisk
Kislov, R. A.; Malova, H. V.; Vasko, I. Y.
2015-09-01
A self-consistent stationary axially symmetric MHD model of the Jovian magnetodisk is constructed. This model is a generalization of the models of plane current sheets that have been proposed earlier in order to describe the structure of the current sheet in the magnetotail of the Earth [1, 2]. The model takes centrifugal force, which is induced by the corotation electric field, and the azimuthal magnetic field into account. The configurations of the magnetic field lines for the isothermic (plasma temperature assumed to be constant) and the isentropic (plasma entropy assumed to be constant) models of the magnetodisk are determined. The dependence of the thickness of the magnetodisk on the distance to Jupiter is obtained. The thickness of the magnetodisk and the magnetic field distribution in the isothermic and isentropic models are similar. The inclusion of a low background plasma pressure results in a considerable reduction in the thickness of the magnetodisk. This effect may be attributed to the fact that centrifugal force prevails over the pressure gradient at large distances from the planet. The mechanism of unipolar induction and the related large-scale current system are analyzed. The direct and return Birkeland currents are determined in the approximation of a weak azimuthal magnetic field. The modeling results agree with theoretical estimates from other studies and experimental data.
two - dimensional mathematical model of water flow in open ...
African Journals Online (AJOL)
ES Obe
1996-09-01
Sep 1, 1996 ... simplification of the system of the governing shallow water equations ... For optional design of the ... models. One of the facilities for preliminary appraisal of the ... distribution. ..... indicated for the individual methods, located ...
Potts models coupled to two-dimensional quantum gravity
Baillie, Clive F.
We perform Monte Carlo simulations using the Wolff cluster algorithm of the q=2 (Ising), 3 and 4 Potts models on dynamical phi-cubed graphs of spherical topology with up to 5000 nodes. We find that the measured critical exponents are in reasonable agreement with those from the exact solution of the Ising model and with those calculated from KPZ scaling for q=3,4 where no exact solution is available.
Two-dimensional biomass combustion modeling of CFB
Energy Technology Data Exchange (ETDEWEB)
Afsin Gungor [Nigde University, Nigde (Turkey). Department of Mechanical Engineering, Faculty of Engineering and Architecture
2008-07-15
In this study, a 2D model for a CFB biomass combustor has been developed which integrates and simultaneously predicts the hydrodynamics, heat transfer and combustion aspects. Combustor hydrodynamic is modeled taking into account previous work. Simulation model calculates the axial and radial distribution of voidage, velocity, particle size distribution, pressure drop, gas emissions and temperature at each time interval for gas and solid phase both for bottom and upper zones. The model results are compared with and validated against experimental data both for small-size and industrial-size biomass combustors which uses different types of biomass fuels given in the literature. As a result of sensitivity analysis, it is observed that: major portion of the combustion will take place in the upper zone, the air staging could improve combustion, for industrial-size CFB biomass combustors and the decrease of NOx adversely results in high CO emissions as air ratio decreases. Unexpected results concerning the emissions is caused by using data of different sized CFBs and is clearly an indicator of the necessity to compare the model results with various sized CFBs as far as possible. 71 refs., 10 figs., 5 tabs.
Halliday, I; Xu, X; Burgin, K
2017-02-01
An extended Benzi-Dellar lattice Boltzmann equation scheme [R. Benzi, S. Succi, and M. Vergassola, Europhys. Lett. 13, 727 (1990)EULEEJ0295-507510.1209/0295-5075/13/8/010; R. Benzi, S. Succi, and M. Vergassola, Phys. Rep. 222, 145 (1992)PRPLCM0370-157310.1016/0370-1573(92)90090-M; P. J. Dellar, Phys. Rev. E 65, 036309 (2002)1063-651X10.1103/PhysRevE.65.036309] is developed and applied to the problem of confirming, at low Re and drop fluid concentration, c, the variation of effective shear viscosity, η_{eff}=η_{1}[1+f(η_{1},η_{2})c], with respect to c for a sheared, two-dimensional, initially crystalline emulsion [here η_{1} (η_{2}) is the fluid (drop fluid) shear viscosity]. Data obtained with our enhanced multicomponent lattice Boltzmann method, using average shear stress and hydrodynamic dissipation, agree well once appropriate corrections to Landau's volume average shear stress [L. Landau and E. M. Lifshitz, Fluid Mechanics, 6th ed. (Pergamon, London, 1966)] are applied. Simulation results also confirm the expected form for f(η_{i},η_{2}), and they provide a reasonable estimate of its parameters. Most significantly, perhaps, the generality of our data supports the validity of Taylor's disputed simplification [G. I. Taylor, Proc. R. Soc. London, Ser. A 138, 133 (1932)1364-502110.1098/rspa.1932.0175] to reduce the effect of one hydrodynamic boundary condition (on the continuity of the normal contraction of stress) to an assumption that interfacial tension is sufficiently strong to maintain a spherical drop shape.
Halliday, I.; Xu, X.; Burgin, K.
2017-02-01
An extended Benzi-Dellar lattice Boltzmann equation scheme [R. Benzi, S. Succi, and M. Vergassola, Europhys. Lett. 13, 727 (1990), 10.1209/0295-5075/13/8/010; R. Benzi, S. Succi, and M. Vergassola, Phys. Rep. 222, 145 (1992), 10.1016/0370-1573(92)90090-M; P. J. Dellar, Phys. Rev. E 65, 036309 (2002), 10.1103/PhysRevE.65.036309] is developed and applied to the problem of confirming, at low Re and drop fluid concentration, c , the variation of effective shear viscosity, ηeff=η1[1 +f (η1,η2) c ] , with respect to c for a sheared, two-dimensional, initially crystalline emulsion [here η1 (η2) is the fluid (drop fluid) shear viscosity]. Data obtained with our enhanced multicomponent lattice Boltzmann method, using average shear stress and hydrodynamic dissipation, agree well once appropriate corrections to Landau's volume average shear stress [L. Landau and E. M. Lifshitz, Fluid Mechanics, 6th ed. (Pergamon, London, 1966)] are applied. Simulation results also confirm the expected form for f (ηi,η2) , and they provide a reasonable estimate of its parameters. Most significantly, perhaps, the generality of our data supports the validity of Taylor's disputed simplification [G. I. Taylor, Proc. R. Soc. London, Ser. A 138, 133 (1932), 10.1098/rspa.1932.0175] to reduce the effect of one hydrodynamic boundary condition (on the continuity of the normal contraction of stress) to an assumption that interfacial tension is sufficiently strong to maintain a spherical drop shape.
Modelling and design of complete photonic band gaps in two-dimensional photonic crystals
Indian Academy of Sciences (India)
Yogita Kalra; R K Sinha
2008-01-01
In this paper, we investigate the existence and variation of complete photonic band gap size with the introduction of asymmetry in the constituent dielectric rods with honeycomb lattices in two-dimensional photonic crystals (PhC) using the plane-wave expansion (PWE) method. Two examples, one consisting of elliptical rods and the other comprising of rectangular rods in honeycomb lattices are considered with a view to estimate the design parameters for maximizing the complete photonic band gap. Further, it has been shown that complete photonic band gap size changes with the variation in the orientation angle of the constituent dielectric rods.
Two-dimensional hydrologic modeling to evaluate aquatic habitat conditions
Pamela Edwards; Frederica Wood; Michael Little; Peter Vila; Peter Vila
2006-01-01
We describe the modeling and mapping procedures used to examine aquatic habitat conditions and habitat suitability of a small river in north- central West Virginia where fish survival and reproduction in specific reaches are poor. The study includes: (1) surveying cross sections of streambed reaches and measuring discharges and corresponding water-surface elevations,...
Improved actions for the two-dimensional sigma-model
Caracciolo, Sergio; Montanari, Andrea; Pelissetto, Andrea
1997-01-01
For the O(N) sigma-model we studied the improvement program for actions with two- and four-spin interactions. An interesting example is an action which is reflection-positive, on-shell improved, and has all the coupling defined on an elementary plaquette. We show the large N solution and preliminary Monte Carlo results for N=3.
Newman, P. A.; Schoeberl, M. R.; Plumb, R. A.
1986-01-01
Calculations of the two-dimensional, species-independent mixing coefficients for two-dimensional chemical models for the troposphere and stratosphere are performed using quasi-geostrophic potential vorticity fluxes and gradients from 4 years of National Meteorological Center data for the four seasons in both hemispheres. Results show that the horizontal mixing coefficient values for the winter lower stratosphere are broadly consistent with those currently employed in two-dimensional models, but the horizontal mixing coefficient values in the northern winter upper stratosphere are much larger than those usually used.
Flow Modelling for partially Cavitating Two-dimensional Hydrofoils
DEFF Research Database (Denmark)
Krishnaswamy, Paddy
2001-01-01
The present work addresses te computational analysis of partial sheet hydrofoil cavitation in two dimensions. Particular attention is given to the method of simulating the flow at the end of the cavity. A fixed-length partially cavitating panel method is used to predict the height of the re...... of the model and comparing the present calculations with numerical results. The flow around the partially cavitating hydrofoil with a re-entrant jet has also been treated with a viscous/inviscid interactive method. The viscous flow model is based on boundary layer theory applied on the compound foil......, consisting of the union of the cavity and the hydrofoil surface. The change in the flow direction in the cavity closure region is seen to have a slightly adverse effect on the viscous pressure distribution. Otherwise, it is seen that the viscous re-entrant jet solution compares favourably with experimental...
Numerical modeling of transient two-dimensional viscoelastic waves
Lombard, Bruno
2010-01-01
This paper deals with the numerical modeling of transient mechanical waves in linear viscoelastic solids. Dissipation mechanisms are described using the Zener model. No time convolutions are required thanks to the introduction of memory variables that satisfy local-in-time differential equations. By appropriately choosing the Zener parameters, it is possible to accurately describe a large range of materials, such as solids with constant quality factors. The evolution equations satisfied by the velocity, the stress, and the memory variables are written in the form of a first-order system of PDEs with a source term. This system is solved by splitting it into two parts: the propagative part is discretized explicitly, using a fourth-order ADER scheme on a Cartesian grid, and the diffusive part is then solved exactly. Jump conditions along the interfaces are discretized by applying an immersed interface method. Numerical experiments of wave propagation in viscoelastic and fluid media show the efficiency of this nu...
Relations between two-dimensional models from dimensional reduction
Energy Technology Data Exchange (ETDEWEB)
Amaral, R.L.P.G.; Natividade, C.P. [Universidade Federal Fluminense, Niteroi, RJ (Brazil). Inst. de Fisica
1998-12-31
In this work we explore the consequences of dimensional reduction of the 3D Maxwell-Chern-Simons and some related models. A connection between topological mass generation in 3D and mass generation according to the Schwinger mechanism in 2D is obtained. Besides, a series of relationships are established by resorting to dimensional reduction and duality interpolating transformations. Nonabelian generalizations are also pointed out. (author) 10 refs.
Model and observed seismicity represented in a two dimensional space
Directory of Open Access Journals (Sweden)
M. Caputo
1976-06-01
Full Text Available In recent years theoretical seismology lias introduced
some formulae relating the magnitude and the seismic moment of earthquakes
to the size of the fault and the stress drop which generated the
earthquake.
In the present paper we introduce a model for the statistics of the
earthquakes based on these formulae. The model gives formulae which
show internal consistency and are also confirmed by observations.
For intermediate magnitudes the formulae reproduce also the trend
of linearity of the statistics of magnitude and moment observed in all the
seismic regions of the world. This linear trend changes into a curve with
increasing slope for large magnitudes and moment.
When a catalogue of the magnitudes and/or the seismic moment of
the earthquakes of a seismic region is available, the model allows to estimate
the maximum magnitude possible in the region.
Phase transitions in the two-dimensional Anisotropic Biquadratic Heisenberg Model
Energy Technology Data Exchange (ETDEWEB)
Moura, A.R., E-mail: armoura@infis.ufu.br [Universidade Federal de Uberlândia (Brazil); Pires, A.S.T., E-mail: antpires@fisica.ufmg.br [Universidade Federal de Minas Gerais (Brazil); Pereira, A.R., E-mail: apereira@ufv.br [Universidade Federal de Viçosa (Brazil)
2014-05-01
In this paper we study the influence of the single-ion anisotropy in the two-dimensional biquadratic Heisenberg model (ABHM) on the square lattice at zero and finite low temperatures. It is common to represent the bilinear and biquadratic terms by J{sub 1}=Jcosθ and J{sub 2}=Jsinθ, respectively, and the many phases present in the model as a function of θ are well documented. However we have adopted a constant value for the bilinear constant (J{sub 1}=1) and small values of the biquadratic term (|J{sub 2}|
A Two-Dimensional PEM Fuel Cell Model
Shi, Zhongying; Wang, Xia; Zhang, Zhuqian
2006-11-01
Proton Exchange Membrane (PEM) fuel cell is a typical low temperature cell, where hydrogen and air are fed into the porous anodic electrode and cathodic electrode though the gas distributors on the bipolar plates, respectively. Activated by the catalyst on anode side, hydrogen will spilt into protons and electrons. Since only protons will be allowed to pass through the membrane, electrons must go through an external circuit. Electrons and protons meet air on cathode side to produce water and heat catalyzed by the catalyst on the cathode side. Numerical simulations are useful tools to describe the basic transport and electrochemical phenomena of PEM fuel cells. The goal of the present work is to develop 2-D computational models of PEM fuel cells, which take into account fluid flow, multi- species transport, current distribution and electrical potential. The velocity field in free channel described by Navier-Stokes equation and the velocity field in porous media described by Darcy’s Law are coupled along the channel-MEA interface. The governing differential equations are solved over a single computational domain, which consists of two gas channel layers, two gas diffusion layers, two catalyst layers as well as a membrane. The model is solved with commercial software COMSOL Multiphysics 3.2b. Parametric study will be conducted to analyze the effects of various parameters on the performance of PEM fuel cells. The results, including the mass concentration, the polarization curve and the velocity distribution, will be presented.
On Regularity Criteria for the Two-Dimensional Generalized Liquid Crystal Model
Directory of Open Access Journals (Sweden)
Yanan Wang
2014-01-01
Full Text Available We establish the regularity criteria for the two-dimensional generalized liquid crystal model. It turns out that the global existence results satisfy our regularity criteria naturally.
Mesh-free Hamiltonian implementation of two dimensional Darwin model
Siddi, Lorenzo; Lapenta, Giovanni; Gibbon, Paul
2017-08-01
A new approach to Darwin or magnetoinductive plasma simulation is presented, which combines a mesh-free field solver with a robust time-integration scheme avoiding numerical divergence errors in the solenoidal field components. The mesh-free formulation employs an efficient parallel Barnes-Hut tree algorithm to speed up the computation of fields summed directly from the particles, avoiding the necessity of divergence cleaning procedures typically required by particle-in-cell methods. The time-integration scheme employs a Hamiltonian formulation of the Lorentz force, circumventing the development of violent numerical instabilities associated with time differentiation of the vector potential. It is shown that a semi-implicit scheme converges rapidly and is robust to further numerical instabilities which can develop from a dominant contribution of the vector potential to the canonical momenta. The model is validated by various static and dynamic benchmark tests, including a simulation of the Weibel-like filamentation instability in beam-plasma interactions.
Two dimensional cellular automaton for evacuation modeling: hybrid shuffle update
Arita, Chikashi; Appert-Rolland, Cécile
2015-01-01
We consider a cellular automaton model with a static floor field for pedestrians evacuating a room. After identifying some properties of real pedestrian flows, we discuss various update schemes, and we introduce a new one, the hybrid shuffle update. The properties specific to pedestrians are incorporated in variables associated to particles called phases, that represent their step cycles. The dynamics of the phases gives naturally raise to some friction, and allows to reproduce several features observed in experiments. We study in particular the crossover between a low- and a high-density regime that occurs when the density of pedestrian increases, the dependency of the outflow in the strength of the floor field, and the shape of the queue in front of the exit.
TWO-DIMENSIONAL MODELLING OF ACCIDENTAL FLOOD WAVES PROPAGATION
Directory of Open Access Journals (Sweden)
Lorand Catalin STOENESCU
2011-05-01
Full Text Available The study presented in this article describes a modern modeling methodology of the propagation of accidental flood waves in case a dam break; this methodology is applied in Romania for the first time for the pilot project „Breaking scenarios of Poiana Uzului dam”. The calculation programs used help us obtain a bidimensional calculation (2D of the propagation of flood waves, taking into consideration the diminishing of the flood wave on a normal direction to the main direction; this diminishing of the flood wave is important in the case of sinuous courses of water or with urban settlements very close to the minor river bed. In the case of Poiana Uzului dam, 2 scenarios were simulated with the help of Ph.D. Eng. Dan Stematiu, plausible scenarios but with very little chances of actually producing. The results were presented as animations with flooded surfaces at certain time steps successively.
Two-Dimensional Coupling Model on Social Deprivation and Its Application
Fu, Yun
This paper qualitatively describes the deprivation under different coupling situations of two-dimensional indicators and then establishes the two-dimensional coupling model on social deprivation, using the social welfare function approach and Foster-Greer-Thorbecke P α method. Finally, this paper applies the model to evaluate the social deprivation of 31 provinces in China under the coupling state of capita disposable income and housing price.
Finite-time scaling via linear driving: application to the two-dimensional Potts model.
Huang, Xianzhi; Gong, Shurong; Zhong, Fan; Fan, Shuangli
2010-04-01
We apply finite-time scaling to the q-state Potts model with q=3 and 4 on two-dimensional lattices to determine its critical properties. This consists in applying to the model a linearly varying external field that couples to one of its q states to manipulate its dynamics in the vicinity of its criticality and that drives the system out of equilibrium and thus produces hysteresis and in defining an order parameter other than the usual one and a nonequilibrium susceptibility to extract coercive fields. From the finite-time scaling of the order parameter, the coercivity, and the hysteresis area and its derivative, we are able to determine systematically both static and dynamic critical exponents as well as the critical temperature. The static critical exponents obtained in general and the magnetic exponent delta in particular agree reasonably with the conjectured ones. The dynamic critical exponents obtained appear to confirm the proposed dynamic weak universality but unlikely to agree with recent short-time dynamic results for q=4. Our results also suggest an alternative way to characterize the weak universality.
Ochiai, Tetsuyuki
2016-01-01
Synthetic gauge field and pseudospin-orbit interaction are implemented in the stacked two-dimensional ring network model proposed by the present author. The model was introduced to simulate light propagation in the corresponding ring-resonator network, and is thus completely bosonic. Without these two items, the system exhibits Floquet-Weyl and Floquet-topological-insulator phases with topologically gapless and gapped band structures, respectively. The synthetic magnetic field implemented in the model results in a three-dimensional Hofstadter-butterfly-type spectrum in a photonic platform. The resulting gaps are characterization by the winding number of relevant S-matrices together with the Chern number of the bulk bands. The pseudospin-orbit interaction is defined as the mixing term between two pseudospin degrees of freedom in the rings, namely, the clockwise and counter-clockwise modes in the rings. It destroys the Floquet-topological-insulator phases, while the Floquet-Weyl phase with multiple Weyl points ...
Chetverikov, A. P.; Ebeling, W.; Velarde, M. G.
2016-09-01
We present computational evidence of the possibility of fast, supersonic or subsonic, nearly loss-free ballistic-like transport of electrons bound to lattice solitons (a form of electron surfing on acoustic waves) along crystallographic axes in two-dimensional anharmonic crystal lattices. First we study the structural changes a soliton creates in the lattice and the time lapse of recovery of the lattice. Then we study the behavior of one electron in the polarization field of one and two solitons with crossing pathways with suitably monitored delay. We show how an electron surfing on a lattice soliton may switch to surf on the second soliton and hence changing accordingly the direction of its path. Finally we discuss the possibility to control the way an excess electron proceeds from a source at a border of the lattice to a selected drain at another border by following appropriate straight pathways on crystallographic axes.
Critical Casimir force scaling functions of the two-dimensional Ising model at finite aspect ratios
Hobrecht, Hendrik; Hucht, Alfred
2017-02-01
We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function Z on an L× M square lattice, wrapped around a torus with aspect ratio ρ =L/M . By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a 2× 2 transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films ρ \\to 0 . Additionally, for the cylinder at criticality our results confirm the predictions from conformal field theory.
DEFF Research Database (Denmark)
Eilbeck, J. C; Lomdahl, P.S.; Olsen, O.H.
1985-01-01
A two-dimensional model of Josephson junction of overlap type is presented. The energy input is provided through induced magnetic fields modeled by a set of boundary conditions. In the limit of a very narrow junction, this model reduces to the one-dimensional model. Further, an equation derived f...
Two-dimensional analytical models for asymmetric fully depleted double-gate strained silicon MOSFETs
Institute of Scientific and Technical Information of China (English)
Liu Hong-Xia; Li Jin; Li Bin; Cao Lei; Yuan Bo
2011-01-01
This paper develops the simple and accurate two-dimensional analytical models for new asymmetric double-gate fully depleted strained-Si MOSFET. The models mainly include the analytical equations of the surface potential, surface electric field and threshold voltage, which are derived by solving two dimensional Poisson equation in strained-Si layer.The models are verified by numerical simulation. Besides offering the physical insight into device physics in the model,the new structure also provides the basic designing guidance for further immunity of short channel effect and drain-induced barrier-lowering of CMOS-based devices in nanometre scale.
A Large Deformation Model for the Elastic Moduli of Two-dimensional Cellular Materials
Institute of Scientific and Technical Information of China (English)
HU Guoming; WAN Hui; ZHANG Youlin; BAO Wujun
2006-01-01
We developed a large deformation model for predicting the elastic moduli of two-dimensional cellular materials. This large deformation model was based on the large deflection of the inclined members of the cells of cellular materials. The deflection of the inclined member, the strain of the representative structure and the elastic moduli of two-dimensional cellular materials were expressed using incomplete elliptic integrals. The experimental results show that these elastic moduli are no longer constant at large deformation, but vary significantly with the strain. A comparison was made between this large deformation model and the small deformation model proposed by Gibson and Ashby.
Degenerate ground states and multiple bifurcations in a two-dimensional q-state quantum Potts model.
Dai, Yan-Wei; Cho, Sam Young; Batchelor, Murray T; Zhou, Huan-Qiang
2014-06-01
We numerically investigate the two-dimensional q-state quantum Potts model on the infinite square lattice by using the infinite projected entangled-pair state (iPEPS) algorithm. We show that the quantum fidelity, defined as an overlap measurement between an arbitrary reference state and the iPEPS ground state of the system, can detect q-fold degenerate ground states for the Z_{q} broken-symmetry phase. Accordingly, a multiple bifurcation of the quantum ground-state fidelity is shown to occur as the transverse magnetic field varies from the symmetry phase to the broken-symmetry phase, which means that a multiple-bifurcation point corresponds to a critical point. A (dis)continuous behavior of quantum fidelity at phase transition points characterizes a (dis)continuous phase transition. Similar to the characteristic behavior of the quantum fidelity, the magnetizations, as order parameters, obtained from the degenerate ground states exhibit multiple bifurcation at critical points. Each order parameter is also explicitly demonstrated to transform under the Z_{q} subgroup of the symmetry group of the Hamiltonian. We find that the q-state quantum Potts model on the square lattice undergoes a discontinuous (first-order) phase transition for q=3 and q=4 and a continuous phase transition for q=2 (the two-dimensional quantum transverse Ising model).
Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models.
Labuhn, Henning; Barredo, Daniel; Ravets, Sylvain; de Léséleuc, Sylvain; Macrì, Tommaso; Lahaye, Thierry; Browaeys, Antoine
2016-06-30
Spin models are the prime example of simplified many-body Hamiltonians used to model complex, strongly correlated real-world materials. However, despite the simplified character of such models, their dynamics often cannot be simulated exactly on classical computers when the number of particles exceeds a few tens. For this reason, quantum simulation of spin Hamiltonians using the tools of atomic and molecular physics has become a very active field over the past years, using ultracold atoms or molecules in optical lattices, or trapped ions. All of these approaches have their own strengths and limitations. Here we report an alternative platform for the study of spin systems, using individual atoms trapped in tunable two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100 per cent. When excited to high-energy Rydberg D states, the atoms undergo strong interactions whose anisotropic character opens the way to simulating exotic matter. We illustrate the versatility of our system by studying the dynamics of a quantum Ising-like spin-1/2 system in a transverse field with up to 30 spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects on the dynamics, we find excellent agreement with ab initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D states has a measurable influence. Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.
USTIFICATION OF A TWO-DIMENSIONAL NONLINEAR SHELL MODEL OF KOITER'S TYPE
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A two-dimensional nonlinear shell model"of Koiter's type"has recently been proposed by the first author. It is shown here that, according to two mutually exclusive sets of assumptions bearing on the associated manifold of admissible inextensional displacements, the leading term of a formal asymptotic expansion of the solution of this two-dimensional model, with the thickness as the"small" parameter, satisfies either the two-dimensional equations of a nonlinearly elastic "membrane" shell or those of a nonlinearly elastic "flexural" shell. These conclusions being identical to those recently drawn by B. Miara, then by V. Lods and B. Miara, for the leading term of a formal asymptotic expansion of the solution of the equations of three-dimensional nonlinear elasticity, again with the thickness as the "small" parameter, the nonlinear shell model of Koiter's type considered here is thus justified, at least formally.
Spin transport in the two-dimensional quantum disordered anisotropic Heisenberg model
Energy Technology Data Exchange (ETDEWEB)
Lima, L.S. [Departamento de Física e Matemática, Centro Federal de Educação Tecnológica de Minas Gerais, 30510-000 Belo Horizonte, MG (Brazil); Pires, A.S.T.; Costa, B.V. [Departamento de Física ICEx, UFMG, CP 702, 31270-901 Belo Horizonte, MG (Brazil)
2014-12-15
We use the self consistent harmonic approximation together with the Linear Response Theory to study the effect of nonmagnetic disorder on spin transport in the quantum diluted two-dimensional anisotropic Heisenberg model with spin S=1 in a square lattice. The model has a BKT transition at zero dilution. We calculate the regular part of the spin conductivity σ{sup reg}(ω) and the Drude weight D{sub S}(T) as a function of the non-magnetic concentration, x. Our calculations show that the spin conductivity drops abruptly to zero at x{sub c}{sup SCHA}≈0.5 indicating that the system changes from an ideal spin conductor state to an insulator. This value is far above the site percolation threshold x{sub c}{sup site}≈0.41. Although the SCHA fails in determining precisely the percolation threshold, both the spin conductivity and the Drude weight show a quite regular behavior inside 0≤x≤x{sub c}{sup SCHA} indicating that the transition stays in the same universality class all along the interval. - Highlights: • The site dilution generates a large influence on regular part of the spin conductivity, σ{sup reg}(ω), and in the Drude weight, D(T). • In a concentration of impurities about x≈0.5, the regular part of the spin conductivity and the Drude weight fall to zero. • In this point we have a change in the state of the system from an ideal spin conductor to a spin insulator.
de Sousa, N; García-Martín, A; Froufe-Pérez, L S; Marqués, M I
2014-01-01
The effect of spatial correlations on the Purcell effect in a bidimensional dispersion of resonant nanoparticles is analyzed. We perform extensive calculations of the fluorescence decay rate of a point emitter embedded in a system of nanoparticles statistically distributed according to a sim- ple 2D lattice-gas model near the critical point. For short range correlations (high temperature thermalization) the Purcell factors present a non-Gaussian long-tailed statistics which evolves to- wards a bimodal distribution as approaching the critical point where the spatial correlation length diverges. Our results suggest long range correlations as a possible origin of the large fluctuations of experimental decay rates in disordered metal films.
Stationary states of the two-dimensional nonlinear Schrödinger model with disorder
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Hendriksen, D.; Christiansen, Peter Leth
1998-01-01
Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrodinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder. In the discr......Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrodinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder...
A Direct Calculation of Critical Exponents of Two-Dimensional Anisotropic Ising Model
Institute of Scientific and Technical Information of China (English)
XIONG Gang; WANG Xiang-Rong
2006-01-01
Using an exact solution of the one-dimensional quantum transverse-field Ising model, we calculate the critical exponents of the two-dimensional anisotropic classicalIsing model (IM). We verify that the exponents are the same as those of isotropic classical IM. Our approach provides an alternative means of obtaining and verifying these well-known results.
