Ferromagnetism and d-wave superconductivity in the 2D Hubbard model
By using the functional renormalization group we compute detailed momentum dependencies of the scale-dependent interaction vertex of the 2D (t,t')-Hubbard model. Compared to previous studies we improve accuracy by separating dominant parts from a remainder term. The former explicitly describe, for example, the interaction of Cooper pairs or spin operators. Applying the method to the repulsive Hubbard model we find d-wave superconductivity or ferromagnetism for larger next-to-nearest neighbor hopping amplitude t' at Van Hove Filling. Both ordering tendencies strongly compete with each other.
On a superconducting instability in the 2D repulsive Hubbard model at low occupancy
A Cooper instability for a weakly interacting 2D repulsive Hubbard model on a square lattice is found at low fermion occupancy. The point is that the previously known results concerning superconductivity under the conditions presented claim the absence of both s- and p-pairings when only nearest neighbors are accounted for. Taking into account next-to-nearest hopping terms in the Hamiltonian one can change the situation so that the l=1 partial scattering amplitude becomes singular. (author). 6 refs
Systematic study of d-wave superconductivity in the 2D repulsive Hubbard model
Maier, T. A.; Jarrell, M.; Schulthess, T.C.; Kent, P. R. C.; White, J. B.
2005-01-01
The cluster size dependence of superconductivity in the conventional two-dimensional Hubbard model, commonly believed to describe high-temperature superconductors, is systematically studied using the Dynamical Cluster Approximation and Quantum Monte Carlo simulations as cluster solver. Due to the non-locality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, the results are independent of the cluster si...
Absence of the d-Density Wave State in 2D Hubbard Model
Macridin, Alexandru; Jarrell, Mark; Maier, Thomas
2004-01-01
Using the Dynamical Cluster Approximation (DCA) we calculate the alternating circulating-current susceptibility and investigate the transition to the d-density wave (DDW) order in the two-dimensional Hubbard model. The 2 x 2 cluster used in the DCA calculation is the smallest that can capture d-wave order; therefore, due to the mean-field character of our calculation, we expect to overestimate d-wave transition temperatures. Despite this, we found no transition to the DDW state. In the pseudo...
A dimensional scaling computation of the electron concentration-dependent ground-state energy for the repulsive Hubbard model is presented, a generalization of Capelle’s analysis of the 2D and 3D Hubbard Hamiltonians with half-filled bands. The computed ground-state energies are compared with the results of mean-field and density matrix functional theories and of quantum Monte Carlo calculations. The comparison indicates that dimensional scaling yields moderately accurate ground-state energies close to and at half filling over the wide range of interaction strengths in the study. By contrast, the accuracy becomes poor at low filling for strong interactions. (author)
Results are presented for the competition between d-wave superconductivity (dSC) and antiferromagnetism (AF) in the ground state of the two-dimensional (2D) Hubbard model, relevant for the high-Tc superconductors (HTSC). Using the variational cluster approach (VCA) we are able to resolve the low energy features at zero temperature and to calculate the spectral function for any wave vector in the Brillouin zone. The cluster calculations reproduce the overall ground-state phase diagram of the HTSC both for hole- and electron-doping. Consistent with experiments, the AF state is found to be significantly more robust for electron doping than for hole doping, resulting from the frustration induced by the next-nearest neighbor hopping in the Hubbard model. Moreover, the system shows a tendency to phase separation into a mixed AF-dSC phase at low and a pure dSC phase at higher doping, where the phase-separation energy is an order of magnitude larger for hole-doping
Maximum Probability Domains for Hubbard Models
Acke, Guillaume; Claeys, Pieter W; Van Raemdonck, Mario; Poelmans, Ward; Van Neck, Dimitri; Bultinck, Patrick
2015-01-01
The theory of Maximum Probability Domains (MPDs) is formulated for the Hubbard model in terms of projection operators and generating functions for both exact eigenstates as well as Slater determinants. A fast MPD analysis procedure is proposed, which is subsequently used to analyse numerical results for the Hubbard model. It is shown that the essential physics behind the considered Hubbard models can be exposed using MPDs. Furthermore, the MPDs appear to be in line with what is expected from Valence Bond Theory-based knowledge.
An algebraic approach to the Hubbard model
de Leeuw, Marius
2015-01-01
We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su(2|2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.
Ventura, P; Li, L; Sofia, S; Basu, S; Demarque, P
2009-01-01
Understanding the reasons of the cyclic variation of the total solar irradiance is one of the most challenging targets of modern astrophysics. These studies prove to be essential also for a more climatologic issue, associated to the global warming. Any attempt to determine the solar components of this phenomenon must include the effects of the magnetic field, whose strength and shape in the solar interior are far from being completely known. Modelling the presence and the effects of a magnetic field requires a 2D approach, since the assumption of radial symmetry is too limiting for this topic. We present the structure of a 2D evolution code that was purposely designed for this scope; rotation, magnetic field and turbulence can be taken into account. Some preliminary results are presented and commented.
Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model.
Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; Neupert, Titus; Maciejko, Joseph
2016-08-26
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. PMID:27610869
Towards a Holographic Bose-Hubbard Model
Fujita, Mitsutoshi; Karch, Andreas; Meyer, Rene; Paquette, Natalie M
2014-01-01
We present a holographic construction of the large-N Bose-Hubbard model. The model is based on Maxwell fields coupled to charged scalar fields on the AdS2 hard wall. We realize the lobe-shaped phase structure of the Bose-Hubbard model and find that the model admits Mott insulator ground states in the limit of large Coulomb repulsion. In the Mott insulator phases, the bosons are localized on each site. At zero hopping we find that the transitions between Mott insulating phases with different fillings correspond to first order level-crossing phase transitions. At finite hopping we find a holographic phase transition between the Mott phase and a non-homogeneous phase. We then analyze the perturbations of fields around both the Mott insulator phase and inhomogeneous phase. We find an almost zero mode in the non-homogeneous phase.
Phase separation in the Hubbard model
Macridin, A.; Jarrell, M.; Maier, Th.
2005-01-01
Phase separation in the Hubbard model is investigated with the dynamical cluster approximation. We find that it is present in the paramagnetic solution for values of filling smaller than one and at finite temperature when a positive next-nearest neighbor hopping is considered. The phase separated region is characterized by a mixture of a strongly correlated metallic and Mott insulating phases. Our results indicate that phase separation is driven by the formation of doped regions with strong a...
Mott transition in the Hubbard model
In this article, the author discuss W. Kohn's criterion for a metal insulator transition, within the framework of a one-band Hubbard model. This and related ideas are applied to 1-dimensional Hubbard systems, and some interesting miscellaneous results discussed. The Jordan-Wigner transformation converting the two species of fermions to two species of hardcore bosons is performed in detail, and the extra phases arising from odd-even effects are explicitly derived. Bosons are shown to prefer zero flux (i.e., diamagnetism) and the corresponding happy fluxes: for the fermions identified. A curios result following from the interplay between orbital diamagnetism and spin polarization is highlighted. A spin-statistics like theorem, showing that the anticommutation relations between fermions of opposite spin are crucial to obtain the SU(2) invariance is pointed out
Activated sludge model No. 2d, ASM2d
Henze, M.
1999-01-01
The Activated Sludge Model No. 2d (ASM2d) presents a model for biological phosphorus removal with simultaneous nitrification-denitrification in activated sludge systems. ASM2d is based on ASM2 and is expanded to include the denitrifying activity of the phosphorus accumulating organisms (PAOs...
Superconducting properties of the attractive Hubbard model
A self-consistent set of equations for the one-electron self-energy in the ladder approximation is derived for the attractive Hubbard model in the superconducting state. The equations provide an extension of a T-matrix formalism recently used to study the effect of electron correlations on normal-state properties. An approximation to the set of equations is solved numerically in the intermediate coupling regime, and the one-particle spectral functions are found to have four peaks. This feature is traced back to a peak in the self-energy, which is related to the formation of real-space bound states. For comparison we extend the moment approach to the superconducting state and discuss the crossover from the weak (BCS) to the intermediate coupling regime from the perspective of single-particle spectral densities. (orig.)
Electron-phonon interaction in the Hubbard model
Superconductivity existence in the Hubbard model is studied, taking into account both electron-phonon and electron-electron interactions. Using Sarker's functional integral formalism a system of equations for the dynamical order parameters is derived. (author). 7 refs
Reexamination of the variational Bose-Hubbard model
Major, Jan; Łącki, Mateusz; Zakrzewski, Jakub
2014-04-01
For strongly interacting bosons in optical lattices, the standard description using the Bose-Hubbard model becomes questionable. The role of excited bands becomes important. In such a situation, we compare results of simulations using the multiband Bose-Hubbard model with a recent proposition based on a time-dependent variational approach. It is shown that the latter, in its original formulation, uses a too small variational space, often leading to spurious effects. Possible expansion of the variational approach is discussed.
Flow equations for the ionic Hubbard model
Hafez, Mohsen; Jafari, S. A.; Abolhassani, M. R.
2009-12-01
Taking the site-diagonal terms of the ionic Hubbard model (IHM) in one and two spatial dimensions, as H, we employ Continuous Unitary Transformations (CUT) to obtain a “classical” effective Hamiltonian in which hopping term has been renormalized to zero. For this Hamiltonian spin gap and charge gap are calculated at half-filling and subject to periodic boundary conditions. Our calculations indicate two transition points. In fixed Δ, as U increases from zero, there is a region in which both spin gap and charge gap are positive and identical; characteristic of band insulators. Upon further increasing U, first transition occurs at U=Uc_1, where spin and charge gaps both vanish and remain zero up to U=Uc_2. A gap-less state in charge and spin sectors characterizes a metal. For U>Uc_2 spin gap remains zero and charge gap becomes positive. This third region corresponds to a Mott insulator in which charge excitations are gaped, while spin excitations remain gap-less.
Quantum Monte Carlo study of bilayer ionic Hubbard model
Jiang, M.; Schulthess, T. C.
2016-04-01
The interaction-driven insulator-to-metal transition has been reported in the ionic Hubbard model (IHM) for moderate interaction U , while its metallic phase only occupies a narrow region in the phase diagram. To explore the enlargement of the metallic regime, we extend the ionic Hubbard model to two coupled layers and study the interplay of interlayer hybridization V and two types of intralayer staggered potentials Δ : one with the same (in-phase) and the other with a π -phase shift (antiphase) potential between layers. Our determinant quantum Monte Carlo (DQMC) simulations at lowest accessible temperatures demonstrate that the interaction-driven metallic phase between Mott and band insulators expands in the Δ -V phase diagram of bilayer IHM only for in-phase ionic potentials; while antiphase potential always induces an insulator with charge density order. This implies possible further extension of the ionic Hubbard model from the bilayer case here to a realistic three-dimensional model.
Hubbard operator density functional theory for Fermionic lattice models
Cheng, Zhengqian; Marianetti, Chris
We formulate an effective action as a functional of Hubbard operator densities whose stationary point delivers all local static information of the interacting lattice model. Using the variational principle, we get a self-consistent equation for Hubbard operator densities. The computational cost of our approach is set by diagonalizing the local Fock space. We apply our method to the one and two band Hubbard model (including crystal field and on-site exchange) in infinite dimensions where the exact solution is known. Excellent agreement is obtained for the one-band model. In the two-band model, good agreement is obtained in the metallic region of the phase diagram in addition to the metal-insulator transition. While our approach does not address frequency dependent observables, it has a negligible computational cost as compared to dynamical mean field theory and could be highly applicable in the context total energies of strongly correlated materials and molecules.
A bespoke single-band Hubbard model material
Griffin, S. M.; Staar, P.; Schulthess, T. C.; Troyer, M.; Spaldin, N. A.
2016-02-01
The Hubbard model, which augments independent-electron band theory with a single parameter to describe electron-electron correlations, is widely regarded to be the "standard model" of condensed-matter physics. The model has been remarkably successful at addressing a range of correlation phenomena in solids, but it neglects many behaviors that occur in real materials, such as phonons, long-range interactions, and, in its simplest form, multiorbital effects. Here, we use ab initio electronic structure methods to design a material whose Hamiltonian matches as closely as possible that of the single-band Hubbard model. Our motivation is to compare the measured properties of our new material to those predicted by reliable theoretical solutions of the Hubbard model to determine the relevance of the model in the description of real materials. After identifying an appropriate crystal class and several appropriate chemistries, we use density-functional theory and dynamical mean-field theory to screen for the desired electronic band structure and metal-insulator transition. We then explore the most promising candidates for structural stability and suitability for doping, and we propose specific materials for subsequent synthesis. Finally, we identify a regime—that should manifest in our bespoke material—in which the single-band Hubbard model on a triangular lattice exhibits exotic d -wave superconductivity.
Critical points of the anyon-Hubbard model
Arcila-Forero, J.; Franco, R.; Silva-Valencia, J.
2016-07-01
Anyons are particles with fractional statistics that exhibit a nontrivial change in the wave function under an exchange of particles. Anyons can be considered to be a general category of particles that interpolate between fermions and bosons. We determined the position of the critical points of the one-dimensional anyon-Hubbard model, which was mapped to a modified Bose-Hubbard model where the tunneling depends on the local density and the interchange angle. We studied the latter model by using the density-matrix renormalization-group method and observed that gapped (Mott insulator) and gapless (superfluid) phases characterized the phase diagram, regardless of the value of the statistical angle. The phase diagram for higher densities was calculated and showed that the Mott lobes increase (decrease) as a function of the statistical angle (global density). The position of the critical point separating the gapped and gapless phases was found using quantum information tools, namely the block von Neumann entropy. We also studied the evolution of the critical point with the global density and the statistical angle and showed that the anyon-Hubbard model with a statistical angle θ =π /4 is in the same universality class as the Bose-Hubbard model with two-body interactions.
Ground state phase diagram of extended attractive Hubbard model
The ground state phase diagram of the extended Hubbard model with intraatomic attraction has been derived in the Hartree-Fock approximation formulated in terms of the Bogoliubov variational approach. For a given value of electron density, the nature of the ordered ground state depends essentially on the sign and the strength of the nearest neighbor coupling. (author)
Stability of ferromagnetism in Hubbard models with nearly flat bands
Whether spin-independent Coulomb interaction in an electron system can be the origin of ferromagnetism has been an open problem for a long time. Recently, a open-quotes constructiveclose quotes approach to this problem has been developed, and the existence of ferromagnetism in the ground states of certain Hubbard models was established rigorously. A special feature of these Hubbard models is that their lowest bands (in the corresponding single-electron problems) are completely flat. Here we study models obtained by adding small but arbitrary translation-invariant perturbation to the hopping Hamiltonian of these flat-band models. The resulting models have nearly flat lowest bands. We prove that the ferromagnetic state is stable against a single-spin flip provided that Coulomb interaction U is sufficiently large. (It is easily found that the same state is unstable against a single-spin flip of U is small enough.) We also prove upper and lower bounds for the dispersion relation of the lowest energy eigenstate with a single flipped spin, which bounds establish that the model has open-quotes healthyclose quotes spin-wave excitation. It is notable that the (local) stability of ferromagnetism is proved in nonsingular Hubbard models, in which we must overcome competition between the kinetic energy and the Coulomb interaction. We also note that this is one of the very few rigorous and robust results which deal with truly non-perturbative phenomena in many-electron systems. The local stability strongly suggests that the Hubbard models with nearly flat bands have ferromagnetic ground states. We believe that the present models can be studied as paradigm models for (insulating) ferromagnetism in itinerant electron systems
Route to supersolidity for the extended Bose-Hubbard model
We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site (U) and nearest-neighbor (V) repulsions. For d-dimensional hypercubic lattices, when 2dVU, in this Rapid Communication, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very large hopping values which could be orders of magnitude higher than that of the well-known case. In particular, the SS-superfluid phase boundary increases linearly as a function of hopping when 2dV > or approx. 1.5U, for which the prospects of observing the SS phase with dipolar Bose gases loaded into optical lattices is much higher.
The 2-site Hubbard and t-J models
Avella, Adolfo; Mancini, Ferdinando; Saikawa, Taiichiro
2001-01-01
The fermionic and bosonic sectors of the 2-site Hubbard model have been exactly solved by means of the equation of motion and Green's function formalism. The exact solution of the t-J model has been also reported to investigate the low-energy dynamics. We have successfully searched for the exact eigenoperators, and the corresponding eigenenergies, having in mind the possibility to use them as an operatorial basis on the lattice. Many local, single-particle, thermodynamical and response proper...
The 2-site Hubbard and {t}-{J} models
Avella, A.; Mancini, F.; Saikawa, T.
2003-12-01
The fermionic and bosonic sectors of the 2-site Hubbard model have been exactly solved by means of the equation of motion and Green’s function formalism. The exact solution of the t- J model has been also reported to investigate the low-energy dynamics. We have successfully searched for the exact eigenoperators, and the corresponding eigenenergies, having in mind the possibility to use them as an operatorial basis on the lattice. Many local, single-particle, thermodynamical and response properties have been studied as functions of the external parameters and compared between the two models and with some numerical and exact results. It has been shown that the 2-site Hubbard model already contains the most relevant energy scales of the Hubbard model: the local Coulomb interaction U and the spin-exchange one J = frac{4t^2}U. As a consequence of this, for some relevant properties (kinetic energy, double occupancy, energy, specific heat and entropy) and as regards the metal-insulator transition issue, it has resulted possible to almost exactly mime the behavior of larger systems, sometimes using a higher temperature to get a comparable level spacing. The 2-site models have been also used as toy models to test the efficiency of the Green’s function formalism for composite operators. The capability to reproduce the exact solutions, obtained by the exact diagonalization technique, gives a firm ground to the approximate treatments based on this formalism.
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.
Extended Bose-Hubbard models with ultracold magnetic atoms
Baier, S.; Mark, M. J.; Petter, D.; Aikawa, K.; Chomaz, L.; Cai, Z.; Baranov, M.; Zoller, P.; Ferlaino, F.
2016-04-01
The Hubbard model underlies our understanding of strongly correlated materials. Whereas its standard form only comprises interactions between particles at the same lattice site, extending it to encompass long-range interactions is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics and their influence on the superfluid-to-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interactions, a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of exotic many-body quantum phases.
Bose-Hubbard model on a checkerboard superlattice
Iskin, Menderes
2011-05-01
We study the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and charge-density-wave insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid-charge-density-wave insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well. This work is supported by Marie Curie International Reintegration Grant (FP7-PEOPLE-IRG-2010-268239).
Local origin of the pseudogap in the attractive Hubbard model
PETERS, Robert; Bauer, Johannes
2015-01-01
We provide a new perspective on the pseudogap physics for attractive fermions as described by the three-dimensional Hubbard model. The pseudogap in the single-particle spectral function, which occurs for temperatures above the critical temperature $T_c$ of the superfluid transition, is often interpreted in terms of preformed, uncondensed pairs. Here we show that the occurrence of pseudogap physics can be consistently understood in terms of local excitations which lead to a splitting of the qu...
Iterated perturbation theory for the attractive Holstein and Hubbard models
Freericks, J. K.; Jarrell, Mark (Eds. )
1994-01-01
A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order iterated perturbation theory is shown to be quite accurate in calculating transition temperatures for retarded interactions, but is not as accurate for the self energy or the irreducible vertex functions themselves. Iterated perturbation theory is carried ...
Bond excitations in the pseudogap phase of the Hubbard Model
Macridin, Alexandru; Jarrell, Mark (Eds. )
2008-01-01
Using the dynamical cluster approximation, we calculate the correlation functions associated with the nearest neighbor bond operator which measure the z component of the spin exchange in the two-dimensional Hubbard model with $U$ equal to the bandwidth. We find that in the pseudogap region, the local bond susceptibility diverges at T=0. This shows the existence of degenerate bond spin excitation and implies quantum criticality and bond order formation when long range correlations are consider...
The one-dimensional extended Bose-Hubbard model
Ramesh V Pai; Rahul Pandit
2003-10-01
We use the finite-size, density-matrix-renormalization-group (DMRG) method to obtain the zero-temperature phase diagram of the one-dimensional, extended Bose-Hubbard model, for mean boson density ρ = 1, in the - plane ( and are respectively, onsite and nearest-neighbour repulsive interactions between bosons). The phase diagram includes superfluid (SF), bosonic-Mott-insulator (MI), and mass-density-wave (MDW) phases. We determine the natures of the quantum phase transitions between these phases.
Entanglement entropies of the quarter filled Hubbard model
We study Rényi and von Neumann entanglement entropies in the ground state of the one dimensional quarter-filled Hubbard model with periodic boundary conditions. We show that they exhibit an unexpected dependence on system size: for L = 4mod 8 the results are in agreement with expectations based on conformal field theory, while for L = 0mod 8 additional contributions arise. We show that these can be understood in terms of a ‘shell-filling’ effect and we develop a conformal field theory approach to calculate the additional contributions to the entropies. These analytic results are found to be in excellent agreement with density matrix renormalization group computations for weak Hubbard interactions. We argue that for larger interactions the presence of a marginal irrelevant operator in the spin sector strongly affects the entropies at the finite sizes accessible numerically and we present an effective way to take them into account. (paper)
Entanglement entropies of the quarter filled Hubbard model
Calabrese, Pasquale; Essler, Fabian H. L.; Läuchli, Andreas M.
2014-09-01
We study Rényi and von Neumann entanglement entropies in the ground state of the one dimensional quarter-filled Hubbard model with periodic boundary conditions. We show that they exhibit an unexpected dependence on system size: for L = 4mod 8 the results are in agreement with expectations based on conformal field theory, while for L = 0mod 8 additional contributions arise. We show that these can be understood in terms of a ‘shell-filling’ effect and we develop a conformal field theory approach to calculate the additional contributions to the entropies. These analytic results are found to be in excellent agreement with density matrix renormalization group computations for weak Hubbard interactions. We argue that for larger interactions the presence of a marginal irrelevant operator in the spin sector strongly affects the entropies at the finite sizes accessible numerically and we present an effective way to take them into account.
Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model
Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-Tc cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)
Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model
Friederich, Simon
2010-12-08
Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-T{sub c} cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)
Path Integral Methods for Single Band Hubbard Model
N. Heydari; Azakov, S.
1997-01-01
We review various ways to express the partition function of the single-band Hubard model as a path integral. The emphasis is made on the derivation of the action in the integrand of the path integral and the results obtained from this approach are discussed only briefly. Since the single-band Hubbard model is a pure fermionic model on the lattice and its Hamiltonian is a polynomial in creation and annihilation fermionic operators, with the help of the fermionic coherent states of holomorp...
Spectral analysis of two-dimensional Bose-Hubbard models
Fischer, David; Hoffmann, Darius; Wimberger, Sandro
2016-04-01
One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple two-dimensional many-body models. Also in two dimensions a transition from regular to chaotic spectral statistics is found and discussed. In particular, we analyze the dependence of the spectral properties on the bond number of the two-dimensional lattices and the applied boundary conditions. For maximal connectivity, the systems behave most regularly in agreement with the applicability of mean-field approaches in the limit of many nearest-neighbor couplings at each site.
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date
Bose–Hubbard model on two-dimensional line graphs
We construct a basis for the many-particle ground states of the positive hopping Bose–Hubbard model on line graphs of finite 2-connected planar bipartite graphs at sufficiently low filling factors. The particles in these states are localized on non-intersecting vertex-disjoint cycles of the line graph which correspond to non-intersecting edge-disjoint cycles of the original graph. The construction works up to a critical filling factor at which the cycles are close-packed. (paper)
Superconductivity in the two-dimensional generalized Hubbard model
Lima, L. S.
2016-08-01
We have used the Green's functions method at finite temperature and the Kubo's formalism, to calculate the electron conductivity σ(ω) in the generalized two-dimensional Hubbard model. We have obtained a behavior superconductor for the system to T > T0. The AC conductivity falls to zero in ω =ω0 , where ω0 depends on Δ, which is the gap of the system. The behavior gotten is according of with the behavior of the superconductors of high Tc where there is a changes abruptly from a Mott's insulator state to superconductor.
Possible phase separation in square and honeycomb Hubbard model: A variational cluster study
Fang, Kun; Fernando, G.W. [Department of Physics, University of Connecticut, Storrs, CT 06269 (United States); Balatsky, A.V. [Institute for Materials Science, Los Alamos, NM 87545 (United States); NORDITA, Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden); Kocharian, A.N., E-mail: armen.kocharian@calstatela.edu [Department of Physics, California State University, Los Angeles, CA 90032 (United States)
2015-10-02
The VCA ground state of the 2D Hubbard model is examined for possible phase separation under hole doping manifested by spatial inhomogeneities of coexisting different electron densities at equilibrium. Phase separation is accompanied by spectral weight loss and first Brillouin zone boundary deformation. Such an instability is observed in square structures and it is absent in honeycomb lattices. To our knowledge, no previous publications have revealed relationship between a Fermi surface instability and phase separation. Our VCA calculations provide strong support for this spontaneous instability, driven by electron correlations in specific lattice geometries, proposed in our earlier publications using exact quantum cluster calculations. - Highlights: • VCA study of possible spontaneous phase separation in 2D square and honeycomb Hubbard lattices. • Phase separation instabilities and density inhomogeneities driven by proximity to level crossing. • Contrasting differences in behaviors of spectral functions in square and honeycomb near first Brillouin zone. • VCA strongly confirms spontaneous phase separation obtained at level crossings in cluster calculations.
Possible phase separation in square and honeycomb Hubbard model: A variational cluster study
The VCA ground state of the 2D Hubbard model is examined for possible phase separation under hole doping manifested by spatial inhomogeneities of coexisting different electron densities at equilibrium. Phase separation is accompanied by spectral weight loss and first Brillouin zone boundary deformation. Such an instability is observed in square structures and it is absent in honeycomb lattices. To our knowledge, no previous publications have revealed relationship between a Fermi surface instability and phase separation. Our VCA calculations provide strong support for this spontaneous instability, driven by electron correlations in specific lattice geometries, proposed in our earlier publications using exact quantum cluster calculations. - Highlights: • VCA study of possible spontaneous phase separation in 2D square and honeycomb Hubbard lattices. • Phase separation instabilities and density inhomogeneities driven by proximity to level crossing. • Contrasting differences in behaviors of spectral functions in square and honeycomb near first Brillouin zone. • VCA strongly confirms spontaneous phase separation obtained at level crossings in cluster calculations
Magnetic properties of three-dimensional Hubbard-sigma model
It is broadly viewed that the magnetism may play an important role in the high-Tc superconductivity in the lamellar CuO2 materials. In this paper, based on a Hubbard-inspired CP1 or S2 nonlinear σ model, we give a quantitative study of some magnetic properties in and around the Neel ordered state of three-dimensional quantum antiferromagnets such as La2CuO4 with and without small hole doping. Our model is a (3+1) dimensional effective field theory describing the low energy spin dynamics of a three-dimensional Hubbard model with a very weak interlayer coupling. The effect of hole dynamics is taken into account in the leading approximation by substituting the CP1 coupling with an 'effective' one determined by the concentration and the one-loop correction of hole fermions. A stationary-phase equation for the one-loop effective potential of S2 model is analyzed numerically. The behavior of Neel temperature, magnetization (long range Neel order), spin correlation length, etc as functions of anisotropic parameter, temperature, hole concentrations, etc are investigated in detail. A phase diagram is also supported by the renormlization group analysis. The results show that our anisotropic field theory model with certain values of parameters could give a reasonably well description of the magnetic properties indicated by some experiments on pure and doped La2CuO4. (author)
Conservation laws in the one-dimensional Hubbard model
We examine the nature, number, and interrelation of conservation laws in the one-dimensional Hubbard model. In previous work by Shastry [Phys. Rev. Lett. 56, 1529 (1986); 56, 2334 (1986); 56, 2453 (1986); J. Stat. Phys. 50, 57 (1988)], who studied the model on a large but finite number of lattice sites (Na), only Na+1 conservation laws, corresponding to Na+1 operators that commute with themselves and the Hamiltonian, were explicitly identified, rather than the ∼2Na conservation laws expected from the solvability and integrability of the model. Using a pseudoparticle approach related to the thermodynamic Bethe ansatz, we discover an additional Na+1 independent conservation laws corresponding to nonlocal, mututally commuting operators, which we call transfer-matrix currents. Further, for the model defined in the whole Hilbert space, we find there are two other independent commuting operators (the squares of the η-spin and spin operators) so that the total number of local plus nonlocal commuting conservation laws for the one-dimensional Hubbard model is 2Na+4. Finally, we introduce an alternative set of 2Na+4 conservation laws which assume particularly simple forms in terms of the pseudoparticle and Yang-particle operators. This set of mutually commuting operators lends itself more readily to calculations of physically relevant correlation functions at finite energy or frequency than the previous set
In these lectures, I shall focus on the matrix formulation of 2-d gravity. In the first one, I shall discuss the main results of the continuum formulation of 2-d gravity, starting from the first renormalization group calculations which led to the concept of the conformal anomaly, going through the Polyakov bosonic string and the Liouville action, up to the recent results on the scaling properties of conformal field theories coupled to 2-d gravity. In the second lecture, I shall discuss the discrete formulation of 2-d gravity in term of random lattices, and the mapping onto random matrix models. The occurrence of critical points in the planar limit and the scaling limit at those critical points will be described, as well as the identification of these scaling limits with continuum 2-d gravity coupled to some matter field theory. In the third lecture, the double scaling limit in the one matrix model, and its connection with continuum non perturbative 2-d gravity, will be presented. The connection with the KdV hierarchy and the general form of the string equation will be discuted. In the fourth lecture, I shall discuss the non-perturbative effects present in the non perturbative solutions, in the case of pure gravity. The Schwinger-Dyson equations for pure gravity in the double scaling limit are described and their compatibility with the solutions of the string equation for pure gravity is shown to be somewhat problematic
Kuno, Yoshihito; Nakafuji, Takashi; Ichinose, Ikuo
2015-12-01
In this paper, we study Bose-Hubbard models on square and honeycomb lattices with complex hopping amplitudes, which are feasible by recent experiments of cold atomic gases in optical lattices. To clarify phase diagrams, we use extended quantum Monte Carlo simulations (eQMC). For the system on the square lattice, the complex hopping is realized by an artificial magnetic field. We found that vortex-solid states form for certain set of magnetic field, i.e., the magnetic field with the flux quanta per plaquette f =p /q , where p and q are co-prime natural numbers. For the system on the honeycomb lattice, we add the next-nearest-neighbor complex hopping. The model is a bosonic analog of the Haldane-Hubbard model. By means of eQMC, we study the model with both weak and strong onsite repulsions. Numerical study shows that the model has a rich phase diagram. We also found that in the system defined on the honeycomb lattice of the cylinder geometry, an interesting edge state appears.
Fermion Coherent State Studies of One-Dimensional Hubbard Model
LIN Ji; GAO Xian-Long; WANG Ke-Lin
2007-01-01
We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and considering the interactions of two pairs electrons and holes. We construct the ground state of the Hubbard model as ｜〉 = [f + ∑′ψc+k1σ1 h+k2σ2 c+k3σ3 h+k4σ4 ∏exp(ρc+k1σ1 h+k2σ2)] [〉0, where ψ and ρ are the coupling constants. Our results are then compared to those of variational methods, density functional theory based on the exact solvable Bethe ansatz solutions, variational Monto-Carlo method (VMC) as well as to the exact result of the infinite system. We find satisfactory agreement between the fermion coherent state scheme and the VMC data, and provide a new picture to deal with the strongly correlated system.
Burcharth, Hans F.; Meinert, Palle; Andersen, Thomas Lykke
This report present the results of 2D physical model tests (length scale 1:50) carried out in a waveflume at Dept. of Civil Engineering, Aalborg University (AAU). The objective of the tests was: To identify cross section design which restrict the overtopping to acceptable levels and to record the...
Andersen, Thomas Lykke; Frigaard, Peter
This report present the results of 2D physical model tests carried out in the shallow wave flume at Dept. of Civil Engineering, Aalborg University (AAU), on behalf of Energy E2 A/S part of DONG Energy A/S, Denmark. The objective of the tests was: to investigate the combined influence of the pile...
Equation of state of the fermionic two-dimensional Hubbard model
LeBlanc, J. P. F.; Gull, Emanuel
2013-10-01
We present results for the equation of state of the two-dimensional Hubbard model on an isotropic square lattice as obtained from a controlled and numerically exact large-cluster dynamical mean field simulation. Our results are obtained for large but finite systems and are extrapolated to infinite system size using a known finite-size scaling relation, and are supplemented by reliable error bars accounting for all sources of errors. We establish the importance of examining the decay of spatial spin correlations to determine whether a sufficiently large cluster has been used and with this in mind we present the energy, entropy, double occupancy, and nearest-neighbor spin correlations extrapolated to the thermodynamic limit. We discuss the implications of these calculations on pseudogap physics of the 2D Hubbard model away from half filling, where we find a strong behavioral shift in energy below a temperature T* which becomes more pronounced for larger clusters. Finally, we provide reference calculations and tables for the equation of state for values of doping away from half filling which are of interest to cold-atom experiments.
Dynamical instability in the S =1 Bose-Hubbard model
Asaoka, Rui; Tsuchiura, Hiroki; Yamashita, Makoto; Toga, Yuta
2016-01-01
We study the dynamical instabilities of superfluid flows in the S =1 Bose-Hubbard model. The time evolution of each spin component in a condensate is calculated based on the dynamical Gutzwiller approximation for a wide range of interactions, from a weakly correlated regime to a strongly correlated regime near the Mott-insulator transition. Owing to the spin-dependent interactions, the superfluid flow of the spin-1 condensate decays at a different critical momentum from a spinless case when the interaction strength is the same. We furthermore calculate the dynamical phase diagram of this model and clarify that the obtained phase boundary has very different features depending on whether the average number of particles per site is even or odd. Finally, we analyze the density and spin modulations that appear in association with the dynamical instability. We find that spin modulations are highly sensitive to the presence of a uniform magnetic field.
Phase transitions in the Hubbard model for the bismuth nickelate
Kojima, Shoya; Nasu, Joji; Koga, Akihisa
2016-07-01
We study low temperature properties of the Hubbard model for the bismuth nickelate, where degenerate orbitals in the nickel ions and a single orbital in the bismuth ions are taken into account, combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method. We discuss the effect of the attractive interactions to mimic the valence skipping phenomenon in the bismuth ions. We demonstrate how the charge and magnetically ordered states are stable against thermal fluctuations. It is furthermore clarified that the ferromagnetically ordered and orbital ordered states are stabilized due to the presence of the orbital degeneracy at low temperatures. The crossover between metallic and insulating states is also discussed.
One-dimensional Hubbard-Luttinger model for carbon nanotubes
Ishkhanyan, H. A.; Krainov, V. P.
2015-06-01
A Hubbard-Luttinger model is developed for qualitative description of one-dimensional motion of interacting Pi-conductivity-electrons in carbon single-wall nanotubes at low temperatures. The low-lying excitations in one-dimensional electron gas are described in terms of interacting bosons. The Bogolyubov transformation allows one to describe the system as an ensemble of non-interacting quasi-bosons. Operators of Fermi excitations and Green functions of fermions are introduced. The electric current is derived as a function of potential difference on the contact between a nanotube and a normal metal. Deviations from Ohm law produced by electron-electron short-range repulsion as well as by the transverse quantization in single-wall nanotubes are discussed. The results are compared with experimental data.
Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model
Results of a renormalization group study for the 2-dimensional Hubbard model close to half-filling at finite temperature are presented. Bosonic degrees of freedom corresponding to antiferromagnetic and d-wave superconducting order are introduced, and flow equations for the corresponding coupling constants are deduced from an exact flow equation for the effective average action. The influence of bosonic fluctuations on the onset of local antiferromagnetic order is discussed. At low enough temperatures and close to half-filling the discrete symmetry of the lattice is broken and incommensurate antiferromagnetic fluctuations dominate. The phase diagram is shown for the parameter regime close to half-filling in the presence of vanishing as well as non-vanishing next-to-nearest-neighbor hopping t'. Finally, the potential emergence of d-wave superconducting order at larger distances from half-filling is discussed.
Conductivite dans le modele de Hubbard bi-dimensionnel a faible couplage
Bergeron, Dominic
Le modele de Hubbard bi-dimensionnel (2D) est souvent considere comme le modele minimal pour les supraconducteurs a haute temperature critique a base d'oxyde de cuivre (SCHT). Sur un reseau carre, ce modele possede les phases qui sont communes a tous les SCHT, la phase antiferromagnetique, la phase supraconductrice et la phase dite du pseudogap. Il n'a pas de solution exacte, toutefois, plusieurs methodes approximatives permettent d'etudier ses proprietes de facon numerique. Les proprietes optiques et de transport sont bien connues dans les SCHT et sont donc de bonne candidates pour valider un modele theorique et aider a comprendre mieux la physique de ces materiaux. La presente these porte sur le calcul de ces proprietes pour le modele de Hubbard 2D a couplage faible ou intermediaire. La methode de calcul utilisee est l'approche auto-coherente a deux particules (ACDP), qui est non-perturbative et inclue l'effet des fluctuations de spin et de charge a toutes les longueurs d'onde. La derivation complete de l'expression de la conductivite dans l'approche ACDP est presentee. Cette expression contient ce qu'on appelle les corrections de vertex, qui tiennent compte des correlations entre quasi-particules. Pour rendre possible le calcul numerique de ces corrections, des algorithmes utilisant, entre autres, des transformees de Fourier rapides et des splines cubiques sont developpes. Les calculs sont faits pour le reseau carre avec sauts aux plus proches voisins autour du point critique antiferromagnetique. Aux dopages plus faibles que le point critique, la conductivite optique presente une bosse dans l'infrarouge moyen a basse temperature, tel qu'observe dans plusieurs SCHT. Dans la resistivite en fonction de la temperature, on trouve un comportement isolant dans le pseudogap lorsque les corrections de vertex sont negligees et metallique lorsqu'elles sont prises en compte. Pres du point critique, la resistivite est lineaire en T a basse temperature et devient
Fermi hyper-netted chain theory on a lattice: The Hubbard model
We review a new lattice version of Fermi Hyper-Netted Chain method for the study of strongly interacting electrons. The ordinary paramagnetic and the spin density wave functions have been correlated with Jastrow-type and e-d correlations, and the corresponding FHNC equations for the pair distribution function, the one body density matrix and the staggered magnetization are discussed. Results for the 1D chain and 2D square lattice models are presented and compared with the available results obtained within Quantum Monte Carlo, variational Monte Carlo and exact diagonalization of a 4x4 Hubbard cluster. Particularly interesting are the strong effects of e-d correlations on E/Nt and on the momentum distribution as well as antiferromagnetic behavior away from half filling found in our FHNC calculations in agreement with other studies. (author). 35 refs, 8 figs, 2 tabs
Bracken, Anthony J.; Ge Xiangyu; Gould, Mark D.; Links, Jon; Zhou Huanqiang [Centre for Mathematical Physics, University of Queensland, Brisbane, QLD (Australia)
2001-06-01
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method. (author)
Dynamical Model and Path Integral Formalism for Hubbard Operators
Foussats, A.; Greco, A. (Anna); Zandron, O. S.