Two-dimensional quantum compass model in a staggered field: some rigorous results
Institute of Scientific and Technical Information of China (English)
He Pei-Song; You Wen-Long; Tian Guang-Shan
2011-01-01
We study the properties of the two-dimensional quantum compass model in a staggered field. Using the PerronFr(o)enius theorem and the reflection positivity method, we rigorously determine the low energy spectrum of this model and its global ground state Ψ0. Furthermore, we show that Ψ0 has a directional long-range order.
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Baungaard, Jens Rane
1996-01-01
A general model for a rotating homogenous flexible robot link is developed. The model describes two-dimensional transverse vibrations induced by the actuator due to misalignment of the actuator axis of rotation relative to the link symmetry axis and due to translational acceleration of the link...
Modeling of the financial market using the two-dimensional anisotropic Ising model
Lima, L. S.
2017-09-01
We have used the two-dimensional classical anisotropic Ising model in an external field and with an ion single anisotropy term as a mathematical model for the price dynamics of the financial market. The model presented allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the facts of financial markets. We have obtained the mean price in terms of the strong of the site anisotropy term Δ which reinforces the sensitivity of the agent's sentiment to external news.
Two dimensional black-hole as a topological coset model of c=1 string theory
Mukhi, S
1993-01-01
We show that a special superconformal coset (with $\\hat c =3$) is equivalent to $c=1$ matter coupled to two dimensional gravity. This identification allows a direct computation of the correlation functions of the $c=1$ non-critical string to all genus, and at nonzero cosmological constant, directly from the continuum approach. The results agree with those of the matrix model. Moreover we connect our coset with a twisted version of a Euclidean two dimensional black hole, in which the ghost and matter systems are mixed.
Simple Two-Dimensional Corrections for One-Dimensional Pulse Tube Models
Lee, J. M.; Kittel, P.; Timmerhaus, K. D.; Radebaugh, R.
2004-01-01
One-dimensional oscillating flow models are very useful for designing pulse tubes. They are simple to use, not computationally intensive, and the physical relationship between temperature, pressure and mass flow are easy to understand when used in conjunction with phasor diagrams. They do not possess, however, the ability to directly calculate thermal and momentum diffusion in the direction transverse to the oscillating flow. To account for transverse effects, lumped parameter corrections, which are obtained though experiment, must be used. Or two-dimensional solutions of the differential fluid equations must be obtained. A linear two-dimensional solution to the fluid equations has been obtained. The solution provides lumped parameter corrections for one-dimensional models. The model accounts for heat transfer and shear flow between the gas and the tube. The complex Nusselt number and complex shear wall are useful in describing these corrections, with phase relations and amplitudes scaled with the Prandtl and Valensi numbers. The calculated ratio, a, between a two-dimensional solution of the oscillating temperature and velocity and a one-dimensional solution for the same shows a scales linearly with Va for Va less than 30. In this region alpha less than 0.5, that is, the enthalpy flow calculated with a two-dimensional model is 50% of a calculation using a one-dimensional model. For Va greater than 250, alpha = 0.8, showing that diffusion is still important even when it is confined to a thing layer near the tube wall.
On two-dimensionalization of three-dimensional turbulence in shell models
DEFF Research Database (Denmark)
Chakraborty, Sagar; Jensen, Mogens Høgh; Sarkar, A.
2010-01-01
Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have been studied and reproduced. Within the framework of shell...
A Two-Dimensional Analytic Thermal Model for a High-Speed PMSM Magnet
CSIR Research Space (South Africa)
Grobler, AJ
2015-11-01
Full Text Available TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 62, NO. 11, NOVEMBER 2015 A Two-Dimensional Analytic Thermal Model for a High-Speed PMSM Magnet Andries J. Groblera, Stanley Robert Holmb, and George van Schoorc a School of Electrical, Electronic...
Proton transport in a membrane protein channel: two-dimensional infrared spectrum modeling.
Liang, C.; Knoester, J.; Jansen, T.L.Th.A.
2012-01-01
We model the two-dimensional infrared (2DIR) spectrum of a proton channel to investigate its applicability as a spectroscopy tool to study the proton transport process in biological systems. Proton transport processes in proton channels are involved in numerous fundamental biochemical reactions. How
Two-dimensional cellular automaton model of traffic flow with open boundaries
Tadaki, S I
1996-01-01
A two-dimensional cellular automaton model of traffic flow with open boundaries are investigated by computer simulations. The outflow of cars from the system and the average velocity are investigated. The time sequences of the outflow and average velocity have flicker noises in a jamming phase. The low density behavior are discussed with simple jam-free approximation.
A Solvable Model in Two-Dimensional Gravity Coupled to a Nonlinear Matter Field
Institute of Scientific and Technical Information of China (English)
YAN Jun; WANG Shun-Jin; TAO Bi-You
2001-01-01
The two-dimensional gravity model with a coupling constant k = 4 and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically. These solutions may be used to describe the naked singularity at the origin.``
Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional non-Abelian spin models.
Borisenko, Oleg; Chelnokov, Volodymyr; Cuteri, Francesca; Papa, Alessandro
2016-07-01
It is argued that two-dimensional U(N) spin models for any N undergo a Berezinskii-Kosterlitz-Thouless (BKT)-like phase transition, similarly to the famous XY model. This conclusion follows from the Berezinskii-like calculation of the two-point correlation function in U(N) models, approximate renormalization group analysis, and numerical investigations of the U(2) model. It is shown, via Monte Carlo simulations, that the universality class of the U(2) model coincides with that of the XY model. Moreover, preliminary numerical results point out that two-dimensional SU(N) spin models with the fundamental and adjoint terms and N>4 exhibit two phase transitions of BKT type, similarly to Z(N) vector models.
Eighth-order phase-field-crystal model for two-dimensional crystallization
Jaatinen, A.; Ala-Nissila, T.
2010-01-01
We present a derivation of the recently proposed eighth order phase field crystal model [Jaatinen et al., Phys. Rev. E 80, 031602 (2009)] for the crystallization of a solid from an undercooled melt. The model is used to study the planar growth of a two dimensional hexagonal crystal, and the results are compared against similar results from dynamical density functional theory of Marconi and Tarazona, as well as other phase field crystal models. We find that among the phase field crystal models...
Logarithmic discretization and systematic derivation of shell models in two-dimensional turbulence.
Gürcan, Ö D; Morel, P; Kobayashi, S; Singh, Rameswar; Xu, S; Diamond, P H
2016-09-01
A detailed systematic derivation of a logarithmically discretized model for two-dimensional turbulence is given, starting from the basic fluid equations and proceeding with a particular form of discretization of the wave-number space. We show that it is possible to keep all or a subset of the interactions, either local or disparate scale, and recover various limiting forms of shell models used in plasma and geophysical turbulence studies. The method makes no use of the conservation laws even though it respects the underlying conservation properties of the fluid equations. It gives a family of models ranging from shell models with nonlocal interactions to anisotropic shell models depending on the way the shells are constructed. Numerical integration of the model shows that energy and enstrophy equipartition seem to dominate over the dual cascade, which is a common problem of two-dimensional shell models.
GIS-based data model and tools for creating and managing two-dimensional cross sections
Whiteaker, Timothy L.; Jones, Norm; Strassberg, Gil; Lemon, Alan; Gallup, Doug
2012-02-01
While modern Geographic Information Systems (GIS) software is robust in handling maps and data in plan view, the software generally falls short when representing features in section view. Further complicating the issue is the fact that geologic cross sections are often drawn by connecting a series of wells together that do not fall along a single straight line. In this case, the x-axis of the cross section represents the distance along the set of individual lines connecting the series of wells, effectively "flattening out" the cross section along this path to create a view of the subsurface with which geologists often work in printed folios. Even 3D-enabled GIS cannot handle this type of cross section. A GIS data model and tools for creating and working with two-dimensional cross sections are presented. The data model and tools create a framework that can be applied using ESRI's ArcGIS software, enabling users to create, edit, manage, and print two-dimensional cross sections from within one of the most well-known GIS software packages. The data model is a component of the arc hydro groundwater data model, which means all two-dimensional cross sections are inherently linked to other features in the hydrogeologic domain, including those represented by xyz coordinates in real world space. Thus, the creation of two-dimensional cross sections can be guided by or completely driven from standard GIS data, and geologic interpretations established on two-dimensional cross sections can be translated back to real world coordinates to create three-dimensional features such as fence diagrams, giving GIS users the capacity to characterize the subsurface environment in a variety of integrated views that was not possible before. A case study for the Sacramento Regional Model in California demonstrates the application of the methodology in support of a regional groundwater management plan.
Model of two-dimensional electron gas formation at ferroelectric interfaces
Energy Technology Data Exchange (ETDEWEB)
Aguado-Puente, P.; Bristowe, N. C.; Yin, B.; Shirasawa, R.; Ghosez, Philippe; Littlewood, P. B.; Artacho, Emilio
2015-07-01
The formation of a two-dimensional electron gas at oxide interfaces as a consequence of polar discontinuities has generated an enormous amount of activity due to the variety of interesting effects it gives rise to. Here, we study under what circumstances similar processes can also take place underneath ferroelectric thin films. We use a simple Landau model to demonstrate that in the absence of extrinsic screening mechanisms, a monodomain phase can be stabilized in ferroelectric films by means of an electronic reconstruction. Unlike in the LaAlO3/SrTiO3 heterostructure, the emergence with thickness of the free charge at the interface is discontinuous. This prediction is confirmed by performing first-principles simulations of free-standing slabs of PbTiO3. The model is also used to predict the response of the system to an applied electric field, demonstrating that the two-dimensional electron gas can be switched on and off discontinuously and in a nonvolatile fashion. Furthermore, the reversal of the polarization can be used to switch between a two-dimensional electron gas and a two-dimensional hole gas, which should, in principle, have very different transport properties. We discuss the possible formation of polarization domains and how such configuration competes with the spontaneous accumulation of free charge at the interfaces.
Measurement of the Equation of State of the Two-Dimensional Hubbard Model
Miller, Luke; Cocchi, Eugenio; Drewes, Jan; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Koehl, Michael
2016-05-01
The subtle interplay between kinetic energy, interactions and dimensionality challenges our comprehension of strongly-correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions, 0 constitute benchmarks for state-of-the-art theoretical approaches.
A two-dimensional analytical model of laminar flame in lycopodium dust particles
Energy Technology Data Exchange (ETDEWEB)
Rahbari, Alireza [Shahid Rajaee Teacher Training University, Tehran (Iran, Islamic Republic of); Shakibi, Ashkan [Iran University of Science and Technology, Tehran (Iran, Islamic Republic of); Bidabadi, Mehdi [Combustion Research Laboratory, Narmak, Tehran (Iran, Islamic Republic of)
2015-09-15
A two-dimensional analytical model is presented to determine the flame speed and temperature distribution of micro-sized lycopodium dust particles. This model is based on the assumptions that the particle burning rate in the flame front is controlled by the process of oxygen diffusion and the flame structure consists of preheat, reaction and post flame zones. In the first step, the energy conservation equations for fuel-lean condition are expressed in two dimensions, and then these differential equations are solved using the required boundary condition and matching the temperature and heat flux at the interfacial boundaries. Consequently, the obtained flame temperature and flame speed distributions in terms of different particle diameters and equivalence ratio for lean mixture are compared with the corresponding experimental data for lycopodium dust particles. Consequently, it is shown that this two-dimensional model demonstrates better agreement with the experimental results compared to the previous models.
Canonical quantization of a two-dimensional model with anomalous breaking of gauge invariance
Girotti, Horacio Oscar; Rothe, Heinz J.; Rothe, Klaus D.
1986-01-01
We investigate in detail the operator quantum dynamics of a two-dimensional model exhibiting anomalous breaking of gauge invariance. The equal-time algebra is systematically obtained by using the Dirac-bracket formalism for constrained systems. For certain values of the regularization parameter the system is shown to undergo drastic changes. For the value of the parameter corresponding to the chiral Schwinger model no operator solutions are found to exist.
Striped periodic minimizers of a two-dimensional model for martensitic phase transitions
Giuliani, Alessandro
2010-01-01
In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional:
On the geometry of classically integrable two-dimensional non-linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Mohammedi, N., E-mail: nouri@lmpt.univ-tours.f [Laboratoire de Mathematiques et Physique Theorique (CNRS - UMR 6083), Universite Francois Rabelais de Tours, Faculte des Sciences et Techniques, Parc de Grandmont, F-37200 Tours (France)
2010-11-11
A master equation expressing the zero curvature representation of the equations of motion of a two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. Special attention is paid to those representations possessing a spectral parameter. Furthermore, a closer connection between integrability and T-duality transformations is emphasised. Finally, new integrable non-linear sigma models are found and all their corresponding Lax pairs depend on a spectral parameter.
The gauging of two-dimensional bosonic sigma models on world-sheets with defects
Gawedzki, Krzysztof; Waldorf, Konrad
2013-01-01
We extend our analysis of the gauging of rigid symmetries in bosonic two-dimensional sigma models with Wess-Zumino terms in the action to the case of world-sheets with defects. A structure that permits a non-anomalous coupling of such sigma models to world-sheet gauge fields of arbitrary topology is analysed, together with obstructions to its existence, and the classification of its inequivalent choices.
Neel order in the two-dimensional S=1/2 Heisenberg Model
Löw, Ute
2007-01-01
The existence of Neel order in the S=1/2 Heisenberg model on the square lattice at T=0 is shown using inequalities set up by Kennedy, Lieb and Shastry in combination with high precision Quantum Monte Carlo data.
A Novel Machine Learning Strategy Based on Two-Dimensional Numerical Models in Financial Engineering
Directory of Open Access Journals (Sweden)
Qingzhen Xu
2013-01-01
Full Text Available Machine learning is the most commonly used technique to address larger and more complex tasks by analyzing the most relevant information already present in databases. In order to better predict the future trend of the index, this paper proposes a two-dimensional numerical model for machine learning to simulate major U.S. stock market index and uses a nonlinear implicit finite-difference method to find numerical solutions of the two-dimensional simulation model. The proposed machine learning method uses partial differential equations to predict the stock market and can be extensively used to accelerate large-scale data processing on the history database. The experimental results show that the proposed algorithm reduces the prediction error and improves forecasting precision.
LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico; Bulik, Ireneusz W.; Chan, Garnet Kin-Lic; Chung, Chia-Min; Deng, Youjin; Ferrero, Michel; Henderson, Thomas M.; Jiménez-Hoyos, Carlos A.; Kozik, E.; Liu, Xuan-Wen; Millis, Andrew J.; Prokof'ev, N. V.; Qin, Mingpu; Scuseria, Gustavo E.; Shi, Hao; Svistunov, B. V.; Tocchio, Luca F.; Tupitsyn, I. S.; White, Steven R.; Zhang, Shiwei; Zheng, Bo-Xiao; Zhu, Zhenyue; Gull, Emanuel; Simons Collaboration on the Many-Electron Problem
2015-10-01
Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.
Leblanc, James
In this talk we present numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice. In order to provide an assessment of our ability to compute accurate results in the thermodynamic limit we employ numerous methods including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock. We illustrate cases where agreement between different methods is obtained in order to establish benchmark results that should be useful in the validation of future results.
Inflation Cosmological Solutions in Two-Dimensional Brans-Dicke Gravity Model
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The purpose of this paper is to study cosmological properties of two-dimensional Brans-Dicke gravity model. For massless scalar field, the new cosmological solutions are found by integration of field equation, these solutions correspond to the inflation solutions with positive cosmological constant. The result of this paper show that the inflation process of universe is controlled by the classical and quantum effect of the scalar field.
Coexistence of Incommensurate Magnetism and Superconductivity in the Two-Dimensional Hubbard Model.
Yamase, Hiroyuki; Eberlein, Andreas; Metzner, Walter
2016-03-04
We analyze the competition of magnetism and superconductivity in the two-dimensional Hubbard model with a moderate interaction strength, including the possibility of incommensurate spiral magnetic order. Using an unbiased renormalization group approach, we compute magnetic and superconducting order parameters in the ground state. In addition to previously established regions of Néel order coexisting with d-wave superconductivity, the calculations reveal further coexistence regions where superconductivity is accompanied by incommensurate magnetic order.
Környei, László; Pleimling, Michel; Iglói, Ferenc
2008-01-01
The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is generally the same due to self-duality. Here we consider a sudden change in the form of the interaction and study the nonequilibrium critical dynamical properties of the nearest-neighbor model. The relaxation of the magnetization and the decay of the autocorrelation function are found to display a power law behavior with characteristic exponents that depend on the universality class of the initial state.
Modeling two-dimensional water flow and bromide transport in a heterogeneous lignitic mine soil
Energy Technology Data Exchange (ETDEWEB)
Buczko, U.; Gerke, H.H. [Brandenburg University of Technology, Cottbus (Germany)
2006-02-15
Water and solute fluxes in lignitic mine soils and in many other soils are often highly heterogeneous. Here, heterogeneity reflects dumping-induced inclined structures and embedded heterogeneous distributions of sediment mixtures and of lignitic fragments. Such two-scale heterogeneity effects may be analyzed through the application of two-dimensional models for calculating water and solute fluxes. The objective of this study was to gain more insight to what extent spatial heterogeneity of soil hydraulic parameters contributes to preferential flow at a lignitic mine soil. The simulations pertained to the 'Barenbrucker Hohe' site in Germany where previously water fluxes and applied tracers had been monitored with a cell lysimeter, and from where a soil block had been excavated for detailed two-dimensional characterization of the hydraulic parameters using pedotransfer functions. Based on those previous studies, scenarios with different distributions of hydraulic parameters were simulated. The results show that spatial variability of hydraulic parameters alone can hardly explain the observed flow patterns. The observed preferential flow at the site was probably caused by additional factors such as hydrophobicity, the presence of root channels, anisotropy in the hydraulic conductivity, and heterogeneous root distributions. To study the relative importance of these other factors by applying two-dimensional flow models to such sites, the experimental database must be improved. Single-continuum model approaches may be insufficient for such sites.
Matoz-Fernandez, D. A.; Linares, D. H.; Ramirez-Pastor, A. J.
2007-01-01
Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior and universality for the isotropic-nematic phase transition in a system of long straight rigid rods of length $k$ ($k$-mers) on two-dimensional lattices. The nematic phase, characterized by a big domain of parallel $k$-mers, is separated from the isotropic state by a continuous transition occurring at a finite density. The determination of the critical exponents, along with the behavi...
Lima, L. S.
2017-02-01
We have used the Dirac's massless quasi-particles together with the Kubo's formula to study the spin transport by electrons in the graphene monolayer. We have calculated the electric conductivity and verified the behavior of the AC and DC currents of this system, that is a relativistic electron plasma. Our results show that the AC conductivity tends to infinity in the limit ω → 0 , similar to the behavior obtained for the spin transport in the two-dimensional frustrated antiferromagnet in the honeycomb lattice. We have made a diagrammatic expansion for the Green's function and we have not gotten significative change in the results.
Phase diagram of a two-dimensional large- Q Potts model in an external field
Tsai, Shan-Ho; Landau, D. P.
2009-04-01
We use a two-dimensional Wang-Landau sampling algorithm to map out the phase diagram of a Q-state Potts model with Q⩽10 in an external field H that couples to one state. Finite-size scaling analyses show that for large Q the first-order phase transition point at H=0 is in fact a triple point at which three first-order phase transition lines meet. One such line is restricted to H=0; another line has H⩽0. The third line, which starts at the H=0 triple point, ends at a critical point (T,H) which needs to be located in a two-dimensional parameter space. The critical field H(Q) is positive and decreases with decreasing Q, which is in qualitative agreement with previous predictions.
Modelling floor heating systems using a validated two-dimensional ground coupled numerical model
DEFF Research Database (Denmark)
Weitzmann, Peter; Kragh, Jesper; Roots, Peter
2005-01-01
the floor. This model can be used to design energy efficient houses with floor heating focusing on the heat loss through the floor construction and foundation. It is found that it is impor-tant to model the dynamics of the floor heating system to find the correct heat loss to the ground, and further......This paper presents a two-dimensional simulation model of the heat losses and tempera-tures in a slab on grade floor with floor heating which is able to dynamically model the floor heating system. The aim of this work is to be able to model, in detail, the influence from the floor construction...... and foundation on the performance of the floor heating sys-tem. The ground coupled floor heating model is validated against measurements from a single-family house. The simulation model is coupled to a whole-building energy simu-lation model with inclusion of heat losses and heat supply to the room above...
FUZZY MODEL FOR TWO-DIMENSIONAL RIVER WATER QUALITY SIMULATION UNDER SUDDEN POLLUTANTS DISCHARGED
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Based on the fuzziness and impreciseness of water environmental system, the fuzzy arithmetic was used to simulate the fuzzy and imprecise relations in modeling river water quality. By defining the parameters of water quality model as symmetrical triangular fuzzy numbers, a two-dimensional fuzzy water quality model for sudden pollutant discharge is established. From the fuzzy model, the pollutant concentrations, corresponding to the specified confidence level of α, can be obtained by means of the α-cut technique and arithmetic operations of triangular fuzzy numbers. Study results reveal that it is feasible in theory and reliable on calculation applying triangular fuzzy numbers to the simulation of river water quality.
Temperature dependence of universal fluctuations in the two-dimensional harmonic XY model.
Palma, G
2006-04-01
We compute exact analytical expressions for the skewness and kurtosis in the two-dimensional harmonic XY model. These quantities correspond to the third and fourth normalized moments of the probability density function (PDF) of the magnetization of the model. From their behavior, we conclude that they depend explicitly on the system temperature even in the thermodynamic limit, and hence the PDF itself must depend on it. Our results correct the hypothesis called universal fluctuations, they confirm and extend previous results which showed a T dependence of the PDF, including perturbative expansions within the XY model up to first order in temperature.
Eighth-order phase-field-crystal model for two-dimensional crystallization
Jaatinen, A.; Ala-Nissilä, Tapio
2010-01-01
We present a derivation of the recently proposed eighth-order phase-field crystal model [A. Jaatinen et al., Phys. Rev. E 80, 031602 (2009)] for the crystallization of a solid from an undercooled melt. The model is used to study the planar growth of a two-dimensional hexagonal crystal, and the results are compared against similar results from dynamical density functional theory of Marconi and Tarazona, as well as other phase-field crystal models. We find that among the phase-field crystal mod...
Neimark-Sacker bifurcation of a two-dimensional discrete-time predator-prey model.
Khan, A Q
2016-01-01
In this paper, we study the dynamics and bifurcation of a two-dimensional discrete-time predator-prey model in the closed first quadrant [Formula: see text]. The existence and local stability of the unique positive equilibrium of the model are analyzed algebraically. It is shown that the model can undergo a Neimark-Sacker bifurcation in a small neighborhood of the unique positive equilibrium and an invariant circle will appear. Some numerical simulations are presented to illustrate our theocratical results and numerically it is shown that the unique positive equilibrium of the system is globally asymptotically stable.
Two-dimensional modeling of apparent resistivity pseudosections in the Cerro Prieto region
Energy Technology Data Exchange (ETDEWEB)
Vega, R.; Martinez, M.
1981-01-01
Using a finite-difference program (Dey, 1976) for two-dimensional modeling of apparent resistivity pseudosections obtained by different measuring arrays, four apparent resistivity pseudosections obtained at Cerro Prieto with a Schlumberger array by CFE personnel were modeled (Razo, 1978). Using geologic (Puente and de la Pena, 1978) and lithologic (Diaz, et al., 1981) data from the geothermal region, models were obtained which show clearly that, for the actual resistivity present in the zone, the information contained in the measured pseudosections is primarily due to the near-surface structure and does not show either the presence of the geothermal reservoir or the granitic basement which underlies it.
Functional scale-free networks in the two-dimensional Abelian sandpile model
Zarepour, M.; Niry, M. D.; Valizadeh, A.
2015-07-01
Recently, the similarity of the functional network of the brain and the Ising model was investigated by Chialvo [Nat. Phys. 6, 744 (2010), 10.1038/nphys1803]. This similarity supports the idea that the brain is a self-organized critical system. In this study we derive a functional network of the two-dimensional Bak-Tang-Wiesenfeld sandpile model as a self-organized critical model, and compare its characteristics with those of the functional network of the brain, obtained from functional magnetic resonance imaging.
Pelizzola, Alessandro
1994-11-01
An explicit formula for the boundary magnetization of a two-dimensional Ising model with a strip of inhomogeneous interactions is obtained by means of a transfer matrix mean-field method introduced by Lipowski and Suzuki. There is clear numerical evidence that the formula is exact By taking the limit where the width of the strip approaches infinity and the interactions have well defined bulk limits, I arrive at the boundary magnetization for a model which includes the Hilhorst-van Leeuwen model. The rich critical behavior of the latter magnetization is thereby rederived with little effort.
DEFF Research Database (Denmark)
Swierczynski, Maciej Jozef; Stroe, Daniel Loan; Knap, Vaclav
2016-01-01
Thermal modeling of lithium-ion batteries is gaining its importance together with increasing power density and compact design of the modern battery systems in order to assure battery safety and long lifetime. Thermal models of lithium-ion batteries are usually either expensive to develop...... and accurate or equivalent thermal circuit based with moderate accuracy and without spatial temperature distribution. This work presents initial results that can be used as a fundament for the cost-efficient development of the two-dimensional thermal model of lithium-ion battery based on multipoint...
Directory of Open Access Journals (Sweden)
Mitsuhiro Numata
2010-11-01
Full Text Available Two dimensional island arrays and honeycomb patterns consisting of ZnO nanocrystal clusters were fabricated on predefined TiO2 seed patterns prepared by vacuum free, aerosol assisted wet-chemical synthesis. The TiO2 seed patterns were prepared by applying an aerosol of a water soluble titanium complex on hexagonally close-packed polystyrene bead arrays for different lengths of time. Scanning electron microscopy revealed that a dot array grows into a honeycomb shape as increasing amounts of the precursor were deposited. ZnO nucleation on substrates with a dot array and honeycomb patterns resulted in the formation of two discrete patterns with contrasting fill fractions of the materials.
Ground-State Transition in a Two-Dimensional Frenkel-Kontorova Model
Institute of Scientific and Technical Information of China (English)
YUAN Xiao-Ping; ZHENG Zhi-Gang
2011-01-01
The ground state of a generalized Frenkel-Kontorova model with a transversaJ degree of freedom is studied. When the coupling strength, K, and the frequency of & single-Atom vibration in the transversaJ direction, ωou are increased, the ground state of the model undergoes a transition from a two-dimensional configuration to a one-dimensional one. This transition can manifest in different ways. Furthermore, we find that the prerequisite of a two-dimensionai ground state is θ≠1//q.%The ground state of a generalized Frenkel-Kontorova model with a transversal degree of freedom is studied.When the coupling strength,K,and the frequency of a single-atom vibration in the transversal direction,ωoy,are increased,the ground state of the model undergoes a transition from a two-dimensional configuration to a one-dimensional one.This transition can manifest in different ways.Furthermore,we find that the prerequisite of a two-dimensional ground state is θ ≠ 1/q.In recent years,the Frenkel-Kontorova (FK) model has been applied to a variety of physical systems,such as adsorbed monolayers,[1,2] Josephsonjunction arrays,[3-5] tribology[6-8] and charge-density waves.[9,10] Experimental and large-scale simulation data at the nanoscale have become available,and more complicated FK-type models have been investigated using simulations of molecular dynamics.[11
Two-dimensional, isothermal, multi-component model for a polymer electrolyte membrane fuel cell
Energy Technology Data Exchange (ETDEWEB)
Mahinpey, N.; Jagannathan, A.; Idem, R. [Regina Univ., SK (Canada). Faculty of Engineering
2007-07-01
A fuel cell is an electrochemical energy conversion device which is more efficient than an internal combustion engine in converting fuel to power. Numerous fuel cell models have been developed by a number of authors accounting for the various physical processes. Earlier models were restricted to being one dimensional, steady-state, and isothermal while more recent two-dimensional models had several limitations. This paper presented the results of a study that developed a two-dimensional computational fluid dynamics model of a polymer electrolyte membrane fuel cell using a finite element method to solve a multi-component transport model coupled with flow in porous media, charge balance, electrochemical kinetics, and rigorous water balance in the membrane. The mass transport, momentum transport, and electrochemical processes occurring in the membrane electrolyte and catalyst layers were modeled. The local equilibrium was assumed at the interfaces and the model was combined with the kinetics and was analytically solved for the anodic and cathodic current using an agglomerate spherical catalyst pellet. The paper compared the modeling results with previously published experimental data. The study investigated the effects of channel and bipolar plate shoulder size, porosity of the electrodes, temperature, relative humidity and current densities on the cell performance. It was concluded that smaller sized channels and bipolar plate shoulders were required to obtain higher current densities, although larger channels were satisfactory at moderate current densities. 13 refs., 5 figs.
Directory of Open Access Journals (Sweden)
A. J. Ramirez-Pastor
2009-09-01
Full Text Available Using Monte Carlo simulations and finite-size scaling analysis, the critical behavior of attractive rigid rods of length $k$ ($k$-mers on square lattices at intermediate density has been studied. A nematic phase, characterized by a big domain of parallel $k$-mers, was found. This ordered phase is separated from the isotropic state by a continuous transition occurring at a intermediate density $heta_c$, which increases linearly with the magnitude of the lateral interactions.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Hai-Feng, E-mail: hanlor@163.com, E-mail: lsb@nuaa.edu.cn [Key Laboratory of Radar Imaging and Microwave Photonics (Nanjing Univ. Aeronaut. Astronaut.), Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Nanjing Artillery Academy, Nanjing 211132 (China); Liu, Shao-Bin, E-mail: hanlor@163.com, E-mail: lsb@nuaa.edu.cn; Jiang, Yu-Chi [Key Laboratory of Radar Imaging and Microwave Photonics (Nanjing Univ. Aeronaut. Astronaut.), Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)
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.
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.
Monte Carlo renormalization-group investigation of the two-dimensional O(4) sigma model
Heller, Urs M.
1988-01-01
An improved Monte Carlo renormalization-group method is used to determine the beta function of the two-dimensional O(4) sigma model. While for (inverse) couplings beta = greater than about 2.2 agreement is obtained with asymptotic scaling according to asymptotic freedom, deviations from it are obtained at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating 'scaling' according to the full beta function. These results contradict recent claims that the model has a critical point at finite coupling.
Thermal metal in network models of a disordered two-dimensional superconductor
Chalker, J. T.; Read, N.; Kagalovsky, V.; Horovitz, B.; Avishai, Y.; Ludwig, A. W.
2002-01-01
We study the symmetry class for localization which arises from models of noninteracting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotation invariance. Two-dimensional systems in this category, which is known as class D, can display phases with three different types of quasiparticle dynamics: metallic, localized, or with a quantized (thermal) Hall conductance. Correspondingly, they can show a variety of delocalization transitions. We illustrate this behavior by investigating numerically the phase diagrams of network models with the appropriate symmetry and show the appearance of the metallic phase.
Digital hardware implementation of a stochastic two-dimensional neuron model.
Grassia, F; Kohno, T; Levi, T
2017-02-22
This study explores the feasibility of stochastic neuron simulation in digital systems (FPGA), which realizes an implementation of a two-dimensional neuron model. The stochasticity is added by a source of current noise in the silicon neuron using an Ornstein-Uhlenbeck process. This approach uses digital computation to emulate individual neuron behavior using fixed point arithmetic operation. The neuron model's computations are performed in arithmetic pipelines. It was designed in VHDL language and simulated prior to mapping in the FPGA. The experimental results confirmed the validity of the developed stochastic FPGA implementation, which makes the implementation of the silicon neuron more biologically plausible for future hybrid experiments.
Two-dimensional model of intrinsic magnetic flux losses in helical flux compression generators
Haurylavets, V V
2012-01-01
Helical Flux Compression Generators (HFCG) are used for generation of mega-amper current and high magnetic fields. We propose the two dimensional HFCG filament model based on the new description of the stator and armature contact point. The model developed enables one to quantitatively describe the intrinsic magnetic flux losses and predict the results of experiments with various types of HFCGs. We present the effective resistance calculations based on the non-linear magnetic diffusion effect describing HFCG performance under the strong conductor heating by currents.
Monte Carlo renormalization-group investigation of the two-dimensional O(4) sigma model
Heller, Urs M.
1988-01-01
An improved Monte Carlo renormalization-group method is used to determine the beta function of the two-dimensional O(4) sigma model. While for (inverse) couplings beta = greater than about 2.2 agreement is obtained with asymptotic scaling according to asymptotic freedom, deviations from it are obtained at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating 'scaling' according to the full beta function. These results contradict recent claims that the model has a critical point at finite coupling.
Energy Technology Data Exchange (ETDEWEB)
Contreras, Anthony Marshall [Univ. of California, Berkeley, CA (United States)
2006-05-20
In order to better understand the fundamental components that govern catalytic activity, two-dimensional model platinum nanocatalyst arrays have been designed and fabricated. These catalysts arrays are meant to model the interplay of the metal and support important to industrial heterogeneous catalytic reactions. Photolithography and sub-lithographic techniques such as electron beam lithography, size reduction lithography and nanoimprint lithography have been employed to create these platinum nanoarrays. Both in-situ and ex-situ surface science techniques and catalytic reaction measurements were used to correlate the structural parameters of the system to catalytic activity.
Halliday, I; Lishchuk, S V; Spencer, T J; Pontrelli, G; Evans, P C
2016-08-01
We present a method for applying a class of velocity-dependent forces within a multicomponent lattice Boltzmann equation simulation that is designed to recover continuum regime incompressible hydrodynamics. This method is applied to the problem, in two dimensions, of constraining to uniformity the tangential velocity of a vesicle membrane implemented within a recent multicomponent lattice Boltzmann simulation method, which avoids the use of Lagrangian boundary tracers. The constraint of uniform tangential velocity is carried by an additional contribution to an immersed boundary force, which we derive here from physical arguments. The result of this enhanced immersed boundary force is to apply a physically appropriate boundary condition at the interface between separated lattice fluids, defined as that region over which the phase-field varies most rapidly. Data from this enhanced vesicle boundary method are in agreement with other data obtained using related methods [e.g., T. Krüger, S. Frijters, F. Günther, B. Kaoui, and J. Harting, Eur. Phys. J. 222, 177 (2013)10.1140/epjst/e2013-01834-y] and underscore the importance of a correct vesicle membrane condition.
Mohammadipour, Omid Reza; Niazmand, Hamid; Succi, Sauro
2017-03-01
In this paper, an alternative approach to implement initial and boundary conditions in the lattice Boltzmann method is presented. The main idea is to approximate the nonequilibrium component of distribution functions as a third-order power series in the lattice velocities and formulate a procedure to determine boundary node distributions by using fluid variables, consistent with such an expansion. The velocity shift associated with the body force effects is included in this scheme, along with an approximation to determine the mass density in complex geometries. Different strategies based on the present scheme are developed to implement velocity and pressure conditions for arbitrarily shaped boundaries, using the D2Q9, D3Q15, D3Q19 and D3Q27 lattices, in two and three space dimensions, respectively. The proposed treatment is tested against several well-established problems, showing second-order spatial accuracy and often improved behavior as compared to various existing methods, with no appreciable computational overhead.
Li, Jun-Jie; Yan, Jia-Bin; Huang, Xiang-Yu
2015-12-01
Meshfree method offers high accuracy and computational capability and constructs the shape function without relying on predefined elements. We comparatively analyze the global weak form meshfree methods, such as element-free Galerkin method (EFGM), the point interpolation method (PIM), and the radial point interpolation method (RPIM). Taking two dimensional Poisson equation as an example, we discuss the support-domain dimensionless size, the field nodes, and background element settings with respect to their effect on calculation accuracy of the meshfree method. RPIM and EFGM are applied to controlled-source two-dimensional electromagnetic modeling with fixed shape parameters. The accuracy of boundary conditions imposed directly and by a penalty function are discussed in the case of forward modeling of two-dimensional magnetotellurics in a homogeneous medium model. The coupling algorithm of EFG-PIM and EFG-RPIM are generated by integrating the PIM or RPIM and EFGM. The results of the numerical modeling suggest the following. First, the proposed meshfree method and corresponding coupled methods are well-suited for electromagnetic numerical modeling. The accuracy of the algorithm is the highest when the support-domain dimensionless size is 1.0 and the distribution of field nodes is consistent with the nodes of background elements. Second, the accuracy of PIM and RPIM are lower than that of EFGM for the Poisson equation but higher than EFGM for the homogeneous medium MT response. Third, RPIM overcomes the matrix inversion problem of PIM and has a wider selection of support-domain dimensionless sizes as compared to RPIM.
Directory of Open Access Journals (Sweden)
Ze-yu MAO
2014-01-01
Full Text Available River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.
D'Archivio, Angelo Antonio; Incani, Angela; Ruggieri, Fabrizio
2011-01-01
In this paper, we use a quantitative structure-retention relationship (QSRR) method to predict the retention times of polychlorinated biphenyls (PCBs) in comprehensive two-dimensional gas chromatography (GC×GC). We analyse the GC×GC retention data taken from the literature by comparing predictive capability of different regression methods. The various models are generated using 70 out of 209 PCB congeners in the calibration stage, while their predictive performance is evaluated on the remaining 139 compounds. The two-dimensional chromatogram is initially estimated by separately modelling retention times of PCBs in the first and in the second column ((1) t (R) and (2) t (R), respectively). In particular, multilinear regression (MLR) combined with genetic algorithm (GA) variable selection is performed to extract two small subsets of predictors for (1) t (R) and (2) t (R) from a large set of theoretical molecular descriptors provided by the popular software Dragon, which after removal of highly correlated or almost constant variables consists of 237 structure-related quantities. Based on GA-MLR analysis, a four-dimensional and a five-dimensional relationship modelling (1) t (R) and (2) t (R), respectively, are identified. Single-response partial least square (PLS-1) regression is alternatively applied to independently model (1) t (R) and (2) t (R) without the need for preliminary GA variable selection. Further, we explore the possibility of predicting the two-dimensional chromatogram of PCBs in a single calibration procedure by using a two-response PLS (PLS-2) model or a feed-forward artificial neural network (ANN) with two output neurons. In the first case, regression is carried out on the full set of 237 descriptors, while the variables previously selected by GA-MLR are initially considered as ANN inputs and subjected to a sensitivity analysis to remove the redundant ones. Results show PLS-1 regression exhibits a noticeably better descriptive and predictive
Spin Dynamics of $La_{2}CuO_{4}$ and the Two-Dimensional Heisenberg Model
Sandvik, A W; Barbara, U C S; Barbara, UC Santa
1994-01-01
The spin-lattice relaxation rate $1/T_1$ and the spin echo decay rate $1/T_{2G}$ for the 2D Heisenberg model are calculated using quantum Monte Carlo and maximum entropy analytic continuation. The results are compared to recent experiments on La$_2$CuO$_4$, as well as predictions based on the non-linear $\\sigma$-model.
Two-dimensional habitat modeling in the Yellowstone/Upper Missouri River system
Waddle, T. J.; Bovee, K.D.; Bowen, Z.H.
1997-01-01
This study is being conducted to provide the aquatic biology component of a decision support system being developed by the U.S. Bureau of Reclamation. In an attempt to capture the habitat needs of Great Plains fish communities we are looking beyond previous habitat modeling methods. Traditional habitat modeling approaches have relied on one-dimensional hydraulic models and lumped compositional habitat metrics to describe aquatic habitat. A broader range of habitat descriptors is available when both composition and configuration of habitats is considered. Habitat metrics that consider both composition and configuration can be adapted from terrestrial biology. These metrics are most conveniently accessed with spatially explicit descriptors of the physical variables driving habitat composition. Two-dimensional hydrodynamic models have advanced to the point that they may provide the spatially explicit description of physical parameters needed to address this problem. This paper reports progress to date on applying two-dimensional hydraulic and habitat models on the Yellowstone and Missouri Rivers and uses examples from the Yellowstone River to illustrate the configurational metrics as a new tool for assessing riverine habitats.
Numerical model for the shear rheology of two-dimensional wet foams with deformable bubbles.
Kähärä, T; Tallinen, T; Timonen, J
2014-09-01
Shearing of two-dimensional wet foam is simulated using an introduced numerical model, and results are compared to those of experiments. This model features realistically deformable bubbles, which distinguishes it from previously used models for wet foam. The internal bubble dynamics and their contact interactions are also separated in the model, making it possible to investigate the effects of the related microscale properties of the model on the macroscale phenomena. Validity of model assumptions was proved here by agreement between the simulated and measured Herschel-Bulkley rheology, and shear-induced relaxation times. This model also suggests a relationship between the shear stress and normal stress as well as between the average degree of bubble deformation and applied shear stress. It can also be used to analyze suspensions of bubbles and solid particles, an extension not considered in this work.
Nogawa, Tomoaki
2011-12-05
The evaporation-condensation transition of the Potts model on a square lattice is numerically investigated by the Wang-Landau sampling method. An intrinsically system-size-dependent discrete transition between supersaturation state and phase-separation state is observed in the microcanonical ensemble by changing constrained internal energy. We calculate the microcanonical temperature, as a derivative of microcanonical entropy, and condensation ratio, and perform a finite-size scaling of them to indicate the clear tendency of numerical data to converge to the infinite-size limit predicted by phenomenological theory for the isotherm lattice gas model. © 2011 American Physical Society.
Nogawa, Tomoaki; Ito, Nobuyasu; Watanabe, Hiroshi
2011-12-01
The evaporation-condensation transition of the Potts model on a square lattice is numerically investigated by the Wang-Landau sampling method. An intrinsically system-size-dependent discrete transition between supersaturation state and phase-separation state is observed in the microcanonical ensemble by changing constrained internal energy. We calculate the microcanonical temperature, as a derivative of microcanonical entropy, and condensation ratio, and perform a finite-size scaling of them to indicate the clear tendency of numerical data to converge to the infinite-size limit predicted by phenomenological theory for the isotherm lattice gas model.
Two Dimensional Incommensurate Spin Excitations and Lattice Fluctuations in La2 - x Bax CuO4
Wagman, J. J.; Carlo, J. P.; van Gastel, G.; Zhao, Y.; Kallin, A. B.; Mazurek, E.; Dabkowska, H. A.; Savicii, A.; Granroth, G. E.; Yamani, Z.; Tun, Z.; Gaulin, B. D.
2013-03-01
'Hour-glass' shaped dispersions of antiferromagnetic (AF) spin fluctuations are a robust feature common to many high temperature superconductors. In 214 cuprates, these phenomena are well known to display a strong dependence on the concentration of holes that are introduced into the copper oxide planes by doping. The incommensurability (IC) of the two dimensional magnetic order in this system is sensitive to hole concentration. Here, we present a series of neutron scattering measurements on single crystals of La2 - x Bax CuO4 (LBCO), with 0 . 035 <= x <= 0 . 095 , a doping range that spans the transition from diagonal to parallel IC ordering wavevectors, and from non-superconducting to superconducting ground states. Our measurements map out the evolution of the spin excitations for energies below ~ 50 meV, and focus on an enhancement in the scattered intensity centered in the 17-20 meV at the AF IC positions. This regime corresponds to the approximate crossing of very dispersive spin excitations and weakly dispersive low lying optic phonons in LBCO. NSERC, Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy
Resonance and Rectification in a Two-Dimensional Frenkel-Kontorova Model with Triangular Symmetry
Institute of Scientific and Technical Information of China (English)
YANG Yang; WANG Cang-Long; DUAN Wen-Shan; CHEN Jian-Min
2011-01-01
The mode-locking phenomena in the dc- and ac-driven overdamped two-dimensional Frenkel-Kontorova model with triangular symmetric structures are studied. The obtained results show that the transverse velocitylongitudinal velocity(vy) can occur when n is an odd number. It is also found in our simulations that the critical depinning force oscillates with the amplitude of ac-driven force, i.e., the system is dominated by the ac-driven force. The oscillatory behavior is strongly determined by the initial phase of ac force.
Topological Invariants of Edge States for Periodic Two-Dimensional Models
Energy Technology Data Exchange (ETDEWEB)
Avila, Julio Cesar; Schulz-Baldes, Hermann, E-mail: schuba@mi.uni-erlangen.de; Villegas-Blas, Carlos [Instituto de Matematicas, UNAM (Mexico)
2013-06-15
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define topological invariants by considering the associated Bott-Maslov indices which can be easily calculated numerically. For time-reversal symmetric systems in the symplectic universality class this leads to a Z{sub 2} -invariant for the edge states. It is shown that the edge state invariants are related to Chern numbers of the bulk systems and also to (spin) edge currents, in the spirit of the theory of topological insulators.
Existence of a line of critical points in a two-dimensional Lebwohl Lasher model
Energy Technology Data Exchange (ETDEWEB)
Shabnam, Sabana [Department of Physics, Lady Brabourne College, Kolkata 700017 (India); DasGupta, Sudeshna, E-mail: sudeshna.dasgupta10@gmail.com [Department of Physics, Lady Brabourne College, Kolkata 700017 (India); Roy, Soumen Kumar [Department of Physics, Jadavpur University, Kolkata 700032 (India)
2016-02-15
Controversy regarding transitions in systems with global symmetry group O(3) has attracted the attention of researchers and the detailed nature of this transition is still not well understood. As an example of such a system in this paper we have studied a two-dimensional Lebwohl Lasher model, using the Wolff cluster algorithm. Though we have not been able to reach any definitive conclusions regarding the order present in the system, from finite size scaling analysis, hyperscaling relations and the behavior of the correlation function we have obtained strong indications regarding the presence of quasi-long range order and the existence of a line of critical points in our system.
Existence of a line of critical points in a two-dimensional Lebwohl Lasher model
Shabnam, Sabana; DasGupta, Sudeshna; Roy, Soumen Kumar
2016-02-01
Controversy regarding transitions in systems with global symmetry group O(3) has attracted the attention of researchers and the detailed nature of this transition is still not well understood. As an example of such a system in this paper we have studied a two-dimensional Lebwohl Lasher model, using the Wolff cluster algorithm. Though we have not been able to reach any definitive conclusions regarding the order present in the system, from finite size scaling analysis, hyperscaling relations and the behavior of the correlation function we have obtained strong indications regarding the presence of quasi-long range order and the existence of a line of critical points in our system.
Topological invariants of edge states for periodic two-dimensional models
Avila, Julio Cesar; Villegas-Blas, Carlos
2012-01-01
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define topological invariants by considering the associated Bott-Maslov indices which can be easily calculated numerically. For time-reversal symmetric systems in the symplectic universality class this leads to a Z_2-invariant for the edge states. It is shown that the edge state invariants are related to Chern numbers of the bulk systems and also to (spin) edge currents, in the spirit of the theory of topological insulators.
Institute of Scientific and Technical Information of China (English)
Xu Zhang; En-min Feng
2004-01-01
This paper studies the two-dimensional layout optimization problem.An optimization model with performance constraints is presented.The layout problem is partitioned intofinite subproblems in terms of graph theory,in such a way of that each subproblem overcomes its on-o inature optimal variable.A minimax problem is constructed that is locally equivalent to each subproblem.By using this minimax problem,we present the optimality function for every subproblem and prove that the first order necessary optimality condition is satisfied at a point if and only if this point is a zero of optimality function.
Two-dimensional airflow modeling underpredicts the wind velocity over dunes.
Michelsen, Britt; Strobl, Severin; Parteli, Eric J R; Pöschel, Thorsten
2015-11-17
We investigate the average turbulent wind field over a barchan dune by means of Computational Fluid Dynamics. We find that the fractional speed-up ratio of the wind velocity over the three-dimensional barchan shape differs from the one obtained from two-dimensional calculations of the airflow over the longitudinal cut along the dune's symmetry axis - that is, over the equivalent transverse dune of same size. This finding suggests that the modeling of the airflow over the central slice of barchan dunes is insufficient for the purpose of the quantitative description of barchan dune dynamics as three-dimensional flow effects cannot be neglected.
Two-dimensional airflow modeling underpredicts the wind velocity over dunes
Britt Michelsen; Severin Strobl; Parteli, Eric J. R.; Thorsten Pöschel
2015-01-01
We investigate the average turbulent wind field over a barchan dune by means of Computational Fluid Dynamics. We find that the fractional speed-up ratio of the wind velocity over the three-dimensional barchan shape differs from the one obtained from two-dimensional calculations of the airflow over the longitudinal cut along the dune’s symmetry axis — that is, over the equivalent transverse dune of same size. This finding suggests that the modeling of the airflow over the central slice of barc...
Scaling of cluster heterogeneity in the two-dimensional Potts model.
Lv, Jian-Ping; Yang, Xianqing; Deng, Youjin
2012-08-01
Cluster heterogeneity, the number of clusters of mutually distinct sizes, has been recently studied for explosive percolation and standard percolation [H. K. Lee et al., Phys. Rev. E 84, 020101(R) (2011); J. D. Noh et al., Phys. Rev. E 84, 010101(R) (2011)]. In this work we study the scaling of various quantities related with cluster heterogeneity in a broader context of two-dimensional q-state Potts model. We predict, via an analytic approach, the critical exponents for most of the measured quantities, and confirm these predications for various q values using extensive Monte Carlo simulations.
Phase Diagram of the Two-Dimensional Ising Model with Dipolar Interaction
Institute of Scientific and Technical Information of China (English)
SUN Gang; CHU Qian-Jin
2001-01-01
We treat the two-dimensional Ising model with the dipolar interaction by the numerical calculation under the restriction that the spin configurations are distributed with a 4 × 4 period. The phase diagram with respect to temperature and dipolar interaction strength is constructed. Most characters of the phase diagram are consistent with those obtained in the references by the Monte Carlo simulation, except that we find a new rectangle phase, which is ordered in the spin structure with the 1 × 2 rectangle.
Nonlinear kinetic modeling and simulations of Raman scattering in a two-dimensional geometry
Directory of Open Access Journals (Sweden)
Bénisti Didier
2013-11-01
Full Text Available In this paper, we present our nonlinear kinetic modeling of stimulated Raman scattering (SRS by the means of envelope equations, whose coefficients have been derived using a mixture of perturbative and adiabatic calculations. First examples of the numerical resolution of these envelope equations in a two-dimensional homogeneous plasma are given, and the results are compared against those of particle-in-cell (PIC simulations. These preliminary comparisons are encouraging since our envelope code provides threshold intensities consistent with those of PIC simulations while requiring computational resources reduced by 4 to 5 orders of magnitude compared to full-kinetic codes.
An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows
Energy Technology Data Exchange (ETDEWEB)
Snider, D.M. [SAIC, Albuquerque, NM (United States); O`Rourke, P.J. [Los Alamos National Lab., NM (United States); Andrews, M.J. [Texas A and M Univ., College Station, TX (United States). Dept. of Mechanical Engineering
1997-06-01
A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.
Nebular Spectra of SN 1998bw Revisited: Detailed Study by One and Two Dimensional Models
Maeda, K; Mazzali, P A; Deng, J
2006-01-01
Refined one- and two-dimensional models for the nebular spectra of the hyper-energetic Type Ic supernova (SN) 1998bw, associated with the gamma-ray burst GRB980425, from 125 to 376 days after B-band maximum are presented. One dimensional, spherically symmetric spectrum synthesis calculations show that reproducing features in the observed spectra, i.e., the sharply peaked [OI] 6300\\AA doublet and MgI] 4570\\AA emission, and the broad [FeII] blend around 5200\\AA, requires the existence of a high-density O-rich core expanding at low velocities ($\\lsim 8,000$ km s$^{-1}$) and of Fe-rich material moving faster than the O-rich material. Synthetic spectra at late phases from aspherical (bipolar) explosion models are also computed with a two-dimensional spectrum synthesis code. The above features are naturally explained by the aspherical model if the explosion is viewed from a direction close to the axis of symmetry ($\\sim 30^{\\rm o}$), since the aspherical model yields a high-density O-rich region confined along the ...
Measuring and modeling two-dimensional irrigation infiltration under film-mulched furrows
Institute of Scientific and Technical Information of China (English)
YongYong Zhang; PuTe Wu; XiNing Zhao; WenZhi Zhao
2016-01-01
Furrow irrigation with film-mulched agricultural beds is being promoted in the arid region of northwest China because it improves water utilization. Two-dimensional infiltration patterns under film-mulched furrows can provide guidelines and criteria for irrigation design and operation. Our objective was to investigate soil water dynamics during ponding irrigation infiltration of mulched furrows in a cross-sectional ridge-furrow configuration, using laboratory experiments and math-ematical simulations. Six experimental treatments, with two soil types (silt loam and sandy loam), were investigated to monitor the wetting patterns and soil water distribution in a cuboid soil chamber. Irrigation of mulched furrows clearly increased water lateral infiltration on ridge shoulders and ridges, due to enhancement of capillary driving force. Increases to both initial soil water content (SWC) and irrigation water level resulted in increased wetted soil volume. Empirical regression equations accurately estimated the wetted lateral distance (Rl) and downward distance (Rd) with elapsed time in a variably wetted soil medium. Optimization of model parameters followed by the Inverse approach resulted in satisfactory agreement between observed and predicted cumulative infiltration and SWC. On the basis of model calibration, HYDRUS-2D model can accurately simulate two-dimensional soil water dynamics under irrigation of mulched furrows. There were significant differences in wetting patterns between unmulched and mulched furrow irrigation using HYDRUS-2D simulation. The Rd under the mulched furrows was 32.14%less than the unmulched furrows. Therefore, film-mulched furrows are recommended in a furrow irrigation system.
A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows
Mininni, P D; Pouquet, A G
2004-01-01
We explore some consequences of the ``alpha model,'' also called the ``Lagrangian-averaged'' model, for two-dimensional incompressible magnetohydrodynamic (MHD) turbulence. This model is an extension of the smoothing procedure in fluid dynamics which filters velocity fields locally while leaving their associated vorticities unsmoothed, and has proved useful for high Reynolds number turbulence computations. We consider several known effects (selective decay, dynamic alignment, inverse cascades, and the probability distribution functions of fluctuating turbulent quantities) in magnetofluid turbulence and compare the results of numerical solutions of the primitive MHD equations with their alpha-model counterparts' performance for the same flows, in regimes where available resolution is adequate to explore both. The hope is to justify the use of the alpha model in regimes that lie outside currently available resolution, as will be the case in particular in three-dimensional geometry or for magnetic Prandtl number...
An evaluation of the role of eddy diffusion in stratospheric interactive two-dimensional models
Schneider, Hans R.; Ko, Malcolm K. W.; Sze, Nien Dak; Shi, Guang-Yu; Wang, Wei-Chyung
1989-01-01
An interactive two-dimensional model of the stratosphere, consisting of a primitive equation dynamics module, a simplified HO(x) ozone model, and a full radiative transfer scheme, is used to study the effect of eddy diffusion in the model. Consideration is given to the effects of nonlocal forcing from dissipation in the model troposphere and frictional drag at mesospheric levels, mechanical damping in the stratosphere itself, and potential vorticity flux due to large scale waves. It is found that the ozone distributions generated with the model are very sensitive to the choice of values for the friction and the eddy diffusion coefficients. It is shown that reasonable latitudinal gradients of ozone may be obtained by using small values for the mechanical damping for the mid- and high-latitude stratopsphere.
Two dimensional, two fluid model for sodium boiling in LMFBR fuel assemblies
Energy Technology Data Exchange (ETDEWEB)
Granziera, M.R.; Kazimi, M.S.
1980-05-01
A two dimensional numerical model for the simulation of sodium boiling transient was developed using the two fluid set of conservation equations. A semiimplicit numerical differencing scheme capable of handling the problems associated with the ill-posedness implied by the complex characteristic roots of the two fluid problems was used, which took advantage of the dumping effect of the exchange terms. Of particular interest in the development of the model was the identification of the numerical problems caused by the strong disparity between the axial and radial dimensions of fuel assemblies. A solution to this problem was found which uses the particular geometry of fuel assemblies to accelerate the convergence of the iterative technique used in the model. Three sodium boiling experiments were simulated with the model, with good agreement between the experimental results and the model predictions.