1998-01-01
In this paper, the possibility to construct a path integral formalism by using the Hubbard operators as field dynamical variables is investigated. By means of arguments coming from the Faddeev-Jackiw symplectic Lagrangian formalism as well as from the Hamiltonian Dirac method, it can be shown that it is not possible to define a classical dynamics consistent with the full algebra of the Hubbard $X$-operators. Moreover, from the Faddeev-Jackiw symplectic algorithm, and in order to satisfy the H...
Antiferromagnetism and d-wave superconductivity in the Hubbard model
The two-dimensional Hubbard model is a promising effective model for the electronic degrees of freedom in the copper-oxide planes of high temperature superconductors. We present a functional renormalization group approach to this model with focus on antiferromagnetism and d-wave superconductivity. In order to make the relevant degrees of freedom more explicitly accessible on all length scales, we introduce composite bosonic fields mediating the interaction between the fermions. Spontaneous symmetry breaking is reflected in a non-vanishing expectation value of a bosonic field. The emergence of a coupling in the d-wave pairing channel triggered by spin wave fluctuations is demonstrated. Furthermore, the highest temperature at which the interaction strength for the electrons diverges in the renormalization flow is calculated for both antiferromagnetism and d-wave superconductivity over a wide range of doping. This ''pseudo-critical'' temperature signals the onset of local ordering. Moreover, the temperature dependence of d-wave superconducting order is studied within a simplified model characterized by a single coupling in the d-wave pairing channel. The phase transition within this model is found to be of the Kosterlitz-Thouless type. (orig.)
Antiferromagnetism and d-wave superconductivity in the Hubbard model
Krahl, H.C.
2007-07-25
The two-dimensional Hubbard model is a promising effective model for the electronic degrees of freedom in the copper-oxide planes of high temperature superconductors. We present a functional renormalization group approach to this model with focus on antiferromagnetism and d-wave superconductivity. In order to make the relevant degrees of freedom more explicitly accessible on all length scales, we introduce composite bosonic fields mediating the interaction between the fermions. Spontaneous symmetry breaking is reflected in a non-vanishing expectation value of a bosonic field. The emergence of a coupling in the d-wave pairing channel triggered by spin wave fluctuations is demonstrated. Furthermore, the highest temperature at which the interaction strength for the electrons diverges in the renormalization flow is calculated for both antiferromagnetism and d-wave superconductivity over a wide range of doping. This ''pseudo-critical'' temperature signals the onset of local ordering. Moreover, the temperature dependence of d-wave superconducting order is studied within a simplified model characterized by a single coupling in the d-wave pairing channel. The phase transition within this model is found to be of the Kosterlitz-Thouless type. (orig.)
Ising tricriticality in the extended Hubbard model with bond dimerization
Ejima, Satoshi; Essler, Fabian H. L.; Lange, Florian; Fehske, Holger
2016-06-01
We explore the quantum phase transition between Peierls and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge c =7 /10 . Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results.
Exact solution of a new class of Hubbard-type models with open boundary conditions
A new class of Hubbard-type models with open boundary conditions in one dimension is studied in the framework of coordinate Bethe ansatz method. The energy spectrum, integrable boundary conditions and the corresponding Bethe ansatz equations are derived. (authors)
Phase diagram of the half-filled ionic Hubbard model
Bag, Soumen; Garg, Arti; Krishnamurthy, H. R.
2015-06-01
We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Δ and the on-site Hubbard U . We find that for a finite Δ and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U =UA F via a first-order phase transition. For U smaller than UA F the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U . We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature TA F(U ,Δ ) [or, equivalently, on decreasing U below UA F(T ,Δ ) ], within both methods, for weak to intermediate values of U /t . In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T , DMFT +CTQMC shows a second phase transition (not seen within DMFT +IPT ) on increasing U beyond UA F. At UN>UA F , when the Neel temperature TN for the effective Heisenberg model becomes lower than T , the AFM order is lost via a second-order transition. For U ≫Δ , TN˜t2/U (1 -x2) , where x =2 Δ /U and thus TN increases with increase in Δ /U . In the three-dimensional parameter space of (U /t ,T /t ,andΔ /t ) , as T increases, the surface of first
Time-of-flight images of Mott insulators in the Hofstadter- Bose-Hubbard model
Işkın, Menderes
2015-01-01
PHYSICAL REVIEW A 92, 023636 (2015) Time-of-flight images of Mott insulators in the Hofstadter-Bose-Hubbard model M. Iskin Department of Physics, Koc¸ University, Rumelifeneri Yolu, 34450 Sarıyer, Istanbul, Turkey (Received 10 April 2015; published 26 August 2015) We analyze the momentum distribution function and its artificial-gauge-field dependence for theMott insulator phases of the Hofstadter-Bose-Hubbard model. By benchmarking the results of the random-phase approximati...
Diffusion dynamics in the disordered Bose Hubbard model
Wadleigh, Laura; Russ, Philip; Demarco, Brian
2016-05-01
We explore the dynamics of diffusion for out-of-equilibrium superfluid, Mott insulator, and Bose glass states using an atomic realization of the disordered Bose Hubbard (DBH) model. Dynamics in strongly correlated systems, especially far from equilibrium, are not well understood. The introduction of disorder further complicates these systems. We realize the DBH model--which has been central to our understanding of quantum phase transitions in disordered systems--using ultracold Rubidium-87 atoms trapped in a cubic disordered optical lattice. By tightly focusing a beam into the center of the gas, we create a hole in the atomic density profile. We achieve Mott insulator, superfluid, or Bose glass states by varying the interaction and disorder strength, and measure the time evolution of the density profile after removing the central barrier. This allows us to infer diffusion rates from the velocities at the edge of the hole and to look for signatures of superfluid puddles in the Bose glass state. We acknowledge funding from NSF Grant PHY 15-05468, NSF Grant DGE-1144245, and ARO Grant W911NF-12-1-0462.
Exact solutions of the high dimensional hard-core Fermi-Hubbard model
PAN; Feng
2001-01-01
［1］Hubbard, J., Electron correlations in narrow energy bands, Proc. R. Soc. London, A, 963, 276: 238.［2］Hubbard, J., Electron correlations in narrow energy bands II. The degenerate band case, Proc. R. Soc. London A, 963, A277: 237.［3］Anderson, P. W., The resonating valence bond state in La2CuOand superconductivity, Science, 987, 235: 96.［4］Lieb, E. H, Wu, F. Y., Absence of Mott transition in an exact solution of the short-range one-band model in one dimension, Phys. Rev. Lett., 968, 20: 445.［5］Ogata, M., Shiba, H., Bethe-ansatz wave function, momentum distribution, and spin correlation in the one-dimensional strongly correlated Hubbard model, Phys. Rev., 990, B4: 326.［6］Ogata, M., Sugiyama, T., Shiba, H., Magnetic-field effects on the correlation functions in the one-dimensional strongly correlated Hubbard model, Phys. Rev., 990, B43: 840.［7］Mei, C., Chen, L., Study of the interaction between two electrons in the single band Hubbard model, Z. Phys., 988, B72: 429.［8］Caspers, W. J., Iske, P. L., Exact spectrum for n electrons in the single band Hubbard model, Physica, 989, A, 57: 033.［9］Kirson, M. W., A dynamical supersymmetry in the Hubbard model, Phys. Rev. Lett., 997, 78: 24.［10］Woynarovich, F., Excitations with complex wavefunctions in a Hubbard chain: II. States with several pairs of complex wavenumbers, J. Phys., 982, C5: 97.
Ground state of the three-band Hubbard model
Yanagisawa, Takashi; Koike, Soh; Yamaji, Kunihiko
2001-11-01
The ground state of the two-dimensional three-band Hubbard model in oxide superconductors is investigated by using the variational Monte Carlo method. The Gutzwiller-projected BCS and spin density wave (SDW) functions are employed in the search for a possible ground state with respect to dependences on electron density. Antiferromagnetic correlations are considerably strong near half-filling. It is shown that the d-wave state may exist away from half-filling for both the hole and electron doping cases. The overall structure of the phase diagram obtained by our calculations qualitatively agrees with experimental indications. The superconducting condensation energy is in reasonable agreement with the experimental value obtained from specific heat and critical magnetic field measurements for optimally doped samples. The inhomogeneous SDW state is also examined near 1/8 doping. Incommensurate magnetic structures become stable due to hole doping in the underdoped region, where the transfer tpp between oxygen orbitals plays an important role in determining a stable stripe structure.
Attractive Hubbard model: Homogeneous Ginzburg-Landau expansion and disorder
Kuchinskii, E. Z.; Kuleeva, N. A.; Sadovskii, M. V.
2016-02-01
We derive a Ginzburg-Landau (GL) expansion in the disordered attractive Hubbard model within the combined Nozieres-Schmitt-Rink and DMFT+Σ approximation. Restricting ourselves to the homogeneous expansion, we analyze the disorder dependence of GL expansion coefficients for a wide range of attractive potentials U, from the weak BCS coupling region to the strong-coupling limit, where superconductivity is described by Bose-Einstein condensation (BEC) of preformed Cooper pairs. We show that for the a semielliptic "bare" density of states of the conduction band, the disorder influence on the GL coefficients A and B before quadratic and quartic terms of the order parameter, as well as on the specific heat discontinuity at the superconducting transition, is of a universal nature at any strength of the attractive interaction and is related only to the general widening of the conduction band by disorder. In general, disorder growth increases the values of the coefficients A and B, leading either to a suppression of the specific heat discontinuity (in the weak-coupling limit), or to its significant growth (in the strong-coupling region). However, this behavior actually confirms the validity of the generalized Anderson theorem, because the disorder dependence of the superconducting transition temperature T c, is also controlled only by disorder widening of the conduction band (density of states).
2-D Model Test of Dolosse Breakwater
Burcharth, Hans F.; Liu, Zhou
1994-01-01
The rational design diagram for Dolos armour should incorporate both the hydraulic stability and the structural integrity. The previous tests performed by Aalborg University (AU) made available such design diagram for the trunk of Dolos breakwater without superstructures (Burcharth et al. 1992). To...... extend the design diagram to cover Dolos breakwaters with superstructure, 2-D model tests of Dolos breakwater with wave wall is included in the project Rubble Mound Breakwater Failure Modes sponsored by the Directorate General XII of the Commission of the European Communities under Contract MAS-CT92......-0042. Furthermore, Task IA will give the design diagram for Tetrapod breakwaters without a superstructure. The more complete research results on Dolosse can certainly give some insight into the behaviour of Tetrapods armour layer of the breakwaters with superstructure. The main part of the experiment was on the...
Surface modelling for 2D imagery
Lieng, Henrik
2014-01-01
Vector graphics provides powerful tools for drawing scalable 2D imagery. With the rise of mobile computers, of different types of displays and image resolutions, vector graphics is receiving an increasing amount of attention. However, vector graphics is not the leading framework for creating and manipulating 2D imagery. The reason for this reluctance of employing vector graphical frameworks is that it is difficult to handle complex behaviour of colour across the 2D domain. ...
Attractive Hubbard model with disorder and the generalized Anderson theorem
Using the generalized DMFT+Σ approach, we study the influence of disorder on single-particle properties of the normal phase and the superconducting transition temperature in the attractive Hubbard model. A wide range of attractive potentials U is studied, from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong-coupling region, where the superconducting transition is due to Bose-Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures much higher than the superconducting transition temperature. We study two typical models of the conduction band with semi-elliptic and flat densities of states, respectively appropriate for three-dimensional and two-dimensional systems. For the semi-elliptic density of states, the disorder influence on all single-particle properties (e.g., density of states) is universal for an arbitrary strength of electronic correlations and disorder and is due to only the general disorder widening of the conduction band. In the case of a flat density of states, universality is absent in the general case, but still the disorder influence is mainly due to band widening, and the universal behavior is restored for large enough disorder. Using the combination of DMFT+Σ and Nozieres-Schmitt-Rink approximations, we study the disorder influence on the superconducting transition temperature Tc for a range of characteristic values of U and disorder, including the BCS-BEC crossover region and the limit of strong-coupling. Disorder can either suppress Tc (in the weak-coupling region) or significantly increase Tc (in the strong-coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of the superconducting critical temperature are essentially due to only the general disorder widening of the conduction band
Quantum simulation of the Hubbard model with dopant atoms in silicon
Salfi, J.; Mol, J. A.; Rahman, R.; Klimeck, G.; Simmons, M. Y.; Hollenberg, L. C. L.; Rogge, S.
2016-04-01
In quantum simulation, many-body phenomena are probed in controllable quantum systems. Recently, simulation of Bose-Hubbard Hamiltonians using cold atoms revealed previously hidden local correlations. However, fermionic many-body Hubbard phenomena such as unconventional superconductivity and spin liquids are more difficult to simulate using cold atoms. To date the required single-site measurements and cooling remain problematic, while only ensemble measurements have been achieved. Here we simulate a two-site Hubbard Hamiltonian at low effective temperatures with single-site resolution using subsurface dopants in silicon. We measure quasi-particle tunnelling maps of spin-resolved states with atomic resolution, finding interference processes from which the entanglement entropy and Hubbard interactions are quantified. Entanglement, determined by spin and orbital degrees of freedom, increases with increasing valence bond length. We find separation-tunable Hubbard interaction strengths that are suitable for simulating strongly correlated phenomena in larger arrays of dopants, establishing dopants as a platform for quantum simulation of the Hubbard model.
Modelling one-dimensional insulating materials with the ionic Hubbard model
The single-particle spectral-weight function of the ionic Hubbard model (IHM) at half-filling shows an abrupt change of regime at a critical value of the coupling constant (Hubbard U). Specifically, this function jumps at the Fermi points kF = ± π/2 from a two-peak to a four-peak structure accompanied by a (non-vanishing) minimum of the single-particle charge gap. This jump separates a weak-coupling regime, the band insulating phase, from a strong-coupling regime which evolves gradually into the Mott-Hubbard phase. We take advantage of this critical behaviour to model several quasi-one-dimensional materials in terms of the IHM instead of the simpler one-band Hubbard model. For instance, the two regimes are physically realized in the angle-resolved photoelectron spectra of (TaSe4)2I, and the blue-bronze K0.3MoO3, respectively
Energy of ground state in B-B'-U-Hubbard model in approximation of static fluctuations
Mironov, G I
2002-01-01
To explain some features of CuO sub 2 base high-temperature superconductors (HTSC) one should take account of possibility of electron transfer to the crystalline structure mode next to the nearest one. It terms of approximation of static fluctuations one calculated the energy of ground state in two-dimensional B-B'-U Hubbard model. Lattice is assumed to consist of two sublattices formed by various type atoms. The calculation results of ground state energy are compared with the precise solution for one-dimensional Hubbard model derived previously. Comparison of the precise and the approximated solutions shows that approximation of static fluctuations describes adequately behavior of the Hubbard studied model within both weak and strong correlation ranges
Density-dependent tunneling in the extended Bose–Hubbard model
Recently, it has become apparent that when the interactions between polar molecules in optical lattices become strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two-dimensional extended Bose–Hubbard model. Using quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V , we show that the ground-state phase diagrams differ significantly from those expected from the standard extended Bose–Hubbard model. (paper)
Density-dependent tunneling in the extended Bose-Hubbard model
Maik, Michał; Hauke, Philipp; Dutta, Omjyoti; Lewenstein, Maciej; Zakrzewski, Jakub
2013-11-01
Recently, it has become apparent that when the interactions between polar molecules in optical lattices become strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two-dimensional extended Bose-Hubbard model. Using quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V , we show that the ground-state phase diagrams differ significantly from those expected from the standard extended Bose-Hubbard model.
Density of States for Hubbard and Emery Model from an Interpolated Self Energy
A Green s Function technique interpolating the self energy between second order perturbation theory and the atomic limit is applied to correlated models. In the doped one band Hubbard model the chemical potential passes a Kondo like resonance, in the three band model it passes the maximum of a correlation induced singlet band. (author)
Coe, J P; D' Amico, I [Department of Physics, University of York, York YO10 5DD (United Kingdom); Franca, V V, E-mail: jpc503@york.ac.uk, E-mail: vivian.franca@physik.uni-freiburg.de, E-mail: ida500@york.ac.uk [Physikalisches Institut, Albert-Ludwigs-Universitaet, Hermann-Herder-Strasse 3, D-79104 Freiburg (Germany)
2011-07-06
We consider the position-space information and linear entropies as proxy measures to the average single-site entanglement-quantified using the von Neumann entropy-of the one-dimensional Hubbard model and of a one-dimensional nanostructure system comprised of an array of quantum-dots. Spatial entanglement in the quantum-dot system is also investigated via the three entropies. We appraise the use of the possible proxy measures in the Hubbard model as an approximation to their use for the nanostructure system.
Afchain, St
2005-02-15
The Hubbard model is the simplest model to describe the behaviour of fermions on a network, it takes into account only fermion scattering and only interactions with other fermions located on the same site. Half-filling means that the total number of fermions is equal to half the number of sites. In the first chapter we show how we can pass trough successive approximations from a very general Hamiltonian to the Hubbard Hamiltonian. The second chapter is dedicated to the passage from the Hamiltonian formalism to the Grassmanian functional formalism. The main idea is to show that the correlation functions of the Hamiltonian approach can be described through fermionic functional integrals which implies the possibility of speaking of the model in terms of field theory. The chapter 3 deals with the main constructive techniques that allow the strict and consistent construction of models inside the frame of field theory. We show by proving the violation of a condition concerning self-energy, that the two-dimensional Hubbard model at half-filling has not the behaviour of a Fermi liquid in the Landau's interpretation. (A.C.)
Metal-insulator transition in three-band Hubbard model
We describe a transition from a metal to an antiferromagnetic (AF) insulator in the three-band Hubbard Hamiltonian for the undoped CuO2 planes of high-temperature superconductors, including local hole correlations. If the realistic parameters are used, one finds the AF ground states with magnetic moment of ≅0.47μB and ≅0.56μB for La2CuO4 and YBa2Cu2O6, respectively. Correlations and the interoxygen hopping reduce drastically the region of the AF long-range order which disappears for the doping of 0.06 hole per unit cell. (orig.)
Classical mapping for Hubbard operators: Application to the double-Anderson model
Li, Bin; Miller, William H. [Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Levy, Tal J.; Rabani, Eran [School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978 (Israel)
2014-05-28
A classical Cartesian mapping for Hubbard operators is developed to describe the nonequilibrium transport of an open quantum system with many electrons. The mapping of the Hubbard operators representing the many-body Hamiltonian is derived by using analogies from classical mappings of boson creation and annihilation operators vis-à-vis a coherent state representation. The approach provides qualitative results for a double quantum dot array (double Anderson impurity model) coupled to fermionic leads for a range of bias voltages, Coulomb couplings, and hopping terms. While the width and height of the conduction peaks show deviations from the master equation approach considered to be accurate in the limit of weak system-leads couplings and high temperatures, the Hubbard mapping captures all transport channels involving transition between many electron states, some of which are not captured by approximate nonequilibrium Green function closures.
Phase diagram of the Hubbard model with arbitrary band filling: renormalization group approach
The finite temperature phase diagram of the Hubbard model in d = 2 and d = 3 is calculated for arbitrary values of the parameter U/t and chemical potential μ using a quantum real space renormalization group. Evidence for a ferromagnetic phase at low temperatures is presented. (author). 15 refs., 5 figs
Phase diagram of exciton condensate in doped two-band Hubbard model
Kuneš, Jan
2014-01-01
Roč. 90, č. 23 (2014), "235140-1"-"235140-8". ISSN 1098-0121 R&D Projects: GA ČR GA13-25251S Institutional support: RVO:68378271 Keywords : Hubbard model * spin-state transition * semiconductor-semimetal transition Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.736, year: 2014
Relative and center-of-mass motion in the attractive Bose-Hubbard model
Sørensen, Ole Søe; Gammelmark, Søren; Mølmer, Klaus
2012-01-01
We present first-principles numerical calculations for few-particle solutions of the attractive Bose-Hubbard model with periodic boundary conditions. We show that the low-energy many-body states found by numerical diagonalization can be written as translational superposition states of compact...
Numerical studies of ground-state fidelity of the Bose-Hubbard model
ŁÄ cki, Mateusz; Damski, Bogdan; Zakrzewski, Jakub
2014-03-01
We compute ground-state fidelity of the one-dimensional Bose-Hubbard model at unit filling factor. To this aim, we apply the density matrix renormalization group algorithm to systems with open and periodic boundary conditions. We find that fidelity differs significantly in the two cases and study its scaling properties in the quantum critical regime.
Metal-insulator transition in three-band Hubbard model
Dutka, J.; Kaminski, M. (Inst. of Physics, Jagiellonian Univ., Cracow (Poland)); Oles, A.M. (Inst. of Physics, Jagiellonian Univ., Cracow (Poland) Max-Planck-Inst., FKF, Stuttgart (Germany))
1992-02-01
We describe a transition from a metal to an antiferromagnetic (AF) insulator in the three-band Hubbard Hamiltonian for the undoped CuO{sub 2} planes of high-temperature superconductors, including local hole correlations. If the realistic parameters are used, one finds the AF ground states with magnetic moment of {approx equal}0.47{mu}{sub B} and {approx equal}0.56{mu}{sub B} for La{sub 2}CuO{sub 4} and YBa{sub 2}Cu{sub 2}O{sub 6}, respectively. Correlations and the interoxygen hopping reduce drastically the region of the AF long-range order which disappears for the doping of 0.06 hole per unit cell. (orig.).
Fermion spectrum of Bose-Fermi-Hubbard model in the phase with Bose-Einstein condensate
We investigate the fermion spectrum within the Bose- Fermi-Hubbard model used for the description of boson-fermion mixtures of ultra-cold atoms in optical lattices. We used the method based on the Hubbard operator approach for an on-site basis. The equation for fermion Green's function in the Bose-Fermi-Hubbard model is built; Green's functions of higher orders are decoupled in the Hubbard-I approximation (the case of the strong on-site interaction). The corresponding spectral densities are calculated. In the case of hard-core bosons, the condition of appearance of additional bands in the fermion spectrum is investigated. It is shown that these bands exist only in the state with a Bose- Einstein condensate and appear because of the mixing of states with different numbers of bosons. These additional bands can be interpreted as a manifestation of composite excitations (when the appearance of a fermion on the site is accompanied by the simultaneous creation (or annihilation) of a boson)
Symmetries and solvable models for evaporating 2D black holes
Cruz Muñoz, José Luis; Navarro-Salas, José; Navarro Navarro, Miguel; Talavera, C. F.
1997-01-01
We study the evaporation process of a 2D black hole in thermal equilibrium when the ingoing radiation is suddenly switched off. We also introduce global symmetries of generic 2D dilaton gravity models which generalize the extra symmetry of the CGHS model. © Elsevier Science B.V
Maximizing entropy of image models for 2-D constrained coding
Forchhammer, Søren; Danieli, Matteo; Burini, Nino; Zamarin, Marco; Ukhanova, Ann
2010-01-01
This paper considers estimating and maximizing the entropy of two-dimensional (2-D) fields with application to 2-D constrained coding. We consider Markov random fields (MRF), which have a non-causal description, and the special case of Pickard random fields (PRF). The PRF are 2-D causal finite context models, which define stationary probability distributions on finite rectangles and thus allow for calculation of the entropy. We consider two binary constraints and revisit the hard square const...
Universal Quantum Computation by Scattering in the Fermi-Hubbard Model
Bao, Ning; Salton, Grant; Thomas, Nathaniel
2014-01-01
The Hubbard model may be the simplest model of particles interacting on a lattice, but simulation of its dynamics remains beyond the reach of current numerical methods. In this article, we show that general quantum computations can be encoded into the physics of wave packets propagating through a planar graph, with scattering interactions governed by the fermionic Hubbard model. Therefore, simulating the model on planar graphs is as hard as simulating quantum computation. We give two different arguments, demonstrating that the simulation is difficult both for wave packets prepared as excitations of the fermionic vacuum, and for hole wave packets at filling fraction one-half in the limit of strong coupling. In the latter case, which is described by the t-J model, there is only reflection and no transmission in the scattering events, as would be the case for classical hard spheres. In that sense, the construction provides a quantum mechanical analog of the Fredkin-Toffoli billiard ball computer.
Competing interactions and symmetry breaking in the Hubbard-Holstein model
Bauer, Johannes
2009-01-01
Competing interactions are often responsible for intriguing phase diagrams in correlated electron systems. Here we analyze the competition of instantaneous short range Coulomb interaction $U$ with the retarded electron-electron interaction induced by an electron-phonon coupling $g$ as described by the Hubbard-Holstein model. The ground state phase diagram of this model in the limit of large dimensions at half filling is established. The study is based on dynamical mean field theory combined w...
Orientational bond and N\\'eel order in the two-dimensional ionic Hubbard model
Hafez-Torbati, Mohsen; Uhrig, Götz S.
2015-01-01
Unconventional phases often occur where two competing mechanisms compensate. An excellent example is the ionic Hubbard model where the alternating local potential $\\delta$, favoring a band insulator (BI), competes with the local repulsion $U$, favoring a Mott insulator (MI). By continuous unitary transformations we derive effective models in which we study the softening of various excitons. The softening signals the instability towards new phases that we describe on the mean-field level. On i...
Class of variational singlet wave functions for the Hubbard model away from half filling
We present a class of variational wave functions for strong-coupling Heisenberg Hubbard models. These are written in the form of three factors---a pair of determinants and a Jastrow function---and are made out of orbitals, a la Hartree-Fock theory, which solve a fictitious one-body problem. The wave functions respect various constraints known from general principles and appear to be potentially useful in understanding the possible behavior of the models in quantitative terms
Effective electron-electron and electron-phonon interactions in the Hubbard-Holstein model
Aprea, G; Di Castro, C.; Grilli, M.; Lorenzana, J.
2006-01-01
We investigate the interplay between the electron-electron and the electron-phonon interaction in the Hubbard-Holstein model. We implement the flow-equation method to investigate within this model the effect of correlation on the electron-phonon effective coupling and, conversely, the effect of phonons in the effective electron-electron interaction. Using this technique we obtain analytical momentum-dependent expressions for the effective couplings and we study their behavior for different ph...
Edge superconducting state in attractive U Kane-Mele-Hubbard model
Yuan, J.; Gao, JH; Chen, WQ; Ye, F; Zhou, Y.; Zhang, FC
2012-01-01
We theoretically investigate the phase transition from topological insulator (TI) to superconductor in the attractive U Kane-Mele-Hubbard model with self-consistent mean field method. We demonstrate the existence of edge superconducting state (ESS), in which the bulk is still an insulator and the superconductivity only appears near the edges. The ESS results from the special energy dispersion of TI, and is a general property of the superconductivity in TI. The phase transition in this model e...
Kalman Filter for Generalized 2-D Roesser Models
SHENG Mei; ZOU Yun
2007-01-01
The design problem of the state filter for the generalized stochastic 2-D Roesser models, which appears when both the state and measurement are simultaneously subjected to the interference from white noise, is discussed. The wellknown Kalman filter design is extended to the generalized 2-D Roesser models. Based on the method of "scanning line by line", the filtering problem of generalized 2-D Roesser models with mode-energy reconstruction is solved. The formula of the optimal filtering, which minimizes the variance of the estimation error of the state vectors, is derived. The validity of the designed filter is verified by the calculation steps and the examples are introduced.
Study of the two-dimensional Hubbard model at half-filling through constructive methods
The Hubbard model is the simplest model to describe the behaviour of fermions on a network, it takes into account only fermion scattering and only interactions with other fermions located on the same site. Half-filling means that the total number of fermions is equal to half the number of sites. In the first chapter we show how we can pass trough successive approximations from a very general Hamiltonian to the Hubbard Hamiltonian. The second chapter is dedicated to the passage from the Hamiltonian formalism to the Grassmanian functional formalism. The main idea is to show that the correlation functions of the Hamiltonian approach can be described through fermionic functional integrals which implies the possibility of speaking of the model in terms of field theory. The chapter 3 deals with the main constructive techniques that allow the strict and consistent construction of models inside the frame of field theory. We show by proving the violation of a condition concerning self-energy, that the two-dimensional Hubbard model at half-filling has not the behaviour of a Fermi liquid in the Landau's interpretation. (A.C.)
Silant’ev, A. V., E-mail: kvvant@rambler.ru [Mari State University (Russian Federation)
2015-10-15
Anticommutator Green’s functions and the energy spectrum of C{sub 60} fullerene are calculated in the approximation of static fluctuations within the Hubbard model. On the basis of this spectrum, an interpretation is proposed for the experimentally observed optical absorption bands of C{sub 60} fullerene. The parameters of C{sub 60} fullerene that characterize it within the Hubbard model are calculated by the optical absorption spectrum.
Detecting phase transitions and crossovers in Hubbard models using the fidelity susceptibility
Huang, Li; Wang, Lei; Werner, Philipp
2016-01-01
A generalized version of the fidelity susceptibility of single-band and multi-orbital Hubbard models is systematically studied using single-site dynamical mean-field theory in combination with a hybridization expansion continuous-time quantum Monte Carlo impurity solver. We find that the fidelity susceptibility is extremely sensitive to changes in the state of the system. It can be used as a numerically inexpensive tool to detect and characterize a broad range of phase transitions and crossovers in Hubbard models, including (orbital-selective) Mott metal-insulator transitions, high-spin to low-spin transitions, Fermi-liquid to non-Fermi-liquid crossovers, and spin-freezing crossovers.
Electronic properties of a generalized Hubbard model at half-filling
A generalized Hubbard model with correlated hoppings is studied at half-filling using exact diagonalization methods. For certain values of the hopping parameters our results for several static and dynamic correlation functions suggest the occurrence of a metal-insulator transition (MIT) at a finite value of the local Coulomb interaction UC. We identify the regions of the hopping parameters where the MIT is of the Mott type. In these regions, for large UC, we find a ferromagnetic ground state. (orig.)
Coexistence of Incommensurate Magnetism and Superconductivity in the Two-Dimensional Hubbard Model.
Yamase, Hiroyuki; Eberlein, Andreas; Metzner, Walter
2016-03-01
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. PMID:26991188
Possibility of superconductivity in the repulsive Hubbard model on the Shastry-Sutherland lattice
Kimura, Takashi; Kuroki, Kazuhiko; Arita, Ryotaro; Aoki, Hideo
2003-01-01
Possibility of superconductivity from electron repulsion in the Shastry-Sutherland lattice, which has a spin gap at half filling, is explored with the repulsive Hubbard model in the fluctuation-exchange approximation. We find that, while superconductivity is not favored around the half-filling, superconductivity is favored around the quarter-filling. Our results suggest that the Fermi surface nesting is more important than the spin dimerization for superconductivity.
Coexistence of incommensurate magnetism and superconductivity in the two-dimensional Hubbard model
Yamase, Hiroyuki; Eberlein, Andreas; Metzner, Walter
2015-01-01
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 Neel order coexisting with d-wave superconductivity, the calculations reveal further coexistence regions where super...
Four-point vertex in the Hubbard model and partial bosonization
Friederich, S.; Krahl, H. C.; Wetterich, C.
2010-01-01
Magnetic and superconducting instabilities in the two-dimensional t-t'-Hubbard model are discussed within a functional renormalization group approach. The fermionic four-point vertex is efficiently parametrized by means of partial bosonization. The exchange of composite bosons in the magnetic, charge density and superconducting channels accounts for the increase of the effective couplings with increasing length scale. We compute the pseudocritical temperature for the onset of local order in v...
Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling
Tam, Ka-Ming; Fotso, H.; Yang, S. -X.; Lee, Tae-Woo; Moreno, J.; Ramanujam, J.; Jarrell, M.
2011-01-01
We find that imposing the crossing symmetry in the iteration process considerably extends the range of convergence for solutions of the parquet equations for the Hubbard model. When the crossing symmetry is not imposed, the convergence of both simple iteration and more complicated continuous loading (homotopy) methods are limited to high temperatures and weak interactions. We modify the algorithm to impose the crossing symmetry without increasing the computational complexity. We also imposed ...
Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields
Li, Yuan-Yuan; Cao, Junpeng [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Yang, Wen-Li [Institute of Modern Physics, Northwest University, Xian 710069 (China); Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, 100048 (China); Shi, Kangjie [Institute of Modern Physics, Northwest University, Xian 710069 (China); Wang, Yupeng, E-mail: yupeng@iphy.ac.cn [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China)
2014-02-15
The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method.
The pairing correlations in the phased t-U Hubbard model
Liu Zi-Xin; Liu Ping; Liu Ya; Wen Sheng-Hui
2004-01-01
In this paper we have studied the phased t U Hubbard model. Using the constrained path Monte Carlo method,we investigated the effects of phase factor on pairing correlation functions in the ground state, and we found that the long-range correlations are dependent on the choice of phase factor, and for some special values of phase factor there exist long-range pairing correlations only in the strong coupling region.
Two-polariton bound states in the Jaynes-Cummings-Hubbard model
We examine the eigenstates of the one-dimensional Jaynes-Cummings-Hubbard model in the two-excitation subspace. We discover that two-excitation bound states emerge when the ratio of vacuum Rabi frequency to the tunneling rate between cavities exceeds a critical value. We determine the critical value as a function of the quasimomentum quantum number, and indicate that the bound states carry a strong correlation in which the two polaritons appear to be spatially confined together.
Spin-state transition and phase separation in multi-orbital Hubbard model
Suzuki, Ryo; Watanabe, Tsutomu; Ishihara, Sumio
2009-01-01
We study spin-state transition and phase separation involving this transition based on the milti-orbital Hubbard model. Multiple spin states are realized by changing the energy separation between the two orbitals and the on-site Hund coupling. By utilizing the variational Monte-Carlo simulation, we analyze the electronic and magnetic structures in hole doped and undoped states. Electronic phase separation occurs between the low-spin band insulating state and the high-spin ferromagnetic metall...
Bosonization study of quantum phase transitions in the one-dimensional asymmetric Hubbard model
Wang, Z. G.; Chen, Y G; Gu, S. J.
2007-01-01
The quantum phase transitions in the one-dimensional asymmetric Hubbard model are investigated with the bosonization approach. The conditions for the phase transition from density wave to phase separation, the correlation functions and their exponents are obtained analytically. Our results show that the difference between the hopping integrals for up- and down-spin electrons is crucial for the happening of the phase separation. When the difference is large enough, the phase separation will ap...
Doping evolution of spin and charge excitations in the Hubbard model
Kung, YF; Nowadnick, EA; Jia, CJ; Johnston, S.; B. Moritz; Scalettar, RT; Devereaux, TP
2015-01-01
© 2015 American Physical Society. To shed light on how electronic correlations vary across the phase diagram of the cuprate superconductors, we examine the doping evolution of spin and charge excitations in the single-band Hubbard model using determinant quantum Monte Carlo (DQMC). In the single-particle response, we observe that the effects of correlations weaken rapidly with doping, such that one may expect the random phase approximation (RPA) to provide an adequate description of the two-p...
Anisotropic Hubbard model on a triangular lattice - spin dynamics in HoMnO3
Saptarshi Ghosh; Avinash Singh
2008-01-01
The recent neutron scattering data for spin-wave dispersion in HoMnO3 are well-described by an anisotropic Hubbard model on a triangular lattice with a planar (XY) spin anisotropy. Best fit indicates that magnetic excitations in HoMnO3 correspond to the strong-coupling limit / > ∼ 15, with planar exchange energy = 42/ ≃ 2.5 meV and planar anisotropy ≃ 0.35 meV.
Lacki, M.; Delande, D; Zakrzewski, J.
2011-01-01
Using Fourier transform on a time series generated by unitary evolution, we extract many-body eigenstates of the Bose-Hubbard model corresponding to low energy excitations, which are generated when the insulator-superfluid phase transition is realized in a typical experiment. The analysis is conducted in a symmetric external potential both without and with and disorder. A simple classification of excitations in the absence disorder is provided. The evolution is performed assuming the presence...
On spectral properties of three-electron systems in the Hubbard model
We investigate spectral properties of a three-electron system in the framework of the Hubbard model. We prove that the essential spectrum of the system in a quartet state consists of a single segment and the three-electron bound state is absent. We show that the essential spectrum of the system in doublet states consists of unification of no more then three segments. We also prove that three-electron bound states exist in doublet states. (authors)
Bethe states for the two-site Bose-Hubbard model: a binomial approach
Santos, Gilberto; Foerster, Angela; Roditi, Itzhak
2015-01-01
We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix for the two-site Bose-Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get and solve a recursion equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.
Quantum Bose-Hubbard model with an evolving graph as a toy model for emergent spacetime
We present a toy model for interacting matter and geometry that explores quantum dynamics in a spin system as a precursor to a quantum theory of gravity. The model has no a priori geometric properties; instead, locality is inferred from the more fundamental notion of interaction between the matter degrees of freedom. The interaction terms are themselves quantum degrees of freedom so that the structure of interactions and hence the resulting local and causal structures are dynamical. The system is a Hubbard model where the graph of the interactions is a set of quantum evolving variables. We show entanglement between spatial and matter degrees of freedom. We study numerically the quantum system and analyze its entanglement dynamics. We analyze the asymptotic behavior of the classical model. Finally, we discuss analogues of trapped surfaces and gravitational attraction in this simple model.
SU(2) symmetry in a Hubbard model with spin-orbit coupling
ZHANG XiZheng; JIN Liang; SONG Zhi
2014-01-01
We study the underlying symmetry in a spin-orbit coupled tight-binding model with Hubbard interaction.It is shown that,in the absence of the on-site interaction,the system possesses the SU(2) symmetry arising from the time reversal symmetry.The influence of the on-site interaction on the symmetry depends on the topology of the networks:The SU(2) symmetry is shown to be the spin rotation symmetry of a simply-connected lattice even in the presence of the Hubbard interaction.On the contrary,the on-site interaction breaks the SU(2) symmetry of a multi-connected lattice.This fact indicates that a discrete spin-orbit coupled system has exclusive features from its counterpart in a continuous system.The obtained rigorous result is illustrated by a simple ring system.