Zhou, Zhenyu; Zhao, Erhai; Liu, W Vincent
2015-03-13
Mott insulators with both spin and orbital degeneracy are pertinent to a large number of transition metal oxides. The intertwined spin and orbital fluctuations can lead to rather exotic phases such as quantum spin-orbital liquids. Here, we consider two-component (spin 1/2) fermionic atoms with strong repulsive interactions on the p band of the optical square lattice. We derive the spin-orbital exchange for quarter filling of the p band when the density fluctuations are suppressed, and show that it frustrates the development of long-range spin order. Exact diagonalization indicates a spin-disordered ground state with ferro-orbital order. The system dynamically decouples into individual Heisenberg spin chains, each realizing a Luttinger liquid accessible at higher temperatures compared to atoms confined to the s band.
Energy Technology Data Exchange (ETDEWEB)
Goldberg, L.F. [Univ. of Minnesota, Minneapolis, MN (United States)
1990-08-01
The activities described in this report do not constitute a continuum but rather a series of linked smaller investigations in the general area of one- and two-dimensional Stirling machine simulation. The initial impetus for these investigations was the development and construction of the Mechanical Engineering Test Rig (METR) under a grant awarded by NASA to Dr. Terry Simon at the Department of Mechanical Engineering, University of Minnesota. The purpose of the METR is to provide experimental data on oscillating turbulent flows in Stirling machine working fluid flow path components (heater, cooler, regenerator, etc.) with particular emphasis on laminar/turbulent flow transitions. Hence, the initial goals for the grant awarded by NASA were, broadly, to provide computer simulation backup for the design of the METR and to analyze the results produced. This was envisaged in two phases: First, to apply an existing one-dimensional Stirling machine simulation code to the METR and second, to adapt a two-dimensional fluid mechanics code which had been developed for simulating high Rayleigh number buoyant cavity flows to the METR. The key aspect of this latter component was the development of an appropriate turbulence model suitable for generalized application to Stirling simulation. A final-step was then to apply the two-dimensional code to an existing Stirling machine for which adequate experimental data exist. The work described herein was carried out over a period of three years on a part-time basis. Forty percent of the first year`s funding was provided as a match to the NASA funds by the Underground Space Center, University of Minnesota, which also made its computing facilities available to the project at no charge.
Finite size scaling analysis of intermittency moments in the two dimensional Ising model
Burda, Z; Peschanski, R; Wosiek, J
1993-01-01
Finite size scaling is shown to work very well for the block variables used in intermittency studies on a 2-d Ising lattice. The intermittency exponents so derived exhibit the expected relations to the magnetic critical exponent of the model. Email contact: pesch@amoco.saclay.cea.fr
Remarks on Two-Dimensional Power Correction in Soft Wall Model
Institute of Scientific and Technical Information of China (English)
HUANG Tao; ZUO Fen
2008-01-01
We present a direct derivation of the two-point correlation function of the vector current in the soft wall model by using the AdS/CFT dictionary. The resulting correlator is exactly the same as the one previously obtained from dispersion relation with the same spectral function as in this model. The coeffcient C2 of the two-dimensional power correction is found to be C2 = -c/2 with c the slope of the Regge trajectory, rather than C2 = -c/3 derived from the strategy of the first quantized string theory. Taking the slope of the p trajectory c ≈ 0.9 CeV2 as input, we then obtain C2 ≈ -0.45 GeV2. The gluon condensate is found to be (αsG2) ≈ 0.064 GeV4, which is almost identical to the QCD sum rule estimation. By comparing these two equivalent derivation of the correlator of scalar glueball operator, we demonstrate that the two-dimensionai correction cannot be eliminated by including the non-leading solution in the bulk-to-boundary propagator, as carried out by Colangelo et al.[arXiv:0711.4747].In other words, the two-dimensional correction does exist in the scalar glueball case. Also it is manifest by using the dispersion relation that the minus sign of gluon condensate and violation of the low energy theorem are related to the subtraction scheme.
A two dimensional thermal network model for a photovoltaic solar wall
Energy Technology Data Exchange (ETDEWEB)
Dehra, Himanshu [1-140 Avenue Windsor, Lachine, Quebec (Canada)
2009-11-15
A two dimensional thermal network model is proposed to predict the temperature distribution for a section of photovoltaic solar wall installed in an outdoor room laboratory in Concordia University, Montreal, Canada. The photovoltaic solar wall is constructed with a pair of glass coated photovoltaic modules and a polystyrene filled plywood board as back panel. The active solar ventilation through a photovoltaic solar wall is achieved with an exhaust fan fixed in the outdoor room laboratory. The steady state thermal network nodal equations are developed for conjugate heat exchange and heat transport for a section of a photovoltaic solar wall. The matrix solution procedure is adopted for formulation of conductance and heat source matrices for obtaining numerical solution of one dimensional heat conduction and heat transport equations by performing two dimensional thermal network analyses. The temperature distribution is predicted by the model with measurement data obtained from the section of a photovoltaic solar wall. The effect of conduction heat flow and multi-node radiation heat exchange between composite surfaces is useful for predicting a ventilation rate through a solar ventilation system. (author)
Development and validation of a two-dimensional fast-response flood estimation model
Energy Technology Data Exchange (ETDEWEB)
Judi, David R [Los Alamos National Laboratory; Mcpherson, Timothy N [Los Alamos National Laboratory; Burian, Steven J [UNIV OF UTAK
2009-01-01
A finite difference formulation of the shallow water equations using an upwind differencing method was developed maintaining computational efficiency and accuracy such that it can be used as a fast-response flood estimation tool. The model was validated using both laboratory controlled experiments and an actual dam breach. Through the laboratory experiments, the model was shown to give good estimations of depth and velocity when compared to the measured data, as well as when compared to a more complex two-dimensional model. Additionally, the model was compared to high water mark data obtained from the failure of the Taum Sauk dam. The simulated inundation extent agreed well with the observed extent, with the most notable differences resulting from the inability to model sediment transport. The results of these validation studies complex two-dimensional model. Additionally, the model was compared to high water mark data obtained from the failure of the Taum Sauk dam. The simulated inundation extent agreed well with the observed extent, with the most notable differences resulting from the inability to model sediment transport. The results of these validation studies show that a relatively numerical scheme used to solve the complete shallow water equations can be used to accurately estimate flood inundation. Future work will focus on further reducing the computation time needed to provide flood inundation estimates for fast-response analyses. This will be accomplished through the efficient use of multi-core, multi-processor computers coupled with an efficient domain-tracking algorithm, as well as an understanding of the impacts of grid resolution on model results.
Research of MPPT for photovoltaic generation based on two-dimensional cloud model
Liu, Shuping; Fan, Wei
2013-03-01
The cloud model is a mathematical representation to fuzziness and randomness in linguistic concepts. It represents a qualitative concept with expected value Ex, entropy En and hyper entropy He, and integrates the fuzziness and randomness of a linguistic concept in a unified way. This model is a new method for transformation between qualitative and quantitative in the knowledge. This paper is introduced MPPT (maximum power point tracking, MPPT) controller based two- dimensional cloud model through analysis of auto-optimization MPPT control of photovoltaic power system and combining theory of cloud model. Simulation result shows that the cloud controller is simple and easy, directly perceived through the senses, and has strong robustness, better control performance.
Eighth-order phase-field-crystal model for two-dimensional crystallization
Jaatinen, A.; Ala-Nissila, T.
2010-12-01
We present a derivation of the recently proposed eighth-order phase-field crystal model [A. Jaatinen , Phys. Rev. E 80, 031602 (2009)10.1103/PhysRevE.80.031602] for the crystallization of a solid from an undercooled melt. The model is used to study the planar growth of a two-dimensional hexagonal crystal, and the results are compared against similar results from dynamical density functional theory of Marconi and Tarazona, as well as other phase-field crystal models. We find that among the phase-field crystal models studied, the eighth-order fitting scheme gives results in good agreement with the density functional theory for both static and dynamic properties, suggesting it is an accurate and computationally efficient approximation to the density functional theory.
A two-dimensional analytical model for short channel junctionless double-gate MOSFETs
Jiang, Chunsheng; Liang, Renrong; Wang, Jing; Xu, Jun
2015-05-01
A physics-based analytical model of electrostatic potential for short-channel junctionless double-gate MOSFETs (JLDGMTs) operated in the subthreshold regime is proposed, in which the full two-dimensional (2-D) Poisson's equation is solved in channel region by a method of series expansion similar to Green's function. The expression of the proposed electrostatic potential is completely rigorous and explicit. Based on this expression, analytical models of threshold voltage, subthreshold swing, and subthreshold drain current for JLDGMTs were derived. Subthreshold behavior was studied in detail by changing different device parameters and bias conditions, including doping concentration, channel thickness, gate length, gate oxide thickness, drain voltage, and gate voltage. Results predicted by all the analytical models agree well with numerical solutions from the 2-D simulator. These analytical models can be used to investigate the operating mechanisms of nanoscale JLDGMTs and to optimize their device performance.
Energy Technology Data Exchange (ETDEWEB)
Sahraoui, Melik [Institut Preparatoire aux Etudes d' Ingenieurs de Tunis (IPEIT) (Tunisia); Kharrat, Chafik; Halouani, Kamel [UR: Micro-Electro-Thermal Systems (METS-ENIS), Industrial Energy Systems Group, Institut Preparatoire aux Etudes d' Ingenieurs de Sfax (IPEIS), University of Sfax, B.P: 1172, 3018 Sfax (Tunisia)
2009-04-15
A two-dimensional CFD model of PEM fuel cell is developed by taking into account the electrochemical, mass and heat transfer phenomena occurring in all of its regions simultaneously. The catalyst layers and membrane are each considered as distinct regions with finite thickness and calculated properties such as permeability, local protonic conductivity, and local dissolved water diffusion. This finite thickness model enables to model accurately the protonic current in these regions with higher accuracy than using an infinitesimal interface. In addition, this model takes into account the effect of osmotic drag in the membrane and catalyst layers. General boundary conditions are implemented in a way taking into consideration any given species concentration at the fuel cell inlet, such as water vapor which is a very important parameter in determining the efficiency of fuel cells. Other operating parameters such as temperature, pressure and porosity of the porous structure are also investigated to characterize their effect on the fuel cell efficiency. (author)
Simple Screened Hydrogen Model of Excitons in Two-Dimensional Materials
DEFF Research Database (Denmark)
Olsen, Thomas; Latini, Simone; Rasmussen, Filip Anselm;
2016-01-01
We present a generalized hydrogen model for the binding energies (EB) and radii of excitons in two-dimensional (2D) materials that sheds light on the fundamental differences between excitons in two and three dimensions. In contrast to the well-known hydrogen model of three-dimensional (3D) excitons...... the recently observed linear scaling of exciton binding energies with band gap. It is also shown that the model accurately reproduces the nonhydrogenic Rydberg series in WS2 and can account for screening from the environment....... that only depends on the excitonic mass and the 2D polarizability α. The model is shown to produce accurate results for 51 transition metal dichalcogenides. Remarkably, over a wide range of polarizabilities the binding energy becomes independent of the mass and we obtain E2DB≈3/(4πα), which explains...
Two-dimensional mathematical model of a reciprocating room-temperature Active Magnetic Regenerator
DEFF Research Database (Denmark)
Petersen, Thomas Frank; Pryds, Nini; Smith, Anders;
2008-01-01
heat exchanger. The model simulates the different steps of the AMR refrigeration cycle and evaluates the performance in terms of refrigeration capacity and temperature span between the two heat exchangers. The model was used to perform an analysis of an AMR with a regenerator made of gadolinium...... and water as the heat transfer fluid. The results show that the AMR is able to obtain a no-load temperature span of 10.9 K in a 1 T magnetic field with a corresponding work input of 93.0 kJ m−3 of gadolinium per cycle. The model shows significant temperature differences between the regenerator and the heat...... transfer fluid during the AMR cycle. This indicates that it is necessary to use two-dimensional models when a parallel-plate regenerator geometry is used....
Finite Element Model for Failure Study of Two-Dimensional Triaxially Braided Composite
Li, Xuetao; Binienda, Wieslaw K.; Goldberg, Robert K.
2010-01-01
A new three-dimensional finite element model of two-dimensional triaxially braided composites is presented in this paper. This meso-scale modeling technique is used to examine and predict the deformation and damage observed in tests of straight sided specimens. A unit cell based approach is used to take into account the braiding architecture as well as the mechanical properties of the fiber tows, the matrix and the fiber tow-matrix interface. A 0 deg / plus or minus 60 deg. braiding configuration has been investigated by conducting static finite element analyses. Failure initiation and progressive degradation has been simulated in the fiber tows by use of the Hashin failure criteria and a damage evolution law. The fiber tow-matrix interface was modeled by using a cohesive zone approach to capture any fiber-matrix debonding. By comparing the analytical results to those obtained experimentally, the applicability of the developed model was assessed and the failure process was investigated.
More on two-dimensional O (N ) models with N =(0 ,1 ) supersymmetry
Peterson, Adam J.; Kurianovych, Evgeniy; Shifman, Mikhail
2016-03-01
We study the behavior of two-dimensional supersymmetric connections of n copies of O (N ) models with an N =(0 ,1 ) heterotic deformation generated by a right-moving fermion. We develop the model in analogy with the connected N =(0 ,2 ) C P (N -1 ) models for the case of a single connecting fermionic superfield. We calculate the effective potential in the large-N limit and determine the vacuum field configurations. Similarly to other supersymmetry (SUSY) connected models we find that SUSY is unbroken under certain conditions despite the vanishing of the Witten index. Specifically, this preservation of SUSY occurs when we have an even number n of O (N ) families. As in previous cases we show that this result follows from a Zn symmetry under a particular exchange of the O (N ) families. This leads to a definition of a modified Witten index, which guarantees the preservation of SUSY in this case.
Two-dimensional models as testing ground for principles and concepts of local quantum physics
Schroer, Bert
2006-02-01
In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g., chiral models, factorizing models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work, I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: (1) a modular interpretation of the chiral model Diff( S)-covariance with a close connection to the recently formulated local covariance principle for QFT in curved spacetime and (2) a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational chiral theories. The SL (2, Z) modular Verlinde relation is a special case of this thermal duality and (within the family of rational models) the matrix S appearing in the thermal duality relation becomes identified with the statistics character matrix S. The relevant angular "Euclideanization" is done in the setting of the Tomita-Takesaki modular formalism of operator algebras. I find it appropriate to dedicate this work to the memory of J.A. Swieca with whom I shared the interest in two-dimensional models as a testing ground for QFT for more than one decade. This is a significantly extended version of an "Encyclopedia of Mathematical Physics" contribution hep-th/0502125.
Two-dimensional models as testing ground for principles and concepts of local quantum physics
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [FU Berlin (Germany). Institut fuer Theoretische Physik
2005-04-15
In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g. chiral models, factoring models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: (1) a modular interpretation of the chiral model Diff(S)-covariance with a close connection to the recently formulated local covariance principle for QFT in curved spacetime and (2) a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational chiral theories. The SL(2,Z) modular Verlinde relation is a special case of this thermal duality and (within the family of rational models) the matrix S appearing in the thermal duality relation becomes identified with the statistics character matrix S. The relevant angular 'Euclideanization' is done in the setting of the Tomita-Takesaki modular formalism of operator algebras. I find it appropriate to dedicate this work to the memory of J. A. Swieca with whom I shared the interest in two-dimensional models as a testing ground for QFT for more than one decade. This is a significantly extended version of an 'Encyclopedia of Mathematical Physics' contribution hep-th/0502125. (author)
Two-dimensional models of early-type fast rotating stars: the ESTER project
Rieutord, Michel
2015-01-01
In this talk I present the latest results of the ESTER project that has taken up the challenge of building two dimensional (axisymmetric) models of stars rotating at any rotation rate. In particular, I focus on main sequence massive and intermediate mass stars. I show what should be expected in such stars as far as the differential rotation and the associated meridional circulation are concerned, notably the emergence of a Stewartson layer along the tangent cylinder of the core. I also indicate what may be inferred about the evolution of an intermediate-mass star at constant angular momentum and how Be stars may form. I finally give some comparisons between models and observations of the gravity darkening on some nearby fast rotators as it has been derived from interferometric observations. In passing, I also discuss how 2D models can help to recover the fundamental parameters of a star.
Chan, B. C.
1986-05-01
A basic, limited scope, fast-running computer model is presented for the solution of two-dimensional, transient, thermally-coupled fluid flow problems. This model is to be the module in the SSC (an LMFBR thermal-hydraulic systems code) for predicting complex flow behavior, as occurs in the upper plenum of the loop-type design or in the sodium pool of the pool-type design. The nonlinear Navier-Stokes equations and the two-equation (two-variable) transport model of turbulence are reduced to a set of linear algebraic equations in an implicit finite difference scheme, based on the control volume approach. These equations are solved iteratively in a line-by-line procedure using the tri-diagonal matrix algorithm. The results of calculational examplers are shown in the computer-generated plots.
Hydrodynamics for a model of a confined quasi-two-dimensional granular gas.
Brey, J Javier; Buzón, V; Maynar, P; García de Soria, M I
2015-05-01
The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and momentum fluxes are calculated to Navier-Stokes order, and the associated transport coefficients are explicitly determined as functions of the coefficient of normal restitution and the velocity parameter involved in the definition of the model. Also an Euler transport term contributing to the energy transport equation is considered. This term arises from the gradient expansion of the rate of change of the temperature due to the inelasticity of collisions, and it vanishes for elastic systems. The hydrodynamic equations are particularized for the relevant case of a system in the homogeneous steady state. The relationship with previous works is analyzed.
Present status of two-dimensional ESTER models: Application to Be stars
Rieutord, M
2013-01-01
ESTER two-dimensional models solve the steady state structure of fast rotating early-type stars including the large scale flows associated with the baroclinicity of the radiative zones. Models are compared successfully to the fundamental parameters of the two main components of the triple system $\\delta$ Velorum that have been derived from interferometric and orbit measurements. Testing the models on the Be star Achernar ($\\alpha$ Eri), we cannot reproduce the data and conclude that this star has left the main sequence and is likely crossing the Herzsprung gap. Computing main sequence evolution of fast rotating stars at constant angular momentum shows that their criticality increases with time suggesting that the Be phenomenon and the ensuing mass ejections is the result of evolution.
An extended two-dimensional mathematical model of vertical ring furnaces
Peter, S.; Charette, A.; Bui, R. T.; Tomsett, A.; Potocnik, V.
1996-04-01
An extended two-dimensional (2-D+) mathematical model of vertical anode baking furnaces has been developed. The work was motivated by the fact that a previous 2-D model was unable to predict the nonuniform baking in the transverse direction, i.e., perpendicular to the longitudinal axis of the furnace. The modeling strategy based on dividing each section in four zones (underlid, pit, underpit, head wall and fire shaft zones) and introducing two symmetry planes in the exterior pits is explained. The basic heat-transfer relations used are also detailed. Selected results shown include draught and oxygen concentration profiles in the flue, gas and anode temperature distributions and fuel consumption in the back fire ramp. Simulation and experimental results are compared.
A two-dimensional model for the study of interpersonal attraction.
Montoya, R Matthew; Horton, Robert S
2014-02-01
We describe a model for understanding interpersonal attraction in which attraction can be understood as a product of the initial evaluations we make about others. The model posits that targets are evaluated on two basic dimensions, capacity and willingness, such that affective and behavioral attraction result from evaluations of (a) a target's capacity to facilitate the perceiver's goals/needs and (b) a target's potential willingness to facilitate those goals/needs. The plausibility of the two-dimensional model of attraction is evaluated vis-à-vis the extant literature on various attraction phenomena including the reciprocity of liking effect, pratfall effect, matching hypothesis, arousal effects, and similarity effect. We conclude that considerable evidence across a wide range of phenomena supports the idea that interpersonal attraction is principally determined by inferences about the target's capacity and willingness.
Statistical mechanics of two-dimensional foams: Physical foundations of the model.
Durand, Marc
2015-12-01
In a recent series of papers, a statistical model that accounts for correlations between topological and geometrical properties of a two-dimensional shuffled foam has been proposed and compared with experimental and numerical data. Here, the various assumptions on which the model is based are exposed and justified: the equiprobability hypothesis of the foam configurations is argued. The range of correlations between bubbles is discussed, and the mean-field approximation that is used in the model is detailed. The two self-consistency equations associated with this mean-field description can be interpreted as the conservation laws of number of sides and bubble curvature, respectively. Finally, the use of a "Grand-Canonical" description, in which the foam constitutes a reservoir of sides and curvature, is justified.
Institute of Scientific and Technical Information of China (English)
XIA Junqiang; WANG Guangqian; WU Baosheng
2004-01-01
Two kinds of bank erosion mechanisms were analyzed, including fluvial and non-fluvial controlled mechanisms, and mechanical methods of simulating the erosion processes of cohesive, non-cohesive and composite riverbanks were improved. Then a two-dimensional numerical model of the channel deformation was developed, consisting of a 2D flow and sediment transport submodel and bank-erosion submodels of different soil riverbanks. In the model, a new technique for updating the bank geometry during the bed evolution was presented, which combines closely two kinds of submodels. The proposed model is capable of not only predicting the processes of flood routing and longitudinal channel deformation in natural rivers, but also simulating the processes of lateral channel deformation, especially the processes of lateral erosion and failure of cohesive, non-cohesive and composite riverbanks.
Two-dimensional modeling of volatile organic compounds adsorption onto beaded activated carbon.
Tefera, Dereje Tamiru; Jahandar Lashaki, Masoud; Fayaz, Mohammadreza; Hashisho, Zaher; Philips, John H; Anderson, James E; Nichols, Mark
2013-10-15
A two-dimensional heterogeneous computational fluid dynamics model was developed and validated to study the mass, heat, and momentum transport in a fixed-bed cylindrical adsorber during the adsorption of volatile organic compounds (VOCs) from a gas stream onto a fixed bed of beaded activated carbon (BAC). Experimental validation tests revealed that the model predicted the breakthrough curves for the studied VOCs (acetone, benzene, toluene, and 1,2,4-trimethylbenzene) as well as the pressure drop and temperature during benzene adsorption with a mean relative absolute error of 2.6, 11.8, and 0.8%, respectively. Effects of varying adsorption process variables such as carrier gas temperature, superficial velocity, VOC loading, particle size, and channelling were investigated. The results obtained from this study are encouraging because they show that the model was able to accurately simulate the transport processes in an adsorber and can potentially be used for enhancing absorber design and operation.
Two-Dimensional ARMA Modeling for Breast Cancer Detection and Classification
Bouaynaya, Nidhal; Schonfeld, Dan
2009-01-01
We propose a new model-based computer-aided diagnosis (CAD) system for tumor detection and classification (cancerous v.s. benign) in breast images. Specifically, we show that (x-ray, ultrasound and MRI) images can be accurately modeled by two-dimensional autoregressive-moving average (ARMA) random fields. We derive a two-stage Yule-Walker Least-Squares estimates of the model parameters, which are subsequently used as the basis for statistical inference and biophysical interpretation of the breast image. We use a k-means classifier to segment the breast image into three regions: healthy tissue, benign tumor, and cancerous tumor. Our simulation results on ultrasound breast images illustrate the power of the proposed approach.
Two-dimensional mathematical model of a packed bed dryer and experimentation
Energy Technology Data Exchange (ETDEWEB)
Basirat-Tabrizi, H.; Saffar-Avval, M.; Assarie, M.R. [Amirkabir University of Technology, Tehran (Iran). Dept. of Mechanical Engineering
2002-04-01
A comprehensive heat and mass transfer model, based on the Eulerian two fluid model (TFM), developed for a packed-bed-drying process. The temperature and moisture content in a particle was considered with the conjugate effects between the gas and particles in a packed bed. Numerical study of the model was carried out on two-dimensional, axi-symmetrical cylindrical coordinates in order to investigate the effects of the different parameters such as particle size, variation of inlet gas temperature on the moisture content, and temperature of solid and gas outlet. For experimental observations, an experimental apparatus was designed and utilized. The theoretical results were then compared to the experimental data, which indicated good agreement. (author)
Synchronizability of Small-World Networks Generated from a Two-Dimensional Kleinberg Model
Directory of Open Access Journals (Sweden)
Yi Zhao
2013-01-01
Full Text Available This paper investigates the synchronizability of small-world networks generated from a two-dimensional Kleinberg model, which is more general than NW small-world network. The three parameters of the Kleinberg model, namely, the distance of neighbors, the number of edge-adding, and the edge-adding probability, are analyzed for their impacts on its synchronizability and average path length. It can be deduced that the synchronizability becomes stronger as the edge-adding probability increases, and the increasing edge-adding probability could make the average path length of the Kleinberg small-world network go smaller. Moreover, larger distance among neighbors and more edges to be added could play positive roles in enhancing the synchronizability of the Kleinberg model. The lorentz oscillators are employed to verify the conclusions numerically.
Test of quantum thermalization in the two-dimensional transverse-field Ising model
Blaß, Benjamin; Rieger, Heiko
2016-12-01
We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems.
Energy Technology Data Exchange (ETDEWEB)
Chair, Noureddine, E-mail: n.chair@ju.edu.jo
2014-02-15
We have recently developed methods for obtaining exact two-point resistance of the complete graph minus N edges. We use these methods to obtain closed formulas of certain trigonometrical sums that arise in connection with one-dimensional lattice, in proving Scott’s conjecture on permanent of Cauchy matrix, and in the perturbative chiral Potts model. The generalized trigonometrical sums of the chiral Potts model are shown to satisfy recursion formulas that are transparent and direct, and differ from those of Gervois and Mehta. By making a change of variables in these recursion formulas, the dimension of the space of conformal blocks of SU(2) and SO(3) WZW models may be computed recursively. Our methods are then extended to compute the corner-to-corner resistance, and the Kirchhoff index of the first non-trivial two-dimensional resistor network, 2×N. Finally, we obtain new closed formulas for variant of trigonometrical sums, some of which appear in connection with number theory. -- Highlights: • Alternative derivation of certain trigonometrical sums of the chiral Potts model are given. • Generalization of these trigonometrical sums satisfy recursion formulas. • The dimension of the space of conformal blocks may be computed from these recursions. • Exact corner-to-corner resistance, the Kirchhoff index of 2×N are given.
Chowdhury, Zahidur R.; Chutinan, Alongkarn; Gougam, Adel B.; Kherani, Nazir P.; Zukotynski, Stefan
2010-06-01
Back Amorphous-Crystalline Silicon Heterojunction (BACH)1 solar cell can be fabricated using low temperature processes while integrating high efficiency features of heterojunction silicon solar cells and back-contact homojunction solar cells. This article presents a two-dimensional modeling study of the BACH cell concept. A parametric study of the BACH cell has been carried out using Sentaurus after benchmarking the software. A detailed model describing the optical generation is defined. Solar cell efficiency of 24.4% is obtained for AM 1.5 global spectrum with VOC of greater than 720 mV and JSC exceeding 40 mA/cm2, considering realistic surface passivation quality and other dominant recombination processes.
Directory of Open Access Journals (Sweden)
Kunal Pathak
2016-09-01
Full Text Available The calcium signaling plays a crucial role in expansion and contraction of cardiac myocytes. This calcium signaling is achieved by calcium diffusion, buffering mechanisms and influx in cardiac myocytes. The various calcium distribution patterns required for achieving calcium signaling in myocytes are still not well understood. In this paper an attempt has been made to develop a model of calcium distribution in myocytes incorporating diffusion of calcium, point source and excess buffer approximation. The model has been developed for a two dimensional unsteady state case. Appropriate boundary conditions and initial condition have been framed. The finite element method has been employed to obtain the solution. The numerical results have been used to study the effect of buffers and source amplitude on calcium distribution in myocytes.
Thermodynamics of the two-dimensional XY model from functional renormalization
Jakubczyk, Pawel
2016-01-01
We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the non-universal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on $\\phi^4$-type truncations. Our computation indicates that such an approximation is insufficient in the high-$T$ phase and a correct analysis of the specific heat profile requires account of an infinite number of interaction vertices.
Hetmaniok, Edyta; Hristov, Jordan; Słota, Damian; Zielonka, Adam
2017-05-01
The paper presents the procedure for solving the inverse problem for the binary alloy solidification in a two-dimensional space. This is a continuation of some previous works of the authors investigating a similar problem but in the one-dimensional domain. Goal of the problem consists in identification of the heat transfer coefficient on boundary of the region and in reconstruction of the temperature distribution inside the considered region in case when the temperature measurements in selected points of the alloy are known. Mathematical model of the problem is based on the heat conduction equation with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependance on the concentration of the alloy component. For describing this concentration the Scheil model is used. Investigated procedure involves also the parallelized Ant Colony Optimization algorithm applied for minimizing a functional expressing the error of approximate solution.
Two-dimensional water quality modeling of Town Creek embayment on Guntersville Reservoir
Energy Technology Data Exchange (ETDEWEB)
Bender, M.D.; Shiao, Ming C.; Hauser, G.E. (Tennessee Valley Authority, Norris, TN (USA). Engineering Lab.); Butkus, S.R. (Tennessee Valley Authority, Norris, TN (USA). Water Quality Dept.)
1990-09-01
TVA investigated water quality of Town Creek embayment using a branched two-dimensional model of Guntersville Reservoir. Simulation results were compared in terms of algal biomass, nutrient concentrations, and volume of embayment with depleted dissolved oxygen. Stratification and flushing play a significant role in the embayment water quality. Storms introduce large loadings of organics, nutrients, and suspended solids. Dissolved oxygen depletion is most severe after storms followed by low flow that fails to flush the embayment. Embayment water quality responses to potential animal waste and erosion controls were explored. Modeling indicated animal waste controls were much more cost-effective than erosion controls. Erosion controls will decrease embayment suspended solids and thereby increase algal biomass due to greater light penetration. 29 refs., 16 figs., 4 tabs.
Benzekry, Sebastien
2010-01-01
Angiogenesis is a key process in the tumoral growth which allows the cancerous tissue to impact on its vasculature in order to improve the nutrient's supply and the metastatic process. In this paper, we introduce a model for the density of metastasis which takes into account for this feature. It is a two dimensional structured equation with a vanishing velocity field and a source term on the boundary. We present here the mathematical analysis of the model, namely the well-posedness of the equation and the asymptotic behavior of the solutions, whose natural regularity led us to investigate some basic properties of the space $\\Wd(\\Om)=\\{V\\in L^1;\\;\\div(GV)\\in L^1\\}$, where $G$ is the velocity field of the equation.
A Two-Dimensional Cloud Model for Condition Assessment of HVDC Converter Transformers
Directory of Open Access Journals (Sweden)
Linjie Zhao
2012-01-01
Full Text Available Converter transformers are the key and the most important components in high voltage direct current (HVDC power transmission systems. Statistics show that the failure rate of HVDC converter transformers is approximately twice of that of transformers in AC power systems. This paper presents an approach integrated with a two-dimensional cloud model and an entropy-based weight model to evaluate the condition of HVDC converter transformers. The integrated approach can describe the complexity of HVDC converter transformers and achieve an effective assessment of their condition. Data from electrical testing, DGA, oil testing, and visual inspection were chosen to form the double-level assessment index system. Analysis results show that the integrated approach is capable of providing a relevant and effective assessment which in turn, provides valuable information for the maintenance of HVDC converter transformers.
A meron cluster solution for the sign problem of the two-dimensional O(3) model
Brechtefeld, F
2002-01-01
The two-dimensional O(3) model at a vacuum angle theta=pi is investigated. This model has a severe sign problem. By a Wolff cluster algorithm an integer or half-integer topological charge is assigned to each cluster. The meron clusters (clusters with half-integer topological charge) are used to construct an improved estimator for the correlation function of two spins at theta=pi. Only configurations with 0 and 2 merons contribute to this correlation function. An algorithm, that generates configurations with only 0 and 2 merons, is constructed and numerical simulations at theta=pi are performed. The numerical results indicate the presence of long range correlations at theta=pi.
Quantum Phase Transition in the Two-Dimensional Random Transverse-Field Ising Model
Pich, C.; Young, A. P.
1998-03-01
We study the quantum phase transition in the random transverse-field Ising model by Monte Carlo simulations. In one-dimension it has been established that this system has the following striking behavior: (i) the dynamical exponent is infinite, and (ii) the exponents for the divergence of the average and typical correlation lengths are different. An important issue is whether this behavior is special to one-dimension or whether similar behavior persists in higher dimensions. Here we attempt to answer this question by studies of the two-dimensional model. Our simulations use the Wolff cluster algorithm and the results are analyzed by anisotropic finite size scaling, paying particular attention to the Binder ratio of moments of the order parameter distribution and the distribution of the spin-spin correlation functions for various distances.
Two-dimensional modeling of stepped planing hulls with open and pressurized air cavities
Directory of Open Access Journals (Sweden)
Konstantin I. Matveev
2012-06-01
Full Text Available A method of hydrodynamic discrete sources is applied for two-dimensional modeling of stepped planing surfaces. The water surface deformations, wetted hull lengths, and pressure distribution are calculated at given hull attitude and Froude number. Pressurized air cavities that improve hydrodynamic performance can also be modeled with the current method. Presented results include validation examples, parametric calculations of a single-step hull, effect of trim tabs, and performance of an infinite series of periodic stepped surfaces. It is shown that transverse steps can lead to higher lift-drag ratio, although at reduced lift capability, in comparison with a stepless hull. Performance of a multi-step configuration is sensitive to the wave pattern between hulls, which depends on Froude number and relative hull spacing.
Velocity selection at large undercooling in a two-dimensional nonlocal model of solidification
Barbieri, Angelo
1987-01-01
The formation of needle-crystal dendrites from an undercooled melt is investigated analytically, applying the method of Caroli et al. (1986) to Langer's (1980) symmetric two-dimensional nonlocal model of solidification with finite anisotropy in the limit of large undercooling. A solution based on the WKB approximation is obtained, and a saddle-point evaluation is performed. It is shown that needle-crystal solutions exist only if the capillary anisotropy is nonzero, in which case a particular value of the growth velocity can be selected. This finding and the expression for the dependence of the selected velocity on the singular perturbation parameter and the strength of the anisotropy are found to be in complete agreement with the results of a boundary-layer model (Langer and Hong, 1986).
Thermodynamics of the two-dimensional XY model from functional renormalization.
Jakubczyk, P; Eberlein, A
2016-06-01
We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the nonuniversal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific-heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on ϕ^{4}-type truncations. Our computation indicates that such an approximation is insufficient in the high-T phase and a correct analysis of the specific-heat profile requires account of an infinite number of interaction vertices.
Danny Raj, M.; Rengaswamy, R.
2017-03-01
A two-dimensional concentrated emulsion exhibits spontaneous rapid destabilization through an avalanche of coalescence events which propagate through the assembly stochastically. We propose a deterministic model to explain the average dynamics of the avalanching process. The dynamics of the avalanche phenomenon is studied as a function of a composite parameter, the decay time ratio, which characterizes the ratio of the propensity of coalescence to cease propagation to that of propagation. When this ratio is small, the avalanche grows autocatalytically to destabilize the emulsion. Using a scaling analysis, we unravel the relation between a local characteristic of the system and a global system wide effect. The anisotropic nature of local coalescence results in a system size dependent transition from nonautocatalytic to autocatalytic behavior. By incorporating uncertainty into the parameters in the model, several possible realizations of the coalescence avalanche are generated. The results are compared with the Monte Carlo simulations to derive insights into how the uncertainty propagates in the system.
Numerical simulations of blast wave characteristics with a two-dimensional axisymmetric room model
Sugiyama, Y.; Homae, T.; Wakabayashi, K.; Matsumura, T.; Nakayama, Y.
2017-01-01
This paper numerically visualizes explosion phenomena in order to discuss blast wave characteristics with a two-dimensional axisymmetric room model. After the shock wave exits via an opening, the blast wave propagates into open space. In the present study, a parametric study was conducted to determine the blast wave characteristics from the room exit by changing the room shape and the mass of the high explosive. Our results show that the blast wave characteristics can be correctly estimated using a scaling factor proposed in the present paper that includes the above parameters. We conducted normalization of the peak overpressure curve using the shock overpressure at the exit and the length scale of the room volume. In the case where the scaling factor has the same value, the normalized peak overpressure curve does not depend on the calculation conditions, and the scaling factor describes the blast wave characteristics emerging from the current room model.
Grain coarsening in two-dimensional phase-field models with an orientation field
Korbuly, Bálint; Pusztai, Tamás; Henry, Hervé; Plapp, Mathis; Apel, Markus; Gránásy, László
2017-05-01
In the literature, contradictory results have been published regarding the form of the limiting (long-time) grain size distribution (LGSD) that characterizes the late stage grain coarsening in two-dimensional and quasi-two-dimensional polycrystalline systems. While experiments and the phase-field crystal (PFC) model (a simple dynamical density functional theory) indicate a log-normal distribution, other works including theoretical studies based on conventional phase-field simulations that rely on coarse grained fields, like the multi-phase-field (MPF) and orientation field (OF) models, yield significantly different distributions. In a recent work, we have shown that the coarse grained phase-field models (whether MPF or OF) yield very similar limiting size distributions that seem to differ from the theoretical predictions. Herein, we revisit this problem, and demonstrate in the case of OF models [R. Kobayashi, J. A. Warren, and W. C. Carter, Physica D 140, 141 (2000), 10.1016/S0167-2789(00)00023-3; H. Henry, J. Mellenthin, and M. Plapp, Phys. Rev. B 86, 054117 (2012), 10.1103/PhysRevB.86.054117] that an insufficient resolution of the small angle grain boundaries leads to a log-normal distribution close to those seen in the experiments and the molecular scale PFC simulations. Our paper indicates, furthermore, that the LGSD is critically sensitive to the details of the evaluation process, and raises the possibility that the differences among the LGSD results from different sources may originate from differences in the detection of small angle grain boundaries.
Review of simplified Pseudo-two-Dimensional models of lithium-ion batteries
Jokar, Ali; Rajabloo, Barzin; Désilets, Martin; Lacroix, Marcel
2016-09-01
Over the last decade, many efforts have been deployed to develop models for the prediction, the control, the optimization and the parameter estimation of Lithium-ion (Li-ion) batteries. It appears that the most successful electrochemical-based model for Li-ion battery is the Pseudo-two-Dimensional model (P2D). Due to the fact that the governing equations are complex, this model cannot be used in real-time applications like Battery Management Systems (BMSs). To remedy the situation, several investigations have been carried out to simplify the P2D model. Mathematical and physical techniques are employed to reduce the order of magnitude of the P2D governing equations. The present paper is a review of the studies on the modeling of Li-ion batteries with simplified P2D models. The assumptions on which these models rest are stated, the calculation methods are examined, the advantages and the drawbacks of the models are discussed and their applications are presented. Suggestions for overcoming the shortcomings of the models are made. Challenges and future directions in the modeling of Li-ion batteries are also discussed.
Institute of Scientific and Technical Information of China (English)
何春山; 李志兵
2003-01-01
The correlation function of a two-dimensionalIsing model is calculated by the corner transfer matrix renormalization group method.We obtain the critical exponent η= 0.2496 with few computer resources.
Wigner crystallization of electrons in deep traps in a two-dimensional dielectric
Energy Technology Data Exchange (ETDEWEB)
Shaimeev, S. S., E-mail: shaimeev@isp.nsc.ru; Gritsenko, V. A. [Institute of Semiconductor Physics (Russian Federation)
2011-03-15
A two-dimensional model is used to examine the spatial distribution of electrons in deep traps in a two-dimensional dielectric. When the trap concentration is much higher than the trapped electron concentration, Coulomb repulsion leads to the formation of a two-dimensional quasi-periodic hexagonal lattice of localized electrons (Wigner glass).
Perez-Morelo, D. J.; Ramirez-Pastor, A. J.; Romá, F.
2012-02-01
We study the two-dimensional Edwards-Anderson spin-glass model using a parallel tempering Monte Carlo algorithm. The ground-state energy and entropy are calculated for different bond distributions. In particular, the entropy is obtained by using a thermodynamic integration technique and an appropriate reference state, which is determined with the method of high-temperature expansion. This strategy provides accurate values of this quantity for finite-size lattices. By extrapolating to the thermodynamic limit, the ground-state energy and entropy of the different versions of the spin-glass model are determined.
Continuous and discrete modeling of the decay of two-dimensional nanostructures
Energy Technology Data Exchange (ETDEWEB)
Castez, Marcos F; Albano, Ezequiel V [Instituto de Investigaciones FisicoquImicas Teoricas y Aplicadas (INIFTA), CCT La Plata, Casilla de Correo 16, Sucursal 4, (1900) La Plata, UNLP, CONICET (Argentina)
2009-07-01
In this work we review some recent research on the surface diffusion-mediated decay of two-dimensional nanostructures. These results include both a continuous, vectorial model and a discrete kinetic Monte Carlo approach. Predictions from the standard linear continuous theory of surface-diffusion-driven interface decay are contrasted with simulational results both from kinetic and morphological points of view. In particular, we focused our attention on high-aspect-ratio nanostructures, where strong deviations from linear theory take place, including nonexponential amplitude decay and the emergence of several interesting nanostructures such as overhangs developing, nanoislands and nanovoids formation, loss of convexity, nanostructures-pinch off and nanostructures-break off, etc. (topical review)
Drude Weight,Optical Conductivity of Two-Dimensional Hubbard Model at Half Filling
Institute of Scientific and Technical Information of China (English)
XU Lei; ZHANG Jun
2008-01-01
We study the Drude weight D and optical conductivity of the two-dimensional (2D) Hubbard model at half filling with staggered magnetic flux (SMF).When SMF being introduced,the hopping integrals are modulated by the magnetic flux.The optical sum rule,which is related to the mean kinetic energy of band electrons,is evaluated for this 2D Hubbard Hamiltonian.Our present result gives the dependence of the kinetic energy,D and the optical conductivity on SMF and U.At half filling D vanishes exponentially with system size.We also find in the frequency dependence of the optical conductivity,there is &function peak at ω≈2|m|U and the incoherent excitations begin to present themselves extended to a higher energy region.
Superconducting phase and pairing fluctuations in the half-filled two-dimensional Hubbard model.
Sentef, Michael; Werner, Philipp; Gull, Emanuel; Kampf, Arno P
2011-09-16
The two-dimensional Hubbard model exhibits superconductivity with d-wave symmetry even at half-filling in the presence of a next-nearest neighbor hopping. Using plaquette cluster dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, we reveal the non-Fermi liquid character of the metallic phase in proximity to the superconducting state. Specifically, the low-frequency scattering rate for momenta near (π, 0) varies nonmonotonically at low temperatures, and the dc conductivity is T linear at elevated temperatures with an upturn upon cooling. Evidence is provided that pairing fluctuations dominate the normal-conducting state even considerably above the superconducting transition temperature.
A two-dimensional volatility basis set – Part 3: Prognostic modeling and NOx dependence
Directory of Open Access Journals (Sweden)
W. K. Chuang
2015-06-01
Full Text Available When NOx is introduced to organic emissions, aerosol production is sometimes, but not always, reduced. Under certain conditions, these interactions will instead increase aerosol concentrations. We expanded the two-dimensional volatility basis set (2-D-VBS to include the effects of NOx on aerosol formation. This includes the formation of organonitrates, where the addition of a nitrate group contributes to a decrease of 2.5 orders of magnitude in volatility. With this refinement, we model outputs from experimental results, such as the atomic N : C ratio, organonitrate mass, and nitrate fragments in AMS measurements. We also discuss the mathematical methods underlying the implementation of the 2-D-VBS and provide the complete code in the Supplemental material. A developer version is available on Bitbucket, an online community repository.
Isotropic model of fractional transport in two-dimensional bounded domains.
Kullberg, A; del-Castillo-Negrete, D; Morales, G J; Maggs, J E
2013-05-01
A two-dimensional fractional Laplacian operator is derived and used to model nonlocal, nondiffusive transport. This integro-differential operator appears in the long-wavelength, fluid description of quantities undergoing non-Brownian random walks without characteristic length scale. To study bounded domains, a mask function is introduced that modifies the kernel in the fractional Laplacian and removes singularities at the boundary. Green's function solutions to the fractional diffusion equation are presented for the unbounded domain and compared to the one-dimensional Cartesian approximations. A time-implicit numerical integration scheme is presented to study fractional diffusion in a circular disk with azimuthal symmetry. Numerical studies of steady-state reveal temperature profiles in which the heat flux and temperature gradient are in the same direction, i.e., uphill transport. The response to off-axis heating, scaling of confinement time with system size, and propagation of cold pulses are investigated.
Directory of Open Access Journals (Sweden)
Dongkyun IM
2011-12-01
Full Text Available River corridors, even if highly modified or degraded, still provide important habitats for numerous biological species, and carry high aesthetic and economic values. One of the keys to urban stream restoration is recovery and maintenance of ecological flows sufficient to sustain aquatic ecosystems. In this study, the Hongje Stream in the Seoul metropolitan area of Korea was selected for evaluating a physically-based habitat with and without habitat structures. The potential value of the aquatic habitat was evaluated by a weighted usable area (WUA using River2D, a two-dimensional hydraulic model. The habitat suitability for Zacco platypus in the Hongje Stream was simulated with and without habitat structures. The computed WUA values for the boulder, spur dike, and riffle increased by about 2%, 7%, and 131%, respectively, after their construction. Also, the three habitat structures, especially the riffle, can contribute to increasing hydraulic heterogeneity and enhancing habitat diversity.
Breakdown of the Nagaoka phase in the two-dimensional t-J model
Eisenberg, E.; Berkovits, R.; Huse, David A.; Altshuler, B. L.
2002-04-01
In the limit of weak exchange J at low hole concentration δ the ground state of the two-dimensional t-J model is believed to be ferromagnetic. We study the leading instability of this Nagaoka state, which emerges with increasing J. Both exact diagonalization of small clusters, and a semiclassical analytical calculation of larger systems show that above a certain critical value of the exchange, Jcr~tδ2, Nagaoka's state is unstable to phase separation. In a finite-size system a bubble of antiferromagnetic Mott insulator appears in the ground state above this threshold. The size of this bubble depends on δ and scales as a power of the system size N.
Nonlocal Coulomb interaction in the two-dimensional spin-1/2 Falicov–Kimball model
Indian Academy of Sciences (India)
S K Bhowmick; N K Ghosh
2012-02-01
The two-dimensional (2D) extended Falicov–Kimball model has been studied to observe the role of nonlocal Coulomb interaction (nc) using an exact diagonalization technique. The f-state occupation ($n^f$), the f–d intersite correlation function (fd), the speciﬁc heat (), entropy () and the speciﬁc heat coefﬁcient () have been examined. Nonlocal Coulomb interaction-induced discontinuous insulator-to-metal transition occurs at a critical f-level energy. More ordered state is obtained with the increase of nc. In the speciﬁc heat curves, two-peak structure as well as a singlepeak structure appears. At low-temperature region, a sharp rise in the speciﬁc heat coefﬁcient is observed. The peak value of shifts to the higher temperature region with nc.
Pairing in the two-dimensional Hubbard model: An exact diagonalization study
Lin, H. Q.; Hirsch, J. E.; Scalapino, D. J.
1988-05-01
We have studied the pair susceptibilities for all possible pair wave functions that fit on a two-dimensional (2D) eight-site Hubbard cluster by exact diagonalization of the Hamiltonian. Band fillings corresponding to four and six electrons were studied (two or four holes in the half-filled band) for a wide range of Hubbard interaction strengths and temperatures. Our results show that all pairing susceptibilities are suppressed by the Hubbard repulsion. We have also carried out perturbation-theory calculations which show that the leading-order U2 contributions to the d-wave pair susceptibility suppresses d-wave pairing over a significant temperature range. These results are consistent with recent Monte Carlo results and provide further evidence suggesting that the 2D Hubbard model does not exhibit superconductivity.
Critical behavior of two-dimensional spin systems under the random-bond six-state clock model
Wu, Raymond P. H.; Lo, Veng-cheong; Huang, Haitao
2012-09-01
The critical behavior of the clock model in two-dimensional square lattice is studied numerically using Monte Carlo method with Wolff algorithm. The Kosterlitz-Thouless (KT) transition is observed in the six-state clock model, where an intermediate phase exists between the low-temperature ordered phase and the high-temperature disordered phase. The bond randomness is introduced to the system by assuming a Gaussian distribution for the coupling coefficients with the mean μ =1 and different values of variance, from σ2=0.1 to σ2=3.0. An abrupt jump in the helicity modulus at the transition, which is the key characteristic of the KT transition, is verified with a stability argument. The critical temperature Tc for both pure and disordered systems is determined from the critical exponent η(Tc)=1/4. The results showed that a small amount of disorder (small σ) reduces the critical temperature of the system, without altering the nature of transition. However, a larger amount of disorder changes the transition from the KT-type into that of non-KT-type.
Palma, G; Zambrano, D
2008-12-01
In this paper we propose a method to study critical systems numerically, which combines collective-mode algorithms and renormalization group on the lattice. This method is an improved version of the Monte Carlo renormalization group in the sense that it has all the advantages of cluster algorithms. As an application we considered the 2D Ising model and studied whether scale invariance or universality are possible underlying mechanisms responsible for the approximate "universal fluctuations" close to a so-called bulk temperature T(L) . "Universal fluctuations" were first proposed in the work of Bramwell, Holdsworth, and Pinton [Nature (London) 396, 552 (1998)] and stated that the probability density function of a global quantity for very dissimilar systems, such as a confined turbulent flow and a two-dimensional (2D) magnetic system, properly normalized to the first two moments, becomes similar to the "universal distribution," originally obtained for magnetization in the 2D XY model in the low-temperature region. The results for the critical exponents and the renormalization-group flow of the probability density function are very accurate and show no evidence to support that the approximate common shape of the PDF should be related to both scale invariance or universal behavior.
Venetsanos, A G; Bartzis, J G; Würtz, J; Papailiou, D D
2003-04-25
A two-dimensional shallow layer model has been developed to predict dense gas dispersion, under realistic conditions, including complex features such as two-phase releases, obstacles and inclined ground. The model attempts to predict the time and space evolution of the cloud formed after a release of a two-phase pollutant into the atmosphere. The air-pollutant mixture is assumed ideal. The cloud evolution is described mathematically through the Cartesian, two-dimensional, shallow layer conservation equations for mixture mass, mixture momentum in two horizontal directions, total pollutant mass fraction (vapor and liquid) and mixture internal energy. Liquid mass fraction is obtained assuming phase equilibrium. Account is taken in the conservation equations for liquid slip and eventual liquid rainout through the ground. Entrainment of ambient air is modeled via an entrainment velocity model, which takes into account the effects of ground friction, ground heat transfer and relative motion between cloud and surrounding atmosphere. The model additionally accounts for thin obstacles effects in three ways. First a stepwise description of the obstacle is generated, following the grid cell faces, taking into account the corresponding area blockage. Then obstacle drag on the passing cloud is modeled by adding flow resistance terms in the momentum equations. Finally the effect of extra vorticity generation and entrainment enhancement behind obstacles is modeled by adding locally into the entrainment formula without obstacles, a characteristic velocity scale defined from the obstacle pressure drop and the local cloud height.The present model predictions have been compared against theoretical results for constant volume and constant flux gravity currents. It was found that deviations of the predicted cloud footprint area change with time from the theoretical were acceptably small, if one models the frictional forces between cloud and ambient air, neglecting the Richardson
Ishola, Kehinde S; Nawawi, Mohd Nm; Abdullah, Khiruddin; Sabri, Ali Idriss Aboubakar; Adiat, Kola Abdulnafiu
2014-01-01
This study attempts to combine the results of geophysical images obtained from three commonly used electrode configurations using an image processing technique in order to assess their capabilities to reproduce two-dimensional (2-D) resistivity models. All the inverse resistivity models were processed using the PCI Geomatica software package commonly used for remote sensing data sets. Preprocessing of the 2-D inverse models was carried out to facilitate further processing and statistical analyses. Four Raster layers were created, three of these layers were used for the input images and the fourth layer was used as the output of the combined images. The data sets were merged using basic statistical approach. Interpreted results show that all images resolved and reconstructed the essential features of the models. An assessment of the accuracy of the images for the four geologic models was performed using four criteria: the mean absolute error and mean percentage absolute error, resistivity values of the reconstructed blocks and their displacements from the true models. Generally, the blocks of the images of maximum approach give the least estimated errors. Also, the displacement of the reconstructed blocks from the true blocks is the least and the reconstructed resistivities of the blocks are closer to the true blocks than any other combined used. Thus, it is corroborated that when inverse resistivity models are combined, most reliable and detailed information about the geologic models is obtained than using individual data sets.
Coupled two-dimensional edge plasma and neutral gas modeling of tokamak scrape-off-layers
Energy Technology Data Exchange (ETDEWEB)
Maingi, R. [North Carolina State Univ., Raleigh, NC (United States)
1992-08-01
The objective of this study is to devise a detailed description of the tokamak scrape-off-layer (SOL), which includes the best available models of both the plasma and neutral species and the strong coupling between the two in many SOL regimes. A good estimate of both particle flux and heat flux profiles at the limiter/divertor target plates is desired. Peak heat flux is one of the limiting factors in determining the survival probability of plasma-facing-components at high power levels. Plate particle flux affects the neutral flux to the pump, which determines the particle exhaust rate. A technique which couples a two-dimensional (2-D) plasma and a 2-D neutral transport code has been developed (coupled code technique), but this procedure requires large amounts of computer time. Relevant physics has been added to an existing two-neutral-species model which takes the SOL plasma/neutral coupling into account in a simple manner (molecular physics model), and this model is compared with the coupled code technique mentioned above. The molecular physics model is benchmarked against experimental data from a divertor tokamak (DIII-D), and a similar model (single-species model) is benchmarked against data from a pump-limiter tokamak (Tore Supra). The models are then used to examine two key issues: free-streaming-limits (ion energy conduction and momentum flux) and the effects of the non-orthogonal geometry of magnetic flux surfaces and target plates on edge plasma parameter profiles.
A Vertical Two-Dimensional Model to Simulate Tidal Hydrodynamics in A Branched Estuary
Institute of Scientific and Technical Information of China (English)
LIU Wen-Cheng; WU Chung-Hsing
2005-01-01
A vertical (laterally averaged) two-dimensional hydrodynamic model is developed for tides, tidal current, and salinity in a branched estuarine system. The governing equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. An explicit scheme is employed to solve the continuity equations. The momentum and mass balance equations are solved implicitly in the Cartesian coordinate system. The tributaries are governed by the same dynamic equations. A control volume at the junctions is designed to conserve mass and volume transport in the finite difference schemes, based on the physical principle of continuum medium of fluid. Predictions by the developed model are compared with the analytic solutions of steady wind-driven circulatory flow and tidal flow. The model results for the velocities and water surface elevations coincide with analytic results. The model is then applied to the Tanshui River estuarine system. Detailed model calibration and verification have been conducted with measured water surface elevations,tidal current, and salinity distributions. The overall performance of the model is in qualitative agreement with the available field data. The calibrated and verified numerical model has been used to quantify the tidal prism and flushing rate in the Tanshui River-Tahan Stream, Hsintien Stream, and Keelung River.
A Monte Carlo Uncertainty Analysis of Ozone Trend Predictions in a Two Dimensional Model. Revision
Considine, D. B.; Stolarski, R. S.; Hollandsworth, S. M.; Jackman, C. H.; Fleming, E. L.