Moment approach for the attractive Hubbard model in two dimensions: superconductivity
Full text. Using the moment of Nolting (Z. Phys. 225, 25 (1972) for the attractive Hubbard model in the superconducting phase, we have derived a set of three non-linear equations, the electron density, the superconducting order parameter, and the narrowing factor. Our starting point is the Ansatz that the diagonal spectral density is composed of three peaks while the off-diagonal spectral functional is composed of two. The third band, or upper Hubbard band, strongly renormalizes the other two, making the energy gap K dependent while the order parameter is pure s-wave. Our approach recuperates the BCS limit, weak coupling (U/t <<1) in a natural way. We solve these non-linear equations in a self-consistent way for intermediate coupling for U/t ∼ -4.0. Here we report the order parameter as function of temperature and compare it with the BCS result. (author)
Moskvin, A. S., E-mail: alexander.moskvin@urfu.ru [Ural Federal University (Russian Federation)
2015-09-15
We discuss the most prominent and intensively studied S = 1 pseudospin formalism for the extended bosonic Hubbard model (EBHM) with the on-site Hilbert space truncated to the three lowest occupation states n = 0, 1, 2. The EBHM Hamiltonian is a paradigmatic model for the highly topical field of ultracold gases in optical lattices. The generalized non-Heisenberg effective pseudospin Hamiltonian does provide a deep link with a boson system and a physically clear description of “the myriad of phases,” from uniform Mott insulating phases and density waves to two types of superfluids and supersolids. We argue that the 2D pseudospin system is prone to a topological phase separation and focus on several types of unconventional skyrmion-like topological structures in 2D boson systems, which have not been analyzed until now. The structures are characterized by a complicated interplay of insulating and two superfluid phases with a single- boson and two-boson condensation, respectively.
Ferromagnetism in the Hubbard model on a lattice of three coupled chains
We study the Hubbard model which is reduced to Mielke's flat-band model on the line graph of the two-leg ladder in a special case. In the flat-band case, the model exhibits saturated ferromagnetism when the electron number corresponds to ((1)/(6)) -filling+1. We show that, even in the non-flat-band case, the model with that number of electrons exhibits ferromagnetism when the on-site interaction is large, and that this is true for ((1)/(6)) -filling. We also give numerical evidence that the model with the nearly flat-band exhibits ferromagnetism for less than ((1)/(6)) -filling
Technical Review of the UNET2D Hydraulic Model
Perkins, William A. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Richmond, Marshall C. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2009-05-18
The Kansas City District of the US Army Corps of Engineers is engaged in a broad range of river management projects that require knowledge of spatially-varied hydraulic conditions such as velocities and water surface elevations. This information is needed to design new structures, improve existing operations, and assess aquatic habitat. Two-dimensional (2D) depth-averaged numerical hydraulic models are a common tool that can be used to provide velocity and depth information. Kansas City District is currently using a specific 2D model, UNET2D, that has been developed to meet the needs of their river engineering applications. This report documents a tech- nical review of UNET2D.
QSAR Models for P-450 (2D6) Substrate Activity
Ringsted, Tine; Nikolov, Nikolai Georgiev; Jensen, Gunde Egeskov;
2009-01-01
activity relationship (QSAR) modelling systems. They cross validated (leave-groups-out) with concordances of 71%, 81% and 82%, respectively. Discrete organic European Inventory of Existing Commercial Chemical Substances (EINECS) chemicals were screened to predict an approximate percentage of CYP 2D6...... substrates. These chemicals are potentially present in the environment. The biological importance of the CYP 2D6 and the use of the software mentioned above were discussed....
Numerical studies of superconductivity in the two-dimensional Hubbard model
The question of superconductivity in the two-dimensional Hubbard model is reviewed. Emphasis is placed on the large-U limit of the single-band model and the relevance of this model to high-temperature superconductivity is discussed. Variational Monte Carlo work has shown that a nominally superconducting Gutzwiller or RVB state has essentially the same energy as the antiferromagnetic state for the half-filled (spin only) case. This state becomes a true d-wave superconductor for the less-than-half-filled (doped) case. This is an interference effect in which the phasing of the Cooper pairs acts to enhance antiferromagnetic spin correlations
Stability of ferromagnetism in Hubbard models with degenerate single-particle ground states
A Hubbard model with a Nd-fold degenerate single-particle ground state has ferromagnetic ground states if the number of electrons is less than or equal to Nd. It is shown rigorously that the local stability of ferromagnetism in such a model implies global stability: the model has only ferromagnetic ground states, if there are no single spin-flip ground states. If the number of electrons is equal to Nd , it is well known that the ferromagnetic ground state is unique if and only if the single-particle density matrix is irreducible. We present a simplified proof for this result. (author)
Numerical investigation of the 3D Hubbard model on a Linux cluster
We investigate numerically the magnetic properties of the 3D Isotropic and Anisotropic Hubbard model at half-filling on a Linux cluster. The behavior of the transition temperature as a function of the anisotropic hopping parameter is qualitatively described. In the Isotropic model we measure the scaling properties of the susceptibility finding agreement with the magnetic critical exponents of the 3D Heisenberg model. We describe several particularities concerning the implementation of our simulation in a cluster of personal computers paying special attention to the issues related with the parallelization of the algorithm
Local moment approach as a quantum impurity solver for the Hubbard model
Barman, Himadri
2016-07-01
The local moment approach (LMA) has presented itself as a powerful semianalytical quantum impurity solver (QIS) in the context of the dynamical mean-field theory (DMFT) for the periodic Anderson model and it correctly captures the low-energy Kondo scale for the single impurity model, having excellent agreement with the Bethe ansatz and numerical renormalization group (NRG) results. However, the most common correlated lattice model, the Hubbard model, has not been explored well within the LMA+DMFT framework beyond the insulating phase. Here in our work, within the framework we complete the filling-interaction phase diagram of the single band Hubbard model at zero temperature. Our formalism is generic to any particle filling and can be extended to finite temperature. We contrast our results with another QIS, namely the iterated perturbation theory (IPT) and show that the second spectral moment sum rule improves better as the Hubbard interaction strength grows stronger in LMA, whereas it severely breaks down after the Mott transition in IPT. For the metallic case, the Fermi liquid (FL) scaling agreement with the NRG spectral density supports the fact that the FL scale emerges from the inherent Kondo physics of the impurity model. We also show that, in the metallic phase, the FL scaling of the spectral density leads to universality which extends to infinite frequency range at infinite correlation strength (strong coupling). At large interaction strength, the off half-filling spectral density forms a pseudogap near the Fermi level and filling-controlled Mott transition occurs as one approaches the half-filling. As a response property, we finally study the zero temperature optical conductivity and find universal features such as absorption peak position governed by the FL scale and a doping independent crossing point, often dubbed the isosbestic point in experiments.
A VARIATIONAL MODEL FOR 2-D MICROPOLAR BLOOD FLOW
He Ji-huan
2003-01-01
The micropolar fluid model is an essential generalization of the well-established Navier-Stokes model in the sense that it takes into account the microstructure of the fluid.This paper is devolted to establishing a variational principle for 2-D incompressible micropolar blood flow.
Spin and charge dynamics in a one-dimensional two-band Hubbard model
A CuO chain with one or two holes doped is studied via the two-band Hubbard model in the large-U limit on a finite cluster. The quasiparticle band is Ek∼0.87J cos(2ka) with the bottom at ka=π/2. The quasiparticles are kinks which have the character of three-spin polarons. The copper spin excitations are incommensurate spin waves. The two doped holes repel each other very slightly, in contrast to the slight attraction in the t-J model. Spin-charge separation also occurs
Quantum phases of the Bose-Hubbard model in optical superlattices
We analyze the quantum phases of multicomponent Bose-Hubbard models in optical superlattices based on a mean-field method, that is, the decoupling approximation. The global phase diagrams exhibit complex patterns with various charge-density-wave orders for both one- and two-component cases. We further calculate the effective spin excitations for the two-component case in the strong-coupling region at unit filling, and show the existence of a spin-density-wave order. The results of our study can be tested straightforwardly with current cold-atom experimental techniques.
Superfluid-Mott-insulator transition in the spin-orbit-coupled Bose-Hubbard model
Işkın, Menderes; Bölükbaşı, Ahmet Tuna
2014-01-01
PHYSICAL REVIEW A 89, 043603 (2014) Superfluid–Mott-insulator transition in the spin-orbit-coupled Bose-Hubbard model A. T. Bolukbasi and M. Iskin Department of Physics, Koc¸ University, Rumelifeneri Yolu, 34450 Sariyer, Istanbul, Turkey (Received 3 January 2014; published 4 April 2014) We consider a square optical lattice in two dimensions and study the effects of both the strength and symmetry of spin-orbit coupling and Zeeman field on the ground-state, i.e.,Mott-insulator...
SDW antiferromagnetic phase in the two-dimensional Hubbard model: Eliashberg approach
Szczes' niak, R. [Institute of Physics, Czestochowa University of Technology, Al. Armii Krajowej 19, 42-200 Czestochowa (Poland)], E-mail: szczesni@mim.pcz.czest.pl
2009-01-19
The two-dimensional Hubbard model was used for the description of the spin density wave (SDW) antiferromagnetic phase. The calculations were conducted in the framework of the Eliashberg formalism. The SDW phase that characterizes with the order parameter of the s-, extended s- or d-wave symmetry has been considered. The Eliashberg equations for the half-filled electron band have been constructed, with a use of which, it has been shown that only the SDW phase of the s-wave symmetry induces in the system. Next, the dependence of the s-wave SDW transition temperature on the value of the on-site Coulomb repulsion parameter was determined.
Eliashberg equations with momentum-dependent kernals for the two-dimensional Hubbard model
Mierzejewski, M.; Zielinski, J.; Entel, P. [Gerhard-Mercator-Univeitat, Duisburg (Germany)
1996-02-01
The authors discuss the impact of the strong electron phonon interactions on the physical properties of correlated electrons in the two-dimensional Hubbard model. An easy access to the physical properties of the superconducting state is obtained by solving the Eliashberg equations with explicit momentum-dependent kernels. In order to facilitate the numerical procedure to solve these equations, correlations are treated within the Gutzwiller approximation (i.e., mean-field-slave boson approximation). The authors results strongly support the view that d-wave symmetry is the most important feature of the superconducting state in the copper oxides. A possible extension beyond the mean field approximation is also presented.
The Mott metal-insulator transition in half-filled two-dimensional Hubbard models
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.
Metal-Insulator Transition in the Hubbard Model: Correlations and Spiral Magnetic Structures
Timirgazin, Marat A.; Igoshev, Petr A.; Arzhnikov, Anatoly K.; Irkhin, Valentin Yu.
2016-03-01
The metal-insulator transition (MIT) for the square, simple cubic, and body-centered cubic lattices is investigated within the t-t^' Hubbard model at half-filling by using both the generalized for the case of spiral order Hartree-Fock approximation (HFA) and Kotliar-Ruckenstein slave-boson approach. It turns out that the magnetic scenario of MIT becomes superior over the non-magnetic one. The electron correlations lead to some suppression of the spiral phases in comparison with HFA. We found the presence of a metallic antiferromagnetic (spiral) phase in the case of three-dimensional lattices.
Pressure dependence of a charge-transfer gap and a three-band Hubbard model
The three-band Hubbard Hamiltonian with an attractive oxygen-oxygen interaction Upp is investigated using the Hartree-Fock approximation. Such a Hamiltonian is assumed to be a generic model for CuO2 planes of high-Tc superconductors. Both superconducting and antiferromagnetic phases are found in the separate regions of the numerically obtained (Upp,δ) phase diagrams, where δ is the hole doping. It is found that the region of stability of the superconducting phase is enhanced with decreasing values of the charge-transfer gap, in good qualitative agreement with the experimental findings
Supersolid and solitonic phases in the one-dimensional extended Bose-Hubbard model
We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.
Mishra, A. K.; Kishore, R.
2016-08-01
We have obtained the exact expressions for the thermoelectric power and the Lorenz number for the infinite U Hubbard model using orthofermion approach. It is found that in one dimension, our results coincide with that of known exact results. In limiting cases, our exact expressions reduce to the known exact results at low and high temperature limits. We present our calculations for one and two dimensions for square as well as triangular lattices. A comparison between the thermoelectric power and Lorenz number for a free Fermi gas and noninteracting orthofermions has also been provided.
DEVELOPMENT OF 2D HUMAN BODY MODELING USING THINNING ALGORITHM
K. Srinivasan
2010-11-01
Full Text Available Monitoring the behavior and activities of people in Video surveillance has gained more applications in Computer vision. This paper proposes a new approach to model the human body in 2D view for the activity analysis using Thinning algorithm. The first step of this work is Background subtraction which is achieved by the frame differencing algorithm. Thinning algorithm has been used to find the skeleton of the human body. After thinning, the thirteen feature points like terminating points, intersecting points, shoulder, elbow, and knee points have been extracted. Here, this research work attempts to represent the body model in three different ways such as Stick figure model, Patch model and Rectangle body model. The activities of humans have been analyzed with the help of 2D model for the pre-defined poses from the monocular video data. Finally, the time consumption and efficiency of our proposed algorithm have been evaluated.
Lattice simulation of 2d Gross-Neveu-type models
Full text: We discuss a Monte Carlo simulation of 2d Gross-Neveu-type models on the lattice. The four-Fermi interaction is written as a Gaussian integral with an auxiliary field and the fermion determinant is included by reweighting. We present results for bulk quantities and correlators and compare them to a simulation using a fermion-loop representation. (author)
For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters
The cell representation of the three-band Hubbard model
Moskalenko, V A; Marinaro, M; Digor, D F; Grecu, D
2002-01-01
The d-p model is reformulated in the representation of the Wannier orthogonalized copper and oxygen orbitals. The exact account of the holes hybridization on the oxygen ions is accomplished in this work in contrast to the other ones. Two diagonalized fermion cells of the oxygen holes mode are used for this purpose alongside with the copper holes mode. These diagonalized modes are characterized by essentially different local energies, that noticeably affects the theory results. The noncommutation of the oxygen Hamiltonian diagonalization operation and the Wannier orbitals orthogonalization by the copper lattice nodes is noted. The cell orbital of the oxygen holes, related to the CuO sub 4 ion complex, proves to be the superposition of these two diagonalized orbitals on our approach. The obtained Hamiltonian constitutes the components sum, the members whereof have the different number of the copper lattice nodes indices. The local component is the high set one. All main states of the cluster representation are ...
Spectral function of the ionic Hubbard model (IHM)
Bulut, Sinan; Atkinson, Bill
2010-03-01
Using two-pole approximations, which are based on the equation of motion method, we calculate the excitation spectrum of the one dimensional IHM. To be specific, we use the composite operator method and the Roth-approximation. Though very simple in nature, these approximations capture the physics of the IHM qualitatively at least. As is predicted by several other numerical and/or theoretical studies, a bond-order (BO) phase is given by these approximate methods. In the BO phase, atoms in the system are dimerized leading to a gap in the excitation spectrum. We find that the BO phase flattens both low and high-energy bands. When the BO phase is suppressed, however, the system can be driven from the band-insulating phase to the metal one by electron-electron repulsions, which is somewhat counter-intuitive. Additionally, two-pole approximations generate a reasonably good DOS spectrum of this model when compared with exact numerical results for small systems.
2D Models for Dust-driven AGB Star Winds
Woitke, P
2006-01-01
New axisymmetric (2D) models for dust-driven winds of C-stars are presented which include hydrodynamics with radiation pressure on dust, equilibrium chemistry and time-dependent dust formation with coupled grey Monte Carlo radiative transfer. Considering the most simple case without stellar pulsation (hydrostatic inner boundary condition) these models reveal a more complex picture of the dust formation and wind acceleration as compared to earlier published spherically symmetric (1D) models. The so-called exterior $\\kappa$-mechanism causes radial oscillations with short phases of active dust formation between longer phases without appreciable dust formation, just like in the 1D models. However, in 2D geometry, the oscillations can be out-of-phase at different places above the stellar atmosphere which result in the formation of dust arcs or smaller caps that only occupy a certain fraction of the total solid angle. These dust structures are accelerated outward by radiation pressure, expanding radially and tangen...
Mott-insulator-to-superfluid transition in the Bose-Hubbard model: A strong-coupling approach
We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory
Johnson, T H; Yuan, Y; Bao, W; Clark, S R; Foot, C; Jaksch, D
2016-06-17
We investigate cold bosonic impurity atoms trapped in a vortex lattice formed by condensed bosons of another species. We describe the dynamics of the impurities by a bosonic Hubbard model containing occupation-dependent parameters to capture the effects of strong impurity-impurity interactions. These include both a repulsive direct interaction and an attractive effective interaction mediated by the Bose-Einstein condensate. The occupation dependence of these two competing interactions drastically affects the Hubbard model phase diagram, including causing the disappearance of some Mott lobes. PMID:27367366
Johnson, T. H.; Yuan, Y.; Bao, W.; Clark, S. R.; Foot, C.; Jaksch, D.
2016-06-01
We investigate cold bosonic impurity atoms trapped in a vortex lattice formed by condensed bosons of another species. We describe the dynamics of the impurities by a bosonic Hubbard model containing occupation-dependent parameters to capture the effects of strong impurity-impurity interactions. These include both a repulsive direct interaction and an attractive effective interaction mediated by the Bose-Einstein condensate. The occupation dependence of these two competing interactions drastically affects the Hubbard model phase diagram, including causing the disappearance of some Mott lobes.
Can the Hubbard model explain the steps observed in the magnetization curve of {Ni4Mo12}?
The low-temperature magnetization curve of the magnetic molecule {Ni4Mo12} features four nonequidistant steps which cannot be explained using a Heisenberg model. In his article, V. Kostyuchenko presents a spin-1 model with biquadratic and three-spin interactions and claims that it is the strong coupling limit of a certain Hubbard model. This spin-1 model correctly predicts the position of the steps in the magnetization curve. We investigate whether the Hubbard model proposed in is really capable of describing {Ni4Mo12}. To this end, we calculate its eigenvalues using numerical exact diagonalization and try to fit its parameters to the experimental magnetization data. We are unable to find suitable fit parameters although the parameter space of the model is only two-dimensional. Therefore, we analyze the strong coupling limit of the Hubbard model and rederive its effective spin model up to order O(U-3). The spin Hamiltonian which we obtain differs from the one presented by Kostyuchenko. We arrive at the final conclusion that the Hubbard model as proposed in is not suited to describe the molecule {Ni4Mo12}.
Mazumdar, S.; Clay, R. T.
2008-01-01
We demonstrate a robust frustration-driven charge-order to superconductivity transition in the half-filled negative-U extended Hubbard model. Superconductivity extends over a broad region of the parameter space. We argue that the model provides the correct insight to understanding unconventional superconductivity in the organic charge-transfer solids and other quarter-filled systems.
Modeling 2D and 3D Horizontal Wells Using CVFA
Chen, Zhangxin; Huan, Guanren; Li, Baoyan
2003-01-01
In this paper we present an application of the recently developed control volume function approximation (CVFA) method to the modeling and simulation of 2D and 3D horizontal wells in petroleum reservoirs. The base grid for this method is based on a Voronoi grid. One of the features of the CVFA is that the flux at the interfaces of control volumes can be accurately computed via function approximations. Also, it reduces grid orientation effects and applies to any shape of eleme...
Long-range orders and spin/orbital freezing in the two-band Hubbard model
Steiner, Karim; Hoshino, Shintaro; Nomura, Yusuke; Werner, Philipp
2016-08-01
We solve the orbitally degenerate two-band Hubbard model within dynamical mean field theory and map out the instabilities to various symmetry-broken phases based on an analysis of the corresponding lattice susceptibilities. Phase diagrams as a function of the Hund coupling parameter J are obtained both for the model with rotationally invariant interaction and for the model with Ising-type anisotropy. For negative J , an intraorbital spin-singlet superconducting phase appears at low temperatures, while the normal state properties are characterized by an orbital-freezing phenomenon. This is the negative-J analog of the recently discovered fluctuating-moment induced s -wave spin-triplet superconductivity in the spin-freezing regime of multiorbital models with J >0 .
A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model
Mark Kelbert
2013-01-01
Full Text Available This paper is the second in a series of papers considering symmetry properties of bosonic quantum systems over 2D graphs, with continuous spins, in the spirit of the Mermin-Wagner theorem. In the model considered here the phase space of a single spin is ℋ1=L2(M, where M is a d-dimensional unit torus M=ℝd/ℤd with a flat metric. The phase space of k spins is ℋk=L2sym(Mk, the subspace of L2(Mk formed by functions symmetric under the permutations of the arguments. The Fock space H=⊕k=0,1,…ℋk yields the phase space of a system of a varying (but finite number of particles. We associate a space H≃H(i with each vertex i∈Γ of a graph (Γ,ℰ satisfying a special bidimensionality property. (Physically, vertex i represents a heavy “atom” or “ion” that does not move but attracts a number of “light” particles. The kinetic energy part of the Hamiltonian includes (i -Δ/2, the minus a half of the Laplace operator on M, responsible for the motion of a particle while “trapped” by a given atom, and (ii an integral term describing possible “jumps” where a particle may join another atom. The potential part is an operator of multiplication by a function (the potential energy of a classical configuration which is a sum of (a one-body potentials U(1(x, x∈M, describing a field generated by a heavy atom, (b two-body potentials U(2(x,y, x,y∈M, showing the interaction between pairs of particles belonging to the same atom, and (c two-body potentials V(x,y, x,y∈M, scaled along the graph distance d(i,j between vertices i,j∈Γ, which gives the interaction between particles belonging to different atoms. The system under consideration can be considered as a generalized (bosonic Hubbard model. We assume that a connected Lie group G acts on M, represented by a Euclidean space or torus of dimension d'≤d, preserving the metric and the volume in M. Furthermore, we suppose that the potentials U(1, U(2, and V are G-invariant. The result
Quantum disordered insulating phase in the frustrated cubic-lattice Hubbard model
Laubach, Manuel; Joshi, Darshan G.; Reuther, Johannes; Thomale, Ronny; Vojta, Matthias; Rachel, Stephan
2016-01-01
In the quest for quantum spin liquids in three spatial dimensions (3D), we study the half-filled Hubbard model on the simple cubic lattice with hopping processes up to third neighbors. Employing the variational cluster approach (VCA), we determine the zero-temperature phase diagram: In addition to a paramagnetic metal at small interaction strength U and various antiferromagnetic insulators at large U , we find an intermediate-U antiferromagnetic metal. Most interestingly, we also identify a nonmagnetic insulating region, extending from intermediate to strong U . Using VCA results in the large-U limit, we establish the phase diagram of the corresponding J1-J2-J3 Heisenberg model. This is qualitatively confirmed—including the nonmagnetic region—using spin-wave theory. Further analysis reveals a striking similarity to the behavior of the J1-J2 square-lattice Heisenberg model, suggesting that the nonmagnetic region may host a 3D spin-liquid phase.
Exactly solvable models for 2D interacting fermions
I discuss many-body models for correlated fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: two-dimensional (2D) fermions in a constant magnetic field and a particular non-local four-point interaction. It is exactly solvable due to a dynamical symmetry corresponding to the Lie algebra gl∞ + gl∞. There is an algorithm to construct all energy eigenvalues and eigenfunctions of this model. The latter are, in general, many-body states with spatial correlations. The model also has a non-trivial zero temperature phase diagram. I point out that this QH model can be obtained from a more realistic one using a truncation procedure generalizing a similar one leading to mean field theory. Applying this truncation procedure to other 2D fermion models I obtain various simplified models of increasing complexity which generalize mean field theory by taking into account non-trivial correlations but nevertheless are treatable by exact methods
Magnetic properties of Hubbard-sigma model with three-dimensionality
It has been broadly accepted that the magnetism may play an important role in the high-Tc superconductivity in the lamellar CuO2 materials. In this paper, based on a Hubbard-inspired CP1 or S2 nonlinear σ model, we give a quantitative study of some magnetic properties in and around the Neel ordered state of three-dimensional quantum antiferromagnets such as La2CuO4 with and without small hole doping. Our model is a (3+1) dimensional effective field theory describing the low energy spin dynamics of a three-dimensional Hubbard model with a very weak interlayer coupling. The effect of hole dynamics is taken into account in the leading approximation by substituting the CP1 coupling and the spin-wave velocity with 'effective' ones determined by the concentration and the one-loop correction of hole fermions. Stationary-phase equations for the one-loop effective potential of S2 model are analyzed. Based on them, various magnetic properties of the system, such as the behavior of Neel temperature, spin correlation length, staggered magnetization, specific heat and susceptibility as functions of anisotropic parameter, temperature, etc. are investigated in detail. The results show that our anisotropic field theory model with certain values of parameters gives a good description of the magnetic properties in both the ordered and the disordered phases indicated by experiments on La2CuO4. The part of the above results is supported by the renormalization-group analysis. In the doped case it is observed that the existence of holes destroys the long-range order and their hopping effect is large. (author)
Orientational bond and Néel order in the two-dimensional ionic Hubbard model
Hafez-Torbati, Mohsen; Uhrig, Götz S.
2016-05-01
Unconventional phases often occur where two competing mechanisms compensate. An excellent example is the ionic Hubbard model where the alternating local potential δ , favoring a band insulator (BI), competes with the local repulsion U , favoring a Mott insulator (MI). By continuous unitary transformations we derive effective models in which we study the softening of various excitons. The softening signals the instability towards new phases that we describe on the mean-field level. On increasing U from the BI in two dimensions, we find a bond-ordered phase breaking orientational symmetry due to a d -wave component. Then, antiferromagnetic order appears coexisting with the d -wave bond order. Finally, the d -wave order vanishes and a Néel-type MI persists.
A Simple Hubbard Model for the Excited States of $\\pi$ Conjugated -acene Molecules
Sadeq, Z S
2015-01-01
In this paper we present a model that elucidates in a simple way the electronic excited states of $\\pi$ conjugated -acene molecules such as tetracene, pentacene, and hexacene. We use a tight-binding and truncated Hubbard model written in the electron-hole basis to describe the low lying excitations with reasonable quantitative accuracy. We are able to produce semi-analytic wavefunctions for the electronic states of the system, which allows us to compute the density correlation functions for various states such as the ground state, the first two singly excited states, and the lowest lying doubly excited state. We show that in this lowest lying doubly excited state, a state which has been speculated as to being involved in the singlet fission process, the electrons and holes behave in a triplet like manner.
Quantum phase transition of light in the Rabi–Hubbard model
We discuss the physics of the Rabi–Hubbard model describing large arrays of coupled cavities interacting with two level atoms via a Rabi nonlinearity. We show that the inclusion of counter-rotating terms in the light–matter interaction, often neglected in theoretical descriptions based on Jaynes–Cumming models, is crucial to stabilize finite-density quantum phases of correlated photons with no need for an artificially engineered chemical potential. We show that the physical properties of these phases and the quantum phase transition occurring between them is remarkably different from those of interacting bosonic massive quantum particles. The competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z2 parity symmetry-breaking quantum phase transition between two gapped phases, a Rabi insulator and a delocalized super-radiant phase. (paper)
Thermodynamics of the Hubbard model on stacked honeycomb and square lattices
Imriška, Jakub; Gull, Emanuel; Troyer, Matthias
2016-07-01
We present a numerical study of the Hubbard model on simply stacked honeycomb and square lattices, motivated by a recent experimental realization of such models with ultracold atoms in optical lattices. We perform simulations with different interlayer coupling and interaction strengths and obtain Néel transition temperatures and entropies. We provide data for the equation of state to enable comparisons of experiments and theory. We find an enhancement of the short-range correlations in the anisotropic lattices compared to the isotropic cubic lattice, in parameter regimes suitable for the interaction driven adiabatic cooling. Supplementary material in the form of one zip file available from the Jounal web page at http://dx.doi.org/10.1140/epjb/e2016-70146-y
Bilayer Hubbard model for 3He: a cluster dynamical mean-field calculation
Inspired by recent experiments on bilayer 3He, we consider a bilayer Hubbard model on a triangular lattice. For appropriate model parameters, we observe a band-selective Mott transition at a critical chemical potential, μc, corresponding to the solidification of the fermions in the first layer. The growth of the effective mass on the metallic side (μ c) is cut off by a first order transition in which the first layer fermions drop out of the Luttinger volume and their spin degrees of freedom become locked in a spin singlet state. These results are obtained from a cluster dynamical mean-field calculation on an eight-site cluster with a quantum Monte Carlo cluster solver.
Panas, J.; Kauch, Anna; Kuneš, Jan; Vollhardt, D.; Byczuk, K.
2015-01-01
Roč. 92, č. 4 (2015), "045102-1"-"045102-9". ISSN 1098-0121 Institutional support: RVO:68378271 Keywords : Bose-Hubbard model * Bose-Einstein condensation * superfluidity Subject RIV: BE - Theoretical Physics Impact factor: 3.736, year: 2014
Zakrzewski, Jakub; Delande, Dominique
2007-01-01
The quantum phase transition point between the insulator and the superfluid phase at unit filling factor of the infinite one-dimensional Bose-Hubbard model is numerically computed with a high accuracy, better than current state of the art calculations. The method uses the infinite system version of the time evolving block decimation algorithm, here tested in a challenging case.
Magnetic phase diagram of the Hubbard model with next-nearest-neighbour hopping
We calculate the magnetic phase diagram of the Hubbard model for a Bethe lattice with nearest-neighbour (NN) hopping t1 and next-nearest-neighbour (NNN) hopping t2 in the limit of infinite coordination. We use the amplitude t2/t1 of the NNN hopping to tune the density of states (DOS) of the non-interacting system from a situation with particle-hole symmetry to an asymmetric one with van-Hove singularities at the lower (t2/t1>0) respectively upper (t2/t12/t1|. For this strongly asymmetric situation, we find rather extended parameter regions with ferromagnetic states and regions with antiferromagnetic states.
Algebraic geometry methods associated to the one-dimensional Hubbard model
Martins, M. J.
2016-06-01
In this paper we study the covering vertex model of the one-dimensional Hubbard Hamiltonian constructed by Shastry in the realm of algebraic geometry. We show that the Lax operator sits in a genus one curve which is not isomorphic but only isogenous to the curve suitable for the AdS/CFT context. We provide an uniformization of the Lax operator in terms of ratios of theta functions allowing us to establish relativistic like properties such as crossing and unitarity. We show that the respective R-matrix weights lie on an Abelian surface being birational to the product of two elliptic curves with distinct J-invariants. One of the curves is isomorphic to that of the Lax operator but the other is solely fourfold isogenous. These results clarify the reason the R-matrix can not be written using only difference of spectral parameters of the Lax operator.
Gutzwiller wave function for finite systems: superconductivity in the Hubbard model.
Tomski, Andrzej; Kaczmarczyk, Jan
2016-05-01
We study the superconducting phase of the Hubbard model using the Gutzwiller variational wave function (GWF) and the recently proposed diagrammatic expansion technique (DE-GWF). The DE-GWF method works on the level of the full GWF and in the thermodynamic limit. Here, we consider a finite-size system to study the accuracy of the results as a function of the system size (which is practically unrestricted). We show that the finite-size scaling used, e.g. in the variational Monte Carlo method can lead to significant, uncontrolled errors. The presented research is the first step towards applying the DE-GWF method in studies of inhomogeneous situations, including systems with impurities, defects, inhomogeneous phases, or disorder. PMID:27023047
Quantum Monte Carlo simulations of the one-dimensional extended Hubbard model
We report preliminary results of an investigation of the thermodynamic properties of the extended Hubbard model in one- dimension, calculated with the world-line Monte Carlo method described by Hirsch et al. With strictly continuous world-lines, we are able to measure the expectation of operators that conserve fermion number locally, such as the energy and (spatial) occupation number. By permitting the world-lines to be ''broken'' stochastically, we may also measure the expectation of operators that conserve fermion number only globally, such as the single-particle Green's function. For a 32 site lattice we present preliminary calculations of the average electron occupancy as a function of wavenumber when U = 4, V = 0 and β = 16. For a half-filled band we find no indications of a Fermi surface. Slightly away from half-filling, we find Fermi-surface-like behavior similar to that found in other numerical investigations. 8 refs., 3 figs
Studies on entanglement entropy for Hubbard model with hole-doping and external magnetic field
By using the density matrix renormalization group (DMRG) method for the one-dimensional (1D) Hubbard model, we have studied the von Neumann entropy of a quantum system, which describes the entanglement of the system block and the rest of the chain. It is found that there is a close relation between the entanglement entropy and properties of the system. The hole-doping can alter the charge-charge and spin-spin interactions, resulting in charge polarization along the chain. By comparing the results before and after the doping, we find that doping favors increase of the von Neumann entropy and thus also favors the exchange of information along the chain. Furthermore, we calculated the spin and entropy distribution in external magnetic filed. It is confirmed that both the charge-charge and the spin-spin interactions affect the exchange of information along the chain, making the entanglement entropy redistribute
Critical points of the Bose–Hubbard model with three-body local interaction
Avila, C.A.; Franco, R. [Departamento de Física, Universidad Nacional de Colombia, A.A. 5997, Bogotá (Colombia); Souza, A.M.C. [Departamento de Física, Universidade Federal de Sergipe, 49100-000 São Cristovão, SE (Brazil); Figueira, M.S. [Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/n, 24210-346 Niterói, Rio de Janeiro (Brazil); Silva-Valencia, J., E-mail: jsilvav@unal.edu.co [Departamento de Física, Universidad Nacional de Colombia, A.A. 5997, Bogotá (Colombia)
2014-09-12
Using the density matrix renormalization group method, we study a one-dimensional system of bosons that interact with a local three-body term. We calculate the phase diagram for higher densities, where the Mott insulator lobes are surrounded by the superfluid phase. We also show that the Mott insulator lobes always grow as a function of the density. The critical points of the Kosterlitz–Thouless transitions were determined through the von Neumann block entropy, and its dependence on the density is given by a power law with a negative exponent. - Highlights: • We studied the Bose–Hubbard model with a local three-body interaction term. • We show that the Mott insulator lobes always grow as a function of the density. • We found a power law dependence of the critical point position with the density.
Critical points of the Bose–Hubbard model with three-body local interaction
Using the density matrix renormalization group method, we study a one-dimensional system of bosons that interact with a local three-body term. We calculate the phase diagram for higher densities, where the Mott insulator lobes are surrounded by the superfluid phase. We also show that the Mott insulator lobes always grow as a function of the density. The critical points of the Kosterlitz–Thouless transitions were determined through the von Neumann block entropy, and its dependence on the density is given by a power law with a negative exponent. - Highlights: • We studied the Bose–Hubbard model with a local three-body interaction term. • We show that the Mott insulator lobes always grow as a function of the density. • We found a power law dependence of the critical point position with the density
Effect of interactions, disorder and magnetic field in the Hubbard model in two dimensions
N Trivedi; P J H Denteneer; D Heidarian; R T Scaletar
2005-06-01
The effects of both interactions and Zeeman magnetic field in disordered electronic systems are explored in the Hubbard model on a square lattice. We investigate the thermodynamic (density, magnetization, density of states) and transport (conductivity) properties using determinantal quantum Monte Carlo and inhomogeneous Hartree Fock techniques. We find that at half filling there is a novel metallic phase at intermediate disorder that is sandwiched between a Mott insulator and an Anderson insulator. The metallic phase is highly inhomogeneous and coexists with antiferromagnetic long-range order. At quarter filling also the combined effects of disorder and interactions produce a conducting state which can be destroyed by applying a Zeeman field, resulting in a magnetic field-driven transition. We discuss the implication of our results for experiments.
Gutzwiller wave function for finite systems: superconductivity in the Hubbard model
Tomski, Andrzej; Kaczmarczyk, Jan
2016-05-01
We study the superconducting phase of the Hubbard model using the Gutzwiller variational wave function (GWF) and the recently proposed diagrammatic expansion technique (DE-GWF). The DE-GWF method works on the level of the full GWF and in the thermodynamic limit. Here, we consider a finite-size system to study the accuracy of the results as a function of the system size (which is practically unrestricted). We show that the finite-size scaling used, e.g. in the variational Monte Carlo method can lead to significant, uncontrolled errors. The presented research is the first step towards applying the DE-GWF method in studies of inhomogeneous situations, including systems with impurities, defects, inhomogeneous phases, or disorder.
2D numerical modelling of meandering channel formation
Y Xiao; G Zhou; F S Yang
2016-03-01
A 2D depth-averaged model for hydrodynamic sediment transport and river morphological adjustment was established. The sediment transport submodel takes into account the influence of non-uniform sediment with bed surface armoring and considers the impact of secondary flow in the direction of bed-loadtransport and transverse slope of the river bed. The bank erosion submodel incorporates a simple simulation method for updating bank geometry during either degradational or aggradational bed evolution. Comparison of the results obtained by the extended model with experimental and field data, and numericalpredictions validate that the proposed model can simulate grain sorting in river bends and duplicate the characteristics of meandering river and its development. The results illustrate that by using its control factors, the improved numerical model can be applied to simulate channel evolution under differentscenarios and improve understanding of patterning processes.
2D numerical modelling of meandering channel formation
XIAO, Y.; ZHOU, G.; YANG, F. S.
2016-03-01
A 2D depth-averaged model for hydrodynamic sediment transport and river morphological adjustment was established. The sediment transport submodel takes into account the influence of non-uniform sediment with bed surface armoring and considers the impact of secondary flow in the direction of bed-load transport and transverse slope of the river bed. The bank erosion submodel incorporates a simple simulation method for updating bank geometry during either degradational or aggradational bed evolution. Comparison of the results obtained by the extended model with experimental and field data, and numerical predictions validate that the proposed model can simulate grain sorting in river bends and duplicate the characteristics of meandering river and its development. The results illustrate that by using its control factors, the improved numerical model can be applied to simulate channel evolution under different scenarios and improve understanding of patterning processes.
Brane Brick Models and 2d (0,2) Triality
Franco, Sebastian; Seong, Rak-Kyeong
2016-01-01
We provide a brane realization of 2d (0,2) Gadde-Gukov-Putrov triality in terms of brane brick models. These are Type IIA brane configurations that are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. Triality translates into a local transformation of brane brick models, whose simplest representative is a cube move. We present explicit examples and construct their triality networks. We also argue that the classical mesonic moduli space of brane brick model theories, which corresponds to the probed Calabi-Yau 4-fold, is invariant under triality. Finally, we discuss triality in terms of phase boundaries, which play a central role in connecting Calabi-Yau 4-folds to brane brick models.
2-D Composite Model for Numerical Simulations of Nonlinear Waves
2000-01-01
－ A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational region Ω is divided into two subregions. In the near-field around a structure, Ω2, the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulence closure model of k-ε equations and numerically solved by the improved VOF method; whereas in the subregion Ω1 (Ω1 = Ω - Ω2) the flow is governed by one-D Boussinesq equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundary of the two subregions. Numerical tests have been conducted for the case of wave propagation and interaction with a wave barrier. It is shown that the composite model can help perform efficient computation of nonlinear waves in a large region with the complicated flow fields near structures taken into account.
Statistical mechanics of shell models for 2D-Turbulence
Aurell, E; Crisanti, A; Frick, P; Paladin, G; Vulpiani, A
1994-01-01
We study shell models that conserve the analogues of energy and enstrophy, hence designed to mimic fluid turbulence in 2D. The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous to the approach to two-dimensional ideal hydrodynamics of Onsager, Hopf and Lee. In the presence of forcing and dissipation we observe a forward flux of enstrophy and a backward flux of energy. These fluxes can be understood as mean diffusive drifts from a source to two sinks in a system which is close to local equilibrium with Lagrange multipliers (``shell temperatures'') changing slowly with scale. The dimensional predictions on the power spectra from a supposed forward cascade of enstrophy, and from one branch of the formal statistical equilibrium, coincide in these shell models at difference to the corresponding predictions for the Navier-Stokes and Euler equations in 2D. This coincidence have previously led to the mistaken conclusion that shell models exhibit a forward ...
Finite state models of constrained 2d data
Justesen, Jørn
2004-01-01
This paper considers a class of discrete finite alphabet 2D fields that can be characterized using tools front finite state machines and Markov chains. These fields have several properties that greatly simplify the analysis of 2D coding methods.......This paper considers a class of discrete finite alphabet 2D fields that can be characterized using tools front finite state machines and Markov chains. These fields have several properties that greatly simplify the analysis of 2D coding methods....
A 2D channel-clogging biofilm model.
Winstanley, H F; Chapwanya, M; Fowler, A C; O'Brien, S B G
2015-09-01
We present a model of biofilm growth in a long channel where the biomass is assumed to have the rheology of a viscous polymer solution. We examine the competition between growth and erosion-like surface detachment due to the flow. A particular focus of our investigation is the effect of the biofilm growth on the fluid flow in the pores, and the issue of whether biomass can grow sufficiently to shut off fluid flow through the pores, thus clogging the pore space. Net biofilm growth is coupled along the pore length via flow rate and nutrient transport in the pore flow. Our 2D model extends existing results on stability of 1D steady state biofilm thicknesses to show that, in the case of flows driven by a fixed pressure drop, full clogging of the pore can indeed happen in certain cases dependent on the functional form of the detachment term. PMID:25240390
On the particle-hole symmetry of the fermionic spinless Hubbard model in D=1
M.T. Thomaz
2014-06-01
Full Text Available We revisit the particle-hole symmetry of the one-dimensional (D=1 fermionic spinless Hubbard model, associating that symmetry to the invariance of the Helmholtz free energy of the one-dimensional spin-1/2 XXZ Heisenberg model, under reversal of the longitudinal magnetic field and at any finite temperature. Upon comparing two regimes of that chain model so that the number of particles in one regime equals the number of holes in the other, one finds that, in general, their thermodynamics is similar, but not identical: both models share the specific heat and entropy functions, but not the internal energy per site, the first-neighbor correlation functions, and the number of particles per site. Due to that symmetry, the difference between the first-neighbor correlation functions is proportional to the z-component of magnetization of the XXZ Heisenberg model. The results presented in this paper are valid for any value of the interaction strength parameter V, which describes the attractive/null/repulsive interaction of neighboring fermions.
Maximizing entropy of image models for 2-D constrained coding
Forchhammer, Søren; Danieli, Matteo; Burini, Nino;
2010-01-01
This paper considers estimating and maximizing the entropy of two-dimensional (2-D) fields with application to 2-D constrained coding. We consider Markov random fields (MRF), which have a non-causal description, and the special case of Pickard random fields (PRF). The PRF are 2-D causal finite...... of the Markov random field defined by the 2-D constraint is estimated to be (upper bounded by) 0.8570 bits/symbol using the iterative technique of Belief Propagation on 2 £ 2 finite lattices. Based on combinatorial bounding techniques the maximum entropy for the constraint was determined to be 0.848....
Cascading rainfall uncertainties into 2D inundation impact models
Souvignet, Maxime; de Almeida, Gustavo; Champion, Adrian; Garcia Pintado, Javier; Neal, Jeff; Freer, Jim; Cloke, Hannah; Odoni, Nick; Coxon, Gemma; Bates, Paul; Mason, David
2013-04-01
Existing precipitation products show differences in their spatial and temporal distribution and several studies have presented how these differences influence the ability to predict hydrological responses. However, an atmospheric-hydrologic-hydraulic uncertainty cascade is seldom explored and how, importantly, input uncertainties propagate through this cascade is still poorly understood. Such a project requires a combination of modelling capabilities, runoff generation predictions based on those rainfall forecasts, and hydraulic flood wave propagation based on the runoff predictions. Accounting for uncertainty in each component is important in decision making for issuing flood warnings, monitoring or planning. We suggest a better understanding of uncertainties in inundation impact modelling must consider these differences in rainfall products. This will improve our understanding of the input uncertainties on our predictive capability. In this paper, we propose to address this issue by i) exploring the effects of errors in rainfall on inundation predictive capacity within an uncertainty framework, i.e. testing inundation uncertainty against different comparable meteorological conditions (i.e. using different rainfall products). Our method cascades rainfall uncertainties into a lumped hydrologic model (FUSE) within the GLUE uncertainty framework. The resultant prediction uncertainties in discharge provide uncertain boundary conditions, which are cascaded into a simplified shallow water 2D hydraulic model (LISFLOOD-FP). Rainfall data captured by three different measurement techniques - rain gauges, gridded data and numerical weather predictions (NWP) models are used to assess the combined input data and model parameter uncertainty. The study is performed in the Severn catchment over the period between June and July 2007, where a series of rainfall events causing record floods in the study area). Changes in flood area extent are compared and the uncertainty envelope is
Multiplons in the two-hole excitation spectra of the one-dimensional Hubbard model
Rausch, Roman; Potthoff, Michael
2016-02-01
Using the density-matrix renormalization group in combination with the Chebyshev polynomial expansion technique, we study the two-hole excitation spectrum of the one-dimensional Hubbard model in the entire filling range from the completely occupied band (n = 2) down to half-filling (n = 1). For strong interactions, the spectra reveal multiplon physics, i.e., relevant final states are characterized by two (doublon), three (triplon), four (quadruplon) and more holes, potentially forming stable compound objects or resonances with finite lifetime. These give rise to several satellites in the spectra with largely different spectral weights as well as to different two-hole, doublon-hole, two-doublon etc continua. The complex multiplon phenomenology is analyzed by interpreting not only local and k-resolved two-hole spectra but also three- and four-hole spectra for the Hubbard model and by referring to effective low-energy models. In addition, a filter-operator technique is presented and applied which allows to extract specific information on the final states at a given excitation energy. While multiplons composed of an odd number of holes do neither form stable compounds nor well-defined resonances unless a nearest-neighbor density interaction V is added to the Hamiltonian, the doublon and the quadruplon are well-defined resonances. The k-resolved four-hole spectrum at n = 2 represents an interesting special case where a completely stable quadruplon turns into a resonance by merging with the doublon-doublon continuum at a critical wave vector. For all fillings with n\\gt 1, the doublon lifetime is strongly k-dependent and is even infinite at the Brillouin zone edges as demonstrated by k-resolved two-hole spectra. This can be traced back to the ‘hidden’ charge-SU(2) symmetry of the model which is explicitly broken off half-filling and gives rise to a massive collective excitation, even for arbitrary higher-dimensional but bipartite lattices.
Duality Between Spin Networks and the 2D Ising Model
Bonzom, Valentin; Costantino, Francesco; Livine, Etera R.
2016-06-01
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.
Effects of Agent's Repulsion in 2d Flocking Models
Moussa, Najem; Tarras, Iliass; Mazroui, M'hammed; Boughaleb, Yahya
In nature many animal groups, such as fish schools or bird flocks, clearly display structural order and appear to move as a single coherent entity. In order to understand the complex behavior of these systems, many models have been proposed and tested so far. This paper deals with an extension of the Vicsek model, by including a second zone of repulsion, where each agent attempts to maintain a minimum distance from the others. The consideration of this zone in our study seems to play an important role during the travel of agents in the two-dimensional (2D) flocking models. Our numerical investigations show that depending on the basic ingredients such as repulsion radius (R1), effect of density of agents (ρ) and noise (η), our nonequilibrium system can undergo a kinetic phase transition from no transport to finite net transport. For different values of ρ, kinetic phase diagrams in the plane (η ,R1) are found. Implications of these findings are discussed.
Magnetic and pair correlations of the Hubbard model with next-nearest-neighbor hopping
A combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping t'=-0.35t as a model for high-temperature superconductors. Magnetic properties are analyzed using the two-particle self-consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite t' and at t'=0 but for two totally different physical reasons. When t'=0, it is induced by antiferromagnetic correlations while at t'=-0.35t it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with T-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the d-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed
Mott-insulator phase of the one-dimensional Bose-Hubbard model: A high-order perturbative study
The one-dimensional Bose-Hubbard model at a unit filling factor is studied by means of a very high-order symbolic perturbative expansion. Analytical expressions are derived for the ground-state quantities such as energy per site, variance of on-site occupation, and correlation functions: j†aj+r> and jnj+r>. These findings are compared to numerics and good agreement is found in the Mott insulator phase. Our results provide analytical approximations to important observables in the Mott phase, and are also of direct relevance to future experiments with ultracold atomic gases placed in optical lattices. We also discuss the symmetry of the Bose-Hubbard model associated with the sign change of the tunneling coupling
Kumar, Manoranjan; Soos, Zolt'an G.
2011-01-01
The bond order wave (BOW) phase of the extended Hubbard model (EHM) in one dimension (1D) is characterized at intermediate correlation $U = 4t$ by exact treatment of $N$-site systems. Linear coupling to lattice (Peierls) phonons and molecular (Holstein) vibrations are treated in the adiabatic approximation. The molar magnetic susceptibility $\\chi_M(T)$ is obtained directly up to $N = 10$. The goal is to find the consequences of a doubly degenerate ground state (gs) and finite magnetic gap $E_...
Properties of the one-dimensional Bose-Hubbard model from a high-order perturbative expansion
Damski, Bogdan; Zakrzewski, Jakub
2015-01-01
We employ a high-order perturbative expansion to characterize the ground state of the Mott phase of the one-dimensional Bose-Hubbard model. We compute for different integer filling factors the energy per lattice site, the two-point and density-density correlations, and expectation values of powers of the on-site number operator determining the local atom number fluctuations (variance, skewness, kurtosis). We compare these expansions to numerical simulations of the infinite-size system to dete...
The Mott insulator phase of the one dimensional Bose-Hubbard model: a high order perturbative study
Damski, Bogdan; Zakrzewski, Jakub
2006-01-01
The one dimensional Bose-Hubbard model at a unit filling factor is studied by means of a very high order symbolic perturbative expansion. Analytical expressions are derived for the ground state quantities such as energy per site, variance of on-site occupation, and different correlation functions. These findings are compared to numerics and good agreement is found in the Mott insulator phase. Our results provide analytical approximations to important observables in the Mott phase, and are als...
Ab initio modeling of 2D layered organohalide lead perovskites
Fraccarollo, Alberto; Cantatore, Valentina; Boschetto, Gabriele; Marchese, Leonardo; Cossi, Maurizio
2016-04-01
A number of 2D layered perovskites A2PbI4 and BPbI4, with A and B mono- and divalent ammonium and imidazolium cations, have been modeled with different theoretical methods. The periodic structures have been optimized (both in monoclinic and in triclinic systems, corresponding to eclipsed and staggered arrangements of the inorganic layers) at the DFT level, with hybrid functionals, Gaussian-type orbitals and dispersion energy corrections. With the same methods, the various contributions to the solid stabilization energy have been discussed, separating electrostatic and dispersion energies, organic-organic intralayer interactions and H-bonding effects, when applicable. Then the electronic band gaps have been computed with plane waves, at the DFT level with scalar and full relativistic potentials, and including the correlation energy through the GW approximation. Spin orbit coupling and GW effects have been combined in an additive scheme, validated by comparing the computed gap with well known experimental and theoretical results for a model system. Finally, various contributions to the computed band gaps have been discussed on some of the studied systems, by varying some geometrical parameters and by substituting one cation in another's place.
Slow dynamics in a two-dimensional Anderson-Hubbard model
Bar Lev, Yevgeny; Reichman, David R.
2016-02-01
We study the real-time dynamics of a two-dimensional Anderson-Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small clusters, we demonstrate that for strong disorder this technique approaches the exact result on all available timescales, while for intermediate disorder, in the vicinity of the many-body localization transition, it produces quantitatively accurate results up to nontrivial times. Our method allows for the treatment of system sizes inaccessible by any numerically exact method and for the complete elimination of finite-size effects for the times considered. We show that for a sufficiently strong disorder the system becomes nonergodic, while for intermediate disorder strengths and for all accessible timescales transport in the system is strictly subdiffusive. We argue that these results are incompatible with a simple percolation picture, but are consistent with the heuristic random resistor network model where subdiffusion may be observed for long times until a crossover to diffusion occurs. The prediction of slow finite-time dynamics in a two-dimensional interacting and disordered system can be directly verified in future cold-atoms experiments.
Phonon-like excitations in the two-state Bose-Hubbard model
I.V. Stasyuk
2015-12-01
Full Text Available The spectrum of phonon-like collective excitations in the system of Bose-atoms in optical lattice (more generally, in the system of quantum particles described by the Bose-Hubbard model is investigated. Such excitations appear due to displacements of particles with respect to their local equilibrium positions. The two-level model taking into account the transitions of bosons between the ground state and the first excited state in potential wells, as well as interaction between them, is used. Calculations are performed within the random phase approximation in the hard-core boson limit. It is shown that excitation spectrum in normal phase consists of the one exciton-like band, while in the phase with BE condensate an additional band appears. The positions, spectral weights and widths of bands strongly depend on chemical potential of bosons and temperature. The conditions of stability of a system with respect to the lowering of symmetry and displacement modulation are discussed.
The method of evaluating quantum partition function for the Hubbard model
The method of evaluation of quantum partition function (QPF) in some four fermion models is proposed. The calculations are carried out by the path integral method. The integral is evaluated by introducing the additional fields (called Hubbard-Stratanovich transformation in some models), integration over fermionic variables, and considering the finite-dimensional approximation of rest integral over bosonic fields in the infinite limit. The result can be represented as a sum of the functional derivatives with respect to the arbitrary bosonic field of the quantum partition of free fermionic theory in the external bosonic field. This expression can be treated in a mean field approximation in closed form (the determinants corresponding to the arbitrary external field are substituted by its mean values corresponding to the mean value of the external fields). The quantum partition function is represented as the integral representation of the function. The approximation for the QPF of the free theory is considered, and the corresponding answer for QPF is studied. A convenient perturbation expansion for ln Z is developed. (author). 6 refs, 1 fig
Solving the parquet equations for the Hubbard model beyond weak coupling.
Tam, Ka-Ming; Fotso, H; Yang, S-X; Lee, Tae-Woo; Moreno, J; Ramanujam, J; Jarrell, M
2013-01-01
We find that imposing crossing symmetry in the iteration process considerably extends the range of convergence for solutions of the parquet equations for the Hubbard model. When crossing symmetry is not imposed, the convergence of both simple iteration and more complicated continuous loading (homotopy) methods is limited to high temperatures and weak interactions. We modify the algorithm to impose the crossing symmetry without increasing the computational complexity. We also imposed time reversal and a subset of the point group symmetries, but they did not further improve the convergence. We elaborate the details of the latency hiding scheme which can significantly improve the performance in the computational implementation. With these modifications, stable solutions for the parquet equations can be obtained by iteration more quickly even for values of the interaction that are a significant fraction of the bandwidth and for temperatures that are much smaller than the bandwidth. This may represent a crucial step towards the solution of two-particle field theories for correlated electron models. PMID:23410464
Study of the multi-orbital Hubbard model at finite temperature
Mukherjee, Anamitra; Dong, Shuai; Alvarez, Gonzalo; Dagotto, Elbio
2014-03-01
Research in pnictide superconductors have clearly established the need for the study of multi-orbital Hubbard models. With this motivation, here we apply a combination of the real-space Exact Diagonalization and Classical Monte Carlo (ED+MC) method, widely used in manganites, with the standard Hartree-Fock mean field (MF) theory to investigate the properties of multiorbital models as a function of temperature. In this approach the MF parameters are treated via a classical MC and the fermions moving in the MF background are solved by exact diagonalization. The temperature dependence of the dynamical spin susceptibility S(q --> , ω) , orbital resolved single particle spectral function A(k --> , ω) , optical conductivity, and real space charge/spin/orbital density maps are calculated at different dopings. These results are relevant in understanding the role of the multiple degrees of freedom in governing the magnetic and transport properties of the Fe based superconductor materials. Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA.
Robust Supersolidity in the V1- V2 Extended Bose-Hubbard Model
Greene, Nicole; Pixley, Jedediah
2016-05-01
Motivated by ultra-cold atomic gases with long-range interactions in an optical lattice we study the effects of the next-nearest neighbor interaction on the extended Bose-Hubbard model on a square lattice. Using the variational Gutzwiller approach with a four-site unit cell we determine the ground state phase diagrams as a function of the model parameters. We focus on the interplay of each interaction between the nearest neighbor (V1) , the next-nearest neighbor (V2) , and the onsite repulsion (U). We find various super-solid phases that can be described by one of the ordering wave-vectors (π, 0), (0, π) , and (π, π) . In the limits V1, V2 U we find phases reminiscent of the limit V2 = 0 but with a richer super solid structure. For V1 qualitatively new super solid phase that is quite stable and occupies a large region of the phase diagram. For sufficiently strong interactions we find various Mott and charge density wave (CDW) insulating phases that can be understood in the classical limit (i.e. no inter-site tunneling). We characterize the nature of each quantum phase transition between Mott/CDW to super-solid to superfluid at the mean field level.
Topological order in 1D super-lattice Bose-Hubbard models
Fleischhauer, Michael; Grusdt, Fabian; Hoening, Michael
2013-05-01
After the discovery of topological insulators as a new state of matter and their consequent classification for free fermions, the question arises what kind of topological order can be supported by incompressible systems of interacting bosons. We consider a 1D super-lattice Hamiltonian with a non-trivial band structure (the Su-Schrieffer-Heeger model) and show that its Mott-insulating (MI) states can be classified by a quantized many-body winding number. This quantization is protected by sub-lattice and time-reversal symmetries, and it allows the implementation of a quantized cyclic pumping process (Thouless pump) in a simple super-lattice Bose-Hubbard model (BHM). For extended BHMs we discuss a connection of such a pump with the fractional quantum Hall effect. Furthermore we show that the quantization of the winding number leads to localized, protected edge states at sharp interfaces between topologically distinct MI phases which can be experimentally realized using Bose-Fermi mixtures in optical superlattices. DMRG simulations show that these edge states manifest themself either in localized density maxima or localized density minima, which can easily be detected. Supported by research center OPTIMAS and graduate school MAINZ.
Frésard, Raymond; Steffen, Kevin; Kopp, Thilo
2016-03-01
Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility–ultimately signalling charge instability and phase separation–and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-boson representation of Kotliar and Ruckenstein. The quasiparticle density of states, the renormalised effective mass and the Landau parameter F s 0 are presented, whereby the positivity of F s 0 – 1 constitutes a criterion for stability. Van Hove singularities in the density of states support possible charge instabilities. A (negative) next-nearest neighbour hopping parameter t' shifts their positions and produces a tendency towards charge instability even for low filling whereas the t'-controlled particle-hole asymmetry of the correlation driven effective mass is small. A region of instability on account of the attractive interaction V is identified, either at half filling in the absence of strong electronic correlations or, in the case of large on-site interaction U, at densities far from half filling.
Robust Supersolidity in the V1- V2 Extended Bose-Hubbard Model
Greene, Nicole; Pixley, Jedediah
2016-05-01
Motivated by ultra-cold atomic gases with long-range interactions in an optical lattice we study the effects of the next-nearest neighbor interaction on the extended Bose-Hubbard model on a square lattice. Using the variational Gutzwiller approach with a four-site unit cell we determine the ground state phase diagrams as a function of the model parameters. We focus on the interplay of each interaction between the nearest neighbor (V1) , the next-nearest neighbor (V2) , and the onsite repulsion (U). We find various super-solid phases that can be described by one of the ordering wave-vectors (π, 0), (0, π) , and (π, π) . In the limits V1, V2 U we find phases reminiscent of the limit V2 = 0 but with a richer super solid structure. For V1
VAM2D: Variably saturated analysis model in two dimensions
This report documents a two-dimensional finite element model, VAM2D, developed to simulate water flow and solute transport in variably saturated porous media. Both flow and transport simulation can be handled concurrently or sequentially. The formulation of the governing equations and the numerical procedures used in the code are presented. The flow equation is approximated using the Galerkin finite element method. Nonlinear soil moisture characteristics and atmospheric boundary conditions (e.g., infiltration, evaporation and seepage face), are treated using Picard and Newton-Raphson iterations. Hysteresis effects and anisotropy in the unsaturated hydraulic conductivity can be taken into account if needed. The contaminant transport simulation can account for advection, hydrodynamic dispersion, linear equilibrium sorption, and first-order degradation. Transport of a single component or a multi-component decay chain can be handled. The transport equation is approximated using an upstream weighted residual method. Several test problems are presented to verify the code and demonstrate its utility. These problems range from simple one-dimensional to complex two-dimensional and axisymmetric problems. This document has been produced as a user's manual. It contains detailed information on the code structure along with instructions for input data preparation and sample input and printed output for selected test problems. Also included are instructions for job set up and restarting procedures. 44 refs., 54 figs., 24 tabs
Superconducting fluctuations in the normal state of the two-dimensional Hubbard model.
Chen, Xi; LeBlanc, J P F; Gull, Emanuel
2015-09-11
We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the d_{x^{2}-y^{2}} superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half filling. We find a change in sign of the vertex contributions to d_{xy} superconductivity from repulsive near half filling to attractive at large doping. p-wave superconductivity is not found at the parameters we study, and s-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shifts towards the electron-doped side in opposition to the van Hove singularity, which moves towards hole doping. We surmise that an increase of the local interaction of the electron-doped compounds would increase T_{c}. PMID:26406843
Orbital nematic order and interplay with magnetism in the two-orbital Hubbard model
Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) on FeSe and iron pnictide families of iron-based superconductors, we have studied the orbital nematic order and its interplay with antiferromagnetism within the two-orbital Hubbard model. We used random phase approximation (RPA) to calculate the dependence of the orbital and magnetic susceptibilities on the strength of interactions and electron density (doping). To account for strong electron correlations not captured by RPA, we further employed non-perturbative variational cluster approximation (VCA) capable of capturing symmetry broken magnetic and orbitally ordered phases. Both approaches show that the electron and hole doping affect the two orders differently. While hole doping tends to suppress both magnetism and orbital ordering, the electron doping suppresses magnetism faster. Crucially, we find a realistic parameter regime for moderate electron doping that stabilizes orbital nematicity in the absence of long-range antiferromagnetic order. This is reminiscent of the non-magnetic orbital nematic phase observed recently in FeSe and a number of iron pnictide materials and raises the possibility that at least in some cases, the observed electronic nematicity may be primarily due to orbital rather than magnetic fluctuations. (paper)
Monte Carlo simulations of two-dimensional Hubbard models with string bond tensor-network states
Song, Jeong-Pil; Wee, Daehyun; Clay, R. T.
2015-03-01
We study charge- and spin-ordered states in the two-dimensional extended Hubbard model on a triangular lattice at 1/3 filling. While the nearest-neighbor Coulomb repulsion V induces charge-ordered states, the competition between on-site U and nearest-neighbor V interactions lead to quantum phase transitions to an antiferromagnetic spin-ordered phase with honeycomb charge order. In order to avoid the fermion sign problem and handle frustrations here we use quantum Monte Carlo methods with the string-bond tensor network ansatz for fermionic systems in two dimensions. We determine the phase boundaries of the several spin- and charge-ordered states and show a phase diagram in the on-site U and the nearest-neighbor V plane. The numerical accuracy of the method is compared with exact diagonalization results in terms of the size of matrices D. We also test the use of lattice symmetries to improve the string-bond ansatz. Work at Mississippi State University was supported by the US Department of Energy grant DE-FG02-06ER46315.
Two-state Bose-Hubbard model in the hard-core boson limit
O.V. Velychk
2011-03-01
Full Text Available Phase transition into the phase with Bose-Einstein (BE condensate in the two-band Bose-Hubbard model with the particle hopping in the excited band only is investigated. Instability connected with such a transition (which appears at excitation energies δ0|, where |t'0| is the particle hopping parameter is considered. The re-entrant behaviour of spinodales is revealed in the hard-core boson limit in the region of positive values of chemical potential. It is found that the order of the phase transition undergoes a change in this case and becomes the first one; the re-entrant transition into the normal phase does not take place in reality. First order phase transitions also exist at negative values of δ (under the condition δ>δcrit≈ − 0.12|t'0|. At μ0|, μ phase diagrams are built and localizations of tricritical points are established. The conditions are found at which the separation on the normal phase and the phase with the BE condensate takes place.
Sato, Ryo; Yokoyama, Hisatoshi
2016-07-01
Band renormalization effects (BRE) are comprehensively studied for a mixed state of dx2 - y2-wave superconducting (d-SC) and antiferromagnetic (AF) orders, in addition to simple d-SC, AF, and normal (paramagnetic) states, by applying a variational Monte Carlo method to a two-dimensional Hubbard (t-t'-U) model. In a weakly correlated regime (U/t ≲ 6), BRE are negligible on all the states studied. As previously shown, the effective band of d-SC is greatly renormalized but the modifications of physical quantities, including energy improvement, are negligible. In contrast, BRE on the AF state considerably affects various features of the system. Because the energy is markedly improved for t'/t t'{L} [t' t'{L}, because the existence of Fermi surfaces near (π ,0) is a requisite for the electron scattering of {q} = (π ,π ). Actually, the coexistent state appears mainly for t'{L}/t < t'/t ≲ 0.2 in the mixed state. Nevertheless, the AF and coexisting states become unstable toward phase separation for - 0.05 ≲ t'/t ≲ 0.2 but become stable at other values of t'/t owing to the energy reduction by the diagonal hopping of doped holes. We show that this instability does not directly correlate with the strength of d-SC.
Antiferromagnetism in three-band Hubbard model: Local-ansatz approach
The ground state of the three-band Hubbard Hamiltonian for CuO2 planes of high-Tc superconductors is investigated. Correlations between holes are included by a local-ansatz approach which starts from the Hartree-Fock approximation and emphasizes the local character of hole correlations. It is found that the hole distribution within CuO2 planes and the region of stability of an antiferromagnetic (AF) ground state are significantly modified by hole correlations. At the filling of one hole per CuO2 unit, and for realistic parameters, the ground state exhibits an AF long-range order. Taking into account the effect of quantum fluctuations, the magnetic moment amounts to 0.47μB which agrees very well with the experimental value for La2CuO4. The order parameter decreases with doping and disappears for the doping of 0.06 hole per unit cell. It is found that the nearest-neighbor oxygen hopping destabilizes AF ground state which proves the importance of this parameter for quantitative analysis. A favorable comparison between the present results and those obtained within variational Monte Carlo, as well as within the Gutzwiller approximation for a similar model, is presented
Antiferromagnetism in three-band Hubbard model: Local-ansatz approach
Dutka, J.; Oles, A.M. (Institute of Physics, Jagellonian University, Reymonta 4, PL-30-059 Krakow, Poland (PL))
1991-03-01
The ground state of the three-band Hubbard Hamiltonian for CuO{sub 2} planes of high-{ital T}{sub {ital c}} superconductors is investigated. Correlations between holes are included by a local-ansatz approach which starts from the Hartree-Fock approximation and emphasizes the local character of hole correlations. It is found that the hole distribution within CuO{sub 2} planes and the region of stability of an antiferromagnetic (AF) ground state are significantly modified by hole correlations. At the filling of one hole per CuO{sub 2} unit, and for realistic parameters, the ground state exhibits an AF long-range order. Taking into account the effect of quantum fluctuations, the magnetic moment amounts to 0.47{mu}{sub {ital B}} which agrees very well with the experimental value for La{sub 2}CuO{sub 4}. The order parameter decreases with doping and disappears for the doping of 0.06 hole per unit cell. It is found that the nearest-neighbor oxygen hopping destabilizes AF ground state which proves the importance of this parameter for quantitative analysis. A favorable comparison between the present results and those obtained within variational Monte Carlo, as well as within the Gutzwiller approximation for a similar model, is presented.
Application of a multisite mean-field theory to the disordered Bose-Hubbard model
We present a multisite formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with intercluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multisite formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott-insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose-glass-to-superfluid transition, one an approximation based on the behavior of the condensate fraction, and one that relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non-self-averaging is discussed.
Quantum Monte Carlo simulation study of two-dimensional Hubbard model
The physical properties of strongly correlated fermionic systems, described by two-dimensional Hubbard model with nearest neighbour hopping have been studied using the path integral formulation along with quantum Monte Carlo simulation technique. The partition function of the fermionic system is evaluated within the usual path integral formulation, treating β, the inverse temperature as imaginary time and dividing it into small discrete intervals. The singlet and triplet pairing correlation functions, nearest-neighbour charge density correlations, local squared magnetic moments, double occupancy and total energy are studied as a function of interaction strength for various band fillings at different temperatures. This study leads to the conclusions that the singlet pairing correlation decreases with increasing interaction strength. The triplet pairing correlations for parallel spins show abrupt behaviour. The extended singlet pairing correlation and triplet pairing correlations for anti-parallel spins show the slightly fluctuating behaviour of finite temperatures. The enhancement of local squared magnetic moment and decrement of double occupancy and increment of total energy with U at finite temperatures for half-filled, one-third-filled and one-fourth-filled bands are also noted. (author)
Importance of Overpressure in 2D Gas Hydrate Modeling
Hauschildt, J.; Unnithan, V.
2005-12-01
Numerical models for sub-seafloor gas hydrate formation [1],[2],[3] which describe the driving fluid transport processes only in the vertical direction, restrict the computationally expensive problem to one dimension. This assumption is only valid in regions where permeable sediments induce no overpressure and where there is little lateral variation of physical properties and boundary conditions. Local accumulations of gas hydrates or authigenic carbonates can significantly reduce the porosity and permeability. In combination with topographic and structural features, subtle but important deviations from the 1D model are considered to occur. This poster shows results obtained from a 2D finite difference model developed for describing the evolution of the gas hydrate zone in structurally complex areas. The discretisation of the terms governing the thermodynamic and transport processes is implemented explicitely in time for the advection and diffusion processes, but implicitely for phase transitions. Although the time scales for transport and phase transitions can differ by several orders of magnitude, this scheme allows for an efficient computation for model runs both over the system's equilibration period in the order of 107 yr or to resolve the effects of sea-level changes within 103 yr. A sensitivity analysis confines the parameter space relevant for hydrate formation influenced by lateral fluid flow, and results for the predicted deviations from a multi-1D model for high gas hydrate fractions and fluid flow rates are presented. References [1] M.K. Davie and B.A. Buffett. Sources of methane for marine gas hydrate: inferences from a comparison of observations and numerical models. Earth and Planetary Science Letters, 206:51-63, 2003. [2] W. Xu and C. Ruppell. Predicting the occurrence, distribution, and evolution of methane hydrate in porous marine sediments. Journal of Geohphysical Research, (B3):5081-5095, 1999. [3] J.B. Klauda and S.I. Sandler. Predictions of
Dynamics of fermionic Hubbard models after interaction quenches in one and two dimensions
Hamerla, Simone Anke
2013-10-15
In the last years the impressive progress on the experimental side led to a variety of new experiments allowing to address systems out of equilibrium. In this way the behavior of such systems far from equilibrium is no longer a purely theoretical issue but indeed observable. New experimental techniques, like particles trapped in optical lattices, render a realization of quantum systems with nearly arbitrary system parameters possible and provide a possibility to study their time evolution. Systems out of equilibrium are characterized by the fact, that these systems are in highly excited states giving rise to totally new fascinating properties. In the present thesis one- and two-dimensional fermionic Hubbard models out of equilibrium are discussed. The system is taken out of equilibrium by a so-called interaction quench. At the beginning the system is prepared in the groundstate of the non-interacting Hamiltonian. At a time t the interaction between the fermions is suddenly turned on so that the time evolution is governed by the whole, interacting Hamiltonian. Hence the system is prepared in the groundstate of one Hamiltonian but evolves according to a different Hamiltonian. Consequently the system ends up in a highly excited state. To describe such a system a method based on an expansion of the Heisenberg equations of motion to highest order possible is developed in this thesis. This method provides an exact description of the time evolution on short and intermediate time scales after the quench. As the method reveal exact results and does not rely on any perturbative assumption, a study of arbitrarily large interaction strengths is possible. Besides, the method is one of the few methods capable of two-dimensional systems. In the following the method used in this thesis is explained and advantages and disadvantages of the approach are thematized. For this purpose the results of the developed iterated equation of motion approach are compared to results obtained in
Split Hubbard bands at low densities
Hansen, Daniel; Perepelitsky, Edward; Shastry, B. Sriram
2011-05-01
We present a numerical scheme for the Hubbard model that throws light on the rather esoteric nature of the upper and lower Hubbard bands, which have been invoked often in literature. We present a self-consistent solution of the ladder-diagram equations for the Hubbard model, and show that these provide, at least in the limit of low densities of particles, a vivid picture of the Hubbard split bands. We also address the currently topical problem of decay of the doublon states that are measured in optical trap studies, using both the ladder scheme and also an exact two-particle calculation of a relevant Green’s function.
Janani, C.; Merino, J.; McCulloch, I. P.; Powell, B. J.
2014-01-01
Motivated by Mo$_3$S$_7$(dmit)$_3$, we investigate the Hubbard model on the triangular necklace lattice at two-thirds filling. We show, using second order perturbation theory, that in the molecular limit, the ground state and the low energy excitations of this model are identical to those of the spin-one Heisenberg chain. The latter model is known to be in the symmetry protected topological Haldane phase. Away from this limit we show, on the basis of symmetry arguments and density matrix reno...
The Bose glass (BG) phase is the Griffiths region of the disordered Bose–Hubbard model (BHM), characterized by finite, quasi-superfluid clusters within a Mott insulating background. We propose to utilize this characterization to identify the complete zero-temperature phase diagram of the disordered BHM in d ⩾ 2 dimensions by analysing the geometric properties of what we call superfluid (SF) clusters, which are defined to be clusters of sites with non-integer expectation values for the local boson occupation number. The Mott insulator phase then is the region in the phase diagram where no SF clusters exist, and the SF phase the region where SF clusters percolate—the BG phase is inbetween: SF clusters exist, but do not percolate. This definition is particularly useful in the context of local mean field (LMF) or Gutzwiller–Ansatz calculations, where we show that an identification of the phases on the basis of global quantities such as the averaged SF order parameter and the compressibility is misleading. We apply the SF cluster analysis to the LMF ground states of the two-dimensional disordered BHM to produce its phase diagram and find (a) an excellent agreement with the phase diagram predicted on the basis of quantum Monte Carlo simulations for the commensurate density n = 1 and (b) large differences to stochastic mean field and other mean field predictions for fixed disorder strength. The relation of the percolation transition of the SF clusters with the onset of non-vanishing SF stiffness indicating the BG to SF transition is discussed. (paper)
A 2D simulation model for urban flood management
Price, Roland; van der Wielen, Jonathan; Velickov, Slavco; Galvao, Diogo
2014-05-01
The European Floods Directive, which came into force on 26 November 2007, requires member states to assess all their water courses and coast lines for risk of flooding, to map flood extents and assets and humans at risk, and to take adequate and coordinated measures to reduce the flood risk in consultation with the public. Flood Risk Management Plans are to be in place by 2015. There are a number of reasons for the promotion of this Directive, not least because there has been much urban and other infrastructural development in flood plains, which puts many at risk of flooding along with vital societal assets. In addition there is growing awareness that the changing climate appears to be inducing more frequent extremes of rainfall with a consequent increases in the frequency of flooding. Thirdly, the growing urban populations in Europe, and especially in the developing countries, means that more people are being put at risk from a greater frequency of urban flooding in particular. There are urgent needs therefore to assess flood risk accurately and consistently, to reduce this risk where it is important to do so or where the benefit is greater than the damage cost, to improve flood forecasting and warning, to provide where necessary (and possible) flood insurance cover, and to involve all stakeholders in decision making affecting flood protection and flood risk management plans. Key data for assessing risk are water levels achieved or forecasted during a flood. Such levels should of course be monitored, but they also need to be predicted, whether for design or simulation. A 2D simulation model (PriceXD) solving the shallow water wave equations is presented specifically for determining flood risk, assessing flood defense schemes and generating flood forecasts and warnings. The simulation model is required to have a number of important properties: -Solve the full shallow water wave equations using a range of possible solutions; -Automatically adjust the time step and
Phase transitions in Bose-Fermi-Hubbard model in the heavy fermion limit: Hard-core boson approach
I.V. Stasyuk
2015-12-01
Full Text Available Phase transitions are investigated in the Bose-Fermi-Hubbard model in the mean field and hard-core boson approximations for the case of infinitely small fermion transfer and repulsive on-site boson-fermion interaction. The behavior of the Bose-Einstein condensate order parameter and grand canonical potential is analyzed as functions of the chemical potential of bosons at zero temperature. The possibility of change of order of the phase transition to the superfluid phase in the regime of fixed values of the chemical potentials of Bose- and Fermi-particles is established. The relevant phase diagrams are built.