1998-01-01
We use Monte Carlo analysis to estimate the uncertainty in predictions of total O3 trends between 1979 and 1995 made by the Goddard Space Flight Center (GSFC) two-dimensional (2D) model of stratospheric photochemistry and dynamics. The uncertainty is caused by gas-phase chemical reaction rates, photolysis coefficients, and heterogeneous reaction parameters which are model inputs. The uncertainty represents a lower bound to the total model uncertainty assuming the input parameter uncertainties are characterized correctly. Each of the Monte Carlo runs was initialized in 1970 and integrated for 26 model years through the end of 1995. This was repeated 419 times using input parameter sets generated by Latin Hypercube Sampling. The standard deviation (a) of the Monte Carlo ensemble of total 03 trend predictions is used to quantify the model uncertainty. The 34% difference between the model trend in globally and annually averaged total O3 using nominal inputs and atmospheric trends calculated from Nimbus 7 and Meteor 3 total ozone mapping spectrometer (TOMS) version 7 data is less than the 46% calculated 1 (sigma), model uncertainty, so there is no significant difference between the modeled and observed trends. In the northern hemisphere midlatitude spring the modeled and observed total 03 trends differ by more than 1(sigma) but less than 2(sigma), which we refer to as marginal significance. We perform a multiple linear regression analysis of the runs which suggests that only a few of the model reactions contribute significantly to the variance in the model predictions. The lack of significance in these comparisons suggests that they are of questionable use as guides for continuing model development. Large model/measurement differences which are many multiples of the input parameter uncertainty are seen in the meridional gradients of the trend and the peak-to-peak variations in the trends over an annual cycle. These discrepancies unambiguously indicate model formulation
Directory of Open Access Journals (Sweden)
Farideh Hosseini
2015-09-01
Full Text Available Introduction As a tumor grows, the demand for oxygen and nutrients increases and it grows further if acquires the ability to induce angiogenesis. In this study, we aimed to present a two-dimensional continuous mathematical model for avascular tumor growth, coupled with a discrete model of angiogenesis. Materials and Methods In the avascular growth model, tumor is considered as a single mass, which uptakes oxygen through diffusion and invades the extracellular matrix (ECM. After the tumor reaches its maximum size in the avascular growth phase, tumor cells may be in three different states (proliferative, quiescent and apoptotic, depending on oxygen availability. Quiescent cells are assumed to secrete tumor angiogenic factors, which diffuse into the surrounding tissue until reaching endothelial cells. The mathematical model for tumor angiogenesis is consisted of a five-point finite difference scheme to simulate the progression of endothelial cells in ECM and their penetration into the tumor. Results The morphology of produced networks was investigated, based on various ECM degradation patterns. The generated capillary networks involved the rules of microvascular branching and anastomosis. Model predictions were in qualitative agreement with experimental observations and might have implications as a supplementary model to facilitate mathematical analyses for anti-cancer therapies. Conclusion Our numerical simulations could facilitate the qualitative comparison between three layers of tumor cells, their TAF-producing abilities and subsequent penetration of micro-vessels in order to determine the dynamics of microvascular branching and anastomosis in ECM and three different parts of the tumor.
Two-dimensional models as testing ground for principles and concepts of local quantum physics
Schrör, B
2005-01-01
In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g. chiral models, factorizing models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) and a modular interpretation of the chiral model Diff(S)-covariance with a close connection to the recently formulated local covariance principle for QFT in curved spacetime. As a special case of the thermal duality, the SL(2,Z) modular Verlinde relation is thus a consequence of the principles of thermal QFT togeth...
Turbulence models and Reynolds analogy for two-dimensional supersonic compression ramp flow
Wang, Chi R.; Bidek, Maleina C.
1994-01-01
Results of the application of turbulence models and the Reynolds analogy to the Navier-Stokes computations of Mach 2.9 two-dimensional compression ramp flows are presented. The Baldwin-Lomax eddy viscosity model and the kappa-epsilon turbulence transport equations for the turbulent momentum flux modeling in the Navier-Stokes equations are studied. The Reynolds analogy for the turbulent heat flux modeling in the energy equation was also studied. The Navier-Stokes equations and the energy equation were numerically solved for the flow properties. The Reynolds shear stress, the skin friction factor, and the surface heat transfer rate were calculated and compared with their measurements. It was concluded that with a hybrid kappa-epsilon turbulence model for turbulence modeling, the present computations predicted the skin friction factors of the 8 deg and 16 deg compression ramp flows and with the turbulent Prandtl number Pr(sub t) = 0.93 and the ratio of the turbulent thermal and momentum transport coefficients mu(sub q)/mu(sub t) = 2/Prt, the present computations also predicted the surface heat transfer rates beneath the boundary layer flow of the 16 compression ramp.
Milgrom Relation Models for Spiral Galaxies from Two-Dimensional Velocity Maps
Barnes, E I; Sellwood, J A; Barnes, Eric I.; Kosowsky, Arthur; Sellwood, Jerry A.
2007-01-01
Using two-dimensional velocity maps and I-band photometry, we have created mass models of 40 spiral galaxies using the Milgrom relation (the basis of modified Newtonian dynamics, or MOND) to complement previous work. A Bayesian technique is employed to compare several different dark matter halo models to Milgrom and Newtonian models. Pseudo-isothermal dark matter halos provide the best statistical fits to the data in a majority of cases, while the Milgrom relation generally provides good fits as well. We also find that Milgrom models give mass-to-light ratios that roughly correlate with galaxy color, as predicted by stellar population models. A subsample of galaxies in the Hydra cluster follow a tight relation between mass-to-light and color, but one that is significantly different from relations found in previous studies. Ruling out the Milgrom relation with rotational kinematics is difficult due to systematic uncertainties in the observations as well as underlying model assumptions. We discuss in detail two...
Directory of Open Access Journals (Sweden)
2015-12-01
Full Text Available Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.
Qin, Mingpu; Zhang, Shiwei
2016-01-01
Ground state properties of the Hubbard model on a two-dimensional square lattice are studied by the auxiliary-field quantum Monte Carlo method. Accurate results for energy, double occupancy, effective hopping, magnetization, and momentum distribution are calculated for interaction strengths of U/t from 2 to 8, for a range of densities including half-filling and n = 0.3, 0.5, 0.6, 0.75, and 0.875. At half-filling, the results are numerically exact. Away from half-filling, the constrained path Monte Carlo method is employed to control the sign problem. Our results are obtained with several advances in the computational algorithm, which are described in detail. We discuss the advantages of generalized Hartree-Fock trial wave functions and its connection to pairing wave functions, as well as the interplay with different forms of Hubbard-Stratonovich decompositions. We study the use of different twist angle sets when applying the twist averaged boundary conditions. We propose the use of quasi-random sequences, whi...
A two-dimensional CFD model of a refrigerated display case
Energy Technology Data Exchange (ETDEWEB)
Stribling, D.; Tassou, S.A. [Brunel Univ., Uxbridge (United Kingdom). Dept. of Mechanical Engineering; Marriott, D. [Safeway Stores plc, Middlesex (United Kingdom)
1997-12-31
The discomfort caused by the cold air overspill from vertical refrigerated display cases in supermarkets is widely accepted as being a problem to customers. This, together with the adverse effect on case performance caused by heat and moisture transfer across the air curtain, suggests that there may be room for improvement in the design and fundamental operation of these display fixtures. This paper presents a two-dimensional computational fluid dynamics (CFD) model of a vertical dairy display case that could be used in the design and optimization of such equipment. Comparisons are also made with experimentally obtained values of velocity and temperature measured around the case in order to assess the accuracy and viability of such a model. Parameters of the computer model, such as the size of the calculation grid, the turbulence model, and the discretization scheme, were also varied to determine their effect on the converged solution, and these results are presented. The CFD model showed good qualitative agreement with measured values and requires only fine tuning to make it quantitatively accurate.
Effect of a levee setback on aquatic resources using two-dimensional flow and bioenergetics models
Black, Robert W.; Czuba, Christiana R.; Magirl, Christopher S.; McCarthy, Sarah; Berge, Hans; Comanor, Kyle
2016-04-05
Watershed restoration is the focus of many resource managers and can include a multitude of restoration actions each with specific restoration objectives. For the White River flowing through the cities of Pacific and Sumner, Washington, a levee setback has been proposed to reconnect the river with its historical floodplain to help reduce flood risks, as well as provide increased habitat for federally listed species of salmonids. The study presented here documents the use of a modeling framework that integrates two-dimensional hydraulic modeling with process-based bioenergetics modeling for predicting how changes in flow from reconnecting the river with its floodplain affects invertebrate drift density and the net rate of energy intake of juvenile salmonids. Modeling results were calculated for flows of 25.9 and 49.3 cubic meters per second during the spring, summer, and fall. Predicted hypothetical future mean velocities and depths were significantly lower and more variable when compared to current conditions. The abundance of low energetic cost and positive growth locations for salmonids were predicted to increase significantly in the study reach following floodplain reconnection, particularly during the summer. This modeling framework presents a viable approach for evaluating the potential fisheries benefits of reconnecting a river to its historical floodplain that integrates our understanding of hydraulic, geomorphology, and organismal biology.
A two-dimensional model of the methane cycle in a sedimentary accretionary wedge
Directory of Open Access Journals (Sweden)
D. E. Archer
2012-08-01
Full Text Available A two-dimensional model of sediment column geophysics and geochemistry has been adapted to the problem of an accretionary wedge formation, patterned after the margin of the Juan de Fuca plate as it subducts under the North American plate. Much of the model description is given in a companion paper about the application of the model to an idealized passive margin setting; here we build on that formulation to simulate the impact of the sediment deformation, as it approaches the subduction zone, on the methane cycle. The active margin configuration of the model shares sensitivities with the passive margin configuration, in that sensitivities to organic carbon deposition and respiration kinetics, and to vertical bubble transport and redissolution in the sediment, are stronger than the sensitivity to ocean temperature. The active margin simulation shows a complex sensitivity of hydrate inventory to plate subduction velocity, with results depending strongly on the geothermal heat flux. In low heat-flux conditions, the model produces a larger inventory of hydrate per meter of coastline in the passive margin than active margin configurations. However, the local hydrate concentrations, as pore volume saturation, are higher in the active setting than in the passive, as generally observed in the field.
TWO-DIMENSIONAL CELLULAR AUTOMATON MODEL FOR THE EVOLUTION OF ACTIVE REGION CORONAL PLASMAS
Energy Technology Data Exchange (ETDEWEB)
López Fuentes, Marcelo [Instituto de Astronomía y Física del Espacio, CONICET-UBA, CC. 67, Suc. 28, 1428 Buenos Aires (Argentina); Klimchuk, James A., E-mail: lopezf@iafe.uba.ar [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States)
2015-02-01
We study a two-dimensional cellular automaton (CA) model for the evolution of coronal loop plasmas. The model is based on the idea that coronal loops are made of elementary magnetic strands that are tangled and stressed by the displacement of their footpoints by photospheric motions. The magnetic stress accumulated between neighbor strands is released in sudden reconnection events or nanoflares that heat the plasma. We combine the CA model with the Enthalpy Based Thermal Evolution of Loops model to compute the response of the plasma to the heating events. Using the known response of the X-Ray Telescope on board Hinode, we also obtain synthetic data. The model obeys easy-to-understand scaling laws relating the output (nanoflare energy, temperature, density, intensity) to the input parameters (field strength, strand length, critical misalignment angle). The nanoflares have a power-law distribution with a universal slope of –2.5, independent of the input parameters. The repetition frequency of nanoflares, expressed in terms of the plasma cooling time, increases with strand length. We discuss the implications of our results for the problem of heating and evolution of active region coronal plasmas.
DEFF Research Database (Denmark)
Baykal, Cüneyt; Ergin, Ayşen; Güler, Işikhan
2014-01-01
transformation model, a two-dimensional depth-averaged numerical waveinduced circulation model, a sediment transport model, and a bottom evolution model. To validate and verify the numerical model, it is applied to several cases of laboratory experiments. Later, the model is applied to a shoreline change problem...
Yamada, Hirofumi
2012-01-01
Based on the strong coupling expansion, we reinvestigate the scaling behavior of the susceptibility chi of two-dimensional O(N) sigma model on the square lattice by the use of Pade-Borel approximants. To exploit the Borel transform, we express the bare coupling g in series expansion in chi. At large N, Pade-Borel approximants exhibit the scaling behavior at the four-loop level. Then, the estimation of the non-perturbative constant associated with the susceptibility is performed for N>=3 and the results are compared with the available theoretical results and Monte Carlo data.
Spin correlations in the two-dimensional quantum s=1/2 XY model
Sznajd, J.
1995-08-01
A quantum version of the Niemeijer-van Leeuwen real-space renormalization-group method is used to study the temperature dependence of the two- and four-spin correlations in the quantum XY model on the triangular lattice. The first-order cumulant expansion results suggest, similarly to other methods, a low-temperature phase of an essentially different kind from that predicted for the classical model. The possible explanation of the origin of the spurious 2D Heisenberg-like nontrivial fixed point in some renormalization-group calculations is also proposed.
Phase diagram and criticality of the two-dimensional prisoner's dilemma model
Santos, M.; Ferreira, A. L.; Figueiredo, W.
2017-07-01
The stationary states of the prisoner's dilemma model are studied on a square lattice taking into account the role of a noise parameter in the decision-making process. Only first neighboring players—defectors and cooperators—are considered in each step of the game. Through Monte Carlo simulations we determined the phase diagrams of the model in the plane noise versus the temptation to defect for a large range of values of the noise parameter. We observed three phases: cooperators and defectors absorbing phases, and a coexistence phase between them. The phase transitions as well as the critical exponents associated with them were determined using both static and dynamical scaling laws.
One- and two-dimensional modelling of overland flow in semiarid shrubland, Jornada basin, New Mexico
Howes, David A.; Abrahams, Athol D.; Pitman, E. Bruce
2006-03-01
Two distributed parameter models, a one-dimensional (1D) model and a two-dimensional (2D) model, are developed to simulate overland flow in two small semiarid shrubland watersheds in the Jornada basin, southern New Mexico. The models are event-based and represent each watershed by an array of 1-m2 cells, in which the cell size is approximately equal to the average area of the shrubs.Each model uses only six parameters, for which values are obtained from field surveys and rainfall simulation experiments. In the 1D model, flow volumes through a fixed network are computed by a simple finite-difference solution to the 1D kinematic wave equation. In the 2D model, flow directions and volumes are computed by a second-order predictor-corrector finite-difference solution to the 2D kinematic wave equation, in which flow routing is implicit and may vary in response to flow conditions.The models are compared in terms of the runoff hydrograph and the spatial distribution of runoff. The simulation results suggest that both the 1D and the 2D models have much to offer as tools for the large-scale study of overland flow. Because it is based on a fixed flow network, the 1D model is better suited to the study of runoff due to individual rainfall events, whereas the 2D model may, with further development, be used to study both runoff and erosion during multiple rainfall events in which the dynamic nature of the terrain becomes an important consideration.
Two-dimensional finite elements model for boron management in agroforestry sites.
Tayfur, Gokmen; Tanji, Kenneth K; Baba, Alper
2010-01-01
Agroforesty systems, which are recommended as a management option to lower the shallow groundwater level and to reuse saline subsurface drainage waters from the tile-drained croplands in the drainage-impacted areas of Jan Joaquin Valley of California, have resulted in excessive boron buildup in the soil root zone. To assess the efficacy of the long-term impacts of soil boron buildup in agroforesty systems, a mathematical model was developed to simulate non-conservative boron transport. The developed dynamic two-dimensional finite element model simulates water flow and boron transport in saturated-unsaturated soil system, including boron sorption and boron uptake by root-water extraction processes. The simulation of two different observed field data sets by the developed model is satisfactory, with mean absolute error of 1.5 mg/L and relative error of 6.5%. Application of the model to three different soils shows that boron adsorption is higher in silt loam soil than that in sandy loam and clay loam soils. This result agrees with the laboratory experimental observations. The results of the sensitivity analysis indicate that boron uptake by root-water extraction process influences the boron concentration distribution along the root zone. Also, absorption coefficient and maximum adsorptive capacity of a soil for boron are found to be sensitive parameters.
Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model
Panajotov, Krassimir; Clerc, Marcel G.; Tlidi, Mustapha
2017-06-01
Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height. Contribution to the Topical Issue "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
Two-Dimensional Core-Collapse Supernova Models with Multi-Dimensional Transport
Dolence, Joshua C; Zhang, Weiqun
2014-01-01
We present new two-dimensional (2D) axisymmetric neutrino radiation/hydrodynamic models of core-collapse supernova (CCSN) cores. We use the CASTRO code, which incorporates truly multi-dimensional, multi-group, flux-limited diffusion (MGFLD) neutrino transport, including all relevant $\\mathcal{O}(v/c)$ terms. Our main motivation for carrying out this study is to compare with recent 2D models produced by other groups who have obtained explosions for some progenitor stars and with recent 2D VULCAN results that did not incorporate $\\mathcal{O}(v/c)$ terms. We follow the evolution of 12, 15, 20, and 25 solar-mass progenitors to approximately 600 milliseconds after bounce and do not obtain an explosion in any of these models. Though the reason for the qualitative disagreement among the groups engaged in CCSN modeling remains unclear, we speculate that the simplifying ``ray-by-ray' approach employed by all other groups may be compromising their results. We show that ``ray-by-ray' calculations greatly exaggerate the ...
Ca2+ movement in smooth muscle cells studied with one- and two-dimensional diffusion models.
Kargacin, G; Fay, F S
1991-11-01
Although many of the processes involved in the regulation of Ca2+ in smooth muscle have been studied separately, it is still not well known how they are integrated into an overall regulatory system. To examine this question and to study the time course and spatial distribution of Ca2+ in cells after activation, one- and two-dimensional diffusion models of the cell that included the major processes thought to be involved in Ca regulation were developed. The models included terms describing Ca influx, buffering, plasma membrane extrusion, and release and reuptake by the sarcoplasmic reticulum. When possible these processes were described with known parameters. Simulations with the models indicated that the sarcoplasmic reticulum Ca pump is probably primarily responsible for the removal of cytoplasmic Ca2+ after cell activation. The plasma membrane Ca-ATPase and Na/Ca exchange appeared more likely to be involved in the long term regulation of Ca2+. Pumping processes in general had little influence on the rate of rise of Ca transients. The models also showed that spatial inhomogeneities in Ca2+ probably occur in cells during the spread of the Ca signal following activation and during the subsequent return of Ca2+ to its resting level.
Analytical solutions of the lattice Boltzmann BGK model
Zou, Q; Doolen, G D; Zou, Qisu; Hou, Shuling; Doolen, Gary D.
1995-01-01
Abstract: Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time representation of these two flows without any approximation.
Two Dimensional Analytical Modeling for SOI and SON MOSFET and Their Performance Comparison
Directory of Open Access Journals (Sweden)
Saptarsi Ghosh
2011-01-01
Full Text Available During last few decade continuous device performance improvements have been achieved through a combination of device scaling, new device structures and material property improvement to its fundamental limits. Conventional silicon (bulk CMOS technology can’t overcome the fundamental physical limitations belong to sub-micro or nanometer region which leads to alternative device technology like Silicon-on-Insulator (SOI technology and its recent innovative modification Silicon-On-Nothing (SON MOSFET. Analytical simulation is very important to understand the relative performance of those devices under different structural and operational parameter variations. For present analytical simulation asymmetric structure of Silicon-On-Insulator (SOI MOSFET and Silicon-On-Nothing (SON MOSFET are considered. The proposed structure of SON MOSFET is similar to that of the SOI MOSFET with the only exception being the oxide layer here is substituted with air which has much lower permittivity than Silicon-dioxide. Variation of threshold voltage against effective channel lengths is compared for both the structures. From our simulation it is observed that the proposed SON model has lower drain to source current (IDS than SOI model. In our modeling based on solution of two dimensional Poisson’s equation short channel effects such as DIBL and fringing field effects are also taken into account. SON is found to provide better suppression of SCE s than SOI. The results predicted by our analytical simulation hold good agreement with experimental results.
A New Paradigm of Modeling Two-Dimensional Overland Watershed Water Quality
Zhang, F.; Yeh, G. G.
2003-12-01
This paper presents the development of sediment and reactive chemical transport under non-isotherm condition in two-dimensional overland watershed system. Through decomposition of reaction network via Gauss-Jordan column reduction, (a) redundant fast reactions and irrelevant kinetic reactions are removed from the system; (b) fast reactions and slow reactions can be decoupled; (c) species reaction equations are transformed into two sets: equilibrium species mass action equations and kinetic-variable reaction equations. This enable our model to include as many types of reactions as possible, choose kinetic-variables instead of chemical species as primary dependent variables, and simplify the reaction terms in transport equations. In our model two options are provided to solve the advection-dispersion transport equation: Lagrangian-Eulerian approach, and Finite Element Method in Conservative Form, and three options to deal with the reaction term: Fully-implicit, Predictor-corrector, and Operator-splitting methods. The production-consumption rate of chemical species is determined by reaction-based formulations. One example problem is employed to demonstrate the design capability of the model and the robustness of the numerical simulations.
Phase diagram and correlation functions of the two-dimensional dissipative quantum XY model
Hou, Changtao; Varma, Chandra M.
2016-11-01
The two-dimensional quantum XY model, with a Caldeira-Leggett form of dissipation, is applicable to the quantum-critical properties of diverse experimental systems, ranging from superconductor to insulator transitions, ferromagnetic and antiferromagnetic transitions in metals, to the loop-current order transition in cuprates. We solve the reexpression of this model in terms of orthogonal topological excitations, vortices, and a variety of instantons, by renormalization group methods. The calculations explain the extraordinary properties of the model discovered in Monte Carlo calculations: the product form of the quantum-critical fluctuations in space and time, a spatial correlation length proportional to the logarithm of the temporal correlation length near the transition from a disordered to a fully ordered state, and the occurrence of a phase with spatial order without temporal order. They are intimately related to the flow of the metric of time in relation to the metric of space, i.e., of the dynamical critical exponent z . These properties appear to be essential in understanding the strange metallic phase found in a variety of quantum-critical transitions as well as the accompanying high-temperature superconductivity.
Efficient two-dimensional magnetotellurics modelling using implicitly restarted Lanczos method
Indian Academy of Sciences (India)
Krishna Kumar; Pravin K Gupta; Sri Niwas
2011-08-01
This paper presents an efficient algorithm, FDA2DMT (Free Decay Analysis for 2D Magnetotellurics (MT)), based on eigenmode approach to solve the relevant partial differential equation, for forward computation of two-dimensional (2D) responses. The main advantage of this approach lies in the fact that only a small subset of eigenvalues and corresponding eigenvectors are required for satisfactory results. This small subset (pre-specified number) of eigenmodes are obtained using shift and invert implementation of Implicitly Restarted Lanczos Method (IRLM). It has been established by experimentation that only 15–20% smallest eigenvalue and corresponding eigenvectors are sufficient to secure the acceptable accuracy. Once the single frequency response is computed using eigenmode approach, the responses for subsequent frequencies can be obtained in negligible time. Experiment design results for validation of FDA2DMT are presented by considering two synthetic models from COMMEMI report, Brewitt-Taylor and Weaver (1976) model and a field data based model from Garhwal Himalaya.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The relationship between desert evolution and change in albedo has been investigated quasi-analytically using a zonal mean two-dimensional energy balance model which considers the radiation transmission process due to thermodynamics and bound- ary layer movement caused by kinetics. A climate state including temperature, zonal wind, meridional wind and vertical wind can be simulated according to the current zonal distribution of albedo. Given desert distribution, characterized by the value and distribution of albedo, the response of climate on albedo has been studied to analyze the evolution of desert climate. One significant result is that the simple model can reproduce mean meridional circulation. Another result indicates that climate corresponds to two equilibria. This happens when the junction temperature between vegetation and desert is higher than a certain critical value. As for the first equilibrium, the desert belt is predicted to move southward in the northern hemisphere with the increasing values of albedo, which corresponds to the current trend of climate change. For the second equilibrium, vegetation will expand northward with increasing values of albedo, which would indicate a narrowing of the desert belt. In order to determine if the two equilibria exist, new physical models are needed.
Design considerations for pulsed-flow comprehensive two-dimensional GC: dynamic flow model approach.
Harvey, Paul McA; Shellie, Robert A; Haddad, Paul R
2010-04-01
A dynamic flow model, which maps carrier gas pressures and carrier gas flow rates through the first dimension separation column, the modulator sample loop, and the second dimension separation column(s) in a pulsed-flow modulation comprehensive two-dimensional gas chromatography (PFM-GCxGC) system is described. The dynamic flow model assists design of a PFM-GCxGC modulator and leads to rapid determination of pneumatic conditions, timing parameters, and the dimensions of the separation columns and connecting tubing used to construct the PFM-GCxGC system. Three significant innovations are introduced in this manuscript, which were all uncovered by using the dynamic flow model. A symmetric flow path modulator improves baseline stability, appropriate selection of the flow restrictors in the first dimension column assembly provides a generally more stable and robust system, and these restrictors increase the modulation period flexibility of the PFM-GCxGC system. The flexibility of a PFM-GCxGC system resulting from these innovations is illustrated using the same modulation interface to analyze Special Antarctic Blend (SAB) diesel using 3 s and 9 s modulation periods.
Probability-changing cluster algorithm for two-dimensional XY and clock models
Tomita, Yusuke; Okabe, Yutaka
2002-05-01
We extend the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm to the study of systems with the vector order parameter. Wolff's idea of the embedded cluster formalism is used for assigning clusters. The Kosterlitz-Thouless (KT) transitions for the two-dimensional (2D) XY and q-state clock models are studied by using the PCC algorithm. Combined with the finite-size scaling analysis based on the KT form of the correlation length, ξ~exp(c/(T/TKT-1)), we determine the KT transition temperature and the decay exponent η as TKT=0.8933(6) and η=0.243(4) for the 2D XY model. We investigate two transitions of the KT type for the 2D q-state clock models with q=6,8,12 and confirm the prediction of η=4/q2 at T1, the low-temperature critical point between the ordered and XY-like phases, systematically.
Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials
Mihalache, D; Skarka, V; Malomed, B A; Leblond, H; Aleksić, N B; Lederer, F
2010-01-01
Complex Ginzburg-Landau (CGL) models of laser media (with the cubic-quintic nonlinearity) do not contain an effective diffusion term, which makes all vortex solitons unstable in these models. Recently, it has been demonstrated that the addition of a two-dimensional periodic potential, which may be induced by a transverse grating in the laser cavity, to the CGL equation stabilizes compound (four-peak) vortices, but the most fundamental "crater-shaped" vortices (CSVs), alias vortex rings, which are, essentially, squeezed into a single cell of the potential, have not been found before in a stable form. In this work we report families of stable compact CSVs with vorticity S=1 in the CGL model with the external potential of two different types: an axisymmetric parabolic trap, and the periodic potential. In both cases, we identify stability region for the CSVs and for the fundamental solitons (S=0). Those CSVs which are unstable in the axisymmetric potential break up into robust dipoles. All the vortices with S=2 a...
Infiltration effects on a two-dimensional molecular dynamics model of landslides
Martelloni, Gianluca
2012-01-01
In this paper we propose a two-dimensional (2D) computational model, based on a molecular dynamics (MD) approach, for deep landslides triggered by rainfall. Our model is based on interacting particles or grains and describes the behavior of a fictitious granular material along a slope consisting of a vertical section, i.e. with a wide thickness. The triggering of the landslide is caused by the passing of two conditions: a threshold speed and a condition on the static friction of the particles, the latter based on the Mohr-Coulomb failure criterion (Coulomb 1776; Mohr 1914). The inter-particle interactions are through a potential that, in the absence of suitable experimental data and due to the arbitrariness of the grain dimension is modeled by means of a potential similar to the Lennard-Jones one (Lennard-Jones 1924), i.e., with an attractive and a repulsive part. For the updating of the particle positions we use a MD method which results to be very suitable to simulate this type of systems (Herrmann and Ludi...
Li, Jingde; Bai, Zhengyu; Croiset, Eric
2016-11-01
A two-dimensional model of nickel/yttria-stabilized zirconia (Ni/YSZ) solid oxide fuel cell (SOFC) was developed for a button cell system. The model integrates the detailed catalytic, electrochemical elementary reactions with ionic/electronic conduction and multiple gas transport processes in SOFC. The model is validated using published experimental data for H2-H2O fuel gas under different cell sizes and operating conditions. The distributions of gas/surface phase species concentration and current density were predicted and the effects of operating temperature, fuel gas composition and fuel channel tube design on the cell performance were studied. The results show that the electrochemical reaction processes occurs mainly within a 20 μm distance from the anode/electrolyte interface and that the Ni catalyst surface is covered mainly by H(s). For the chamber channel design, the calculations show that the tube chamber should have a diameter no smaller than the cathode electrode to obtain the best SOFC performance.
Understanding Ground Motion in Las Vegas: Insights from Data Analysis and Two-Dimensional Modeling
Energy Technology Data Exchange (ETDEWEB)
Rodgers, A; Tkalcic, H; McCallen, D
2004-02-05
Seismic ground motions are amplified in low velocity sedimentary basins relative to adjacent sites on high velocity hard rock. We used historical recordings of NTS nuclear explosions and earthquake recordings in Las Vegas Valley to quantify frequency-dependent basin amplification using Standard Spectral Ratios. We show that amplifications, referred to as site response, can reach a factor of 10 in the frequency band 0.4-2.0 Hz. Band-averaged site response between 0.4-2.0 Hz is strongly correlated with basin depth. However, it is also well known that site response is related to shallow shear-wave velocity structure. We simulated low frequency (f<1Hz) ground motion and site response with two-dimensional elastic finite difference simulations. We demonstrate that physically plausible models of the shallow subsurface, including low velocity sedimentary structure, can predict relative amplification as well as some of the complexity in the observed waveforms. This study demonstrates that site response can be modeled without invoking complex and computationally expensive three-dimensional structural models.