Paul, Saurabh; Johnson, P R; Tiesinga, Eite
2016-01-01
We show that for ultra-cold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pair-wise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine...
Properties of the one-dimensional Bose-Hubbard model from a high-order perturbative expansion
Damski, Bogdan; Zakrzewski, Jakub
2015-12-01
We employ a high-order perturbative expansion to characterize the ground state of the Mott phase of the one-dimensional Bose-Hubbard model. We compute for different integer filling factors the energy per lattice site, the two-point and density-density correlations, and expectation values of powers of the on-site number operator determining the local atom number fluctuations (variance, skewness, kurtosis). We compare these expansions to numerical simulations of the infinite-size system to determine their range of applicability. We also discuss a new sum rule for the density-density correlations that can be used in both equilibrium and non-equilibrium systems.
How to control pairing fluctuations: SU(2) slave-rotor gauge theory of the Hubbard model
Kim, Ki-Seok
2006-01-01
We study how to incorporate Mott physics in the BCS-type superconductor, motivated from the fact that high $T_c$ superconductivity results from a Mott insulator via hole doping. The U(1) slave-rotor representation was proposed to take local density fluctuations into account non-perturbatively, describing the Mott-Hubbard transition at half filling. Since this decomposition cannot control local pairing fluctuations, the U(1) slave-rotor representation does not give a satisfactory treatment for...
Phase separation instabilities and magnetism in two dimensional square and honeycomb Hubbard model
The variational cluster approximation is applied to rigorously calculate intrinsic local electron correlations in bipartite square and honeycomb Hubbard lattices. The Mott–Hubbard gap at half filling is manifested by a smooth metal–insulator transition in both lattices in agreement with the generic two-dimensional phase diagram. However, a density variation with the chemical potential shows the distinct structural differences away from half filling. The square lattice exhibits electron density discontinuity accompanied with spontaneous transition from antiferromagnetic Mott–Hubbard insulator into nonmagnetic metal. The spectral density anomaly and spin susceptibility peaks also are signaling on coexistence of hole rich metallic and hole poor insulating regions. In contrast, honeycomb lattice does not show density anomaly but displays a smooth transition with continuous evolution of a homogenous metallic state. These calculations provide strong evidence for spontaneous phase separation instability found in our quantum cluster calculations at moderate U - Highlights: • Variational cluster approximation (VCA) captures phase separation in various lattices under doping. • The conditions are formulated for continuous and discontinuous transitions. • Discontinuous phase separation is found in square lattices under doping and pressure. • Honeycomb lattice displays continuous evolution of a homogenous metallic state. • Spectral function anomaly in square geometry displays the folding of the first Brillouin zone
The Implementation of C-ID, R2D2 Model on Learning Reading Comprehension
Rayanto, Yudi Hari; Rusmawan, Putu Ngurah
2016-01-01
The purposes of this research are to find out, (1) whether C-ID, R2D2 model is effective to be implemented on learning Reading comprehension, (2) college students' activity during the implementation of C-ID, R2D2 model on learning Reading comprehension, and 3) college students' learning achievement during the implementation of C-ID, R2D2 model on…
Le modele de Hubbard bidimensionnel a faible couplage: Thermodynamique et phenomenes critiques
Roy, Sebastien
Une etude systematique du modele de Hubbard en deux dimensions a faible couplage a l'aide de la theorie Auto-Coherente a Deux Particules (ACDP) dans le diagramme temperature-dopage-interaction-sauts permet de mettre en evidence l'influence des fluctuations magnetiques sur les proprietes thermodynamiques du systeme electronique sur reseau. Le regime classique renormalise a temperature finie pres du dopage nul est marque par la grandeur de la longueur de correlation de spin comparee a la longueur thermique de de Broglie et est caracterisee par un accroissement drastique de la longueur de correlation de spin. Cette croissance exponentielle a dopage nul marque la presence d'un pic de chaleur specifique en fonction de la temperature a basse temperature. Une temperature de crossover est alors associee a la temperature a laquelle la longueur de correlation de spin est egale a la longueur thermique de de Broglie. C'est a cette temperature caracteristique, ou est observee l'ouverture du pseudogap dans le poids spectral, que se situe le maximum du pic de chaleur specifique. La presence de ce pic a des consequences sur l'evolution du potentiel chimique avec le dopage lorsque l'uniformite thermodynamique est respectee. Les contraintes imposees par les lois de la thermodynamique font en sorte que l'evolution du potentiel chimique avec le dopage est non triviale. On demontre entre autres que le potentiel chimique est proportionnel a la double occupation qui est reliee au moment local. Par ailleurs, une derivation de la fonction de mise a l'echelle de la susceptibilite de spin a frequence nulle au voisinage d'un point critique marque sans equivoque la presence d'un point critique quantique en dopage pour une valeur donnee de l'interaction. Ce point critique, associe a une transition de phase magnetique en fonction du dopage a temperature nulle, induit un comportement non trivial sur les proprietes physiques du systeme a temperature finie. L'approche quantitative ACDP permet de
Chae, Dongho; Constantin, Peter; Wu, Jiahong
2014-09-01
We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time for all time. In addition, we introduce a variant of the 2D Boussinesq equations which is perhaps a more faithful companion of the 3D axisymmetric Euler equations than the usual 2D Boussinesq equations.
Dallaire-Demers, Pierre-Luc; Wilhelm, Frank K.
2016-03-01
Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model whose thermodynamic properties can be computed from its grand-canonical potential. In general, there is no closed-form expression of the grand-canonical potential for lattices of more than one spatial dimension, but solutions can be numerically approximated using cluster methods. To model long-range effects such as order parameters, a powerful method to compute the cluster's Green's function consists of finding its self-energy through a variational principle. This allows the possibility of studying various phase transitions at finite temperature in the Fermi-Hubbard model. However, a classical cluster solver quickly hits an exponential wall in the memory (or computation time) required to store the computation variables. Here it is shown theoretically that the cluster solver can be mapped to a subroutine on a quantum computer whose quantum memory usage scales linearly with the number of orbitals in the simulated cluster and the number of measurements scales quadratically. A quantum computer with a few tens of qubits could therefore simulate the thermodynamic properties of complex fermionic lattices inaccessible to classical supercomputers.
Two-component Bose-Hubbard model with higher-angular-momentum states
Pietraszewicz, Joanna; Sowiński, Tomasz; Brewczyk, Mirosław; Zakrzewski, Jakub; Lewenstein, Maciej; Gajda, Mariusz
2012-05-01
Bose-Hubbard Hamiltonian of cold two-component Bose gas of spinor chromium atoms is studied. Dipolar interactions of magnetic moments while tuned resonantly by an ultralow magnetic field can lead to a transfer of atoms from the ground to excited Wannier states with a nonvanishing angular orbital momentum. Hence we propose the way of creating Px+iPy orbital superfluid. The spin introduces an additional degree of control and leads to a variety of different stable phases of the system. The Mott insulator of atoms in a superposition of the ground and vortex Wannier states as well as a superposition of the Mott insulator with orbital superfluid are predicted.
The selection of soil models parameters in Plaxis 2D
O.V. Sokolova
2014-06-01
Full Text Available Finite element method is often used to solve complex geotechnical problems. The application of FEM-based programs demands special attention to setting models parameters and simulating soil behavior. The paper considers the problem of the model selection to describe the behavior of soils when calculating soil settlement in the check task, referring to complicated geotechnical conditions of Saint Petersburg. The obtained settlement values in Linear Elastic model, Mohr – Coulomb model, Hardening Soil model and Hardening Soil Small model were compared. The paper presents results of calibrating parameters for a geotechnical model obtained on the data of compression testing. The necessity of prior calculations to evaluate the accuracy of a soil model is confirmed.
Spiral magnetism in the single-band Hubbard model: the Hartree–Fock and slave-boson approaches
The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree–Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistically large Hubbard U by the correlation effects if nesting is absent and van Hove singularities are well away from the paramagnetic phase Fermi level. The magnetic phase separation plays an important role in the formation of magnetic states, the corresponding phase regions being especially wide in the vicinity of half-filling. The details of non-collinear and collinear magnetic ordering for different cubic lattices are discussed. (paper)
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...
Modeling Overlapping Laminations in Magnetic Core Materials Using 2-D Finite-Element Analysis
Jensen, Bogi Bech; Guest, Emerson David; Mecrow, Barrie C.
2015-01-01
This paper describes a technique for modeling overlapping laminations in magnetic core materials using two-dimensional finite-element (2-D FE) analysis. The magnetizing characteristic of the overlapping region is captured using a simple 2-D FE model of the periodic overlapping geometry and a comp...
Kuno, Yoshihito; Sakane, Shinya; Kasamatsu, Kenichi; Ichinose, Ikuo; Matsui, Tetsuo
2016-01-01
In this paper, we study atomic quantum simulations of $(1+1)$-dimensional($(1+1)$D) U(1) gauge-Higgs models (GHMs) defined on a lattice. We explain how U(1) lattice GHMs appear from an extended Bose-Hubbard model (EBHM) describing ultra-cold atoms with a nearest neighbor repulsion in a 1D optical lattice. We first study a phase diagram of the 1D EBHM at low fillings by means of a quantum Monte-Carlo(MC) simulation. Next, we study the EBHM at large fillings and also GHMs by the MC simulations in the path-integral formalism and show that there are four phases, i.e., the Higgs phase(superfluid), the confinement phase (Mott insulator), and phases corresponding to the density wave and the supersolid. With the obtained phase diagrams, we investigate the relationship between the two models. Finally, we study real-time dynamic of an electric flux in the GHMs by the Gross-Pitaevskii equations and the truncated Wigner approximation.
2D semiclassical model for high harmonic generation from gas
陈黎明; 余玮; 张杰; 陈朝阳; 江文勉
2000-01-01
The electron behavior in laser field is described in detail. Based on the 1D semiclassical model, a 20 semiclassical model is proposed analytically using 3D DC-tunneling ionization theory. Lots of harmonic features are explained by this model, including the analytical demonstration of the maximum electron energy 3.17 Up. Finally, some experimental phenomena such as the increase of the cutoff harmonic energy with the decrease of pulse duration and the "anomalous" fluctuations in the cutoff region are explained by this model.
2-D Model Test Study of the Suape Breakwater, Brazil
Andersen, Thomas Lykke; Burcharth, Hans F.; Sopavicius, A.;
This report deals with a two-dimensional model test study of the extension of the breakwater in Suape, Brazil. One cross-section was tested for stability and overtopping in various sea conditions. The length scale used for the model tests was 1:35. Unless otherwise specified all values given in...
2D modelling and assessment of divertor performance for ITER
The results of the ITER divertor modelling performed during the EDA are summarised in the paper. Studies on the operating window and optimisation of the divertor geometry are presented together with preliminary results on the start-up limiter performance. The issue of model validation against the experimental data which is crucial for extrapolation to ITER is also addressed. (author)
Practical aspects of a 2-D edge-plasma model
The poloidal divertor configuration is considered the most promising solution to the particle and energy exhaust problem for a tokamak reactor. The scrape-off layer plasma surrounding the core and the high-recycling plasma near the divertor plates can be modelled by fluid equations for particle, momentum and energy transport. A numerical code (B2) based on a two-dimensional multi-fluid model has been developed for the study of edge plasmas in tokamaks. In this report we identify some key features of this model as applied to the DIII-D tokamak. 2 refs., 1 fig
Vibration induced flow in hoppers: DEM 2D polygon model
无
2008-01-01
A two-dimensional discrete element model (DEM) simulation of cohesive polygonal particles has been developed to assess the benefit of point source vibration to induce flow in wedge-shaped hoppers. The particle-particle interaction model used is based on a multi-contact principle.The first part of the study investigated particle discharge under gravity without vibration to determine the critical orifice size (Be) to just sustain flow as a function of particle shape. It is shown that polygonal-shaped particles need a larger orifice than circular particles. It is also shown that Be decreases as the number of particle vertices increases. Addition of circular particles promotes flow of polygons in a linear manner.The second part of the study showed that vibration could enhance flow, effectively reducing Be. The model demonstrated the importance of vibrator location (height), consistent with previous continuum model results, and vibration amplitude in enhancing flow.
Percolation properties of the 2D Heisenberg model
Allès, B; Criado, C; Pepé, M
1999-01-01
We analyze the percolation properties of certain clusters defined on configurations of the 2--dimensional Heisenberg model thermalized at a temperature T=0.5. We find that, given any direction in O(3) space, \\vec{n}, the spins almost perpendicular to \\vec{n} form a percolating cluster. Given a fixed configuration, this is true for any \\vec{n}. We briefly comment on the critical properties of the model.
A fully coupled 2D model of equiaxed eutectic solidification
Charbon, Ch.; LeSar, R.
1995-12-31
We propose a model of equiaxed eutectic solidification that couples the macroscopic level of heat diffusion with the microscopic level of nucleation and growth of the eutectic grains. The heat equation with the source term corresponding to the latent heat release due to solidification is calculated numerically by means of an implicit finite difference method. In the time stepping scheme, the evolution of solid fraction is deduced from a stochastic model of nucleation and growth which uses the local temperature (interpolated from the FDM mesh) to determine the local grain density and the local growth rate. The solid-liquid interface of each grain is tracked by using a subdivision of each grain perimeter in a large number of sectors. The state of each sector (i.e. whether it is still in contact with the liquid or already captured by an other grain) and the increase of radius of each grain during one time step allows one to compute the increase of solid fraction. As for deterministic models, the results of the model are the evolution of temperature and of solid fraction at any point of the sample. Moreover the model provides a complete picture of the microstructure, thus not limiting the microstructural information to the average grain density but allowing one to compute any stereological value of interest. We apply the model to the solidification of gray cast iron.
Simulation of subgrid orographic precipitation with an embedded 2-D cloud-resolving model
Jung, Joon-Hee; Arakawa, Akio
2016-03-01
By explicitly resolving cloud-scale processes with embedded two-dimensional (2-D) cloud-resolving models (CRMs), superparameterized global atmospheric models have successfully simulated various atmospheric events over a wide range of time scales. Up to now, however, such models have not included the effects of topography on the CRM grid scale. We have used both 3-D and 2-D CRMs to simulate the effects of topography with prescribed "large-scale" winds. The 3-D CRM is used as a benchmark. The results show that the mean precipitation can be simulated reasonably well by using a 2-D representation of topography as long as the statistics of the topography such as the mean and standard deviation are closely represented. It is also shown that the use of a set of two perpendicular 2-D grids can significantly reduce the error due to a 2-D representation of topography.
Google Earth as a tool in 2-D hydrodynamic modeling
Chien, Nguyen Quang; Keat Tan, Soon
2011-01-01
A method for coupling virtual globes with geophysical hydrodynamic models is presented. Virtual globes such as Google TM Earth can be used as a visualization tool to help users create and enter input data. The authors discuss techniques for representing linear and areal geographical objects with KML (Keyhole Markup Language) files generated using computer codes (scripts). Although virtual globes offer very limited tools for data input, some data of categorical or vector type can be entered by users, and then transformed into inputs for the hydrodynamic program by using appropriate scripts. An application with the AnuGA hydrodynamic model was used as an illustration of the method. Firstly, users draw polygons on the Google Earth screen. These features are then saved in a KML file which is read using a script file written in the Lua programming language. After the hydrodynamic simulation has been performed, another script file is used to convert the resulting output text file to a KML file for visualization, where the depths of inundation are represented by the color of discrete point icons. The visualization of a wind speed vector field was also included as a supplementary example.
Conservation laws and LETKF with 2D Shallow Water Model
Zeng, Yuefei; Janjic, Tijana
2016-04-01
Numerous approaches have been proposed to maintain physical conservation laws in the numerical weather prediction models. However, to achieve a reliable prediction, adequate initial conditions are also necessary, which are produced by a data assimilation algorithm. If an ensemble Kalman filters (EnKF) is used for this purpose, it has been shown that it could yield unphysical analysis ensemble that for example violates principles of mass conservation and positivity preservation (e.g. Janjic et al 2014) . In this presentation, we discuss the selection of conservation criteria for the analysis step, and start with testing the conservation of mass, energy and enstrophy. The simple experiments deal with nonlinear shallow water equations and simulated observations that are assimilated with LETKF (Localized Ensemble Transform Kalman Filter, Hunt et al. 2007). The model is discretized in a specific way to conserve mass, angular momentum, energy and enstrophy. The effects of the data assimilation on the conserved quantities (of mass, energy and enstrophy) depend on observation covarage, localization radius, observed variable and observation operator. Having in mind that Arakawa (1966) and Arakawa and Lamb (1977) showed that the conservation of both kinetic energy and enstrophy by momentum advection schemes in the case of nondivergent flow prevents systematic and unrealistic energy cascade towards high wave numbers, a cause of excessive numerical noise and possible eventual nonlinear instability, we test the effects on prediction depending on the type of errors in the initial condition. The performance with respect to nonlinear energy cascade is assessed as well.
Point Contacts in Modeling Conducting 2D Planar Structures
Thiel, David V; Hettenhausen, Jan; Lewis, Andrew
2015-01-01
Use of an optimization algorithm to improve performance of antennas and electromagnetic structures usually ends up in planar unusual shapes. Using rectangular conducting elements the proposed structures sometimes have connections with only one single point in common between two neighboring areas. The single point connections (point crossing) can affect the electromagnetic performance of the structure. In this letter, we illustrate the influence of point crossing on dipole and loop antennas using MoM, FDTD, and FEM solvers. Current distribution, radiation pattern, and impedance properties for different junctions are different. These solvers do not agree in the modeling of the point crossing junctions which is a warning about uncertainty in using such junctions. However, solvers agree that a negligible change in the junction would significantly change the antenna performance. We propose that one should consider both bridging and chamfering of the conflicting cells to find optimized structures. This reduces the ...
Multiflavor bosonic Hubbard models in the first excited Bloch band of an optical lattice
We propose that by exciting ultracold atoms from the zeroth to the first Bloch band in an optical lattice, multiflavor bosonic Hubbard Hamiltonians can be realized in a different way. In these systems, each flavor hops in a separate direction and on-site exchange terms allow pairwise conversion between different flavors. Using band-structure calculations, we determine the parameters entering these Hamiltonians and derive the mean-field ground-state phase diagram for two effective Hamiltonians (two dimensional, two flavors, and three dimensional, three flavors). Further, we estimate the stability of atoms in the first band using second-order perturbation theory and find lifetimes that can be considerably (10-100 times) longer than the relevant time scale associated with intersite hopping dynamics, suggesting that quasiequilibrium can be achieved in these metastable states
2D modelling of polycrystalline silicon thin film solar cells
Leendertz Caspar
2013-07-01
Full Text Available The influence of grain boundary (GB properties on device parameters of polycrystalline silicon (poly-Si thin film solar cells is investigated by two-dimensional device simulation. A realistic poly-Si thin film model cell composed of antireflection layer, (n+-type emitter, thick p-type absorber, and (p+-type back surface field was created. The absorber consists of a low-defect crystalline Si grain with an adjacent highly defective grain boundary layer. The performances of a reference cell without GB, one with n-type and one with p-type GB, respectively, are compared. The doping concentration and defect density at the GB are varied. It is shown that the impact of the grain boundary on the poly-Si cell is twofold: a local potential barrier is created at the GB, and a part of the photogenerated current flows within the GB. Regarding the cell performance, a highly doped n-type GB is less critical in terms of the cell’s short circuit current than a highly doped p-type GB, but more detrimental in terms of the cell’s open circuit voltage and fill factor.
We investigate the two-dimensional attractive Hubbard model with quantum Monte Carlo techniques to reveal the crossover from a BCS-type superconductivity in the weak-coupling regime to a superconductivity properly described by a Bose-Einstein condensation (BEC) of local, preformed pairs. The crossover from BCS to BEC is particularly well exposed in the temperature dependence of both the spin susceptibility and the double occupancy, as well as by the appearance of a pseudogap in the density of states far above Tc. These features are also mirrored in the shape of the specific-heat peak around Tc, the separation of the temperature regimes where pair formation and their condensation occur, and in the transfer of spectral weight from the single-particle excitation branch to a pair band in the normal state. copyright 1996 The American Physical Society
Phases and transitions in the spin-1 Bose-Hubbard model: Systematics of a mean-field theory
We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulator, that arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are of first order at finite temperatures. Our systematic study yields rich phase diagrams that include first-order and second-order transitions and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems
The electronic structure of the high-Tc copper oxides is calculated by means of an extended two-dimensional three-band Hubbard model in the unrestricted Hartree-Fock approximation. The influence of the coupling parameters on the obtained bands, as well as their doping dependence are investigated especially at the Fermi surface. Results are discussed in the light of recent experimental data for the cuprate Fermi surfaces. A comparative analysis of these conflicting data on the basis of our results sheds some light on the interpretation of the measured band structures. The direct oxygen-oxygen hopping interaction is found to be essential in fitting experimental results, suggesting that, in the doped regime, the oxygen band plays a key role at least in the near-EF region. Antiferromagnetic correlations among copper atoms turn out as well to be crucial. The results agree remarkably well with previous local-density calculations and with spectroscopic measurements
Phase boundary between spin singlet and triplet superconductivity in the extended Hubbard model with exchange interaction on a square lattice is calculated within meanfield approximation. Basically, antiferromagnetic exchange interaction J is advantageous for the singlet pairing, while ferromagnetic J prefers the triplet pairing. When off-site interaction V is repulsive, the singlet phase and the triplet phase are separated by normal state in the phase diagram against V and J. If V is effectively attractive, however, the singlet and triplet states can compete against each other. We calculate the phase boundary between singlet and triplet phase for various band filling. It is shown that the triplet phase penetrates rather deeply into antiferromagnetic exchange regime for lower band filling, whereas the penetration of the singlet phase is confined in a narrow range of ferromagnetic exchange regime.
Momentum structure of the self-energy and its parametrization for the two-dimensional Hubbard model
Pudleiner, P.; Schäfer, T.; Rost, D.; Li, G.; Held, K.; Blümer, N.
2016-05-01
We compute the self-energy for the half-filled Hubbard model on a square lattice using lattice quantum Monte Carlo simulations and the dynamical vertex approximation. The self-energy is strongly momentum-dependent, but it can be parametrized via the noninteracting energy-momentum dispersion ɛk, except for pseudogap features right at the Fermi edge. That is, it can be written as Σ (ɛk,ω ) , with two energylike parameters (ɛ , ω ) instead of three (kx, ky, and ω ). The self-energy has two rather broad and weakly dispersing high-energy features and a sharp ω =ɛk feature at high temperatures, which turns to ω =-ɛk at low temperatures. Altogether this yields a Z - and reversed-Z -like structure, respectively, for the imaginary part of Σ (ɛk,ω ) . We attribute the change of the low-energy structure to antiferromagnetic spin fluctuations.
An effective depression filling algorithm for DEM-based 2-D surface flow modelling
Zhu, D.; Ren, Q.; Xuan, Y.; Y. Chen; I. D. Cluckie
2013-01-01
The surface runoff process in fluvial/pluvial flood modelling is often simulated employing a two-dimensional (2-D) diffusive wave approximation described by grid based digital elevation models (DEMs). However, this approach may cause potential problems when using the 2-D surface flow model which exchanges flows through adjacent cells, with conventional sink removal algorithms which also allow for flow exchange along diagonal directions, due to the existence of artificial dep...
2-D model for pollutant dispersion at the coastal outfall off Paradip
Suryanarayana, A.; Babu, M.T.; Vethamony, P.; Gouveia, A.D
Simulation of dispersion of the effluent discharge has been carried out using 2-D Model to verify the advection and diffusion of the pollutant patch of the proposed effluent disposal off Paradip, Orissa, India. The simulation of dispersion...
Ghostine, Rabih
2014-12-01
In open channel networks, flow is usually approximated by the one-dimensional (1D) Saint-Venant equations coupled with an empirical junction model. In this work, a comparison in terms of accuracy and computational cost between a coupled 1D-2D shallow water model and a fully two-dimensional (2D) model is presented. The paper explores the ability of a coupled model to simulate the flow processes during supercritical flows in crossroads. This combination leads to a significant reduction in the computational time, as a 1D approach is used in branches and a 2D approach is employed in selected areas only where detailed flow information is essential. Overall, the numerical results suggest that the coupled model is able to accurately simulate the main flow processes. In particular, hydraulic jumps, recirculation zones, and discharge distribution are reasonably well reproduced and clearly identified. Overall, the proposed model leads to a 30% reduction in run times. © 2014 International Association for Hydro-Environment Engineering and Research.
Comparison of 1D and 2D modelling with soil erosion model SMODERP
Kavka, Petr; Weyskrabova, Lenka; Zajicek, Jan
2013-04-01
The contribution presents a comparison of a runoff simulated by profile method (1D) and spatially distributed method (2D). Simulation model SMODERP is used for calculation and prediction of soil erosion and surface runoff from agricultural land. SMODERP is physically based model that includes the processes of infiltration (Phillips equation), surface runoff (kinematic wave based equation), surface retention, surface roughness and vegetation impact on runoff. 1D model was developed in past, new 2D model was developed in last two years. The model is being developed at the Department of Irrigation, Drainage and Landscape Engineering, Civil Engineering Faculty, CTU in Prague. 2D model was developed as a tool for widespread GIS software ArcGIS. The physical relations were implemented through Python script. This script uses ArcGIS system tools for raster and vectors treatment of the inputs. Flow direction is calculated by Steepest Descent algorithm in the preliminary version of 2D model. More advanced multiple flow algorithm is planned in the next version. Spatially distributed models enable to estimate not only surface runoff but also flow in the rills. Surface runoff is described in the model by kinematic wave equation. Equation uses Manning roughness coefficient for surface runoff. Parameters for five different soil textures were calibrated on the set of forty measurements performed on the laboratory rainfall simulator. For modelling of the rills a specific sub model was created. This sub model uses Manning formula for flow estimation. Numerical stability of the model is solved by Courant criterion. Spatial scale is fixed. Time step is dynamically changed depending on how flow is generated and developed. SMODERP is meant to be used not only for the research purposes, but mainly for the engineering practice. We also present how the input data can be obtained based on available resources (soil maps and data, land use, terrain models, field research, etc.) and how can
Bose-Hubbard model in a ring-shaped optical lattice with high filling factors
The high-barrier quantum tunneling regime of a Bose-Einstein condensate confined in a ring-shaped optical lattice is investigated. By means of a change of basis transformation, connecting the set of ''vortex'' Bloch states and a Wannier-like set of localized wave functions, we derive a generalized Bose-Hubbard Hamiltonian. In addition to the usual hopping rate terms, such a Hamiltonian takes into account interaction-driven tunneling processes, which are shown to play a principal role at high filling factors, when the standard hopping rate parameter turns out to be negative. By calculating the energy and atomic current of a Bloch state, we show that such a hopping rate must be replaced by an effective hopping rate parameter containing the additional contribution an interaction-driven hopping rate. Such a contribution turns out to be crucial at high filling factors, since it preserves the positivity of the effective hopping rate parameter. Level crossings between the energies per particle of a Wannier-like state and the superfluid ground state are interpreted as a signature of the transition to configurations with macroscopically occupied states at each lattice site.
Simulation of Cardiac Arrhythmias Using a 2D Heterogeneous Whole Heart Model
Balakrishnan, Minimol; Chakravarthy, V. Srinivasa; Guhathakurta, Soma
2015-01-01
Simulation studies of cardiac arrhythmias at the whole heart level with electrocardiogram (ECG) gives an understanding of how the underlying cell and tissue level changes manifest as rhythm disturbances in the ECG. We present a 2D whole heart model (WHM2D) which can accommodate variations at the cellular level and can generate the ECG waveform. It is shown that, by varying cellular-level parameters like the gap junction conductance (GJC), excitability, action potential duration (APD) and freq...
DEVELOPMENT OF COUPLED 1D-2D MATHEMATICAL MODELS FOR TIDAL RIVERS
XU Zu-xin; YIN Hai-long
2004-01-01
Some coupled 1D-2D hydrodynamic and water quality models depicting tidal water bodies with complex topography were presented. For the coupled models, finite element method was used to solve the governing equations so as to study tidal rivers with complex topography. Since the 1D and 2D models were coupled, the principle of model coupling was proposed to account appropriately for the factors of water level, flow and pollutant flux and the related dynamical behavior was simulated. Specifically the models were used to probe quantitative pollution contribution of receiving water from neighboring Jiangsu and Zhejiang Provinces to the pollution in the Huangpu River passing through Shanghai City. Numerical examples indicated that the developed coupled 1D-2D models are applicable in tidal river network region of Shanghai.
Liu, Guangkun; Kaushal, Nitin; Li, Shaozhi; Bishop, Christopher B.; Wang, Yan; Johnston, Steve; Alvarez, Gonzalo; Moreo, Adriana; Dagotto, Elbio
2016-06-01
A recently introduced one-dimensional three-orbital Hubbard model displays orbital-selective Mott phases with exotic spin arrangements such as spin block states [J. Rincón et al., Phys. Rev. Lett. 112, 106405 (2014), 10.1103/PhysRevLett.112.106405]. In this publication we show that the constrained-path quantum Monte Carlo (CPQMC) technique can accurately reproduce the phase diagram of this multiorbital one-dimensional model, paving the way to future CPQMC studies in systems with more challenging geometries, such as ladders and planes. The success of this approach relies on using the Hartree-Fock technique to prepare the trial states needed in CPQMC. We also study a simplified version of the model where the pair-hopping term is neglected and the Hund coupling is restricted to its Ising component. The corresponding phase diagrams are shown to be only mildly affected by the absence of these technically difficult-to-implement terms. This is confirmed by additional density matrix renormalization group and determinant quantum Monte Carlo calculations carried out for the same simplified model, with the latter displaying only mild fermion sign problems. We conclude that these methods are able to capture quantitatively the rich physics of the several orbital-selective Mott phases (OSMP) displayed by this model, thus enabling computational studies of the OSMP regime in higher dimensions, beyond static or dynamic mean-field approximations.
Hemodynamic simulation of the heart using a 2D model and MR data
Adeler, Pernille Thorup; Thomsen, Per Grove; Barker, Vincent A.
2002-01-01
Computational models of the blood flow in the heart are a useful tool for studying the functioning of the heart. The purpose of this thesis is to achieve a better understanding of hemodynamics of the normal and diseased hearts through the use of a computational model and magnetic resonance (MR) data. We present a 2D computational model of the blood flow in the left side of the heart. The work is based on Peskin and McQueen's 2D model dimensioned to data on the dog heart, which we improve and ...
Analysis of vegetation effect on waves using a vertical 2-D RANS model
A vertical two-dimensional (2-D) model has been applied in the simulation of wave propagation through vegetated water bodies. The model is based on an existing model SOLA-VOF which solves the Reynolds-Averaged Navier-Stokes (RANS) equations with the finite difference method on a staggered rectangula...
Tidal regime in Gulf of Kutch, west coast of India, by 2D model
Unnikrishnan, A; Gouveia, A; Vethamony, P.
A 2D barotropic numerical model is developed for the Gulf of Kutch with a view to synthesize available information on tides and currents in the Gulf. A comparison of model results with moored current meter observations shows that the model...
Fast 2D flood modelling using GPU technology - recent applications and new developments
Crossley, Amanda; Lamb, Rob; Waller, Simon; Dunning, Paul
2010-05-01
In recent years there has been considerable interest amongst scientists and engineers in exploiting the potential of commodity graphics hardware for desktop parallel computing. The Graphics Processing Units (GPUs) that are used in PC graphics cards have now evolved into powerful parallel co-processors that can be used to accelerate the numerical codes used for floodplain inundation modelling. We report in this paper on experience over the past two years in developing and applying two dimensional (2D) flood inundation models using GPUs to achieve significant practical performance benefits. Starting with a solution scheme for the 2D diffusion wave approximation to the 2D Shallow Water Equations (SWEs), we have demonstrated the capability to reduce model run times in ‘real-world' applications using GPU hardware and programming techniques. We then present results from a GPU-based 2D finite volume SWE solver. A series of numerical test cases demonstrate that the model produces outputs that are accurate and consistent with reference results published elsewhere. In comparisons conducted for a real world test case, the GPU-based SWE model was over 100 times faster than the CPU version. We conclude with some discussion of practical experience in using the GPU technology for flood mapping applications, and for research projects investigating use of Monte Carlo simulation methods for the analysis of uncertainty in 2D flood modelling.
The extended Bose–Hubbard model for a double-well potential with pair tunneling is studied through both exact diagonalization and mean field theory (MFT). When pair tunneling is strong enough, the ground state wavefunction predicted by the MFT is complex and doubly degenerate while the quantum ground state wavefunction is always real and unique. The time reversal symmetry is spontaneously broken when the system transfers from the quantum ground state into one of the mean field ground states upon a small perturbation. As the gap between the lowest two levels decreases exponentially with particle number, the required perturbation inducing the spontaneous symmetry breaking (SSB) is infinitesimal for particle number of typical cold atom systems. The quantum ground state is further analyzed with the Penrose–Onsager criterion, and is found to be a fragmented condensate. The state also develops the pair correlation and has non-vanishing pair order parameter instead of the conventional single particle order parameter. When this model is generalized to optical lattice, a pair superfluid can be generated. The mean field ground state can be regarded as effective ground state in this simple model. The detailed computation for this model enables us to offer an in-depth discussion of the relation between SSB and effective ground state, giving a glimpse on how nonlinearity arises in the SSB of a quantum system. (paper)
Brehm, Sascha
2009-02-26
Two-particle excitations, such as spin and charge excitations, play a key role in high-T{sub c} cuprate superconductors (HTSC). Due to the antiferromagnetism of the parent compound the magnetic excitations are supposed to be directly related to the mechanism of superconductivity. In particular, the so-called resonance mode is a promising candidate for the pairing glue, a bosonic excitation mediating the electronic pairing. In addition, its interactions with itinerant electrons may be responsible for some of the observed properties of HTSC. Hence, getting to the bottom of the resonance mode is crucial for a deeper understanding of the cuprate materials. To analyze the corresponding two-particle correlation functions we develop in the present thesis a new, non-perturbative and parameter-free technique for T=0 which is based on the Variational Cluster Approach (VCA, an embedded cluster method for one-particle Green's functions). Guided by the spirit of the VCA we extract an effective electron-hole vertex from an isolated cluster and use a fully renormalized bubble susceptibility {chi}{sub 0} including the VCA one-particle propagators. Within our new approach, the magnetic excitations of HTSC are shown to be reproduced for the Hubbard model within the relevant strong-coupling regime. Exceptionally, the famous resonance mode occurring in the underdoped regime within the superconductivity-induced gap of spin-flip electron-hole excitations is obtained. Its intensity and hourglass dispersion are in good overall agreement with experiments. Furthermore, characteristic features such as the position in energy of the resonance mode and the difference of the imaginary part of the susceptibility in the superconducting and the normal states are in accord with Inelastic Neutron Scattering (INS) experiments. For the first time, a strongly-correlated parameter-free calculation revealed these salient magnetic properties supporting the S=1 magnetic exciton scenario for the
Two-particle excitations, such as spin and charge excitations, play a key role in high-Tc cuprate superconductors (HTSC). Due to the antiferromagnetism of the parent compound the magnetic excitations are supposed to be directly related to the mechanism of superconductivity. In particular, the so-called resonance mode is a promising candidate for the pairing glue, a bosonic excitation mediating the electronic pairing. In addition, its interactions with itinerant electrons may be responsible for some of the observed properties of HTSC. Hence, getting to the bottom of the resonance mode is crucial for a deeper understanding of the cuprate materials. To analyze the corresponding two-particle correlation functions we develop in the present thesis a new, non-perturbative and parameter-free technique for T=0 which is based on the Variational Cluster Approach (VCA, an embedded cluster method for one-particle Green's functions). Guided by the spirit of the VCA we extract an effective electron-hole vertex from an isolated cluster and use a fully renormalized bubble susceptibility χ0 including the VCA one-particle propagators. Within our new approach, the magnetic excitations of HTSC are shown to be reproduced for the Hubbard model within the relevant strong-coupling regime. Exceptionally, the famous resonance mode occurring in the underdoped regime within the superconductivity-induced gap of spin-flip electron-hole excitations is obtained. Its intensity and hourglass dispersion are in good overall agreement with experiments. Furthermore, characteristic features such as the position in energy of the resonance mode and the difference of the imaginary part of the susceptibility in the superconducting and the normal states are in accord with Inelastic Neutron Scattering (INS) experiments. For the first time, a strongly-correlated parameter-free calculation revealed these salient magnetic properties supporting the S=1 magnetic exciton scenario for the resonance mode. Besides the
2D Path Solutions from a Single Layer Excitable CNN Model
Karahaliloglu, Koray
2007-01-01
An easily implementable path solution algorithm for 2D spatial problems, based on excitable/programmable characteristics of a specific cellular nonlinear network (CNN) model is presented and numerically investigated. The network is a single layer bioinspired model which was also implemented in CMOS technology. It exhibits excitable characteristics with regionally bistable cells. The related response realizes propagations of trigger autowaves, where the excitable mode can be globally preset and reset. It is shown that, obstacle distributions in 2D space can also be directly mapped onto the coupled cell array in the network. Combining these two features, the network model can serve as the main block in a 2D path computing processor. The related algorithm and configurations are numerically experimented with circuit level parameters and performance estimations are also presented. The simplicity of the model also allows alternative technology and device level implementation, which may become critical in autonomous...
Pair correlations in doped Hubbard ladders
Dolfi, Michele; Bauer, Bela; Keller, Sebastian; Troyer, Matthias
2015-11-01
Hubbard ladders are an important stepping stone to the physics of the two-dimensional Hubbard model. While many of their properties are accessible to numerical and analytical techniques, the question of whether weakly hole-doped Hubbard ladders are dominated by superconducting or charge-density-wave correlations has so far eluded a definitive answer. In particular, previous numerical simulations of Hubbard ladders have seen a much faster decay of superconducting correlations than expected based on analytical arguments. We revisit this question using a state-of-the-art implementation of the density matrix renormalization group algorithm that allows us to simulate larger system sizes with higher accuracy than before. Performing careful extrapolations of the results, we obtain improved estimates for the Luttinger liquid parameter and the correlation functions at long distances. Our results confirm that, as suggested by analytical considerations, superconducting correlations become dominant in the limit of very small doping.
Optimal implicit 2-D finite differences to model wave propagation in poroelastic media
Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.
2016-08-01
Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite differences (FD) to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (linear systems of equations through Thomas' algorithm.
Universality and Non-Perturbative Definitions of 2D Quantum Gravity from Matrix Models
Miramontes, J. Luis; Guillen, Joaquin Sanchez
1991-01-01
The universality of the non-perturbative definition of Hermitian one-matrix models following the quantum, stochastic, or $d=1$-like stabilization is discussed in comparison with other procedures. We also present another alternative definition, which illustrates the need of new physical input for $d=0$ matrix models to make contact with 2D quantum gravity at the non-perturbative level.
Universality and nonperturbative definitions of 2D quantum gravity from matrix models
The universality of the nonperturbative definition of Hermitian one-matrix models following the quantum stochastic, or d = 1-like stabilization is discussed in comparison with other procedures. The authors also present another alternative definition, which illustrates the need of new physical input for d = 0 matrix models to make contact with 2D quantum gravity at the nonperturbative level
Comparison between 2D turbulence model ESEL and experimental data from AUG and COMPASS tokamaks
Ondac, Peter; Horacek, Jan; Seidl, Jakub;
2015-01-01
In this article we have used the 2D fluid turbulence numerical model, ESEL, to simulate turbulent transport in edge tokamak plasma. Basic plasma parameters from the ASDEX Upgrade and COMPASS tokamaks are used as input for the model, and the output is compared with experimental observations obtained...
Bond formation effects on the metal-insulator transition in the half-filled kagome Hubbard model
Higa, Ryota; Asano, Kenichi
2016-06-01
We study the metal-insulator transition in the half-filled Hubbard model on a Kagome lattice using the variational cluster approximation. The strong coupling limit of the model corresponds to the S =1 /2 Kagome Heisenberg antiferromagnet, which is known to have a singlet ground state, although its detail is still debated. As the results of the cluster methods generally depend much on the choice of the unit cluster, we have chosen the clusters that are compatible with these singlet ground states in the strong coupling case found so far, which basically consist of even number of sites. It is found that the correlated electrons on the Kagome lattice have a strong tendency to form valence-bond structures, which are the resonation of electrons on a single bond or several bonds forming loops. The zero-temperature metal-insulator transition at some interaction strength is possibly driven by the formation of such short range valence bonds and shows a second order character, which is distinctive from the Brinkman-Rice scenario. The electrons on these valence bonds further localizes onto each site as the interaction increases, and the valence bonds of electrons finally turn into magnetic singlet bonds between localized S =1 /2 spins, which are consistent with the ground states of the Kagome antiferromagnet.
Exact solution of the 1D Hubbard model with NN and NNN interactions in the narrow-band limit
Mancini, Ferdinando; Plekhanov, Evgeny; Sica, Gerardo
2013-10-01
We present the exact solution, obtained by means of the Transfer Matrix (TM) method, of the 1D Hubbard model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) Coulomb interactions in the atomic limit ( t = 0). The competition among the interactions ( U, V 1, and V 2) generates a plethora of T = 0 phases in the whole range of fillings. U, V 1, and V 2 are the intensities of the local, NN and NNN interactions, respectively. We report the T = 0 phase diagram, in which the phases are classified according to the behavior of the principal correlation functions, and reconstruct a representative electronic configuration for each phase. In order to do that, we make an analytic limit T → 0 in the transfer matrix, which allows us to obtain analytic expressions for the ground state energies even for extended transfer matrices. Such an extension of the standard TM technique can be easily applied to a wide class of 1D models with the interaction range beyond NN distance, allowing for a complete determination of the T = 0 phase diagrams.
Validation of DYSTOOL for unsteady aerodynamic modeling of 2D airfoils
From the point of view of wind turbine modeling, an important group of tools is based on blade element momentum (BEM) theory using 2D aerodynamic calculations on the blade elements. Due to the importance of this sectional computation of the blades, the National Renewable Wind Energy Center of Spain (CENER) developed DYSTOOL, an aerodynamic code for 2D airfoil modeling based on the Beddoes-Leishman model. The main focus here is related to the model parameters, whose values depend on the airfoil or the operating conditions. In this work, the values of the parameters are adjusted using available experimental or CFD data. The present document is mainly related to the validation of the results of DYSTOOL for 2D airfoils. The results of the computations have been compared with unsteady experimental data of the S809 and NACA0015 profiles. Some of the cases have also been modeled using the CFD code WMB (Wind Multi Block), within the framework of a collaboration with ACCIONA Windpower. The validation has been performed using pitch oscillations with different reduced frequencies, Reynolds numbers, amplitudes and mean angles of attack. The results have shown a good agreement using the methodology of adjustment for the value of the parameters. DYSTOOL have demonstrated to be a promising tool for 2D airfoil unsteady aerodynamic modeling
Validation of DYSTOOL for unsteady aerodynamic modeling of 2D airfoils
González, A.; Gomez-Iradi, S.; Munduate, X.
2014-06-01
From the point of view of wind turbine modeling, an important group of tools is based on blade element momentum (BEM) theory using 2D aerodynamic calculations on the blade elements. Due to the importance of this sectional computation of the blades, the National Renewable Wind Energy Center of Spain (CENER) developed DYSTOOL, an aerodynamic code for 2D airfoil modeling based on the Beddoes-Leishman model. The main focus here is related to the model parameters, whose values depend on the airfoil or the operating conditions. In this work, the values of the parameters are adjusted using available experimental or CFD data. The present document is mainly related to the validation of the results of DYSTOOL for 2D airfoils. The results of the computations have been compared with unsteady experimental data of the S809 and NACA0015 profiles. Some of the cases have also been modeled using the CFD code WMB (Wind Multi Block), within the framework of a collaboration with ACCIONA Windpower. The validation has been performed using pitch oscillations with different reduced frequencies, Reynolds numbers, amplitudes and mean angles of attack. The results have shown a good agreement using the methodology of adjustment for the value of the parameters. DYSTOOL have demonstrated to be a promising tool for 2D airfoil unsteady aerodynamic modeling.
Paul, Saurabh; Johnson, P. R.; Tiesinga, Eite
2016-04-01
We show that, for ultracold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pairwise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine the strength of the two- and three-body interactions for scattering from van der Waals potentials and near Fano-Feshbach resonances. For van der Waals potentials, which for example describe scattering of alkaline-earth atoms, we find that the pairwise interaction can only be turned off for species with a small negative scattering length, leaving the 88Sr isotope a possible candidate. Interestingly, for collisional magnetic Feshbach resonances this restriction does not apply and there often exist magnetic fields where the two-body interaction is small. We illustrate this result for several known narrow resonances between alkali-metal atoms as well as chromium atoms. Finally, we compare the size of the three-body interaction with hopping rates and describe limits due to three-body recombination.
A tractable direct optimization algorithm is developed to optimize orbitals in the Slater determinants (S-dets) in a resonating Hartree-Fock (Res HF) wave function. We reduce the variation space using the orbitals to put the first order energy variation in the steepest descent direction. The orbitals in the next iteration are determined so as to minimize the energy functional including up to the second order variation. This algorithm is applied to the one dimensional Hubbard model of half-filling. The optimized S-dets much deviate from the trial S-dets prepared from the HF calculations. The Res HF ground state generated with a few-S-dets explains from 99.9 to 95.0 % of the ground state correlation energy in all the correlation regimes. We have spin correlation functions with the correct short and long range behaviors and the lowest triplet and singlet spin excitations with correct dispersion, suggesting that the optimization of orbitals incorporates long range spin fluctuations and their mode-mode couplings. (author)
Chen, Qi-Hui; Li, Peng; Su, Haibin
2016-06-29
By generalizing the traditional single-site strong coupling expansion approach to a cluster one, we study the zero-temperature phase diagram of bosonic atoms in a trimerized Kagomé optical lattice. Some new features are present in this system. Due to the strong intra-trimer hopping interaction, there will be a new Mott insulator (MI), which is by definition incompressible but with a fractional filling per trimer. This is different from the traditional MI, which has an integral filling and originates only from the repulsive interaction between particles. We investigate the MI-to-superfluid transition and the nature of the fractional MI by calculating the critical exponents of phase transitions and the low-lying energy excitation spectra of quasiparticles (quasihole). We will show how the low-energy properties of this system can be understood qualitatively as a Bose-Hubbard model in triangular lattice from the point of view of the cluster strong coupling expansion. We also discuss how our results are related to experiment by studying the Bragg spectroscopy. PMID:27165440
Kumar, Sanjeev; Chakraborty, Prabuddha B.
2015-03-01
We investigate the influence of diagonal and off-diagonal disorder potentials on superconductivity in an attractive Hubbard model. The study is motivated by recent experimental and theoretical interest in understanding the microscopic mechanism by which impurities destroy superconductivity. In order to capture the spatial correlations accurately, we make use of the real-space Bogoliubov-de Gennes mean field method. We find that the response of a superconductor to disorder crucially depends, even qualitatively, on the type of disorder considered. Superconductivity is suppressed spatially homogeneously by off-diagonal (kinetic) disorder in comparison to the suppression by diagonal (potential) disorder which proceeds via the formation of strongly superconducting islands. Moreover, the non-superconducting phase is gapless in the case of kinetic disorder, suggesting a fermionic superconductor-insulator transition (SIT). This is in sharp contrast to the SIT tuned by diagonal disorder, which is understood to be bosonic in nature. A qualitatively distinct mechanism that allows for a BCS-like suppression of superconductivity with increasing disorder is, in fact, consistent with recent experiments on amorphous Bi films.
The simulation of 3D mass models in 2D digital mammography and breast tomosynthesis
Shaheen, Eman, E-mail: eman.shaheen@uzleuven.be; De Keyzer, Frederik; Bosmans, Hilde; Ongeval, Chantal Van [Department of Radiology, University Hospitals Leuven, Herestraat 49, 3000 Leuven (Belgium); Dance, David R.; Young, Kenneth C. [National Coordinating Centre for the Physics of Mammography, Royal Surrey County Hospital, Guildford GU2 7XX, United Kingdom and Department of Physics, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford GU2 7XH (United Kingdom)
2014-08-15
Purpose: This work proposes a new method of building 3D breast mass models with different morphological shapes and describes the validation of the realism of their appearance after simulation into 2D digital mammograms and breast tomosynthesis images. Methods: Twenty-five contrast enhanced MRI breast lesions were collected and each mass was manually segmented in the three orthogonal views: sagittal, coronal, and transversal. The segmented models were combined, resampled to have isotropic voxel sizes, triangularly meshed, and scaled to different sizes. These masses were referred to as nonspiculated masses and were then used as nuclei onto which spicules were grown with an iterative branching algorithm forming a total of 30 spiculated masses. These 55 mass models were projected into 2D projection images to obtain mammograms after image processing and into tomographic sequences of projection images, which were then reconstructed to form 3D tomosynthesis datasets. The realism of the appearance of these mass models was assessed by five radiologists via receiver operating characteristic (ROC) analysis when compared to 54 real masses. All lesions were also given a breast imaging reporting and data system (BIRADS) score. The data sets of 2D mammography and tomosynthesis were read separately. The Kendall's coefficient of concordance was used for the interrater observer agreement assessment for the BIRADS scores per modality. Further paired analysis, using the Wilcoxon signed rank test, of the BIRADS assessment between 2D and tomosynthesis was separately performed for the real masses and for the simulated masses. Results: The area under the ROC curves, averaged over all observers, was 0.54 (95% confidence interval [0.50, 0.66]) for the 2D study, and 0.67 (95% confidence interval [0.55, 0.79]) for the tomosynthesis study. According to the BIRADS scores, the nonspiculated and the spiculated masses varied in their degrees of malignancy from normal (BIRADS 1) to highly
The simulation of 3D mass models in 2D digital mammography and breast tomosynthesis
Purpose: This work proposes a new method of building 3D breast mass models with different morphological shapes and describes the validation of the realism of their appearance after simulation into 2D digital mammograms and breast tomosynthesis images. Methods: Twenty-five contrast enhanced MRI breast lesions were collected and each mass was manually segmented in the three orthogonal views: sagittal, coronal, and transversal. The segmented models were combined, resampled to have isotropic voxel sizes, triangularly meshed, and scaled to different sizes. These masses were referred to as nonspiculated masses and were then used as nuclei onto which spicules were grown with an iterative branching algorithm forming a total of 30 spiculated masses. These 55 mass models were projected into 2D projection images to obtain mammograms after image processing and into tomographic sequences of projection images, which were then reconstructed to form 3D tomosynthesis datasets. The realism of the appearance of these mass models was assessed by five radiologists via receiver operating characteristic (ROC) analysis when compared to 54 real masses. All lesions were also given a breast imaging reporting and data system (BIRADS) score. The data sets of 2D mammography and tomosynthesis were read separately. The Kendall's coefficient of concordance was used for the interrater observer agreement assessment for the BIRADS scores per modality. Further paired analysis, using the Wilcoxon signed rank test, of the BIRADS assessment between 2D and tomosynthesis was separately performed for the real masses and for the simulated masses. Results: The area under the ROC curves, averaged over all observers, was 0.54 (95% confidence interval [0.50, 0.66]) for the 2D study, and 0.67 (95% confidence interval [0.55, 0.79]) for the tomosynthesis study. According to the BIRADS scores, the nonspiculated and the spiculated masses varied in their degrees of malignancy from normal (BIRADS 1) to highly
Impact of high speed civil transports on stratospheric ozone. A 2-D model investigation
Kinnison, D.E.; Connell, P.S. [Lawrence Livermore National Lab., CA (United States)
1997-12-31
This study investigates the effect on stratospheric ozone from a fleet of proposed High Speed Civil Transports (HSCTs). The new LLNL 2-D operator-split chemical-radiative-transport model of the troposphere and stratosphere is used for this HSCT investigation. This model is integrated in a diurnal manner, using an implicit numerical solver. Therefore, rate coefficients are not modified by any sort of diurnal average factor. This model also does not make any assumptions on lumping of chemical species into families. Comparisons to previous model-derived HSCT assessment of ozone change are made, both to the previous LLNL 2-D model and to other models from the international assessment modeling community. The sensitivity to the NO{sub x} emission index and sulfate surface area density is also explored. (author) 7 refs.
Comparison of 3-D finite element model of ashlar masonry with 2-D numerical models of ashlar masonry
Beran, Pavel
2016-06-01
3-D state of stress in heterogeneous ashlar masonry can be also computed by several suitable chosen 2-D numerical models of ashlar masonry. The results obtained from 2-D numerical models well correspond to the results obtained from 3-D numerical model. The character of thermal stress is the same. While using 2-D models the computational time is reduced more than hundredfold and therefore this method could be used for computation of thermal stresses during long time periods with 10 000 of steps.
Global 6DOF Pose Estimation from Untextured 2D City Models
Arth, Clemens; Pirchheim, Christian; Ventura, Jonathan; Lepetit, Vincent
2015-01-01
We propose a method for estimating the 3D pose for the camera of a mobile device in outdoor conditions, using only an untextured 2D model. Previous methods compute only a relative pose using a SLAM algorithm, or require many registered images, which are cumbersome to acquire. By contrast, our method returns an accurate, absolute camera pose in an absolute referential using simple 2D+height maps, which are broadly available, to refine a first estimate of the pose provided by the device's senso...
N=2, D=4 supersymmetric σ-models and Hamiltonian mechanics
A deep similarity is established between the Hamiltonian mechanics of point particle and supersymmetric N=2, D=4 σ-models formulated within harmonic superspace. An essential part of the latter, the sphere S2, comes out as a counterpart of the time variable. (author). 7 refs
A simple model for 2D image upconversion of incoherent light
Dam, Jeppe Seidelin; Pedersen, Christian; Tidemand-Lichtenberg, Peter
2011-01-01
We present a simple theoretical model for 2 dimensional (2-D) image up-conversion of incoherent light. While image upconversion has been known for more than 40 years, the technology has been hindered by very low conversion quantum efficiency (~10-7). We show that our implementation compared to...
Park, Elisa L.
2009-01-01
The purpose of this study is to understand the dynamics of Korean students' international mobility to study abroad by using the 2-D Model. The first D, "the driving force factor," explains how and what components of the dissatisfaction with domestic higher education perceived by Korean students drives students' outward mobility to seek foreign…
Parallelized CCHE2D flow model with CUDA Fortran on Graphics Process Units
This paper presents the CCHE2D implicit flow model parallelized using CUDA Fortran programming technique on Graphics Processing Units (GPUs). A parallelized implicit Alternating Direction Implicit (ADI) solver using Parallel Cyclic Reduction (PCR) algorithm on GPU is developed and tested. This solve...
Mechanical Modelling of Pultrusion Process: 2D and 3D Numerical Approaches
Baran, Ismet; Hattel, Jesper Henri; Akkerman, Remko;
2015-01-01
mechanical analysis should be performed. In the present work, the two dimensional (2D) quasi-static plane strain mechanical model for the pultrusion of a thick square profile developed by the authors is further improved using generalized plane strain elements. In addition to that, a more advanced 3D thermo...
Structure of a model salt bridge in solution investigated with 2D-IR spectroscopy
Huerta-Viga, Adriana; Amirjalayer, Saeed; Woutersen, Sander
2013-01-01
Salt bridges are known to be important for the stability of protein conformation, but up to now it has been difficult to study their geometry in solution. Here we characterize the spatial structure of a model salt bridge between guanidinium (Gdm+) and acetate (Ac-) using two-dimensional vibrational (2D-IR) spectroscopy. We find that as a result of salt bridging the infrared response of Gdm+ and Ac- change significantly, and in the 2D-IR spectrum, salt bridging of the molecules appears as cross peaks. From the 2D-IR spectrum we determine the relative orientation of the transition-dipole moments of the vibrational modes involved in the salt bridge, as well as the coupling between them. In this manner we reconstruct the geometry of the solvated salt bridge.
Justification for a 2D versus 3D fingertip finite element model during static contact simulations.
Harih, Gregor; Tada, Mitsunori; Dolšak, Bojan
2016-10-01
The biomechanical response of a human hand during contact with various products has not been investigated in details yet. It has been shown that excessive contact pressure on the soft tissue can result in discomfort, pain and also cumulative traumatic disorders. This manuscript explores the benefits and limitations of a simplified two-dimensional vs. an anatomically correct three-dimensional finite element model of a human fingertip. Most authors still use 2D FE fingertip models due to their simplicity and reduced computational costs. However we show that an anatomically correct 3D FE fingertip model can provide additional insight into the biomechanical behaviour. The use of 2D fingertip FE models is justified when observing peak contact pressure values as well as displacement during the contact for the given studied cross-section. On the other hand, an anatomically correct 3D FE fingertip model provides a contact pressure distribution, which reflects the fingertip's anatomy. PMID:26856769
Molecular Dynamics implementation of BN2D or 'Mercedes Benz' water model
Scukins, Arturs; Bardik, Vitaliy; Pavlov, Evgen; Nerukh, Dmitry
2015-05-01
Two-dimensional 'Mercedes Benz' (MB) or BN2D water model (Naim, 1971) is implemented in Molecular Dynamics. It is known that the MB model can capture abnormal properties of real water (high heat capacity, minima of pressure and isothermal compressibility, negative thermal expansion coefficient) (Silverstein et al., 1998). In this work formulas for calculating the thermodynamic, structural and dynamic properties in microcanonical (NVE) and isothermal-isobaric (NPT) ensembles for the model from Molecular Dynamics simulation are derived and verified against known Monte Carlo results. The convergence of the thermodynamic properties and the system's numerical stability are investigated. The results qualitatively reproduce the peculiarities of real water making the model a visually convenient tool that also requires less computational resources, thus allowing simulations of large (hydrodynamic scale) molecular systems. We provide the open source code written in C/C++ for the BN2D water model implementation using Molecular Dynamics.
The 2dF Galaxy Redshift Survey: Voids and hierarchical scaling models
Croton, D J; Gaztañaga, E; Baugh, C M; Norberg, P; Baldry, I K; Bland-Hawthorn, J; Bridges, T J; Cannon, R; Cole, S; Collins, C; Couch, W; Dalton, G B; De Propris, R; Driver, S P; Efstathiou, G P; Ellis, Richard S; Frenk, C S; Glazebrook, K; Jackson, C; Lahav, O; Lewis, I; Lumsden, S; Maddox, S; Madgwick, D; Peacock, J A; Peterson, B A; Sutherland, W; Taylor, K
2004-01-01
We study the void distribution in the completed 2dFGRS using counts-in-cells to measure the reduced void probability function (VPF). Theoretically, the VPF connects the distribution of voids to the moments of galaxy clustering of all orders. The reduced VPF measured from the 2dFGRS is in excellent agreement with the paradigm of hierarchical scaling of the galaxy clustering moments. This scaling results in a universal form for the VPF when plotted as a function of $\\Nbar\\xibar_2$, where $\\Nbar$ is the expected mean number of galaxies and $\\bar{\\xi_2}$ is the volume-averaged 2-point correlation function. Models of galaxy clustering which display hierarchical scaling yield different predictions for the reduced VPF. The accuracy of our measurement of the VPF from the 2dFGRS is such that we can rule out, at a very high significance, popular models for clustering, such as the lognormal distribution. We demonstrate that the negative binomial model gives a very good approximation to the 2dFGRS data over a wide range ...
The 2dF Galaxy Redshift Survey: voids and hierarchical scaling models
Croton, Darren J.; Colless, Matthew; Gaztañaga, Enrique; Baugh, Carlton M.; Norberg, Peder; Baldry, I. K.; Bland-Hawthorn, J.; Bridges, T.; Cannon, R.; Cole, S.; Collins, C.; Couch, W.; Dalton, G.; de Propris, R.; Driver, S. P.; Efstathiou, G.; Ellis, R. S.; Frenk, C. S.; Glazebrook, K.; Jackson, C.; Lahav, O.; Lewis, I.; Lumsden, S.; Maddox, S.; Madgwick, D.; Peacock, J. A.; Peterson, B. A.; Sutherland, W.; Taylor, K.
2004-08-01
We measure the redshift-space reduced void probability function (VPF) for 2dFGRS volume-limited galaxy samples covering the absolute magnitude range MbJ-5log10h=-18 to -22. Theoretically, the VPF connects the distribution of voids to the moments of galaxy clustering of all orders, and can be used to discriminate clustering models in the weakly non-linear regime. The reduced VPF measured from the 2dFGRS is in excellent agreement with the paradigm of hierarchical scaling of the galaxy clustering moments. The accuracy of our measurement is such that we can rule out, at a very high significance, popular models for galaxy clustering, including the lognormal distribution. We demonstrate that the negative binomial model gives a very good approximation to the 2dFGRS data over a wide range of scales, out to at least 20 h-1 Mpc. Conversely, the reduced VPF for dark matter in a Λ cold dark matter (ΛCDM) universe does appear to be lognormal on small scales but deviates significantly beyond ~4 h-1 Mpc. We find little dependence of the 2dFGRS reduced VPF on galaxy luminosity. Our results hold independently in both the North and South Galactic Pole survey regions.
Reliability of a Novel Model for Drug Release from 2D HPMC-Matrices
Rumiana Blagoeva
2010-04-01
Full Text Available A novel model of drug release from 2D-HPMC matrices is considered. Detailed mathematical description of matrix swelling and the effect of the initial drug loading are introduced. A numerical approach to solution of the posed nonlinear 2D problem is used on the basis of finite element domain approximation and time difference method. The reliability of the model is investigated in two steps: numerical evaluation of the water uptake parameters; evaluation of drug release parameters under available experimental data. The proposed numerical procedure for fitting the model is validated performing different numerical examples of drug release in two cases (with and without taking into account initial drug loading. The goodness of fit evaluated by the coefficient of determination is presented to be very good with few exceptions. The obtained results show better model fitting when accounting the effect of initial drug loading (especially for larger values.
Stochastic 2-D Models of Galaxy Disk Evolution. The Galaxy M33
Mineikis, Tadas; Vansevičius, Vladas
2015-01-01
We have developed a fast numerical 2-D model of galaxy disk evolution (resolved along the galaxy radius and azimuth) by adopting a scheme of parameterized stochastic self-propagating star formation. We explore the parameter space of the model and demonstrate its capability to reproduce 1-D radial profiles of the galaxy M33: gas surface density, surface brightness in the i and GALEX FUV passbands, and metallicity.
Nishimori point in random-bond Ising and Potts models in 2D
A. Honecker; Jacobsen, J. L.; Picco, M.; Pujol, P.
2001-01-01
We study the universality class of the fixed points of the 2D random bond q-state Potts model by means of numerical transfer matrix methods. In particular, we determine the critical exponents associated with the fixed point on the Nishimori line. Precise measurements show that the universality class of this fixed point is inconsistent with percolation on Potts clusters for q=2, corresponding to the Ising model, and q=3
A U(1) Current Algebra Model Coupled to 2D-Gravity
Stoilov, M.; Zaikov, R.
1993-01-01
We consider a simple model of a scalar field with $U(1)$ current algebra gauge symmetry coupled to $2D$-gravity in order to clarify the origin of Stuckelberg symmetry in the $w_{\\infty}$-gravity theory. An analogous symmetry takes place in our model too. The possible central extension of the complete symmetry algebra and the corresponding critical dimension have been found. The analysis of the Hamiltonian and the constraints shows that the generators of the current algebra, the reparametrizat...
Ice shelf flexures modeled with a 2-D elastic flow line model
Y. V. Konovalov
2011-10-01
Full Text Available Ice shelf flexures modeling was performed using a 2-D finite-difference elastic model, which takes into account sub-ice-shelf sea water flow. The sub-ice water flow was described by the wave equation for the sub-ice-shelf pressure perturbations (Holdsworth and Glynn, 1978. In the model ice shelf flexures result from variations in ocean pressure due to changes in prescribed sea levels. The numerical experiments were performed for a flow line down one of the fast flowing ice streams of the Academy of Sciences Ice Cap. The profile includes a part of the adjacent ice shelf. The numerical experiments were carried out for harmonic incoming pressure perturbations P' and the ice shelf flexures were obtained for a wide spectrum of the pressure perturbations frequencies, ranging from tidal periods down to periods of a few seconds (0.004..0.02 Hz. The amplitudes of the ice shelf deflections obtained by the model achieve a maxima at about T ≈ 165 s in concordance with previous investigations of the impact of waves on Antarctic ice shelves (Bromirski et al., 2010. The explanation of the effect is found in the solution of the corresponding eigenvalue problem revealing the existence of a resonance at these high frequencies.
Cluster Model for Wave-Like Motions of a 2D Vertically Vibrated Granular System
The fact that trapezoid clusters exist in 2D vertically vibrated granular systems leads us to construct a cluster model, in which wave-like motions are explained as the result of cluster-plate and cluster-cluster collisions. By analyzing the collision of one cluster with the plate in detail, we deduce a basic equation from velocity relationship, which could be separated into two correlative equations: one relates wave-like motion with exciting acceleration, and we call it the excitation condition; the other relates wavelength with exciting frequency, viz., the dispersion relation. The theoretical results are in agreement with the experimental ones, which supports the idea of the cluster model. Moreover, from the cluster model, we also predict a possibility of abnormal dispersion relation of a 2D granular system. (fundamental areas of phenomenology(including applications))
Numerical Methods and Comparisons for 1D and Quasi 2D Streamer Propagation Models
Huang, Mengmin; Guan, Huizhe; Zeng, Rong
2016-01-01
In this work, we propose four different strategies to simulate the one-dimensional (1D) and quasi two-dimensional (2D) model for streamer propagation. Each strategy involves of one numerical method for solving Poisson's equation and another method for solving continuity equations in the models, and a total variation diminishing three-stage Runge-Kutta method in temporal discretization. The numerical methods for Poisson's equation include finite volume method, discontinuous Galerkin methods, mixed finite element method and least-squared finite element method. The numerical method for continuity equations is chosen from the family of discontinuous Galerkin methods. The accuracy tests and comparisons show that all of these four strategies are suitable and competitive in streamer simulations from the aspects of accuracy and efficiency. By applying any strategy in real simulations, we can study the dynamics of streamer propagations and influences due to the change of parameters in both of 1D and quasi 2D models. T...
Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models
Luther, K.; Haitjema, H. M.
2000-04-01
We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.
COMPARISON BETWEEN 2D TURBULENCE MODEL ESEL AND EXPERIMENTAL DATA FROM AUG AND COMPASS TOKAMAKS
Peter Ondac
2015-04-01
Full Text Available In this article we have used the 2D fluid turbulence numerical model, ESEL, to simulate turbulent transport in edge tokamak plasma. Basic plasma parameters from the ASDEX Upgrade and COMPASS tokamaks are used as input for the model, and the output is compared with experimental observations obtained by reciprocating probe measurements from the two machines. Agreements were found in radial profiles of mean plasma potential and temperature, and in a level of density fluctuations. Disagreements, however, were found in the level of plasma potential and temperature fluctuations. This implicates a need for an extension of the ESEL model from 2D to 3D to fully resolve the parallel dynamics, and the coupling from the plasma to the sheath.
2D and 3D numerical models on compositionally buoyant diapirs in the mantle wedge
Hasenclever, Jörg; Morgan, Jason Phipps; Hort, Matthias; Rüpke, Lars H.
2011-11-01
We present 2D and 3D numerical model calculations that focus on the physics of compositionally buoyant diapirs rising within a mantle wedge corner flow. Compositional buoyancy is assumed to arise from slab dehydration during which water-rich volatiles enter the mantle wedge and form a wet, less dense boundary layer on top of the slab. Slab dehydration is prescribed to occur in the 80-180 km deep slab interval, and the water transport is treated as a diffusion-like process. In this study, the mantle's rheology is modeled as being isoviscous for the benefit of easier-to-interpret feedbacks between water migration and buoyant viscous flow of the mantle. We use a simple subduction geometry that does not change during the numerical calculation. In a large set of 2D calculations we have identified that five different flow regimes can form, in which the position, number, and formation time of the diapirs vary as a function of four parameters: subduction angle, subduction rate, water diffusivity (mobility), and mantle viscosity. Using the same numerical method and numerical resolution we also conducted a suite of 3D calculations for 16 selected parameter combinations. Comparing the 2D and 3D results for the same model parameters reveals that the 2D models can only give limited insights into the inherently 3D problem of mantle wedge diapirism. While often correctly predicting the position and onset time of the first diapir(s), the 2D models fail to capture the dynamics of diapir ascent as well as the formation of secondary diapirs that result from boundary layer perturbations caused by previous diapirs. Of greatest importance for physically correct results is the numerical resolution in the region where diapirs nucleate, which must be high enough to accurately capture the growth of the thin wet boundary layer on top of the slab and, subsequently, the formation, morphology, and ascent of diapirs. Here 2D models can be very useful to quantify the required resolution, which we
An effective depression filling algorithm for DEM-based 2-D surface flow modelling
D. Zhu
2013-02-01
Full Text Available The surface runoff process in fluvial/pluvial flood modelling is often simulated employing a two-dimensional (2-D diffusive wave approximation described by grid based digital elevation models (DEMs. However, this approach may cause potential problems when using the 2-D surface flow model which exchanges flows through adjacent cells, with conventional sink removal algorithms which also allow for flow exchange along diagonal directions, due to the existence of artificial depression in DEMs. In this paper, we propose an effective method for filling artificial depressions in DEM so that the problem can be addressed. We firstly analyse two types of depressions in DEMs and demonstrate the issues caused by the current depression filling algorithms using the surface flow simulations from the MIKE SHE model built for a medium-sized basin in Southeast England. The proposed depression-filling algorithm for 2-D overland flow modelling is applied and evaluated by comparing the simulated flows at the outlet of the catchment represented by DEMs at various resolutions (50 m, 100 m and 200 m. The results suggest that the existence of depressions in DEMs can substantially influence the overland flow estimation and the new depression filling algorithm is shown to be effective in tackling this issue based upon the comparison of simulations for sink-dominated and sink-free DEMs, especially in the areas with relatively flat topography.
TRENT2D WG: a smart web infrastructure for debris-flow modelling and hazard assessment
Zorzi, Nadia; Rosatti, Giorgio; Zugliani, Daniel; Rizzi, Alessandro; Piffer, Stefano
2016-04-01
Mountain regions are naturally exposed to geomorphic flows, which involve large amounts of sediments and induce significant morphological modifications. The physical complexity of this class of phenomena represents a challenging issue for modelling, leading to elaborate theoretical frameworks and sophisticated numerical techniques. In general, geomorphic-flows models proved to be valid tools in hazard assessment and management. However, model complexity seems to represent one of the main obstacles to the diffusion of advanced modelling tools between practitioners and stakeholders, although the UE Flood Directive (2007/60/EC) requires risk management and assessment to be based on "best practices and best available technologies". Furthermore, several cutting-edge models are not particularly user-friendly and multiple stand-alone software are needed to pre- and post-process modelling data. For all these reasons, users often resort to quicker and rougher approaches, leading possibly to unreliable results. Therefore, some effort seems to be necessary to overcome these drawbacks, with the purpose of supporting and encouraging a widespread diffusion of the most reliable, although sophisticated, modelling tools. With this aim, this work presents TRENT2D WG, a new smart modelling solution for the state-of-the-art model TRENT2D (Armanini et al., 2009, Rosatti and Begnudelli, 2013), which simulates debris flows and hyperconcentrated flows adopting a two-phase description over a mobile bed. TRENT2D WG is a web infrastructure joining advantages offered by the software-delivering model SaaS (Software as a Service) and by WebGIS technology and hosting a complete and user-friendly working environment for modelling. In order to develop TRENT2D WG, the model TRENT2D was converted into a service and exposed on a cloud server, transferring computational burdens from the user hardware to a high-performing server and reducing computational time. Then, the system was equipped with an
Gao, Shou-Ting; Ping, Fan; Li, Xiao-Fan; Tao, Wei-Kuo
2004-01-01
Although dry/moist potential vorticity is a useful physical quantity for meteorological analysis, it cannot be applied to the analysis of 2D simulations. A convective vorticity vector (CVV) is introduced in this study to analyze 2D cloud-resolving simulation data associated with 2D tropical convection. The cloud model is forced by the vertical velocity, zonal wind, horizontal advection, and sea surface temperature obtained from the TOGA COARE, and is integrated for a selected 10-day period. The CVV has zonal and vertical components in the 2D x-z frame. Analysis of zonally-averaged and mass-integrated quantities shows that the correlation coefficient between the vertical component of the CVV and the sum of the cloud hydrometeor mixing ratios is 0.81, whereas the correlation coefficient between the zonal component and the sum of the mixing ratios is only 0.18. This indicates that the vertical component of the CVV is closely associated with tropical convection. The tendency equation for the vertical component of the CVV is derived and the zonally-averaged and mass-integrated tendency budgets are analyzed. The tendency of the vertical component of the CVV is determined by the interaction between the vorticity and the zonal gradient of cloud heating. The results demonstrate that the vertical component of the CVV is a cloud-linked parameter and can be used to study tropical convection.
Parameterising root system growth models using 2D neutron radiography images
Schnepf, Andrea; Felderer, Bernd; Vontobel, Peter; Leitner, Daniel
2013-04-01
Root architecture is a key factor for plant acquisition of water and nutrients from soil. In particular in view of a second green revolution where the below ground parts of agricultural crops are important, it is essential to characterise and quantify root architecture and its effect on plant resource acquisition. Mathematical models can help to understand the processes occurring in the soil-plant system, they can be used to quantify the effect of root and rhizosphere traits on resource acquisition and the response to environmental conditions. In order to do so, root architectural models are coupled with a model of water and solute transport in soil. However, dynamic root architectural models are difficult to parameterise. Novel imaging techniques such as x-ray computed tomography, neutron radiography and magnetic resonance imaging enable the in situ visualisation of plant root systems. Therefore, these images facilitate the parameterisation of dynamic root architecture models. These imaging techniques are capable of producing 3D or 2D images. Moreover, 2D images are also available in the form of hand drawings or from images of standard cameras. While full 3D imaging tools are still limited in resolutions, 2D techniques are a more accurate and less expensive option for observing roots in their environment. However, analysis of 2D images has additional difficulties compared to the 3D case, because of overlapping roots. We present a novel algorithm for the parameterisation of root system growth models based on 2D images of root system. The algorithm analyses dynamic image data. These are a series of 2D images of the root system at different points in time. Image data has already been adjusted for missing links and artefacts and segmentation was performed by applying a matched filter response. From this time series of binary 2D images, we parameterise the dynamic root architecture model in the following way: First, a morphological skeleton is derived from the binary
2D axisymmetric model of particle acceleration in colliding shock flows system
Gladilin, P. E.; Bykov, A. M.; Osipov, S. M.; Romanskiy, V. I.
2015-12-01
We present the 2D axisymmetric model of particle acceleration at colliding shocks from supernova remnant and stellar wind from the nearby star. The model is the expansion of the previously developed plane-parallel model and takes into account three three-dimensional structure of the stellar wind and the supernova remnant shock. Numerical and analytical calculations provides the energetic and spatial distributions of the particles accelerated by colliding shock flows system. The presented model can be used in calculations of the emission spectra of different stellar associations and star clusters with colliding shock flows.
Dotsenko, V S; Pujol, P; Dotsenko, Vladimir; Picco, Marco; Pujol, Pierre
1995-01-01
We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series around the conformal field theories representing the pure models. We obtain a crossover in the amplitude for the correlation function for the Ising model which doesn't change the critical exponent, and a shift in the critical exponent produced by randomness in the case of the Potts model. A comparison with numerical data is discussed briefly.
2D edge plasma modeling extended up to the main chamber
Dekeyser, W., E-mail: wouter.dekeyser@mech.kuleuven.be [Department of Mechanical Engineering, Katholieke Universiteit Leuven, Celestijnenlaan 300A, 3001 Leuven (Belgium); Baelmans, M. [Department of Mechanical Engineering, Katholieke Universiteit Leuven, Celestijnenlaan 300A, 3001 Leuven (Belgium); Reiter, D.; Boerner, P.; Kotov, V. [Institut fuer Plasmaphysik, Forschungszentrum Juelich GmbH, EURATOM-Association, Trilateral Euregio Cluster, D-52425 Juelich (Germany)
2011-08-01
Far SOL plasma flow, and hence main chamber recycling and plasma surface interaction, are today still only very poorly described by current 2D fluid edge codes, such as B2, UEDGE or EDGE2D, due to a common technical limitation. We have extended the B2 plasma fluid solver in the current ITER version of B2-EIRENE (SOLPS4.3) to allow plasma solutions to be obtained up to the 'real vessel wall', at least on the basis of ad hoc far SOL transport models. We apply here the kinetic Monte Carlo Code EIRENE on such plasma solutions to study effects of this model refinement on main chamber fluxes and sputtering, for an ITER configuration. We show that main chamber sputtering may be significantly modified both due to thermalization of CX neutrals in the far SOL and poloidally highly asymmetric plasma wall contact, as compared to hitherto applied teleportation of particle fluxes across this domain.