Critical properties of XY model on two-dimensional layered magnetic films
Institute of Scientific and Technical Information of China (English)
Wang Yi; Liu Xiao-Yan; Sun Lei; Zhang Xing; Han Ru-Qi
2006-01-01
Using Monte Carlo simulations, we have investigated the classical XY model on triangular lattices of ultra-thin film structures with middle ferromagnetic layers sandwiched between two antiferromagnetic layers. The internal energy,the specific heat, the chirality and the chiral susceptibility are calculated in order to clarify phase transitions and critical phenomena. From the finite-size scaling analyses, the values of critical exponents are determined. In a range of interaction parameters, we find that the chirality steeply goes up as temperature increases in a temperature range;correspondingly the value of a critical exponent for this change is estimated.
Curvature-driven coarsening in the two-dimensional Potts model.
Loureiro, Marcos P O; Arenzon, Jeferson J; Cugliandolo, Leticia F; Sicilia, Alberto
2010-02-01
We study the geometric properties of polymixtures after a sudden quench in temperature. We mimic these systems with the q -states Potts model on a square lattice with and without weak quenched disorder, and their evolution with Monte Carlo simulations with nonconserved order parameter. We analyze the distribution of hull-enclosed areas for different initial conditions and compare our results with recent exact and numerical findings for q=2 (Ising) case. Our results demonstrate the memory of the presence or absence of long-range correlations in the initial state during the coarsening regime and exhibit superuniversality properties.
Verification of the two-dimensional hydrodynamic model based on remote sensing
Sazonov, Alexey; Mikhailukova, Polina; Krylenko, Inna; Frolova, Natalya; Kireeva, Mariya
2016-04-01
Mathematical modeling methods are used more and more actively to evaluate possible damage, identify potential flood zone and the influence of individual factors affecting the river during the passage of the flood. Calculations were performed by means of domestic software complex «STREAM-2D» which is based on the numerical solution of two-dimensional St. Venant equations. One of the major challenges in mathematical modeling is the verification of the model. This is usually made using data on water levels from hydrological stations: the smaller the difference of the actual level and the simulated one, the better the quality of the model used. Data from hydrological stations are not always available, so alternative sources of verification, such as remote sensing, are increasingly used. The aim of this work is to develop a method of verification of hydrodynamic model based on a comparison of actual flood zone area, which in turn is determined on the basis of the automated satellite image interpretation methods for different imaging systems and flooded area obtained in the course of the model. The study areas are Lena River, The North Dvina River, Amur River near Blagoveshchensk. We used satellite images made by optical and radar sensors: SPOT-5/HRG, Resurs-F, Radarsat-2. Flooded area were calculated using unsupervised classification (ISODATA and K-mean) for optical images and segmentation for Radarsat-2. Knowing the flow rate and the water level at a given date for the upper and lower limits of the model, respectively, it is possible to calculate flooded area by means of program STREAM-2D and GIS technology. All the existing vector layers with the boundaries of flooding are included in a GIS project for flood area calculation. This study was supported by the Russian Science Foundation, project no. 14-17-00155.
Coexistence in the two-dimensional May-Leonard model with random rates
He, Q.; Mobilia, M.; Täuber, U. C.
2011-07-01
We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-) steady state in two-dimensional stochastic May-Leonard models of mobile individuals, allowing for particle exchanges with nearest-neighbors and hopping onto empty sites. We therefore consider a class of four-state three-species cyclic predator-prey models whose total particle number is not conserved. We demonstrate that quenched disorder in either the reaction or in the mobility rates hardly impacts the dynamical evolution, the emergence and structure of spiral patterns, or the mean extinction time in this system. We also show that direct particle pair exchange processes promote the formation of regular spiral structures. Moreover, upon increasing the rates of mobility, we observe a remarkable change in the extinction properties in the May-Leonard system (for small system sizes): (1) as the mobility rate exceeds a threshold that separates a species coexistence (quasi-) steady state from an absorbing state, the mean extinction time as function of system size N crosses over from a functional form ˜ e c N / N (where c is a constant) to a linear dependence; (2) the measured histogram of extinction times displays a corresponding crossover from an (approximately) exponential to a Gaussian distribution. The latter results are found to hold true also when the mobility rates are randomly distributed.
Institute of Scientific and Technical Information of China (English)
Thien-Tong Nguyen; Doyoung Byun
2008-01-01
In the "modified quasi-steady" approach, two-dimensional (2D) aerodynamic models of flapping wing motions are analyzed with focus on different types of wing rotation and different positions of rotation axis to explain the force peak at the end of each half stroke. In this model, an additional velocity of the mid chord position due to rotation is superimposed on the translational relative velocity of air with respect to the wing. This modification produces augmented forces around the end of eachstroke. For each case of the flapping wing motions with various combination of controlled translational and rotational velocities of the wing along inclined stroke planes with thin figure-of-eight trajectory, discussions focus on lift-drag evolution during one stroke cycle and efficiency of types of wing rotation. This "modified quasi-steady" approach provides a systematic analysis of various parameters and their effects on efficiency of flapping wing mechanism. Flapping mechanism with delayed rotation around quarter-chord axis is an efficient one and can be made simple by a passive rotation mechanism so that it can be useful for robotic application.
Experiment and modeling of a two-dimensional piezoelectric energy harvester
Yang, Yaowen; Wu, Hao; Kiong Soh, Chee
2015-12-01
Vibration energy harvesting using piezoelectric materials has attracted much research interest in recent years. Numerous efforts have been devoted to improving the efficiency of vibration energy harvesters and broadening their bandwidths. In most reported literature, energy harvesters are designed to harvest energy from vibration source with a specific excitation direction. However, a practical environmental vibration source may include multiple components from different directions. Thus, it is an important concern to design a vibration energy harvester to be adaptive to multiple excitation directions. In this article, a piezoelectric energy harvester with frame configuration is proposed to achieve two-dimensional (2D) vibration energy harvesting. The harvester works in two fundamental modes, i.e., its vertical and horizontal vibration modes. By tuning the structural parameters, the harvester can capture vibration energy from arbitrary directions in a 2D plane. Experimental studies are carried out to prove its feasibility. A finite element model and an equivalent circuit model are built to simulate the system and validate the experiment outcomes. The study of this 2D energy harvester indicates its promising potential in practical vibration scenarios.
Directory of Open Access Journals (Sweden)
Franceschini Barbara
2005-02-01
Full Text Available Abstract Background Modeling the complex development and growth of tumor angiogenesis using mathematics and biological data is a burgeoning area of cancer research. Architectural complexity is the main feature of every anatomical system, including organs, tissues, cells and sub-cellular entities. The vascular system is a complex network whose geometrical characteristics cannot be properly defined using the principles of Euclidean geometry, which is only capable of interpreting regular and smooth objects that are almost impossible to find in Nature. However, fractal geometry is a more powerful means of quantifying the spatial complexity of real objects. Methods This paper introduces the surface fractal dimension (Ds as a numerical index of the two-dimensional (2-D geometrical complexity of tumor vascular networks, and their behavior during computer-simulated changes in vessel density and distribution. Results We show that Ds significantly depends on the number of vessels and their pattern of distribution. This demonstrates that the quantitative evaluation of the 2-D geometrical complexity of tumor vascular systems can be useful not only to measure its complex architecture, but also to model its development and growth. Conclusions Studying the fractal properties of neovascularity induces reflections upon the real significance of the complex form of branched anatomical structures, in an attempt to define more appropriate methods of describing them quantitatively. This knowledge can be used to predict the aggressiveness of malignant tumors and design compounds that can halt the process of angiogenesis and influence tumor growth.
A two-dimensional (azimuthal-axial) particle-in-cell model of a Hall thruster
Energy Technology Data Exchange (ETDEWEB)
Coche, P.; Garrigues, L., E-mail: laurent.garrigues@laplace.univ-tlse.fr [LAPLACE (Laboratoire Plasma et Conversion d' Energie), Université de Toulouse, UPS, INPT Toulouse 118, route de Narbonne, F-31062 Toulouse cedex 9 (France); CNRS, LAPLACE, F-31062 Toulouse (France)
2014-02-15
We have developed a two-dimensional Particle-In-Cell model in the azimuthal and axial directions of the Hall thruster. A scaling method that consists to work at a lower plasma density to overcome constraints on time-step and grid-spacing is used. Calculations are able to reproduce the breathing mode due to a periodic depletion of neutral atoms without the introduction of a supplementary anomalous mechanism, as in fluid and hybrid models. Results show that during the increase of the discharge current, an electron-cyclotron drift instability (frequency in the range of MHz and wave number on the order of 3000 rad s{sup −1}) is formed in the region of the negative gradient of magnetic field. During the current decrease, an axial electric wave propagates from the channel toward the exhaust (whose frequency is on the order of 400 kHz) leading to a broadening of the ion energy distribution function. A discussion about the influence of the scaling method on the calculation results is also proposed.
Numerical Simulations of an atmospheric pressure discharge using a two dimensional fluid model
Iqbal, Muhammad M.; Turner, Miles M.
2008-10-01
We present numerical simulations of a parallel-plate dielectric barrier discharge using a two-dimensional fluid model with symmetric boundary conditions in pure helium and He-N2 gases at atmospheric pressure. The periodic stationary pattern of electrons and molecular helium ions density is shown at different times during one breakdown pulse for the pure helium gas. The temporal behavior of the helium metastables and excimers species density is examined and their influences on the discharge characteristics are exhibited for an APD. The atmospheric pressure discharge modes (APGD and APTD) are affected with small N2 impurities and the discharge mode structures are described under different operating conditions. The uniform and filamentary behavior of the discharge is controlled with the variable relative permittivity of the dielectric barrier material. The influence of nitrogen impurities plays a major role for the production of the filaments in the after glow phase of He-N2 discharge and the filaments are clearly observed with the increased recombination coefficient of nitrogen ions. The creation and annihilation mechanism of filaments is described with the production and destruction of nitrogen ions at different applied voltages and driving frequencies for a complete cycle. The results of the fluid model are validated by comparison with the experimental atmospheric pressure discharge results in He-N2 plasma discharge.
a Numerical Test of Kpz Scaling:. Potts Models Coupled to Two-Dimensional Quantum Gravity
Baillie, C. F.; Johnston, D. A.
We perform Monte-Carlo simulations using the Wolff cluster algorithm of the q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of spherical topology with up to 5000 nodes. We find that the measured critical exponents are in reasonable agreement with those from the exact solution of the Ising model and with those calculated from KPZ scaling for q=3, 4 where no exact solution is available. Using Binder’s cumulant we find that the q=10 Potts model displays a first order phase transition on a dynamical graph, as it does on a fixed lattice. We also examine the internal geometry of the graphs generated in the simulation, finding a linear relationship between ring length probabilities and the central charge of the Potts model.
A Numerical Test of KPZ Scaling Potts Models Coupled to Two-Dimensional Quantum Gravity
Baillie, C F
1992-01-01
We perform Monte Carlo simulations using the Wolff cluster algorithm of the q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of spherical topology with up to 5000 nodes. We find that the measured critical exponents are in reasonable agreement with those from the exact solution of the Ising model and with those calculated from KPZ scaling for q=3,4 where no exact solution is available. Using Binder's cumulant we find that the q=10 Potts model displays a first order phase transition on a dynamical graph, as it does on a fixed lattice. We also examine the internal geometry of the graphs generated in the simulation, finding a linear relationship between ring length probabilities and the central charge of the Potts model
Murase, Yohsuke; Ito, Nobuyasu
2008-01-01
Values of dynamic critical exponents are numerically estimated for various models with the nonequilibrium relaxation method to test the dynamic universality hypothesis. The dynamics used here are single-spin update with Metropolis-type transition probabities. The estimated values of nonequilibrium relaxation exponent of magnetization λm (=β/zν) of Ising models on bcc and fcc lattices are estimated to be 0.251(3) and 0.252(3), respectively, which are consistent with the value of the model on simple-cubic lattice, 0.250(2). The dynamic critical exponents of three-states Potts models on square, honeycomb and triangular lattices are also estimated to be 2.193(5), 2.198(4), and 2.199(3), respectively. They are consistent within the error bars. It is also confirmed that Ising models with regularly modulated coupling constants on square lattice have the same dynamic critical exponents with the uniformly ferromagnetic Ising model.
Energy Technology Data Exchange (ETDEWEB)
Considine, D.B.; Douglass, A.R.; Jackman, C.H. [Applied Research Corp., Landover, MD (United States)]|[NASA, Goddard Space Flight Center, Greenbelt, MD (United States)
1995-02-01
The Goddard Space Flight Center (GSFC) two-dimensional model of stratospheric photochemistry and dynamics has been used to calculate the O3 response to stratospheric aircraft (high-speed civil transport (HSCT)) emissions. The sensitivity of the model O3 response was examined for systematic variations of five parameters and two reaction rates over a wide range, expanding on calculations by various modeling groups for the NASA High Speed Research Program and the World Meteorological Organization. In all, 448 model runs were required to test the effects of variations in the latitude, altitude, and magnetitude of the aircraft emissions perturbation, the background chlorine levels, the background sulfate aerosol surface area densities, and the rates of two key reactions. No deviation from previous conclusions concerning the response of O3 to HSCTs was found in this more exhaustive exploration of parameter space. Maximum O3 depletions occur for high-altitude, low altitude HSCT perturbations. Small increases in global total O3 can occur for low-altitude, high-altitude injections. Decreasing aerosol surface area densities and background chlorine levels increases the sensitivity of model O3 to the HSCT perturbations. The location of the aircraft emissions is the most important determinant of the model response. Response to the location of the HSCT emissions is not changed qualitatively by changes in background chlorine and aerosol loading. The response is also not very sensitive to changes in the rates of the reactions NO + HO2 yields NO2 + OH and HO2 + O3 yields OH + 2O2 over the limits of their respective uncertainties. Finally, levels of lower stratospheric HO(sub x) generally decrease when the HSCT perturbation is included, even though there are large increases in H2O due to the perturbation.
2015-01-01
A two-dimensional single-phase model is developed for the steady-state and transient analysis of polymer electrolyte membrane fuel cells (PEMFC). Based on diluted and concentrated solution theories, viscous flow is introduced into a phenomenological multi-component modeling framework in the membrane. Characteristic variables related to the water uptake are discussed. A ButlereVolmer formulation of the current-overpotential relationship is developed based on an elementary mechanism of elect...
Hu, W.; Wang, L.-J.; Chen, H.; Holbach, A.; Zheng, B.-H.; Norra, S.; Westrich, B.
2012-04-01
After impoundment of the Three Gorges Reservoir (TGR) in 2003, hydrological regimes of the Yangtze River, upstream and downstream of the Three Gorges Dam, have been changed enormously, leading to significant environmental, ecological and social impacts. Nutrients and pollutants from agriculture, industry and municipalities are of concern due to their impact on the aquatic environment and hence, transport behavior of sediment associated pollutants must be modeled and analyzed to establish a sustainable water reservoir management. As part of the Chinese-German Yangtze-Project [1], two-dimensional numerical model TELEMAC is applied to study the dissolved and particulate pollutant transport at different locations of concern in the TGR. In-situ measurement campaigns for morphology and water quality data using mobile measuring device (MINIBAT) are carried out to provide detailed information for the different water bodies at different time. Additional morphological data are taken from cross-section profiles in the literature, the digital elevation model (DEM) of Shuttle Radar Topography Mission (SRTM) from CGIAR. Daily and hourly water level and discharge, suspended sediment concentration and pollutant loads are obtained from the authorities and extracted from literature. The model describes the spatial-temporal flow field, transport and dispersion of sediment associated pollutants with emphasis on the dynamic interaction and mutual influence of the river Yangtze, its major tributaries and adjacent lagoon-like dead water bodies due to the 30 meter annual reservoir water level fluctuation. Since algae bloom, especially in the tributaries and side arms of the mainstream, is one of the major issues occurred after 2003, the results of the numerical modeling together with the statistical analysis of the MINIBAT measurements are used for the eutrophication status analysis. Acknowledgments The Yangtze-Project is funded by the Federal Ministry of Education and Research (BMBF
Nonequilibrium critical dynamics of the two-dimensional Ashkin-Teller model at the Baxter line
Fernandes, H. A.; da Silva, R.; Caparica, A. A.; de Felício, J. R. Drugowich
2017-04-01
We investigate the short-time universal behavior of the two-dimensional Ashkin-Teller model at the Baxter line by performing time-dependent Monte Carlo simulations. First, as preparatory results, we obtain the critical parameters by searching the optimal power-law decay of the magnetization. Thus, the dynamic critical exponents θm and θp, related to the magnetic and electric order parameters, as well as the persistence exponent θg, are estimated using heat-bath Monte Carlo simulations. In addition, we estimate the dynamic exponent z and the static critical exponents β and ν for both order parameters. We propose a refined method to estimate the static exponents that considers two different averages: one that combines an internal average using several seeds with another, which is taken over temporal variations in the power laws. Moreover, we also performed the bootstrapping method for a complementary analysis. Our results show that the ratio β /ν exhibits universal behavior along the critical line corroborating the conjecture for both magnetization and polarization.
A Method for Geometry Optimization in a Simple Model of Two-Dimensional Heat Transfer
Peng, Xiaohui; Protas, Bartosz
2013-01-01
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations and involving a one-dimensional cooling element represented by a contour on which interface boundary conditions are specified. The problem consists in finding an optimal shape of the cooling element which will ensure that the solution in a given region is close (in the least squares sense) to some prescribed target distribution. We formulate this problem as PDE-constrained optimization and the locally optimal contour shapes are found using a gradient-based descent algorithm in which the Sobolev shape gradients are obtained using methods of the shape-differential calculus. The main novelty of this work is an accurate and efficient approach to the evaluation of the shape gradients based on a boundary-integral formulation which exploits certain analytical properties of the sol...
Electron-phonon vertex in the two-dimensional one-band Hubbard model
Huang, Z. B.; Hanke, W.; Arrigoni, E.; Scalapino, D. J.
2003-12-01
Using quantum Monte Carlo techniques, we study the effects of electronic correlations on the effective electron-phonon (el-ph) coupling in a two-dimensional one-band Hubbard model. We consider a momentum-independent bare ionic el-ph coupling. In the weak- and intermediate-correlation regimes, we find that the on-site Coulomb interaction U acts to effectively suppress the ionic el-ph coupling at all electron and phonon momenta. In this regime, our numerical simulations are in good agreement with the results of perturbation theory to order U2. However, entering the strong-correlation regime, we find that the forward-scattering process stops decreasing and begins to substantially increase as a function of U, leading to an effective el-ph coupling which is peaked in the forward direction. Whereas at weak and intermediate Coulomb interactions, screening is the dominant correlation effect suppressing the el-ph coupling, at larger U values irreducible vertex corrections become more important and give rise to this increase. These vertex corrections depend crucially on the renormalized electronic structure of the strongly correlated system.
Jin, Wang; Penington, Catherine J.; McCue, Scott W.; Simpson, Matthew J.
2016-10-01
Two-dimensional collective cell migration assays are used to study cancer and tissue repair. These assays involve combined cell migration and cell proliferation processes, both of which are modulated by cell-to-cell crowding. Previous discrete models of collective cell migration assays involve a nearest-neighbour proliferation mechanism where crowding effects are incorporated by aborting potential proliferation events if the randomly chosen target site is occupied. There are two limitations of this traditional approach: (i) it seems unreasonable to abort a potential proliferation event based on the occupancy of a single, randomly chosen target site; and, (ii) the continuum limit description of this mechanism leads to the standard logistic growth function, but some experimental evidence suggests that cells do not always proliferate logistically. Motivated by these observations, we introduce a generalised proliferation mechanism which allows non-nearest neighbour proliferation events to take place over a template of r≥slant 1 concentric rings of lattice sites. Further, the decision to abort potential proliferation events is made using a crowding function, f(C), which accounts for the density of agents within a group of sites rather than dealing with the occupancy of a single randomly chosen site. Analysing the continuum limit description of the stochastic model shows that the standard logistic source term, λ C(1-C), where λ is the proliferation rate, is generalised to a universal growth function, λ C f(C). Comparing the solution of the continuum description with averaged simulation data indicates that the continuum model performs well for many choices of f(C) and r. For nonlinear f(C), the quality of the continuum-discrete match increases with r.
Numerical Modeling of Two-Dimensional Temperature Dynamics Across Ice-Wedge Polygons
Garayshin, Viacheslav V.
The ice wedges on the North Slope of Alaska have been forming for many millennia, when the ground cracked and the cracks were filled with snowmelt water. The infiltrated water then became frozen and turned into ice. When the annual and summer air temperatures become higher, the depth of the active layer increases. A deeper seasonal thawing may cause melting of ice wedges from their tops. Consequently, the ground starts to settle and a trough begins to form above the ice wedge. The forming trough creates a local temperature anomaly in the surrounding ground, and the permafrost located immediately under the trough starts degrading further. Once the trough is formed, the winter snow cover becomes deeper at the trough area further degrading the permafrost. In this thesis we present a computational approach to study the seasonal temperature dynamics of the ground surrounding an ice wedge and ground subsidence associated with ice wedge degradation. A thermo-mechanical model of the ice wedge based on principles of macroscopic thermodynamics and continuum mechanics was developed and will be presented. The model includes heat conduction and quasi-static mechanical equilibrium equations, a visco-elastic rheology for ground deformation, and an empirical formula which relates unfrozen water content to temperature. The complete system is reduced to a computationally convenient set of coupled equations for temperature, ground displacement and ground porosity in a two-dimensional domain. A finite element method and an implicit scheme in time were utilized to construct a non-linear system of equations, which was solved iteratively. The model employs temperature and moisture content data collected from a field experiment at the Next-Generation Ecosystem Experiments (NGEE) sites in Barrow, Alaska. The model describes seasonal dynamics of temperature and the long-term ground motion near the ice wedges and helps to explain destabilization of the ice wedges north of Alaska's Brooks
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L.O.
1985-12-01
Matrix nonlinear sigma models are discussed and the matrix nonlinear sigma model in the case of N x ..cap alpha..N rectangular matrices is considered. The authors show that in two-dimensional Euclidean space, the model is renormalizable with respect to ..cap alpha.. and 1/N. The fulfillment of the chirality identity is demonstrated in the operator expansion for the renormalized theory.
Two-dimensional thermal modeling of power monolithic microwave integrated circuits (MMIC's)
Fan, Mark S.; Christou, Aris; Pecht, Michael G.
1992-01-01
Numerical simulations of the two-dimensional temperature distributions for a typical GaAs MMIC circuit are conducted, aiming at understanding the heat conduction process of the circuit chip and providing temperature information for device reliability analysis. The method used is to solve the two-dimensional heat conduction equation with a control-volume-based finite difference scheme. In particular, the effects of the power dissipation and the ambient temperature are examined, and the criterion for the worst operating environment is discussed in terms of the allowed highest device junction temperature.
On the two-dimensional dynamical Ising model in the phase coexistence region
Martinelli, F.
1994-09-01
We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of side L, in the absence of an external field and at large inverse temperature β. We first consider the gap in the spectrum of the generator of the dynamics in two different cases: with plus and open boundary conditions. We prove that, when the symmetry under global spin flip is broken by the boundary conditions, the gap is much larger than the case in which the symmetry is present. For this latter we compute exactly the asymptotics of -(1/β L) log(gap) as L→∞ and show that it coincides with the surface tension along one of the coordinate axes. As a consequence we are able to study quite precisely the large deviations in time of the magnetization and to obtain an upper bound on the spin-spin time correlation in the infinite-volume plus phase. Our results establish a connection between the dynamical large deviations and those of the equilibrium Gibbs measure studied by Shlosman in the framework of the rigorous description of the Wulff shape for the Ising model. Finally we show that, in the case of open boundary conditions, it is possible to rescale the time with L in such a way that, as L→∞, the finite-dimensional distributions of the time-rescaled magnetization converge to those of a symmetric continuous-time Markov chain on the two-state space {- m *(β), m *(β)}, m *(β) being the spontaneous magnetization. Our methods rely upon a novel combination of techniques for bounding from below the gap of symmetric Markov chains on complicated graphs, developed by Jerrum and Sinclair in their Markov chain approach to hard computational problems, and the idea of introducing "block Glauber dynamics" instead of the standard single-site dynamics, in order to put in evidence more effectively the effect of the boundary conditions in the approach to equilibrium.
Two-dimensional spectroscopy of molecular excitons in a model dimer system
Halpin, Alexei
The physics of molecular excitons has been the subject of many recent studies using electronic two-dimensional photon-echo spectroscopy (2DPE), particularly in the context of light harvesting in photosynthesis. Since the spectra for multichromophoric aggregates are congested, particularly so at room temperature, we present a study of a model dimer comprised of identical chromophores with a well defined electronic coupling strength, to provide clear signatures for coherences between vibronic excitons in 2D spectra. We begin by describing the design of a broadband passively phase-stabilized interferometer for collection of 2D spectra, which also allows for the investigation of state preparation in 2D spectroscopy by using shaped excitation pulses. In experiments on the model dimer we observe strong oscillating off-diagonal features in the 2D spectra which are present only before the onset of dephasing, which occurs in less than 100 fs due to strong system-bath coupling. This is in contrast with the parent dye, where low amplitude oscillations associated with Raman active vibrations persist for several ps following excitation. The results of this comparative study indicate that the signals observed earlier in photosynthetic proteins likely reflect vibrational motion in isolated pigments, and not delocalized quantum coherence. While long-lived vibrational coherences are of questionable biological relevance at face value, we conclude with a discussion on initial findings using coherently controlled 2D spectroscopy, where we observe long-lived signatures associated to vibronic coherences at room temperature. These results point to new directions of study using multidimensional spectroscopy to unravel the role of coherence in excitation energy transfer in molecular aggregates in an experimentally direct fashion.
Danila, Bogdan; Mocanu, Gabriela
2015-01-01
We investigate the transition to Self Organized Criticality in a two-dimensional model of a flux tube with a background flow. The magnetic induction equation, represented by a partial differential equation with a stochastic source term, is discretized and implemented on a two dimensional cellular automaton. The energy released by the automaton during one relaxation event is the magnetic energy. As a result of the simulations we obtain the time evolution of the energy release, of the system control parameter, of the event lifetime distribution and of the event size distribution, respectively, and we establish that a Self Organized Critical state is indeed reached by the system. Moreover, energetic initial impulses in the magnetohydrodynamic flow can lead to one dimensional signatures in the magnetic two dimensional system, once the Self Organized Critical regime is established. The applications of the model for the study of Gamma Ray Bursts is briefly considered, and it is shown that some astrophysical paramet...
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L.O.
1985-06-01
Matrix nonlinear sigma-model is considered in the case of rectangular matrices of the dimension Nx..alpha..N. Renormalizability of the model with respect to ..alpha.. and 1/N is demonstrated for the case of two-dimensional Euclidean space. Validity of the chiral identity is proved in the operator expansion for the renormalized theory.
Geometrical mutual information at the tricritical point of the two-dimensional Blume-Capel model
Mandal, Ipsita; Melko, Roger G
2016-01-01
The spin-1 classical Blume-Capel model on a square lattice is known to exhibit a finite-temperature phase transition described by the tricritical Ising CFT in 1+1 space-time dimensions. This phase transition can be accessed with classical Monte Carlo simulations, which, via a replica-trick calculation, can be used to study the shape-dependence of the classical R\\'enyi entropies for a torus divided into two cylinders. From the second R\\'enyi entropy, we calculate the Geometrical Mutual Information (GMI) introduced by St\\'ephan et. al. [Phys. Rev. Lett. 112, 127204 (2014)] and use it to extract a numerical estimate for the value of the central charge near the tricritical point. By comparing to the known CFT result, $c=7/10$, we demonstrate how this type of GMI calculation can be used to estimate the position of the tricritical point in the phase diagram.