Hybrid 2D-3D modelling of GTA welding with filler wire addition
Traidia, Abderrazak
2012-07-01
A hybrid 2D-3D model for the numerical simulation of Gas Tungsten Arc welding is proposed in this paper. It offers the possibility to predict the temperature field as well as the shape of the solidified weld joint for different operating parameters, with relatively good accuracy and reasonable computational cost. Also, an original approach to simulate the effect of immersing a cold filler wire in the weld pool is presented. The simulation results reveal two important observations. First, the weld pool depth is locally decreased in the presence of filler metal, which is due to the energy absorption by the cold feeding wire from the hot molten pool. In addition, the weld shape, maximum temperature and thermal cycles in the workpiece are relatively well predicted even when a 2D model for the arc plasma region is used. © 2012 Elsevier Ltd. All rights reserved.
A Neural-FEM tool for the 2-D magnetic hysteresis modeling
Cardelli, E.; Faba, A.; Laudani, A.; Lozito, G. M.; Riganti Fulginei, F.; Salvini, A.
2016-04-01
The aim of this work is to present a new tool for the analysis of magnetic field problems considering 2-D magnetic hysteresis. In particular, this tool makes use of the Finite Element Method to solve the magnetic field problem in real device, and fruitfully exploits a neural network (NN) for the modeling of 2-D magnetic hysteresis of materials. The NS has as input the magnetic inductions components B at the k-th simulation step and returns as output the corresponding values of the magnetic field H corresponding to the input pattern. It is trained by vector measurements performed on the magnetic material to be modeled. This input/output scheme is directly implemented in a FEM code employing the magnetic potential vector A formulation. Validations through measurements on a real device have been performed.
Non-equilibrium critical vortex dynamics of disordered 2D XY-model
Popov, Ivan S.; Prudnikov, Pavel V.; Prudnikov, Vladimir V.
2016-02-01
Vortex dynamics and clustering in non-equilibrium critical relaxation of disordered 2D XY-model are investigated for different initial states. Time dependencies of vortex concentration and clusters sizes are studied for different spin concentrations. The anomalous slow down of clustering in disordered system are explained by pinning of vortices on defects. The calculated temperature dependence of transverse stiffness allows to estimate critical temperature Tbkt and applicability of spin-wave approximation for disordered system.
Exotic magnetisation plateaus in a quasi-2D Shastry-Sutherland model
Foltin, G. R.; Manmana, S. R.; Schmidt, K. P.
2014-01-01
We find unconventional Mott insulators in a quasi-2D version of the Shastry-Sutherland model in a magnetic field. In our realization on a 4-leg tube geometry, these are stabilized by correlated hopping of localized magnetic excitations. Using perturbative continuous unitary transformations (pCUTs, plus classical approximation or exact diagonalization) and the density matrix renormalisation group method (DMRG), we identify prominent magnetization plateaus at magnetizations M=1/8, M=3/16, M=1/4...
Anisotropy effects and friction maps in the framework of the 2d PT model
Fajardo, O.Y. [Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, E-50009 Zaragoza (Spain); Gnecco, E. [Instituto Madrileño de Estudios Avanzados, IMDEA Nanociencia, 28049 Madrid (Spain); Mazo, J.J., E-mail: juanjo@unizar.es [Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, E-50009 Zaragoza (Spain)
2014-12-15
We present a series of numerical simulations on the friction–anisotropy behavior and stick–slip dynamics of a point mass in the framework of a 2d Prandtl–Tomlinson model. Results for three representative surface lattice are shown: square, hexagonal and honeycomb. Curves for scan angle dependence of static friction force, and kinetic one at T=0 K and T=300 K are shown. Friction force maps are computed at different directions.
Anisotropy effects and friction maps in the framework of the 2d PT model
We present a series of numerical simulations on the friction–anisotropy behavior and stick–slip dynamics of a point mass in the framework of a 2d Prandtl–Tomlinson model. Results for three representative surface lattice are shown: square, hexagonal and honeycomb. Curves for scan angle dependence of static friction force, and kinetic one at T=0 K and T=300 K are shown. Friction force maps are computed at different directions
Effects of vegetation on high waters in 2D hydraulic modeling
Müller, Matej
2009-01-01
Due to increasing impervious surfaces and climate change, the frequency of high water is increasing in recent decades. In parallel, the damage produced by them also increases. The need for preparedness for such events and for constructing flood measures grows. Hydraulic analysis are necessary for the assessment of the flood hazard and for flood extension forecasting. In recent years the development of advanced computers increased the use of complex 2D hydraulic models. The accuracy of such...
TMRPres2D: high quality visual representation of transmembrane protein models.
Spyropoulos, Ioannis C; Liakopoulos, Theodore D; Bagos, Pantelis G; Hamodrakas, Stavros J
2004-11-22
The 'TransMembrane protein Re-Presentation in 2-Dimensions' (TMRPres2D) tool, automates the creation of uniform, two-dimensional, high analysis graphical images/models of alpha-helical or beta-barrel transmembrane proteins. Protein sequence data and structural information may be acquired from public protein knowledge bases, emanate from prediction algorithms, or even be defined by the user. Several important biological and physical sequence attributes can be embedded in the graphical representation. PMID:15201184
A 2D wavenumber domain phase model for ground moving vehicles in synthetic aperture radar imagery
In this paper, fundamental phase characteristics of moving vehicles in synthetic aperture radar (SAR) data are reviewed. A 2D phase model for a moving point scatterer is expressed in terms of range and azimuth wavenumbers. The moving point scatterer impulse response is then the 2D Fourier transform of the associated complex sinusoid. Numerical computation of the 2D phase for arbitrary relative radar-point scatter motion is organized as a composition of functions expressing time, frequency and angle in terms of wavenumber vectors. An analytic model for the phase is subsequently derived in the special case that the Doppler cone angle is 90°. With that model it is observed that the map from velocity and acceleration to quadratic phase is not one-to-one and therefore the associated inverse problem is ill-posed. An example of moving vehicle Doppler energy dispersion and corresponding phase measured in clutter suppressed SAR image data is provided. Clutter suppression is achieved by application of spacetime adaptive processing. (paper)
APPLICATION OF MULTIGRID METHOD IN 2-D MATHEMATICAL MODEL IN OPEN CHANNELS
无
2000-01-01
In 2-D mathematical model, one of the important problems is to improve computational speed. The multigrid method is a new rapid iteration method developed in the resent 20 years, and it has been widely used in many fields, but in sediment mathematical model it has been rarely used, especially in plane mathematical model with large scale computational scope. In this paper, the multigrid method is introduced and expected to be used widely in this field. And it is verified that the more layers are adopted, the higher convergent speed will be reached in computation.
Innovative Machine Vision Technique for 2D/3D Complex and Irregular Surfaces Modelling
Shahzad Anwar
2012-09-01
Full Text Available This study propose and demonstrates a novel technique incorporating multilayer perceptron (MLP neural networks for feature extraction with Photometric stereo based image capture techniques for the analysis of complex and irregular 2D profiles and 3D surfaces. In order to develop the method and to ensure that it is capable of modelling non-axisymmetric and complex 2D/3D profiles, the network was initially trained and tested on 2D profiles, and subsequently using objects consisting of between 1 and 4 hemispherical 3D forms. To test the capability of the proposed model, random noise was added to 2D profiles. 3D objects were coated with various degrees of coarsenesses (ranging from low-high. The gradient of each surface normal was quantified in terms of the slant and tilt angles of the vector about the x and y axis respectively. The slant and tilt angles were obtained from the bump maps and these data were subsequently employed for training of a NN that had x and y as inputs and slant and tilt angles as outputs. The network employed had the following architecture: MLP and a Levenberg-Marquardt algorithm (LMA for training the network for 12,000 epochs. At each point on the surface the network was consulted to predict slant and tilt and the actual slant and tilt was subtracted, giving a measure of surface irregularity. The network was able to model the underlying asymmetrical geometry with an accuracy regression analysis R-value of 0.93 for a single 3D hemispheres and 0.90 for four adjacent 3D non-axisymmetric hemispheres.
Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects
Stasińska, Julia; Łacki, Mateusz; Dutta, Omjyoti; Zakrzewski, Jakub; Lewenstein, Maciej
2014-12-01
We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the site-dependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the model with chemical-potential disorder. These triple points, however, cease to exist after the addition of the hopping disorder.
A simple 2-D inundation model for incorporating flood damage in urban drainage planning
A. Pathirana
2008-11-01
Full Text Available In this paper a new inundation model code is developed and coupled with Storm Water Management Model, SWMM, to relate spatial information associated with urban drainage systems as criteria for planning of storm water drainage networks. The prime objective is to achive a model code that is simple and fast enough to be consistently be used in planning stages of urban drainage projects.
The formulation for the two-dimensional (2-D surface flow model algorithms is based on the Navier Stokes equation in two dimensions. An Alternating Direction Implicit (ADI finite difference numerical scheme is applied to solve the governing equations. This numerical scheme is used to express the partial differential equations with time steps split into two halves. The model algorithm is written using C++ computer programming language.
This 2-D surface flow model is then coupled with SWMM for simulation of both pipe flow component and surcharge induced inundation in urban areas. In addition, a damage calculation block is integrated within the inundation model code.
The coupled model is shown to be capable of dealing with various flow conditions, as well as being able to simulate wetting and drying processes that will occur as the flood flows over an urban area. It has been applied under idealized and semi-hypothetical cases to determine detailed inundation zones, depths and velocities due to surcharged water on overland surface.
The two-loop renormalization group (RG) calculation is considerably extended here for the two-dimensional (2D) fermionic effective field theory model, which includes only the so-called “hot spots” that are connected by the spin-density-wave (SDW) ordering wavevector on a Fermi surface generated by the 2D t−t′ Hubbard model at low hole doping. We compute the Callan–Symanzik RG equation up to two loops describing the flow of the single-particle Green’s function, the corresponding spectral function, the Fermi velocity, and some of the most important order-parameter susceptibilities in the model at lower energies. As a result, we establish that–in addition to clearly dominant SDW correlations–an approximate (pseudospin) symmetry relating a short-range incommensurated-wave charge order to the d-wave superconducting order indeed emerges at lower energy scales, which is in agreement with recent works available in the literature addressing the 2D spin-fermion model. We derive implications of this possible electronic phase in the ongoing attempt to describe the phenomenology of the pseudogap regime in underdoped cuprates
Universal behavior of entanglement in 2D quantum critical dimer models
We examine the scaling behavior of the entanglement entropy for the 2D quantum dimer model (QDM) at criticality and derive the universal finite sub-leading correction γQCP. We compute the value of γQCP without approximation working directly with the wavefunction of a generalized 2D QDM at the Rokhsar–Kivelson QCP in the continuum limit. Using the replica approach, we construct the conformal boundary state corresponding to the cyclic identification of n-copies along the boundary of the observed region. We find that the universal finite term is γQCP = lnR − 1/2 where R is the compactification radius of the Bose field theory quantum Lifshitz model, the effective field theory of the 2D QDM at quantum criticality. We also demonstrated that the entanglement spectrum of the critical wavefunction on a large but finite region is described by the characters of the underlying conformal field theory. It is shown that this is formally related to the problems of quantum Brownian motion on n-dimensional lattices or equivalently a system of strings interacting with a brane containing a background electromagnetic field and can be written as an expectation value of a vertex operator
Sankar, I. V.; Chatterjee, Ashok
2016-05-01
The quantum phase transition from a spin-density wave phase to a charge-density wave phase is studied within the framework of the one-dimensional Holstein-Hubbard model. The phonons are first eliminated by using a variational phonon state and the effective electronic Hamiltonian is then exactly solved using the Bethe ansatz technique to get the ground state energy. The entanglement entropy is finally calculated to show the possibility of existence of an intervening metallic phase at the cross-over region of the spin-density and charge-density wave phases in the thermodynamic limit at half-filling.
It has been shown that the spin-density wave instability does not coexist with s-like anisotropic superconductivity in the molecular field approach to the nearly half-filled two-dimensional Hubbard model. The phase diagram of the interplay of normal state, spin density wave, d-wave and extended s-wave superconducting orderings has been constructed. The possibility of the first order transition from the normal state and the superconducting state to the SDW-phase has been discussed. (author). 14 refs, 2 figs
Nested 1D-2D approach for urban surface flood modeling
Murla, Damian; Willems, Patrick
2015-04-01
Floods in urban areas as a consequence of sewer capacity exceedance receive increased attention because of trends in urbanization (increased population density and impermeability of the surface) and climate change. Despite the strong recent developments in numerical modeling of water systems, urban surface flood modeling is still a major challenge. Whereas very advanced and accurate flood modeling systems are in place and operation by many river authorities in support of flood management along rivers, this is not yet the case in urban water management. Reasons include the small scale of the urban inundation processes, the need to have very high resolution topographical information available, and the huge computational demands. Urban drainage related inundation modeling requires a 1D full hydrodynamic model of the sewer network to be coupled with a 2D surface flood model. To reduce the computational times, 0D (flood cones), 1D/quasi-2D surface flood modeling approaches have been developed and applied in some case studies. In this research, a nested 1D/2D hydraulic model has been developed for an urban catchment at the city of Gent (Belgium), linking the underground sewer (minor system) with the overland surface (major system). For the overland surface flood modelling, comparison was made of 0D, 1D/quasi-2D and full 2D approaches. The approaches are advanced by considering nested 1D-2D approaches, including infiltration in the green city areas, and allowing the effects of surface storm water storage to be simulated. An optimal nested combination of three different mesh resolutions was identified; based on a compromise between precision and simulation time for further real-time flood forecasting, warning and control applications. Main streets as mesh zones together with buildings as void regions constitute one of these mesh resolution (3.75m2 - 15m2); they have been included since they channel most of the flood water from the manholes and they improve the accuracy of
Brane brick models, toric Calabi-Yau 4-folds and 2d (0,2) quivers
Franco, Sebastián; Lee, Sangmin; Seong, Rak-Kyeong
2016-02-01
We introduce brane brick models, a novel type of Type IIA brane configurations consisting of D4-branes ending on an NS5-brane. Brane brick models are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. They fully encode the infinite class of 2 d (generically) {N}=(0,2) gauge theories on the worldvolume of the D1-branes and streamline their connection to the probed geometries. For this purpose, we also introduce new combinatorial procedures for deriving the Calabi-Yau associated to a given gauge theory and vice versa.
Complex zeros of the 2 d Ising model on dynamical random lattices
Ambjørn, J.; Anagnostopoulos, K. N.; Magnea, U.
1998-04-01
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2 d quantum gravity for complex magnetic field and for complex temperature. We compute the zeros by using the exact solution coming from a two matrix model and by Monte Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional patterns in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of singularities near the critical point.
On Spectral Laws of 2D--Turbulence in Shell Models
Frick, Peter; Aurell, Erik
1993-01-01
We consider a class of shell models of 2D-turbulence. They conserve inertially the analogues of energy and enstrophy, two quadratic forms in the shell amplitudes. Inertially conserving two quadratic integrals leads to two spectral ranges. We study in detail the one characterized by a forward cascade of enstrophy and spectrum close to Kraichnan's $k^{-3}$--law. In an inertial range over more than 15 octaves, the spectrum falls off as $k^{-3.05\\pm 0.01}$, with the same slope in all models. We i...
On the 2D zero modes' algebra of the SU(n) WZNW model
Hadjiivanov, Ludmil
2014-01-01
A quantum group covariant extension of the chiral parts of the Wess-Zumino-Novikov-Witten model on a compact Lie group G gives rise to two matrix algebras with non-commutative entries. These are generated by "chiral zero modes" which combine in the 2D model into "Q-operators" which encode information about the internal symmetry and the fusion ring. We review earlier results about the SU(n) WZNW Q-algebra and its Fock representation for n=2 and display the first steps towards their generalization to higher n.
Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers
Franco, Sebastian; Seong, Rak-Kyeong
2015-01-01
We introduce brane brick models, a novel type of Type IIA brane configurations consisting of D4-branes ending on an NS5-brane. Brane brick models are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. They fully encode the infinite class of 2d (generically) N=(0,2) gauge theories on the worldvolume of the D1-branes and streamline their connection to the probed geometries. For this purpose, we also introduce new combinatorial procedures for deriving the Calabi-Yau associated to a given gauge theory and vice versa.
Canonical vs. micro-canonical sampling methods in a 2D Ising model
Canonical and micro-canonical Monte Carlo algorithms were implemented on a 2D Ising model. Expressions for the internal energy, U, inverse temperature, Z, and specific heat, C, are given. These quantities were calculated over a range of temperature, lattice sizes, and time steps. Both algorithms accurately simulate the Ising model. To obtain greater than three decimal accuracy from the micro-canonical method requires that the more complicated expression for Z be used. The overall difference between the algorithms is small. The physics of the problem under study should be the deciding factor in determining which algorithm to use. 13 refs., 6 figs., 2 tabs
Topological edge states in the one-dimensional super-lattice Bose-Hubbard model
Grusdt, Fabian; Höning, Michael; Fleischhauer, Michael
2013-01-01
We analyze interacting ultra-cold bosonic atoms in a one-dimensional (1D) super-lattice potential with alternating tunneling rates t_1 and t_2 and inversion symmetry, which is the bosonic analogue of the Su-Schrieffer-Heeger (SSH) model. A Z2 topological order parameter is introduced which is quantized for the Mott insulating (MI) phases. Depending on the ratio t_1/t_2 the n=1/2 MI phase is topologically non-trivial, which results in many-body edge states at open boundaries. In contrast to th...
Topological Edge States in the One-Dimensional Superlattice Bose-Hubbard Model
Grusdt, Fabian; Höning, Michael; Fleischhauer, Michael
2013-06-01
We analyze interacting ultracold bosonic atoms in a one-dimensional superlattice potential with alternating tunneling rates t1 and t2 and inversion symmetry, which is the bosonic analogue of the Su-Schrieffer-Heeger model. A Z2 topological order parameter is introduced which is quantized for the Mott insulating (MI) phases. Depending on the ratio t1/t2 the n=1/2 MI phase is topologically nontrivial, which results in many-body edge states at open boundaries. In contrast to the Su-Schrieffer-Heeger model the bosonic counterpart lacks chiral symmetry and the edge states are no longer midgap. This leads to a generalization of the bulk-edge correspondence, which we discuss in detail. The edge states can be observed in cold atom experiments by creating a step in the effective confining potential, e.g., by a second heavy atom species, which leads to an interface between two MI regions with filling n=1 and n=1/2. The shape and energy of the edge states as well as the conditions for their occupation are determined analytically in the strong coupling limit and in general by density-matrix renormalization group simulations.
Graphene as a model system for 2D fracture behavior of perfect and defective solids
P. Hess
2015-10-01
Full Text Available A 2D bond-breaking model is presented that allows the extraction of the intrinsic line or edge energy, fracture toughness, and strain energy release rate of graphene from measured and calculated 2D Young’s moduli and 2D pristine strengths. The ideal fracture stress of perfect graphene is compared with the critical fracture stresses of defective graphene sheets containing different types of imperfections. This includes (multiple vacancies in the subnanometer range, grain boundaries, slits in the nanometer region, and artificial pre-cracks with sizes of 30 nm to 1 μm. Independent of the type of defect, a common dependence of the critical fracture strength on the square root of half defect size is observed. Furthermore, the results suggest the applicability of the Griffith relation at length scales of several nanometers. This observation is not consistent with simulations pointing to the existence of a flaw tolerance for defects with nanometer size. According to simulations for quasi-static growth of pre-existing cracks, the atomic mechanism may also consist of an alternating sequence of bond-breaking and bond-rotation steps with a straight extension of the crack path. Independent of the exact atomic failure mechanism brittle fracture of graphene is generally assumed at low temperatures.
2D-3D Registration of CT Vertebra Volume to Fluoroscopy Projection: A Calibration Model Assessment
P. Bifulco
2010-01-01
Full Text Available This study extends a previous research concerning intervertebral motion registration by means of 2D dynamic fluoroscopy to obtain a more comprehensive 3D description of vertebral kinematics. The problem of estimating the 3D rigid pose of a CT volume of a vertebra from its 2D X-ray fluoroscopy projection is addressed. 2D-3D registration is obtained maximising a measure of similarity between Digitally Reconstructed Radiographs (obtained from the CT volume and real fluoroscopic projection. X-ray energy correction was performed. To assess the method a calibration model was realised a sheep dry vertebra was rigidly fixed to a frame of reference including metallic markers. Accurate measurement of 3D orientation was obtained via single-camera calibration of the markers and held as true 3D vertebra position; then, vertebra 3D pose was estimated and results compared. Error analysis revealed accuracy of the order of 0.1 degree for the rotation angles of about 1 mm for displacements parallel to the fluoroscopic plane, and of order of 10 mm for the orthogonal displacement.
Methodology for Modeling 2-D Groundwater Motion in a Geographic Information System (GIS)
From the mid-1950's through the 1980's, the U.S. Department of Energy's Savannah River Site (SRS) produced nuclear materials for the weapons stockpile, for medical and industrial applications, and for space exploration. A legacy of this production is groundwater contamination located near previous production sites. This contamination is comprised mainly of heavy metals, organic degreasers, and radionuclides such as tritium. To monitor this contamination, a network of more than 1000 groundwater wells has been established across SRS. As a result of this contamination, extensive remediation activities are ongoing at SRS. Modeling the 3-D flow and transport of groundwater to support these efforts is a time consuming and arduous task involving discretizing a model domain representing geological and hydrogeological surfaces, specifying appropriate boundary conditions, and calibrating the model to measured piezometric and potentiometric data. For SRS areas where the groundwater motion is essentially 2-D with negligible vertical gradients, a simplified modeling capability was developed in a GIS software framework providing the capability to simulate 2-D groundwater motion with results that could be obtained in hours, versus weeks or months often required for a full 3-D model
Comparison of 1D and 2D CSR Models with Application to the FERMI@ELETTRA Bunch Compressors
Bassi, G.; Ellison, J.A.; Heinemann, K.
2011-03-28
We compare our 2D mean field (Vlasov-Maxwell) treatment of coherent synchrotron radiation (CSR) effects with 1D approximations of the CSR force which are commonly implemented in CSR codes. In our model we track particles in 4D phase space and calculate 2D forces [1]. The major cost in our calculation is the computation of the 2D force. To speed up the computation and improve 1D models we also investigate approximations to our exact 2D force. As an application, we present numerical results for the Fermi{at}Elettra first bunch compressor with the configuration described in [1].
Comparison of 1D and 2D CSR Models with Application to the FERMI(at)ELETTRA Bunch Compressors
We compare our 2D mean field (Vlasov-Maxwell) treatment of coherent synchrotron radiation (CSR) effects with 1D approximations of the CSR force which are commonly implemented in CSR codes. In our model we track particles in 4D phase space and calculate 2D forces (1). The major cost in our calculation is the computation of the 2D force. To speed up the computation and improve 1D models we also investigate approximations to our exact 2D force. As an application, we present numerical results for the Fermi(at)Elettra first bunch compressor with the configuration described in (1).
Heo, Jingu; Savvides, Marios
2012-12-01
In this paper, we propose a novel method for generating a realistic 3D human face from a single 2D face image for the purpose of synthesizing new 2D face images at arbitrary poses using gender and ethnicity specific models. We employ the Generic Elastic Model (GEM) approach, which elastically deforms a generic 3D depth-map based on the sparse observations of an input face image in order to estimate the depth of the face image. Particularly, we show that Gender and Ethnicity specific GEMs (GE-GEMs) can approximate the 3D shape of the input face image more accurately, achieving a better generalization of 3D face modeling and reconstruction compared to the original GEM approach. We qualitatively validate our method using publicly available databases by showing each reconstructed 3D shape generated from a single image and new synthesized poses of the same person at arbitrary angles. For quantitative comparisons, we compare our synthesized results against 3D scanned data and also perform face recognition using synthesized images generated from a single enrollment frontal image. We obtain promising results for handling pose and expression changes based on the proposed method. PMID:22201062
2D cellular automaton model for the evolution of active region coronal plasmas
Fuentes, Marcelo López
2016-01-01
We study a 2D 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 (EBTEL) model to compute the response of the plasma to the heating events. Using the known response of the XRT 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 t...
Global regularity for the 2D Oldroyd-B model in the corotational case
Ye, Zhuan; Xu, Xiaojing
2016-09-01
This paper is dedicated to the Oldroyd-B model with fractional dissipation $(-\\Delta)^{\\alpha}\\tau$ for any $\\alpha>0$. We establish the global smooth solutions to the Oldroyd-B model in the corotational case with arbitrarily small fractional powers of the Laplacian in two spatial dimensions. The methods described here are quite different from the tedious iterative approach used in recent paper \\cite{XY}. Moreover, in the Appendix we provide some a priori estimates to the Oldroyd-B model in the critical case which may be useful and of interest for future improvement. Finally, the global regularity to to the Oldroyd-B model in the corotational case with $-\\Delta u$ replaced by $(-\\Delta)^{\\gamma}u$ for $\\gamma>1$ are also collected in the Appendix. Therefore our result is more closer to the resolution of the well-known global regularity issue on the critical 2D Oldroyd-B model.
Sakr, Ahmed Hamdi; Hossain, Ekram
2014-01-01
While cognitive radio enables spectrum-efficient wireless communication, radio frequency (RF) energy harvesting from ambient interference is an enabler for energy-efficient wireless communication. In this paper, we model and analyze cognitive and energy harvesting-based D2D communication in cellular networks. The cognitive D2D transmitters harvest energy from ambient interference and use one of the channels allocated to cellular users (in uplink or downlink), which is referred to as the D2D c...
Verification of Numerical Modeling in 2-D Wave Propagation in Rock
LEI Wei-dong; HEFNY Ashraf; TENG Jun; ZHAO Jian; SONG Hong-wei
2005-01-01
Compressional harmonic wave propagation from a cylindrical tunnel or borehole in an intact rock is the basis for investigation of the practical explosion waves in a fractured rock mass. The amplitudes of the radial stress wave obtained from the universal distinct element code (UDEC) were compared with the analytical solutions for two cases with different conditions. Good agreements between the UDEC results and the analytical solutions have been achieved. It indicates that UDEC can model 2-D dynamic problems at a high degree of accuracy.
Nishimori point in the 2D +/- J random-bond Ising model
A. Honecker; Picco, M.; Pujol, P.
2000-01-01
We study the universality class of the Nishimori point in the 2D +/- J random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free-energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value p_c = 0.1094 +/- 0.0002 and estimate nu = 1.33 +/- 0.03. Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge c = 0.464 +/- 0.004. The mai...
Prominence Parameters from 2D Modeling of Lyman Lines Measured with SUMER
Gunár, Stanislav; Heinzel, Petr; Schmieder, B.; Anzer, U.
San Francisco: Astronomical Society of the Pacific, 2007 - (Heinzel, P.; Dorotovič, I.; Rutten, R.), s. 317-320. (ASP Conference Series. 368). ISBN 978-1-583812-36-5. [Solar Physics Meeting. Coimbra (PT), 09.10.2006-13.10.2006] Grant ostatní: EU(XE) ESA-PECS project NO. 9030 Institutional research plan: CEZ:AV0Z10030501 Source of funding: V - iné verejné zdroje Keywords : solar prominence * Lyman series lines * 2D modeling Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics
A quasi 2D semianalytical model for the potential profile in hetero and homojunction tunnel FETs
Villani, F.; Gnani, E.; Gnudi, A.; Reggiani, S.; Baccarani, G.
2015-11-01
A quasi 2D semianalytical model for the potential profile in hetero and homojunction tunnel FETs is developed and compared with full-quantum simulation results. It will be shown that the pure analytical solution perfectly matches results at high VDS. However, a coupling with the numerical solution of the 1D Poisson equation in the radial direction is necessary at low VDS, in order to properly account for the charge density in equilibrium with the drain contact. With such an approach we are able to correctly predict the potential profile for both the linear and saturation regimes.
Non-Fragile Controller Design for 2-D Discrete Uncertain Systems Described by the Roesser Model
Amit Dhawan
2012-01-01
This paper is concerned with the design problem of non-fragile controller for a class of two-dimensional (2-D) discrete uncertain systems described by the Roesser model. The parametric uncertainties are assumed to be norm-bounded. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A new linear matrix inequality (LMI) based suf...
Entanglement entropy through conformal interfaces in the 2D Ising model
Brehm, Enrico M
2015-01-01
We consider the entanglement entropy for the 2D Ising model at the conformal fixed point in the presence of interfaces. More precisely, we investigate the situation where the two subsystems are separated by a defect line that preserves conformal invariance. Using the replica trick, we compute the entanglement entropy between the two subsystems. We observe that the entropy, just like in the case without defects, shows a logarithmic scaling behavior with respect to the size of the system. Here, the prefactor of the logarithm depends on the strength of the defect encoded in the transmission coefficient. We also commend on the supersymmetric case.
Fusion of Critical Defect Lines in the 2D Ising Model
Bachas, Costas; Brunner, Ilka; Roggenkamp, Daniel
2013-01-01
Two defect lines separated by a distance delta look from much larger distances like a single defect. In the critical theory, when all scales are large compared to the cutoff scale, this fusion of defect lines is universal. We calculate the universal fusion rule in the critical 2D Ising model and show that it is given by the Verlinde algebra of primary fields, combined with group multiplication in O(1,1)/Z_2. Fusion is in general singular and requires the subtraction of a divergent Casimir ene...
3D reconstruction of femoral shape using a two 2D radiographs and statistical parametric model
In medical imaging, X-ray CT scanner or MRI system are quite useful to acquire 3D shapes of internal organs or bones. However, these apparatuses are generally very expensive and of large size. They also need a prior arrangement, and thus, they are unsuitable for an urgent fracture diagnosis in emergency treatment. This paper proposes a method to estimate a 3D shape of patient's femur from only two radiographs using a parametric femoral model. Firstly, we develop the parametric femoral model utilizing statistical procedure of 3D femoral models by CT images of 51 patients. Then, the pose and shape parameters of the parametric model are estimated from two 2D images using a distance map constructed by the Level Set Method. Experiments using synthesized images and radiographs of a phantom femur are carried out to verify the performance of the proposed technique. (author)
Quasi 2D hydrodynamic modelling of the flooded hinterland due to dyke breaching on the Elbe River
S. Huang
2007-01-01
Full Text Available In flood modeling, many 1D and 2D combination and 2D models are used to simulate diversion of water from rivers through dyke breaches into the hinterland for extreme flood events. However, these models are too demanding in data requirements and computational resources which is an important consideration when uncertainty analysis using Monte Carlo techniques is used to complement the modeling exercise. The goal of this paper is to show the development of a quasi-2D modeling approach, which still calculates the dynamic wave in 1D but the discretisation of the computational units are in 2D, allowing a better spatial representation of the flow in the hinterland due to dyke breaching without a large additional expenditure on data pre-processing and computational time. A 2D representation of the flow and velocity fields is required to model sediment and micro-pollutant transport. The model DYNHYD (1D hydrodynamics from the WASP5 modeling package was used as a basis for the simulations. The model was extended to incorporate the quasi-2D approach and a Monte-Carlo Analysis was used to conduct a flood sensitivity analysis to determine the sensitivity of parameters and boundary conditions to the resulting water flow. An extreme flood event on the Elbe River, Germany, with a possible dyke breach area was used as a test case. The results show a good similarity with those obtained from another 1D/2D modeling study.
Dynamical study of 2D and 3D barred galaxy models
Manos, T
2008-01-01
We study the dynamics of 2D and 3D barred galaxy analytical models, focusing on the distinction between regular and chaotic orbits with the help of the Smaller ALigment Index (SALI), a very powerful tool for this kind of problems. We present briefly the method and we calculate the fraction of chaotic and regular orbits in several cases. In the 2D model, taking initial conditions on a Poincar\\'{e} $(y,p_y)$ surface of section, we determine the fraction of regular and chaotic orbits. In the 3D model, choosing initial conditions on a cartesian grid in a region of the $(x, z, p_y)$ space, which in coordinate space covers the inner disc, we find how the fraction of regular orbits changes as a function of the Jacobi constant. Finally, we outline that regions near the $(x,y)$ plane are populated mainly by regular orbits. The same is true for regions that lie either near to the galactic center, or at larger relatively distances from it.
Yan, Bo; Li, Yuguo; Liu, Ying
2016-07-01
In this paper, we present an adaptive finite element (FE) algorithm for direct current (DC) resistivity modeling in 2-D generally anisotropic conductivity structures. Our algorithm is implemented on an unstructured triangular mesh that readily accommodates complex structures such as topography and dipping layers and so on. We implement a self-adaptive, goal-oriented grid refinement algorithm in which the finite element analysis is performed on a sequence of refined grids. The grid refinement process is guided by an a posteriori error estimator. The problem is formulated in terms of total potentials where mixed boundary conditions are incorporated. This type of boundary condition is superior to the Dirichlet type of conditions and improves numerical accuracy considerably according to model calculations. We have verified the adaptive finite element algorithm using a two-layered earth with azimuthal anisotropy. The FE algorithm with incorporation of mixed boundary conditions achieves high accuracy. The relative error between the numerical and analytical solutions is less than 1% except in the vicinity of the current source location, where the relative error is up to 2.4%. A 2-D anisotropic model is used to demonstrate the effects of anisotropy upon the apparent resistivity in DC soundings.
Stochastic dynamics of phase singularities under ventricular fibrillation in 2D Beeler-Reuter model
Akio Suzuki
2011-09-01
Full Text Available The dynamics of ventricular fibrillation (VF has been studied extensively, and the initiation mechanism of VF has been elucidated to some extent. However, the stochastic dynamical nature of sustained VF remains unclear so far due to the complexity of high dimensional chaos in a heterogeneous system. In this paper, various statistical mechanical properties of sustained VF are studied numerically in 2D Beeler-Reuter-Drouhard-Roberge (BRDR model with normal and modified ionic current conductance. The nature of sustained VF is analyzed by measuring various fluctuations of spatial phase singularity (PS such as velocity, lifetime, the rates of birth and death. It is found that the probability density function (pdf for lifetime of PSs is independent of system size. It is also found that the hyper-Gamma distribution serves as a universal pdf for the counting number of PSs for various system sizes and various parameters of our model tissue under VF. Further, it is demonstrated that the nonlinear Langevin equation associated with a hyper-Gamma process can mimic the pdf and temporal variation of the number of PSs in the 2D BRDR model.
EDGE2D modelling of edge profiles obtained in JET diagnostic optimized configuration
Kallenbach, A [MPI fuer Plasmaphysik, EURATOM Association, D-85748 Garching (Germany); Andrew, Y [EURATOM/UKAEA Fusion Association, Culham (United Kingdom); Beurskens, M [FOM-Rijnhuizen, Ass. Euratom-FOM, TEC (Netherlands); Corrigan, G [EURATOM/UKAEA Fusion Association, Culham (United Kingdom); Eich, T [MPI fuer Plasmaphysik, EURATOM Association, D-85748 Garching (Germany); Jachmich, S [ERM, Brussels (Belgium); Kempenaars, M [FOM-Rijnhuizen, Ass. Euratom-FOM, TEC (Netherlands); Korotkov, A [EURATOM/UKAEA Fusion Association, Culham (United Kingdom); Loarte, A [EFDA Close Support Unit, Garching (Germany); Matthews, G [EURATOM/UKAEA Fusion Association, Culham (United Kingdom); Monier-Garbet, P [CEA Cadarache (France); Saibene, G [EFDA Close Support Unit, Garching (Germany); Spence, J [EURATOM/UKAEA Fusion Association, Culham (United Kingdom); Suttrop, W [MPI fuer Plasmaphysik, EURATOM Association, D-85748 Garching (Germany)
2004-03-01
Nine type-I ELMy H-mode discharges in diagnostic optimized configuration in JET are analysed with the EDGE2D/NIMBUS package. EDGE2D solves the fluid equations for the conservation of particles, momentum and energy for hydrogenic and impurity ions, while neutrals are followed with the two-dimensional Monte Carlo module NIMBUS. Using external boundary conditions from the experiment, the perpendicular heat conductivities {chi}{sub i,e} and the particle transport coefficients D, v are varied until good agreement between code result and measured data is obtained. A step-like ansatz is used for the edge transport parameters for the outer core region, the edge transport barrier and the outer scrape-off layer. The time-dependent effect of edge localized modes on the edge profiles is simulated with an ad hoc ELM model based on the repetitive increase of the transport coefficients {chi}{sub i,e} and D. The values of the transport coefficients are matched to experimental data mapped to the outer midplane, in the course of which radial shifts of experimental profiles of the order of 1 cm caused by the accuracy limit of the equilibrium reconstruction are taken into account. Simulated divertor profiles obtained from the upstream transport ansatz and the experimental boundary conditions agree with measurements, except a small region localized at the separatrix strike points which is supposed to be affected by direct ion losses. The integrated analysis using EDGE2D modelling, although still limited by the marginal spatial resolution of individual diagnostics, allows the characterization of profiles in the edge/pedestal region and supplies additional information on the separatrix position. The steep density gradient zone inside the separatrix shrinks compared to the electron temperature with increasing density, indicating the effect of the neutral penetration depth becoming shorter than the region of reduced transport.
Uncertainties in modelling Mt. Pinatubo eruption with 2-D AER model and CCM SOCOL
Kenzelmann, P.; Weisenstein, D.; Peter, T.; Luo, B. P.; Rozanov, E.; Fueglistaler, S.; Thomason, L. W.