Schapers, T; Nitta, J; Heersche, HB; Takayanagi, H
2002-01-01
The spin dependent conductance of a ferromagnet/two-dimensional electron gas ferromagnet structure is theoretically examined in the ballistic transport regime. It is shown that the spin signal can be improved considerably by making use of the spin filtering effect of a barrier at the ferromagnet two
Collapse arresting in an inhomogeneous two-dimensional nonlinear Schrodinger model
DEFF Research Database (Denmark)
Schjødt-Eriksen, Jens; Gaididei, Yuri Borisovich; Christiansen, Peter Leth
2001-01-01
Collapse of (2 + 1)-dimensional beams in the inhomogeneous two-dimensional cubic nonlinear Schrodinger equation is analyzed numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams that in a homogeneous medium would collapse may...
Energy Technology Data Exchange (ETDEWEB)
Walder, Brennan J.; Davis, Michael C.; Grandinetti, Philip J. [Department of Chemistry, Ohio State University, 100 West 18th Avenue, Columbus, Ohio 43210 (United States); Dey, Krishna K. [Department of Physics, Dr. H. S. Gour University, Sagar, Madhya Pradesh 470003 (India); Baltisberger, Jay H. [Division of Natural Science, Mathematics, and Nursing, Berea College, Berea, Kentucky 40403 (United States)
2015-01-07
A new two-dimensional Nuclear Magnetic Resonance (NMR) experiment to separate and correlate the first-order quadrupolar and chemical/paramagnetic shift interactions is described. This experiment, which we call the shifting-d echo experiment, allows a more precise determination of tensor principal components values and their relative orientation. It is designed using the recently introduced symmetry pathway concept. A comparison of the shifting-d experiment with earlier proposed methods is presented and experimentally illustrated in the case of {sup 2}H (I = 1) paramagnetic shift and quadrupolar tensors of CuCl{sub 2}⋅2D{sub 2}O. The benefits of the shifting-d echo experiment over other methods are a factor of two improvement in sensitivity and the suppression of major artifacts. From the 2D lineshape analysis of the shifting-d spectrum, the {sup 2}H quadrupolar coupling parameters are 〈C{sub q}〉 = 118.1 kHz and 〈η{sub q}〉 = 0.88, and the {sup 2}H paramagnetic shift tensor anisotropy parameters are 〈ζ{sub P}〉 = − 152.5 ppm and 〈η{sub P}〉 = 0.91. The orientation of the quadrupolar coupling principal axis system (PAS) relative to the paramagnetic shift anisotropy principal axis system is given by (α,β,γ)=((π)/2 ,(π)/2 ,0). Using a simple ligand hopping model, the tensor parameters in the absence of exchange are estimated. On the basis of this analysis, the instantaneous principal components and orientation of the quadrupolar coupling are found to be in excellent agreement with previous measurements. A new point dipole model for predicting the paramagnetic shift tensor is proposed yielding significantly better agreement than previously used models. In the new model, the dipoles are displaced from nuclei at positions associated with high electron density in the singly occupied molecular orbital predicted from ligand field theory.
Gauge theories and integrable lattice models
Witten, Edward
1989-08-01
Investigations of new knot polynomials discovered in the last few years have shown them to be intimately connected with soluble models of two dimensional lattice statistical mechanics. In this paper, these results, which in time may illuminate the whole question of why integrable lattice models exist, are reconsidered from the point of view of three dimensional gauge theory. Expectation values of Wilson lines in three dimensional Chern-Simons gauge theories can be computed by evaluating the partition functions of certain lattice models on finite graphs obtained by projecting the Wilson lines to the plane. The models in question — previously considered in both the knot theory and statistical mechanics — are IRF models in which the local Boltzmann weights are the matrix elements of braiding matrices in rational conformal field theories. These matrix elements, in turn, can be presented in three dimensional gauge theory in terms of the expectation value of a certain tetrahedral configuration of Wilson lines. This representation makes manifest a surprising symmetry of the braiding matrix elements in conformal field theory.
Bera, A. K.; Yusuf, S. M.; Kumar, Amit; Ritter, C.
2017-03-01
The crystal structure, magnetic ground state, and the temperature-dependent microscopic spin-spin correlations of the frustrated honeycomb lattice antiferromagnet N a2C o2Te O6 have been investigated by powder neutron diffraction. A long-range antiferromagnetic (AFM) ordering has been found below TN˜24.8 K . The magnetic ground state, determined to be zigzag antiferromagnetic and characterized by a propagation vector k =(1 /2 0 0 ) , occurs due to the competing exchange interactions up to third-nearest neighbors within the honeycomb lattice. The exceptional existence of a limited magnetic correlation length along the c axis (perpendicular to the honeycomb layers in the a b planes) has been found even at 1.8 K, well below the TN˜24.8 K . The observed limited correlation along the c axis is explained by the disorder distribution of the Na ions within the intermediate layers between honeycomb planes. The reduced ordered moments mCo (1 )=2.77 (3 ) μB/C o2 + and mCo (2 )=2.45 (2 ) μB/C o2 + at 1.8 K reflect the persistence of spin fluctuations in the ordered state. Above TN˜24.8 K , the presence of short-range magnetic correlations, manifested by broad diffuse magnetic peaks in the diffraction patterns, has been found. Reverse Monte Carlo analysis of the experimental diffuse magnetic scattering data reveals that the spin correlations are mainly confined within the two-dimensional honeycomb layers (a b plane) with a correlation length of ˜12 Å at 25 K. The nature of the spin arrangements is found to be similar in both the short-range and long-range ordered magnetic states. This implies that the short-range correlation grows with decreasing temperature and leads to the zigzag AFM ordering at T ≤TN . The present study provides a comprehensive picture of the magnetic correlations over the temperature range above and below the TN and their relation to the crystal structure. The role of intermediate soft Na layers on the magnetic coupling between honeycomb planes is
Wetting transition in the two-dimensional Blume-Capel model: A Monte Carlo study
Albano, Ezequiel V.; Binder, Kurt
2012-06-01
The wetting transition of the Blume-Capel model is studied by a finite-size scaling analysis of L×M lattices where competing boundary fields ±H1 act on the first or last row of the L rows in the strip, respectively. We show that using the appropriate anisotropic version of finite-size scaling, critical wetting in d=2 is equivalent to a “bulk” critical phenomenon with exponents α=-1, β=0, and γ=3. These concepts are also verified for the Ising model. For the Blume-Capel model, it is found that the field strength H1c(T) where critical wetting occurs goes to zero when the bulk second-order transition is approached, while H1c(T) stays nonzero in the region where in the bulk a first-order transition from the ordered phase, with nonzero spontaneous magnetization, to the disordered phase occurs. Interfaces between coexisting phases then show interfacial enrichment of a layer of the disordered phase which exhibits in the second-order case a finite thickness only. A tentative discussion of the scaling behavior of the wetting phase diagram near the tricritical point is also given.
Energy Technology Data Exchange (ETDEWEB)
Hummel, D.W.; Langton, S.E.; Ball, M.R.; Novog, D.R.; Buijs, A., E-mail: hummeld@mcmaster.ca [McMaster Univ., Hamilton, Ontario (Canada)
2013-07-01
Discrepancies have been observed among a number of recent reactor physics studies in support of the PT-SCWR pre-conceptual design, including differences in lattice-level predictions of infinite neutron multiplication factor, coolant void reactivity, and radial power profile. As a first step to resolving these discrepancies, a lattice-level benchmark problem was designed based on the 78-element plutonium-thorium PT-SCWR fuel design under a set of prescribed local conditions. This benchmark problem was modeled with a suite of both deterministic and Monte Carlo neutron transport codes. The results of these models are presented here as the basis of a code-to-code comparison. (author)
Landim, C.; Lemire, P.
2016-07-01
We consider the two-dimensional Blume-Capel model with zero chemical potential and small magnetic field evolving on a large but finite torus. We obtain sharp estimates for the transition time, we characterize the set of critical configurations, and we prove the metastable behavior of the dynamics as the temperature vanishes.
Corboz, P.
2016-01-01
An infinite projected entangled-pair state (iPEPS) is a variational tensor network ansatz for two-dimensional wave functions in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension D. We show that for the doped Hubbard model in the strongly correlated reg
Bondarenko, Anna S.; Jansen, Thomas L. C.
2015-01-01
In this paper, we present a novel benchmarking method for validating the modelling of vibrational spectra for the amide I region of proteins. We use the linear absorption spectra and two-dimensional infrared spectra of four experimentally well-studied proteins as a reference and test nine combinatio
Shoushtari, Seyed Mohammad Hossein Jazayeri; Cartwright, Nick; Perrochet, Pierre; Nielsen, Peter
2017-01-01
This paper presents a new laboratory dataset on the moisture-pressure relationship above a dispersive groundwater wave in a two-dimensional vertical unconfined sand flume aquifer driven by simple harmonic forcing. A total of five experiments were conducted in which all experimental parameters were kept constant except for the oscillation period, which ranged from 268 s to 2449 s between tests. Moisture content and suction head sensor pairings were co-located at two locations in the unsaturated zone both approximately 0.2 m above the mean watertable elevation and respectively 0.3 m and 0.75 m from the driving head boundary. For all oscillation periods except for the shortest (T = 268s), the formation of a hysteretic moisture-pressure scanning loop was observed. Consistent with the decay of the saturated zone groundwater wave, the size of the observed moisture-pressure scanning loops decayed with increasing distance landward and the decay rate is larger for the shorter oscillation periods. At the shortest period (T = 268s), the observed moisture-pressure relationship was observed to be non-hysteretic but with a capillary capacity that differs from that of the static equilibrium wetting and drying curves. This finding is consistent with observations from existing one-dimensional vertical sand column experiments. The relative damping of the moisture content with distance landward is higher than that for the suction head consistent with the fact that transmission of pressure through a porous medium occurs more readily than mass transfer. This is further supported by the fact that observed phase lags for the unsaturated zone variables (i.e. suction head and moisture content) relative to the driving head are greater than the saturated zone variables (i.e. piezometric head). Harmonic analysis of the data reveals no observable generation of higher harmonics in either moisture or pressure despite the strongly non-linear relationship between the two. In addition, a phase lag
Ba8CoNb6O24 : A spin-1/2 triangular-lattice Heisenberg antiferromagnet in the two-dimensional limit
Rawl, R.; Ge, L.; Agrawal, H.; Kamiya, Y.; Dela Cruz, C. R.; Butch, N. P.; Sun, X. F.; Lee, M.; Choi, E. S.; Oitmaa, J.; Batista, C. D.; Mourigal, M.; Zhou, H. D.; Ma, J.
2017-02-01
The perovskite Ba8CoNb6O24 comprises equilateral effective spin-1/2 Co2 + triangular layers separated by six nonmagnetic layers. Susceptibility, specific heat, and neutron scattering measurements combined with high-temperature series expansions and spin-wave calculations confirm that Ba8CoNb6O24 is basically a two-dimensional magnet with no detectable spin anisotropy and no long-range magnetic ordering down to 0.06 K. In other words, Ba8CoNb6O24 is very close to be a realization of the paradigmatic spin-1/2 triangular Heisenberg model, which is not expected to exhibit symmetry breaking at finite temperatures according to the Mermin and Wagner theorem.
Computer model of two-dimensional solute transport and dispersion in ground water
Konikow, Leonard F.; Bredehoeft, J.D.
1978-01-01
This report presents a model that simulates solute transport in flowing ground water. The model is both general and flexible in that it can be applied to a wide range of problem types. It is applicable to one- or two-dimensional problems involving steady-state or transient flow. The model computes changes in concentration over time caused by the processes of convective transport, hydrodynamic dispersion, and mixing (or dilution) from fluid sources. The model assumes that the solute is non-reactive and that gradients of fluid density, viscosity, and temperature do not affect the velocity distribution. However, the aquifer may be heterogeneous and (or) anisotropic. The model couples the ground-water flow equation with the solute-transport equation. The digital computer program uses an alternating-direction implicit procedure to solve a finite-difference approximation to the ground-water flow equation, and it uses the method of characteristics to solve the solute-transport equation. The latter uses a particle- tracking procedure to represent convective transport and a two-step explicit procedure to solve a finite-difference equation that describes the effects of hydrodynamic dispersion, fluid sources and sinks, and divergence of velocity. This explicit procedure has several stability criteria, but the consequent time-step limitations are automatically determined by the program. The report includes a listing of the computer program, which is written in FORTRAN IV and contains about 2,000 lines. The model is based on a rectangular, block-centered, finite difference grid. It allows the specification of any number of injection or withdrawal wells and of spatially varying diffuse recharge or discharge, saturated thickness, transmissivity, boundary conditions, and initial heads and concentrations. The program also permits the designation of up to five nodes as observation points, for which a summary table of head and concentration versus time is printed at the end of the
Construction of two-dimensional quantum field models through Longo-Witten endomorphisms
Tanimoto, Yoh
2013-01-01
We present a procedure to construct families of local, massive and interacting Haag-Kastler nets on the two-dimensional spacetime through an operator-algebraic method. An existence proof of local observable is given without relying on modular nuclearity. By a similar technique, another family of wedge-local nets is constructed using certain endomorphisms of conformal nets recently studied by Longo and Witten.
Graphene as a Prototypical Model for Two-Dimensional Continuous Mechanics
Directory of Open Access Journals (Sweden)
Philippe Lambin
2017-08-01
Full Text Available This paper reviews a few problems where continuous-medium theory specialized to two-dimensional media provides a qualitatively correct picture of the mechanical behavior of graphene. A critical analysis of the parameters involved is given. Among other results, a simple mathematical description of a folded graphene sheet is proposed. It is also shown how the graphene–graphene adhesion interaction is related to the cleavage energy of graphite and its C 33 bulk elastic constant.
An immersed interface method for two-dimensional modelling of stratified flow in pipes
Berthelsen, Petter Andreas
2004-01-01
This thesis deals with the construction of a numerical method for solving two-dimensional elliptic interface problems, such as fully developed stratified flow in pipes. Interface problems are characterized by its non-smooth and often discontinuous behaviour along a sharp boundary separating the fluids or other materials. Classical numerical schemes are not suitable for these problems due to the irregular geometry of the interface. Standard finite difference discretization across the interface...
Dynamics of kinks in one- and two-dimensional hyperbolic models with quasidiscrete nonlinearities.
Rotstein, H G; Mitkov, I; Zhabotinsky, A M; Epstein, I R
2001-06-01
We study the evolution of fronts in the Klein-Gordon equation when the nonlinear term is inhomogeneous. Extending previous works on homogeneous nonlinear terms, we describe the derivation of an equation governing the front motion, which is strongly nonlinear, and, for the two-dimensional case, generalizes the damped Born-Infeld equation. We study the motion of one- and two-dimensional fronts finding a much richer dynamics than in the homogeneous system case, leading, in most cases, to the stabilization of one phase inside the other. For a one-dimensional front, the function describing the inhomogeneity of the nonlinear term acts as a "potential function" for the motion of the front, i.e., a front initially placed between two of its local maxima asymptotically approaches the intervening minimum. Two-dimensional fronts, with radial symmetry and without dissipation can either shrink to a point in finite time, grow unboundedly, or their radius can oscillate, depending on the initial conditions. When dissipation effects are present, the oscillations either decay spirally or not depending on the value of the damping dissipation parameter. For fronts with a more general shape, we present numerical simulations showing the same behavior.
Magnons in a two-dimensional transverse-field XXZ model
Kar, Satyaki; Wierschem, Keola; Sengupta, Pinaki
2017-07-01
The XXZ model on a square lattice in the presence of a transverse magnetic field is studied within the spin-wave theory to investigate the resulting canted antiferromagnet. The small- and large-field regimes are probed separately both for easy-axis and easy-plane scenarios which reveal an unentangled factorized ground state at an intermediate value of the field. Goldstone modes are obtained for the field-free XY antiferromagnet as well as for the isotropic antiferromagnet with field up to its saturation value. Moreover, for an easy-plane anisotropy, we find that there exists a nonzero field, where magnon degeneracy appears as a result of restoration of a U(1) sublattice symmetry and that, across that field, there occurs a magnon band crossing. For completeness, we then obtain the system phase diagram for S =1 /2 via large-scale quantum Monte Carlo simulations using the stochastic series expansion technique. Our numerical method is based on a quantization of spin along the direction of the applied magnetic field and does not suffer from a sign problem, unlike comparable algorithms based on a spin quantization along the axis of anisotropy. With this formalism, we are also able to obtain powder averages of the transverse and longitudinal magnetizations, which may be useful for understanding experimental measurements on polycrystalline samples.
Lattice Boltzmann model with nearly constant density.
Fang, Hai-ping; Wan, Rong-zheng; Lin, Zhi-fang
2002-09-01
An improved lattice Boltzmann model is developed to simulate fluid flow with nearly constant fluid density. The ingredient is to incorporate an extra relaxation for fluid density, which is realized by introducing a feedback equation in the equilibrium distribution functions. The pressure is dominated by the moving particles at a node, while the fluid density is kept nearly constant and explicit mass conservation is retained as well. Numerical simulation based on the present model for the (steady) plane Poiseuille flow and the (unsteady) two-dimensional Womersley flow shows a great improvement in simulation results over the previous models. In particular, the density fluctuation has been reduced effectively while achieving a relatively large pressure gradient.
New statistical lattice model with double honeycomb symmetry
Naji, S.; Belhaj, A.; Labrim, H.; Bhihi, M.; Benyoussef, A.; El Kenz, A.
2014-04-01
Inspired from the connection between Lie symmetries and two-dimensional materials, we propose a new statistical lattice model based on a double hexagonal structure appearing in the G2 symmetry. We first construct an Ising-1/2 model, with spin values σ = ±1, exhibiting such a symmetry. The corresponding ground state shows the ferromagnetic, the antiferromagnetic, the partial ferrimagnetic and the topological ferrimagnetic phases depending on the exchange couplings. Then, we examine the phase diagrams and the magnetization using the mean field approximation (MFA). Among others, it has been suggested that the present model could be localized between systems involving the triangular and the single hexagonal lattice geometries.
Numerical model for two-dimensional hydrodynamics and energy transport. [VECTRA code
Energy Technology Data Exchange (ETDEWEB)
Trent, D.S.
1973-06-01
The theoretical basis and computational procedure of the VECTRA computer program are presented. VECTRA (Vorticity-Energy Code for TRansport Analysis) is designed for applying numerical simulation to a broad range of intake/discharge flows in conjunction with power plant hydrological evaluation. The code computational procedure is based on finite-difference approximation of the vorticity-stream function partial differential equations which govern steady flow momentum transport of two-dimensional, incompressible, viscous fluids in conjunction with the transport of heat and other constituents.
Modeling A.C. Electronic Transport through a Two-Dimensional Quantum Point Contact
Energy Technology Data Exchange (ETDEWEB)
Aronov, I.E.; Beletskii, N.N.; Berman, G.P.; Campbell, D.K.; Doolen, G.D.; Dudiy, S.V.
1998-12-07
We present the results on the a.c. transport of electrons moving through a two-dimensional (2D) semiconductor quantum point contact (QPC). We concentrate our attention on the characteristic properties of the high frequency admittance ({omega}{approximately}0 - 50 GHz), and on the oscillations of the admittance in the vicinity of the separatrix (when a channel opens or closes), in presence of the relaxation effects. The experimental verification of such oscillations in the admittance would be a strong confirmation of the semi-classical approach to the a.c. transport in a QPC, in the separatrix region.
A discontinuous Galerkin method for two-dimensional PDE models of Asian options
Hozman, J.; Tichý, T.; Cvejnová, D.
2016-06-01
In our previous research we have focused on the problem of plain vanilla option valuation using discontinuous Galerkin method for numerical PDE solution. Here we extend a simple one-dimensional problem into two-dimensional one and design a scheme for valuation of Asian options, i.e. options with payoff depending on the average of prices collected over prespecified horizon. The algorithm is based on the approach combining the advantages of the finite element methods together with the piecewise polynomial generally discontinuous approximations. Finally, an illustrative example using DAX option market data is provided.
Zhao, Qiang; Dong, Zhiwei
2016-11-01
We have developed two-dimensional Arbitrary Lagrangian Eulerian (ALE) code which is used to study the physical processes, the plasma absorption, the crater profile, and the temperature distribution on metallic target and below the surface. The ALE method overcomes problems with Lagrangian moving mesh distortion by mesh smoothing and conservative quantities remapping from Lagrangian mesh to smoothed one. The results of numerical simulation of pulsed laser ablation are presented. The study presents particular interest for the analysis of experimental results obtained during pulsed laser ablation.
Modeling strong motions produced by earthquakes with two-dimensional numerical codes
Helmberger, Donald V.; Vidale, John E.
1988-01-01
We present a scheme for generating synthetic point-source seismograms for shear dislocation sources using line source (two-dimensional) theory. It is based on expanding the complete three-dimensional solution of the wave equation expressed in cylindrical coordinates in an asymptotic form which provides for the separation of the motions into SH and P-SV systems. We evaluate the equations of motion with the aid of the Cagniard-de Hoop technique and derive close-formed expressions appropriate fo...
Spin-Orbit Splitting in Semiconductor Quantum Dots with a Two-Dimensional Ring Model
Institute of Scientific and Technical Information of China (English)
FENG Jun-Sheng; LIU Zheng
2009-01-01
We present a theoretical study of the energy levels with two-dimensional ring confining potential in the presence of the Rashba spin-orbit interaction.The features of some low-lying states in various strengths of the Rashba spin-orbit interaction are investigated.The Rashba spin-orbit splitting can also be influenced by the width of the potential barrier.The computed results show that the spin-polarized electronic states can be more easily achieved in a weakly confined dot when the confinement strength for the Rashba spin-orbit interaction is larger than a critical value.
Modeling of pressure sensors based on two-dimensional photonic crystals
Institute of Scientific and Technical Information of China (English)
Xuehui XIONG; Ping LU; Deming LIU
2009-01-01
A pressure sensor based on the two-dimensional photonic crystal (2D PC) has been proposed. Under the condition of different pressure, the photonic band gap of the sensor has been studied by means of the plane wave expansion method (PWM). The results show that there is a good linear relation between the cutoff wavelength and the pressure. Apart from being easily implemented, the presented 2D PC pressure sensor holds many characteristics such as high-pressure sensitivity and convenience in achieving demanded pressure range.
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics
Mohseni, F; Succi, S; Herrmann, H J
2015-01-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfv\\'en waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to $\\sigma^{-\\frac{1}{2}}$, $\\sigma$ being the conductivity, w...
SOME PROGRESS IN THE LATTICE BOLTMANN MODEL
Institute of Scientific and Technical Information of China (English)
FENG SHI-DE; TSUTAHARA MICHIHISA; JI ZHONG-ZHEN
2001-01-01
A lattice Boltzmann equation model has been developed by using the equilibrium distribution function of the Maxwell-Boltzmann-like form, which is third order in fluid velocity uα. The criteria of energy conservation between the macroscopic physical quantities and the microscopic particles are introduced into the model, thus the thermal hydrodynamic equations containing the effect of buoyancy force can be recovered in terms of the Taylor and ChapmanEnskog asymptotic expansion methods. The two-dimensional thermal convection phenomena in a square cavity and between two concentric cylinders have been calculated by implementing a heat flux boundary condition. Both numerical results are in good agreement with the conventional numerical results.
Jiao, Huiqing; Zhao, Chengyi; Sheng, Yu; Chen, Yan; Shi, Jianchu; Li, Baoguo
2017-04-01
Water shortage and soil salinization increasingly become the main constraints for sustainable development of agriculture in Southern Xinjiang, China. Mulched drip irrigation, as a high-efficient water-saving irrigation method, has been widely applied in Southern Xinjiang for cotton production. In order to analyze the reasonability of describing the three-dimensional soil water and salt transport processes under mulched drip irrigation with a relatively simple two-dimensional model, a field experiment was conducted from 2007 to 2015 at Aksu of Southern Xinjiang, and soil water and salt transport processes were simulated through the three-dimensional and two-dimensional models based on COMSOL. Obvious differences were found between three-dimensional and two-dimensional simulations for soil water flow within the early 12 h of irrigation event and for soil salt transport in the area within 15 cm away from drip tubes during the whole irrigation event. The soil water and salt contents simulated by the two-dimensional model, however, agreed well with the mean values between two adjacent emitters simulated by the three-dimensional model, and also coincided with the measurements as corresponding RMSE less than 0.037 cm3 cm-3 and 1.80 g kg-1, indicating that the two-dimensional model was reliable for field irrigation management. Subsequently, the two-dimensional model was applied to simulate the dynamics of soil salinity for five numerical situations and for a widely adopted irrigation pattern in Southern Xinjiang (about 350 mm through mulched drip irrigation during growing season of cotton and total 400 mm through flooding irrigations before sowing and after harvesting). The simulation results indicated that the contribution of transpiration to salt accumulation in root layer was about 75% under mulched drip irrigation. Moreover, flooding irrigations before sowing and after harvesting were of great importance for salt leaching of arable layer, especially in bare strip where
Corner wetting in the two-dimensional Ising model: Monte Carlo results
Albano, E. V.; DeVirgiliis, A.; Müller, M.; Binder, K.
2003-01-01
Square L × L (L = 24-128) Ising lattices with nearest neighbour ferromagnetic exchange are considered using free boundary conditions at which boundary magnetic fields ± h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field -h acts. For temperatures T less than the critical temperature Tc of the bulk, this boundary condition leads to the formation of two domains with opposite orientations of the magnetization direction, separated by an interface which for T larger than the filling transition temperature Tf (h) runs from the upper left corner to the lower right corner, while for T interface is localized either close to the lower left corner or close to the upper right corner. Numerous theoretical predictions for the critical behaviour of this 'corner wetting' or 'wedge filling' transition are tested by Monte Carlo simulations. In particular, it is shown that for T = Tf (h) the magnetization profile m(z) in the z-direction normal to the interface is simply linear and the interfacial width scales as w propto L, while for T > Tf (h) it scales as w proptosurd L. The distribution P (ell) of the interface position ell (measured along the z-direction from the corners) decays exponentially for T Tf (h). Furthermore, the Monte Carlo data are compatible with langleellrangle propto (Tf (h) - T)-1 and a finite size scaling of the total magnetization according to M(L, T) = tilde M {(1 - T/Tf (h))nubot L} with nubot = 1. Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.
Lattice Boltzmann model for nanofluids
Energy Technology Data Exchange (ETDEWEB)
Xuan Yimin; Yao Zhengping [Nanjing University of Science and Technology, School of Power Engineering, Nanjing (China)
2005-01-01
A nanofluid is a particle suspension that consists of base liquids and nanoparticles and has great potential for heat transfer enhancement. By accounting for the external and internal forces acting on the suspended nanoparticles and interactions among the nanoparticles and fluid particles, a lattice Boltzmann model is proposed for simulating flow and energy transport processes inside the nanofluids. First, we briefly introduce the conventional lattice Boltzmann model for multicomponent systems. Then, we discuss the irregular motion of the nanoparticles and inherent dynamic behavior of nanofluids and describe a lattice Boltzmann model for simulating nanofluids. Finally, we conduct some calculations for the distribution of the suspended nanoparticles. (orig.)
Validating two-dimensional leadership models on three-dimensionally structured fish schools
Nagy, Máté; Holbrook, Robert I.; Biro, Dora; Burt de Perera, Theresa
2017-01-01
Identifying leader–follower interactions is crucial for understanding how a group decides where or when to move, and how this information is transferred between members. Although many animal groups have a three-dimensional structure, previous studies investigating leader–follower interactions have often ignored vertical information. This raises the question of whether commonly used two-dimensional leader–follower analyses can be used justifiably on groups that interact in three dimensions. To address this, we quantified the individual movements of banded tetra fish (Astyanax mexicanus) within shoals by computing the three-dimensional trajectories of all individuals using a stereo-camera technique. We used these data firstly to identify and compare leader–follower interactions in two and three dimensions, and secondly to analyse leadership with respect to an individual's spatial position in three dimensions. We show that for 95% of all pairwise interactions leadership identified through two-dimensional analysis matches that identified through three-dimensional analysis, and we reveal that fish attend to the same shoalmates for vertical information as they do for horizontal information. Our results therefore highlight that three-dimensional analyses are not always required to identify leader–follower relationships in species that move freely in three dimensions. We discuss our results in terms of the importance of taking species' sensory capacities into account when studying interaction networks within groups.