2009-04-01
Large volcanic eruptions may introduce a strong forcing on climate. They challenge the skills of climate models. In addition to the short time attenuation of solar light by ashes the formation of stratospheric sulphate aerosols, due to volcanic sulphur dioxide injection into the lower stratosphere, may lead to a significant enhancement of the global albedo. The sulphate aerosols have a residence time of about 2 years. As a consequence of the enhanced sulphate aerosol concentration both the stratospheric chemistry and dynamics are strongly affected. Due to absorption of longwave and near infrared radiation the temperature in the lower stratosphere increases. So far chemistry climate models overestimate this warming [Eyring et al. 2006]. We present an extensive validation of extinction measurements and model runs of the eruption of Mt. Pinatubo in 1991. Even if Mt. Pinatubo eruption has been the best quantified volcanic eruption of this magnitude, the measurements show considerable uncertainties. For instance the total amount of sulphur emitted to the stratosphere ranges from 5-12 Mt sulphur [e.g. Guo et al. 2004, McCormick, 1992]. The largest uncertainties are in the specification of the main aerosol cloud. SAGE II, for instance, could not measure the peak of the aerosol extinction for about 1.5 years, because optical termination was reached. The gap-filling of the SAGE II [Thomason and Peter, 2006] using lidar measurements underestimates the total extinctions in the tropics for the first half year after the eruption by 30% compared to AVHRR [Rusell et. al 1992]. The same applies to the optical dataset described by Stenchikov et al. [1998]. We compare these extinction data derived from measurements with extinctions derived from AER 2D aerosol model calculations [Weisenstein et al., 2007]. Full microphysical calculations with injections of 14, 17, 20 and 26 Mt SO2 in the lower stratosphere were performed. The optical aerosol properties derived from SAGE II
Well-posedness and generalized plane waves simulations of a 2D mode conversion model
Imbert-Gérard, Lise-Marie
2015-01-01
Certain types of electro-magnetic waves propagating in a plasma can undergo a mode conversion process. In magnetic confinement fusion, this phenomenon is very useful to heat the plasma, since it permits to transfer the heat at or near the plasma center. This work focuses on a mathematical model of wave propagation around the mode conversion region, from both theoretical and numerical points of view. It aims at developing, for a well-posed equation, specific basis functions to study a wave mode conversion process. These basis functions, called generalized plane waves, are intrinsically based on variable coefficients. As such, they are particularly adapted to the mode conversion problem. The design of generalized plane waves for the proposed model is described in detail. Their implementation within a discontinuous Galerkin method then provides numerical simulations of the process. These first 2D simulations for this model agree with qualitative aspects studied in previous works.
A coupled $2\\times2$D Babcock-Leighton solar dynamo model. II. Reference dynamo solutions
Lemerle, Alexandre
2016-01-01
In this paper we complete the presentation of a new hybrid $2\\times2$D flux transport dynamo (FTD) model of the solar cycle based on the Babcock-Leighton mechanism of poloidal magnetic field regeneration via the surface decay of bipolar magnetic regions (BMRs). This hybrid model is constructed by allowing the surface flux transport (SFT) simulation described in Lemerle et al. 2015 to provide the poloidal source term to an axisymmetric FTD simulation defined in a meridional plane, which in turn generates the BMRs required by the SFT. A key aspect of this coupling is the definition of an emergence function describing the probability of BMR emergence as a function of the spatial distribution of the internal axisymmetric magnetic field. We use a genetic algorithm to calibrate this function, together with other model parameters, against observed cycle 21 emergence data. We present a reference dynamo solution reproducing many solar cycle characteristics, including good hemispheric coupling, phase relationship betwe...
Boontian, Nittaya
2012-01-01
Carbon sources are considered as one of the most important factors in the performance of enhanced biological phosphorus removal (EBPR). Disintegrated sludge (DS) can act as carbon source to increase the efficiency of EBPR. This research explores the influence of DS upon phosphorus removal efficiency using mathematical simulation modeling. Activated Sludge Model No. 2d (ASM2d) is one of the most useful of activated sludge (AS) models. This is because ASM2d can express the integrated mechanisms...
Non-interacting systems with bounded disorder have been shown to exhibit sharp density of state peaks at the band edge which coincide with an energy range of abruptly suppressed localization. Recent work has shown that these features also occur in the presence of on-site interactions in ensembles of two-site Anderson–Hubbard systems at half filling. Here we demonstrate that this effect in interacting systems persists away from half filling, and moreover that energy regions with suppressed localization continue to appear in ensembles of larger systems despite a loss of sharp features in the density of states. (paper)
Daley, P; Wortis, R
2016-05-01
Non-interacting systems with bounded disorder have been shown to exhibit sharp density of state peaks at the band edge which coincide with an energy range of abruptly suppressed localization. Recent work has shown that these features also occur in the presence of on-site interactions in ensembles of two-site Anderson-Hubbard systems at half filling. Here we demonstrate that this effect in interacting systems persists away from half filling, and moreover that energy regions with suppressed localization continue to appear in ensembles of larger systems despite a loss of sharp features in the density of states. PMID:27022884
Modeling and 2-D discrete simulation of dislocation dynamics for plastic deformation of metal
Liu, Juan; Cui, Zhenshan; Ou, Hengan; Ruan, Liqun
2013-05-01
Two methods are employed in this paper to investigate the dislocation evolution during plastic deformation of metal. One method is dislocation dynamic simulation of two-dimensional discrete dislocation dynamics (2D-DDD), and the other is dislocation dynamics modeling by means of nonlinear analysis. As screw dislocation is prone to disappear by cross-slip, only edge dislocation is taken into account in simulation. First, an approach of 2D-DDD is used to graphically simulate and exhibit the collective motion of a large number of discrete dislocations. In the beginning, initial grains are generated in the simulation cells according to the mechanism of grain growth and the initial dislocation is randomly distributed in grains and relaxed under the internal stress. During the simulation process, the externally imposed stress, the long range stress contribution of all dislocations and the short range stress caused by the grain boundaries are calculated. Under the action of these forces, dislocations begin to glide, climb, multiply, annihilate and react with each other. Besides, thermal activation process is included. Through the simulation, the distribution of dislocation and the stress-strain curves can be obtained. On the other hand, based on the classic dislocation theory, the variation of the dislocation density with time is described by nonlinear differential equations. Finite difference method (FDM) is used to solve the built differential equations. The dislocation evolution at a constant strain rate is taken as an example to verify the rationality of the model.
Modeling floods in a dense urban area using 2D shallow water equations
Mignot, E.; Paquier, A.; Haider, S.
2006-07-01
SummaryA code solving the 2D shallow water equations by an explicit second-order scheme is used to simulate the severe October 1988 flood in the Richelieu urban locality of the French city of Nîmes. A reference calculation using a detailed description of the street network and of the cross-sections of the streets, considering impervious residence blocks and neglecting the flow interaction with the sewer network provides a mean peak water elevation 0.13 m lower than the measured flood marks with a standard deviation between the measured and computed water depths of 0.53 m. Sensitivity analysis of various topographical and numerical parameters shows that globally, the results keep the same level of accuracy, which reflects both the stability of the calculation method and the smoothening of results. However, the local flow modifications due to change of parameter values can drastically modify the local water depths, especially when the local flow regime is modified. Furthermore, the flow distribution to the downstream parts of the city can be altered depending on the set of parameters used. Finally, a second event, the 2002 flood, was simulated with the calibrated model providing results similar to 1988 flood calculation. Thus, the article shows that, after calibration, a 2D model can be used to help planning mitigation measures in a dense urban area.
Interpretation of gravity data using 2-D continuous wavelet transformation and 3-D inverse modeling
Roshandel Kahoo, Amin; Nejati Kalateh, Ali; Salajegheh, Farshad
2015-10-01
Recently the continuous wavelet transform has been proposed for interpretation of potential field anomalies. In this paper, we introduced a 2D wavelet based method that uses a new mother wavelet for determination of the location and the depth to the top and base of gravity anomaly. The new wavelet is the first horizontal derivatives of gravity anomaly of a buried cube with unit dimensions. The effectiveness of the proposed method is compared with Li and Oldenburg inversion algorithm and is demonstrated with synthetics and real gravity data. The real gravity data is taken over the Mobrun massive sulfide ore body in Noranda, Quebec, Canada. The obtained results of the 2D wavelet based algorithm and Li and Oldenburg inversion on the Mobrun ore body had desired similarities to the drill-hole depth information. In all of the inversion algorithms the model non-uniqueness is the challenging problem. Proposed method is based on a simple theory and there is no model non-uniqueness on it.
2D-hybrid particle model with non-linear electron distribution
A 2D, hybrid (particle-ion, fluid-electron) simulation code characterized by the solution of the non-linear modified Poisson equation, which results assuming the Boltzmann distribution for the electrons, is presented. The field solution is achieved through an iterative procedure. Anyhow a new scheme is considered. The potential is not obtained by directly solving the finite difference equation but via the Green's function method. The procedure begins with the first guess for the potential. This is found through the solution of the linearized modified Poisson equation. The Green's function for this equation, in the 2D case which is considered, can be found analytically in terms of the Newmann functions. Once the potential corresponding to the linearized modified Poisson equation is known, the first approximation of the electron (Boltzmann) distribution can be calculated. This distribution, plus the one given by the (particle) ions, is considered as the source term for the Poisson equation (which now is not modified since the fluid electron component is taken into account in the source term itself). The solution of this Poisson equation gives the second approximation of the electric potential and is still obtained via the Green's function method (as it comes from the Coulomb law, modified for the 2D case). Each time step this procedure can be iterated according to the desired accuracy. The last iteration cycle is different: in fact the direct solution for the electric field can be obtained, without numerical differencing from the potential. It is sufficient in this case to consider the electric field Green's functions (x- and y-component) for the Poisson equation (in place of the electric potential Green's function). The first results obtained with this new code are here presented and compared with previous simulation runs based on a linearized Boltzmann distribution model. 3 refs
Be2D: A model to understand the distribution of meteoric 10Be in soilscapes
Campforts, Benjamin; Vanacker, Veerle; Vanderborght, Jan; Govers, Gerard
2016-04-01
Cosmogenic nuclides have revolutionised our understanding of earth surface process rates. They have become one of the standard tools to quantify soil production by weathering, soil redistribution and erosion. Especially Beryllium-10 has gained much attention due to its long half-live and propensity to be relatively conservative in the landscape. The latter makes 10Be an excellent tool to assess denudation rates over the last 1000 to 100 × 103 years, bridging the anthropogenic and geological time scale. Nevertheless, the mobility of meteoric 10Be in soil systems makes translation of meteoric 10Be inventories into erosion and deposition rates difficult. Here we present a coupled soil hillslope model, Be2D, that is applied to synthetic and real topography to address the following three research questions. (i) What is the influence of vertical meteoric Be10 mobility, caused by chemical mobility, clay translocation and bioturbation, on its lateral redistribution over the soilscape, (ii) How does vertical mobility influence erosion rates and soil residence times inferred from meteoric 10Be inventories and (iii) To what extent can a tracer with a half-life of 1.36 Myr be used to distinguish between natural and human-disturbed soil redistribution rates? The model architecture of Be2D is designed to answer these research questions. Be2D is a dynamic model including physical processes such as soil formation, physical weathering, clay migration, bioturbation, creep, overland flow and tillage erosion. Pathways of meteoric 10Be mobility are simulated using a two step approach which is updated each timestep. First, advective and diffusive mobility of meteoric 10Be is simulated within the soil profile and second, lateral redistribution because of lateral soil fluxes is calculated. The performance and functionality of the model is demonstrated through a number of synthetic and real model runs using existing datasets of meteoric 10Be from case-studies in southeastern US. Brute
Estimating nitrogen losses in furrow irrigated soil amended by compost using HYDRUS-2D model
Iqbal, Shahid; Guber, Andrey; Zaman Khan, Haroon; ullah, Ehsan
2014-05-01
Furrow irrigation commonly results in high nitrogen (N) losses from soil profile via deep infiltration. Estimation of such losses and their reduction is not a trivial task because furrow irrigation creates highly nonuniform distribution of soil water that leads to preferential water and N fluxes in soil profile. Direct measurements of such fluxes are impractical. The objective of this study was to assess applicability of HYDRUS-2D model for estimating nitrogen balance in manure amended soil under furrow irrigation. Field experiments were conducted in a sandy loam soil amended by poultry manure compost (PMC) and pressmud compost (PrMC) fertilizers. The PMC and PrMC contained 2.5% and 0.9% N and were applied at 5 rates: 2, 4, 6, 8 and 10 ton/ha. Plots were irrigated starting from 26th day from planting using furrows with 1x1 ridge to furrow aspect ratio. Irrigation depths were 7.5 cm and time interval between irrigations varied from 8 to 15 days. Results of the field experiments showed that approximately the same corn yield was obtained with considerably higher N application rates using PMC than using PrMC as a fertilizer. HYDRUS-2D model was implemented to evaluate N fluxes in soil amended by PMC and PrMC fertilizers. Nitrogen exchange between two pools of organic N (compost and soil) and two pools of mineral N (soil NH4-N and soil NO3-N) was modeled using mineralization and nitrification reactions. Sources of mineral N losses from soil profile included denitrification, root N uptake and leaching with deep infiltration of water. HYDRUS-2D simulations showed that the observed increases in N root water uptake and corn yields associated with compost application could not be explained by the amount of N added to soil profile with the compost. Predicted N uptake by roots significantly underestimated the field data. Good agreement between simulated and field-estimated values of N root uptake was achieved when the rate of organic N mineralization was increased
Complex-temperature properties of the Ising model on 2D heteropolygonal lattices
Matveev, V; Matveev, Victor; Shrock, Robert
1995-01-01
Using exact results, we determine the complex-temperature phase diagrams of the 2D Ising model on three regular heteropolygonal lattices, (3 \\cdot 6 \\cdot 3 \\cdot 6) (kagom\\'{e}), (3 \\cdot 12^2), and (4 \\cdot 8^2) (bathroom tile), where the notation denotes the regular n-sided polygons adjacent to each vertex. We also work out the exact complex-temperature singularities of the spontaneous magnetisation. A comparison with the properties on the square, triangular, and hexagonal lattices is given. In particular, we find the first case where, even for isotropic spin-spin exchange couplings, the nontrivial non-analyticities of the free energy of the Ising model lie in a two-dimensional, rather than one-dimensional, algebraic variety in the z=e^{-2K} plane.
SO(3) vortices and disorder in the 2d SU(2) chiral model
Kovács, T G
1995-01-01
We study the correlation function of the 2d SU(2) principal chiral model on the lattice. By rewriting the model in terms of Z(2) degrees of freedom coupled to SO(3) vortices we show that the vortices play a crucial role in disordering the correlations at low temperature. Using a series of exact transformations we prove that, if satisfied, certain inequalities between vortex correlations imply exponential fall-off of the correlation function at arbitrarily low temperatures. We also present some Monte Carlo evidence that these correlation inequalities are indeed satisfied. Our method can be easily translated to the language of 4d SU(2) gauge theory to establish the role of corresponding SO(3) monopoles in maintaining confinement at small couplings.
A VERTICAL 2D MATHEMATICAL MODEL FOR HYDRODYNAMIC FLOWS WITH FREE SURFACE IN σ COORDINATE
无
2006-01-01
Numerical models with hydrostatic pressure have been widely utilized in studying flows in rivers, estuaries and coastal areas. The hydrostatic assumption is valid for the large-scale surface flows where the vertical acceleration can be ignored, but for some particular cases the hydrodynamic pressure is important. In this paper, a vertical 2D mathematical model with non-hydrostatic pressure was implemented in the σ coordinate. A fractional step method was used to enable the pressure to be decomposed into hydrostatic and hydrodynamic components and the predictor-corrector approach was applied to integration in time domain. Finally, several computational cases were studied to validate the importance of contributions of the hydrodynamic pressure.
2D and 3D numerical modeling of seismic waves from explosion sources
Over the last decade, nonlinear and linear 2D axisymmetric finite difference codes have been used in conjunction with far-field seismic Green's functions to simulate seismic waves from a variety of sources. In this paper we briefly review some of the results and conclusions that have resulted from numerical simulations and explosion modeling in support of treaty verification research at S-CUBED in the last decade. We then describe in more detail the results from two recent projects. Our goal is to provide a flavor for the kinds of problems that can be examined with numerical methods for modeling excitation of seismic waves from explosions. Two classes of problems have been addressed; nonlinear and linear near-source interactions. In both classes of problems displacements and tractions are saved on a closed surface in the linear region and the representation theorem is used to propagate the seismic waves to the far-field
Singularities of the Partition Function for the Ising Model Coupled to 2D Quantum Gravity
Ambjørn, J.; Anagnostopoulos, K. N.; Magnea, U.
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2D quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We compute the zeros by using the exact solution coming from a two-matrix model and by Monte-Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional curves in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of the singularities near the critical point. Despite the small size of the systems studied, we can obtain a reasonable estimate of the (known) critical exponents.
On Spectral Laws of 2D-Turbulence in Shell Models
Frick, P; Frick, Peter; Aurell, Erik
1993-01-01
We consider a class of shell models of 2D-turbulence. They conserve inertially the analogues of energy and enstrophy, two quadratic forms in the shell amplitudes. Inertially conserving two quadratic integrals leads to two spectral ranges. We study in detail the one characterized by a forward cascade of enstrophy and spectrum close to Kraichnan's $k^{-3}$--law. In an inertial range over more than 15 octaves, the spectrum falls off as $k^{-3.05\\pm 0.01}$, with the same slope in all models. We identify a ``spurious'' intermittency effect, in that the energy spectrum over a rather wide interval adjoing the viscous cut-off, is well approximated by a power-law with fall-off significantly steeper than $k^{-3}$.
Optimal implicit 2-D finite differences to model wave propagation in poroelastic media
Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.
2016-05-01
Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite-differences to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (waves (for a porous media saturated with fluid). The numerical dispersion and stability conditions are derived using von Neumann analysis, showing that over a wide range of porous materials the Courant condition governs the stability and this optimal implicit scheme improves the stability of explicit schemes. High order explicit finite-differences (FD) can be replaced by some lower order optimal implicit FD so computational cost will not be as expensive while maintaining the accuracy. Here we compute weights for the optimal implicit FD scheme to attain an accuracy of γ = 10-8. The implicit spatial differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.
A New Material Model for 2D FE Analysis of Adhesively Bonded Composite Joints
Libin ZHAO
2014-12-01
Full Text Available Effective and convenient stress analysis techniques play important roles in the analysis and design of adhesively bonded composite joints. A new material model is presented at the level of composite ply according to the orthotropic elastic mechanics theory and plane strain assumption. The model proposed has the potential to reserve nature properties of laminates with ply-to-ply modeling. The equivalent engineering constants in the model are obtained only by the material properties of unidirectional composites. Based on commercial FE software ABAQUS, a 2D FE model of a single-lap adhesively bonded joint was established conveniently by using the new model without complex modeling process and much professional knowledge. Stress distributions in adhesive were compared with the numerical results by Tsai and Morton and interlaminar stresses between adhesive and adherents were compared with the results from a detailed 3D FE analysis. Good agreements in both cases verify the validity of the proposed model. DOI: http://dx.doi.org/10.5755/j01.ms.20.4.5960
2D time-domain finite-difference modeling for viscoelastic seismic wave propagation
Fan, Na; Zhao, Lian-Feng; Xie, Xiao-Bi; Ge, Zengxi; Yao, Zhen-Xing
2016-07-01
Real Earth media are not perfectly elastic. Instead, they attenuate propagating mechanical waves. This anelastic phenomenon in wave propagation can be modeled by a viscoelastic mechanical model consisting of several standard linear solids. Using this viscoelastic model, we approximate a constant Q over a frequency band of interest. We use a four-element viscoelastic model with a tradeoff between accuracy and computational costs to incorporate Q into 2D time-domain first-order velocity-stress wave equations. To improve the computational efficiency, we limit the Q in the model to a list of discrete values between 2 and 1000. The related stress and strain relaxation times that characterize the viscoelastic model are pre-calculated and stored in a database for use by the finite-difference calculation. A viscoelastic finite-difference scheme that is second-order in time and fourth-order in space is developed based on the MacCormack algorithm. The new method is validated by comparing the numerical result with analytical solutions that are calculated using the generalized reflection/transmission coefficient method. The synthetic seismograms exhibit greater than 95 per cent consistency in a two-layer viscoelastic model. The dispersion generated from the simulation is consistent with the Kolsky-Futterman dispersion relationship.
Transforming 2d Cadastral Data Into a Dynamic Smart 3d Model
Tsiliakou, E.; Labropoulos, T.; Dimopoulou, E.
2013-08-01
3D property registration has become an imperative need in order to optimally reflect all complex cases of the multilayer reality of property rights and restrictions, revealing their vertical component. This paper refers to the potentials and multiple applications of 3D cadastral systems and explores the current state-of-the art, especially the available software with which 3D visualization can be achieved. Within this context, the Hellenic Cadastre's current state is investigated, in particular its data modeling frame. Presenting the methodologies and specifications addressing the registration of 3D properties, the operating cadastral system's shortcomings and merits are pointed out. Nonetheless, current technological advances as well as the availability of sophisticated software packages (proprietary or open source) call for 3D modeling. In order to register and visualize the complex reality in 3D, Esri's CityEngine modeling software has been used, which is specialized in the generation of 3D urban environments, transforming 2D GIS Data into Smart 3D City Models. The application of the 3D model concerns the Campus of the National Technical University of Athens, in which a complex ownership status is established along with approved special zoning regulations. The 3D model was built using different parameters based on input data, derived from cadastral and urban planning datasets, as well as legal documents and architectural plans. The process resulted in a final 3D model, optimally describing the cadastral situation and built environment and proved to be a good practice example of 3D visualization.
Mo, Yike; Greenhalgh, Stewart A.; Robertsson, Johan O. A.; Karaman, Hakki
2015-05-01
Lateral velocity variations and low velocity near-surface layers can produce strong scattered and guided waves which interfere with reflections and lead to severe imaging problems in seismic exploration. In order to investigate these specific problems by laboratory seismic modelling, a simple 2D ultrasonic model facility has been recently assembled within the Wave Propagation Lab at ETH Zurich. The simulated geological structures are constructed from 2 mm thick metal and plastic sheets, cut and bonded together. The experiments entail the use of a piezoelectric source driven by a pulse amplifier at ultrasonic frequencies to generate Lamb waves in the plate, which are detected by piezoelectric receivers and recorded digitally on a National Instruments recording system, under LabVIEW software control. The 2D models employed were constructed in-house in full recognition of the similitude relations. The first heterogeneous model features a flat uniform low velocity near-surface layer and deeper dipping and flat interfaces separating different materials. The second model is comparable but also incorporates two rectangular shaped inserts, one of low velocity, the other of high velocity. The third model is identical to the second other than it has an irregular low velocity surface layer of variable thickness. Reflection as well as transmission experiments (crosshole & vertical seismic profiling) were performed on each model. The two dominant Lamb waves recorded are the fundamental symmetric mode (non-dispersive) and the fundamental antisymmetric (flexural) dispersive mode, the latter normally being absent when the source transducer is located on a model edge but dominant when it is on the flat planar surface of the plate. Experimental group and phase velocity dispersion curves were determined and plotted for both modes in a uniform aluminium plate. For the reflection seismic data, various processing techniques were applied, as far as pre-stack Kirchhoff migration. The
Coronary arteries motion modeling on 2D x-ray images
Gao, Yang; Sundar, Hari
2012-02-01
During interventional procedures, 3D imaging modalities like CT and MRI are not commonly used due to interference with the surgery and radiation exposure concerns. Therefore, real-time information is usually limited and building models of cardiac motion are difficult. In such case, vessel motion modeling based on 2-D angiography images become indispensable. Due to issues with existing vessel segmentation algorithms and the lack of contrast in occluded vessels, manual segmentation of certain branches is usually necessary. In addition, such occluded branches are the most important vessels during coronary interventions and obtaining motion models for these can greatly help in reducing the procedure time and radiation exposure. Segmenting different cardiac phases independently does not guarantee temporal consistency and is not efficient for occluded branches required manual segmentation. In this paper, we propose a coronary motion modeling system which extracts the coronary tree for every cardiac phase, maintaining the segmentation by tracking the coronary tree during the cardiac cycle. It is able to map every frame to the specific cardiac phase, thereby inferring the shape information of the coronary arteries using the model corresponding to its phase. Our experiments show that our motion modeling system can achieve promising results with real-time performance.
The combined effect of attraction and orientation zones in 2D flocking models
Iliass, Tarras; Cambui, Dorilson
2016-01-01
In nature, many animal groups, such as fish schools or bird flocks, clearly display structural order and appear to move as a single coherent entity. In order to understand the complex motion of these systems, we study the Vicsek model of self-propelled particles (SPP) which is an important tool to investigate the behavior of collective motion of live organisms. This model reproduces the biological behavior patterns in the two-dimensional (2D) space. Within the framework of this model, the particles move with the same absolute velocity and interact locally in the zone of orientation by trying to align their direction with that of the neighbors. In this paper, we model the collective movement of SPP using an agent-based model which follows biologically motivated behavioral rules, by adding a second region called the attraction zone, where each particles move towards each other avoiding being isolated. Our main goal is to present a detailed numerical study on the effect of the zone of attraction on the kinetic phase transition of our system. In our study, the consideration of this zone seems to play an important role in the cohesion. Consequently, in the directional orientation, the zone that we added forms the compact particle group. In our simulation, we show clearly that the model proposed here can produce two collective behavior patterns: torus and dynamic parallel group. Implications of these findings are discussed.
Time domain numerical modeling of wave propagation in 2D acoustic / porous media
Chiavassa, Guillaume
2011-01-01
Numerical methods are developed to simulate the wave propagation in 2D heterogeneous fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot's equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect pores. Well-possedness of the initial-boundary value problem is proven. Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context: a fourth-order ADER scheme with Strang splitting for time-marching; a space-time mesh-refinement to capture the slow compressional wave predicted by Biot's theory; and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution. Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions, demonstrating the accuracy of the approach...
Universality Class of the Nishimori Point in the 2D +/-J Random-Bond Ising Model
Honecker, A.; Picco, M.; Pujol, P.
2001-07-01
We study the universality class of the Nishimori point in the 2D +/-J random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value pc = 0.1094+/-0.0002 and estimate ν = 1.33+/-0.03. Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge c = 0.464+/-0.004. The main qualitative result is the fact that percolation is now excluded as a candidate for describing the universality class of this fixed point.
Universality Class of the Nishimori Point in the 2D {+-}J Random-Bond Ising Model
Honecker, A.; Picco, M.; Pujol, P.
2001-07-23
We study the universality class of the Nishimori point in the 2D {+-}J random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value p{sub c}=0.1094{+-}0.0002 and estimate {nu}=1.33{+-}0.03 . Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge c=0.464{+-}0.004 . The main qualitative result is the fact that percolation is now excluded as a candidate for describing the universality class of this fixed point.
The strong-weak coupling symmetry in 2D Φ4 field models
B.N.Shalaev
2005-01-01
Full Text Available It is found that the exact beta-function β(g of the continuous 2D gΦ4 model possesses two types of dual symmetries, these being the Kramers-Wannier (KW duality symmetry and the strong-weak (SW coupling symmetry f(g, or S-duality. All these transformations are explicitly constructed. The S-duality transformation f(g is shown to connect domains of weak and strong couplings, i.e. above and below g*. Basically it means that there is a tempting possibility to compute multiloop Feynman diagrams for the β-function using high-temperature lattice expansions. The regular scheme developed is found to be strongly unstable. Approximate values of the renormalized coupling constant g* found from duality symmetry equations are in an agreement with available numerical results.
Transition from static to kinetic friction: Insights from a 2D model
Trømborg, Jørgen; Amundsen, David Skålid; Thøgersen, Kjetil; Malthe-Sørenssen, Anders
2013-01-01
We describe a 2D spring-block model for the transition from static to kinetic friction at an elastic slider/rigid substrate interface obeying a minimalistic friction law (Amontons-Coulomb). By using realistic boundary conditions, a number of previously unexplained experimental results on precursory micro-slip fronts are successfully reproduced. From the analysis of the interfacial stresses, we derive a prediction for the evolution of the precursor length as a function of the applied loads, as well as an approximate relationship between microscopic and macroscopic friction coefficients. We show that the stress build-up due to both elastic loading and micro-slip-related relaxations depend only weakly on the underlying shear crack propagation dynamics. Conversely, crack speed depends strongly on both the instantaneous stresses and the friction coefficients, through a non-trivial scaling parameter.
Structure-approximating inverse protein folding problem in the 2D HP model.
Gupta, Arvind; Manuch, Ján; Stacho, Ladislav
2005-12-01
The inverse protein folding problem is that of designing an amino acid sequence which has a particular native protein fold. This problem arises in drug design where a particular structure is necessary to ensure proper protein-protein interactions. In this paper, we show that in the 2D HP model of Dill it is possible to solve this problem for a broad class of structures. These structures can be used to closely approximate any given structure. One of the most important properties of a good protein (in drug design) is its stability--the aptitude not to fold simultaneously into other structures. We show that for a number of basic structures, our sequences have a unique fold. PMID:16379538
2D XXZ model ground state properties using an analytic Lanczos expansion
A formalism was developed for calculating arbitrary expectation values for any extensive lattice Hamiltonian system using a new analytic Lanczos expansion, or plaquette expansion, and a recently proved exact theorem for ground state energies. The ground state energy, staggered magnetisation and the excited state gap of the 2D anisotropic antiferromagnetic Heisenberg Model are then calculated using this expansion for a range of anisotropy parameters and compared to other moment based techniques, such as the t-expansion, and spin-wave theory and series expansion methods. It was found that far from the isotropic point all moment methods give essentially very similar results, but near the isotopic point the plaquette expansion is generally better than the others. 20 refs., 6 tabs
Surface delta interaction in the g7/2 - d5/2 model space
Yu, Xiaofei; Zamick, Larry
2016-05-01
Using an attractive surface delta interaction we obtain wave functions for 2 neutrons (or neutron holes) in the g7/2 -d5/2 model space. If we take the single particle energies to be degenerate we find that the g factors for I = 2 , 4 and 6 are all the same G (J) =gl, the orbital g factor of the nucleon. For a free neutron gl = 0, so in this case all 2 particles or 2 holes' g factors are equal to zero. Only the orbital part of the g-factors contributes - the spin part cancels out. We then consider the effects of introducing a single energy splitting between the 2 orbits. We make a linear approximation for all other n values.
An application of the distributed hydrologic model CASC2D to a tropical montane watershed
Marsik, Matt; Waylen, Peter
2006-11-01
SummaryIncreased stormflow in the Quebrada Estero watershed (2.5 km 2), in the northwestern Central Valley tectonic depression of Costa Rica, reportedly has caused flooding of the city of San Ramón in recent decades. Although scientifically untested, urban expansion was deemed the cause and remedial measures were recommended by the Programa de Investigación en Desarrollo Humano Sostenible (ProDUS). CASC2D, a physically-based, spatially explicit hydrologic model, was constructed and calibrated to a June 10th 2002 storm that delivered 110.5 mm of precipitation in 4.5 h visibly exceeded the bankfull stage (0.9 m) of the Quebrada flooding portions of San Ramón. The calibrated hydrograph showed a peak discharge 16.68% (2.5 m 3 s -1) higher, an above flood stage duration 20% shorter, and time to peak discharge 11 min later than the same observed discharge hydrograph characteristics. Simulations of changing land cover conditions from 1979 to 1999 showed an increase also in the peak discharge, above flood stage duration, and time to peak discharge. Analysis using a modified location quotient identified increased urbanization in lower portions of the watershed over the time period studied. These results suggest that increased urbanization in the Quebrada Estero watershed have increased flooding peaks, and durations above threshold, confirming the ProDUS report. These results and the CASC2D model offer an easy-to-use, pragmatic planning tool for policymakers in San Ramón to assess future development scenarios and their potential flooding impacts to San Ramón.
Assessment of the Impacts of Compensation Flow Changes Upon Instream Habitat Using 2D Modelling
Mould, D. C.; Lane, S. N.; Christmas, M.
2004-05-01
Many millstone-grit rivers in northern England are impounded. In such cases the water company in the area has to release compensation flows from the reservoirs, traditionally to meet industrial needs: these flows are rarely set with ecology in mind; and have commonly involved constant flow. Dam overtopping may create spates, but spawning in many fish species is prompted by a spate flow in the early autumn when dams are rarely full enough to overtop. Such flows are important for fine sediment flushing and controlling the wetted useable area for spawning. Classical physical habitat modelling for instream habitat has been largely reliant upon 1D approaches, such as the Instream Flow Incremental Methodology (IFIM). Here we use a 2D finite element model (FESWMS), to simulate changes in instream habitat with variations in the compensation flow regimes. The spatial resolution of 2D models can be adapted to the scale of fish habitats so providing better representation of the reach-scale flow processes (such as slack water in the margins, wetting and drying) than the 1D case. The model is applied to the Rivers Rivelin and Loxley in Sheffield, Northern England. At the confluence of the two rivers, the compensation flow level is set at 30.6 Thousand Cubic Metres per Day (TCMD). Due to historical reasons, the compensation is not divided equally, as the Loxley receives 28 TCMD whilst the Rivelin receives only 2.6 TCMD. The model is used to simulate a transfer of 6 TCMD from the Loxley to the Rivelin. After validation, model predictions are combined with available habitat requirement data (e.g. velocity and depth needs) to develop an index of change in habitat suitability in terms of first order variables (e.g. velocity, depth and wetted useable area). This suggests that the change in compensation may significantly improve instream ecology in relation to macroinvertebrates, brown trout (Salmo trutta) and bullhead (Cottus gobio) in the Rivelin without causing detrimental impacts
Graded Poisson-Sigma models and dilaton-deformed 2D supergravity algebra
Supergravity extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. On the other hand, obstructions may reduce the allowed range of fields as given by the bosonic theory, or even prohibit any extension in certain cases. In our present work we relate the finite W-algebras inherent in the gPSM algebra of constraints to supergravity algebras (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of the dilaton field. With very straightforward and natural assumptions on them - like the one linking the anti-commutator of certain fermionic charges to the Hamiltonian constraint without deformation - we are able not only to remove the ambiguities but, at the same time, the singularities referred to above. Thus all especially interesting bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.) under these conditions possess a unique fermionic extension and are free from new singularities. The superspace supergravity model of Howe is found as a special case of this supergravity action. For this class of models the relation between bosonic potential and prepotential does not introduce obstructions as well. (author)
Spin Circuit Model for 2D Channels with Spin-Orbit Coupling
Hong, Seokmin; Sayed, Shehrin; Datta, Supriyo
2016-03-01
In this paper we present a general theory for an arbitrary 2D channel with “spin momentum locking” due to spin-orbit coupling. It is based on a semiclassical model that classifies all the channel electronic states into four groups based on the sign of the z-component of the spin (up (U), down (D)) and the sign of the x-component of the velocity (+, -). This could be viewed as an extension of the standard spin diffusion model which uses two separate electrochemical potentials for U and D states. Our model uses four: U+, D+, U-, and D-. We use this formulation to develop an equivalent spin circuit that is also benchmarked against a full non-equilibrium Green’s function (NEGF) model. The circuit representation can be used to interpret experiments and estimate important quantities of interest like the charge to spin conversion ratio or the maximum spin current that can be extracted. The model should be applicable to topological insulator surface states with parallel channels as well as to other layered structures with interfacial spin-orbit coupling.
Thermochemical Nonequilibrium 2D Modeling of Nitrogen Inductively Coupled Plasma Flow
Yu, Minghao; Yusuke, Takahashi; Hisashi, Kihara; Ken-ichi, Abe; Kazuhiko, Yamada; Takashi, Abe; Satoshi, Miyatani
2015-09-01
Two-dimensional (2D) numerical simulations of thermochemical nonequilibrium inductively coupled plasma (ICP) flows inside a 10-kW inductively coupled plasma wind tunnel (ICPWT) were carried out with nitrogen as the working gas. Compressible axisymmetric Navier-Stokes (N-S) equations coupled with magnetic vector potential equations were solved. A four-temperature model including an improved electron-vibration relaxation time was used to model the internal energy exchange between electron and heavy particles. The third-order accuracy electron transport properties (3rd AETP) were applied to the simulations. A hybrid chemical kinetic model was adopted to model the chemical nonequilibrium process. The flow characteristics such as thermal nonequilibrium, inductive discharge, effects of Lorentz force were made clear through the present study. It was clarified that the thermal nonequilibrium model played an important role in properly predicting the temperature field. The prediction accuracy can be improved by applying the 3rd AETP to the simulation for this ICPWT. supported by Grant-in-Aid for Scientific Research (No. 23560954), sponsored by the Japan Society for the Promotion of Science
Secure D2D Communication in Large-Scale Cognitive Cellular Networks: A Wireless Power Transfer Model
Liu, Yuanwei; Wang, Lifeng; Zaidi, Syed Ali Raza; Elkashlan, Maged; Duong, Trung Q.
2015-01-01
In this paper, we investigate secure device-to-device (D2D) communication in energy harvesting large-scale cognitive cellular networks. The energy constrained D2D transmitter harvests energy from multiantenna equipped power beacons (PBs), and communicates with the corresponding receiver using the spectrum of the primary base stations (BSs). We introduce a power transfer model and an information signal model to enable wireless energy harvesting and secure information transmission. In the power...
A new model for two-dimensional numerical simulation of pseudo-2D gas-solids fluidized beds
Li, Tingwen; Zhang, Yongmin
2013-10-11
Pseudo-two dimensional (pseudo-2D) fluidized beds, for which the thickness of the system is much smaller than the other two dimensions, is widely used to perform fundamental studies on bubble behavior, solids mixing, or clustering phenomenon in different gas-solids fluidization systems. The abundant data from such experimental systems are very useful for numerical model development and validation. However, it has been reported that two-dimensional (2D) computational fluid dynamic (CFD) simulations of pseudo-2D gas-solids fluidized beds usually predict poor quantitative agreement with the experimental data, especially for the solids velocity field. In this paper, a new model is proposed to improve the 2D numerical simulations of pseudo-2D gas-solids fluidized beds by properly accounting for the frictional effect of the front and back walls. Two previously reported pseudo-2D experimental systems were simulated with this model. Compared to the traditional 2D simulations, significant improvements in the numerical predictions have been observed and the predicted results are in better agreement with the available experimental data.
LBQ2D, Extending the Line Broadened Quasilinear Model to TAE-EP Interaction
Ghantous, Katy; Gorelenkov, Nikolai; Berk, Herbert
2012-10-01
The line broadened quasilinear model was proposed and tested on the one dimensional electrostatic case of the bump on tailfootnotetextH.L Berk, B. Breizman and J. Fitzpatrick, Nucl. Fusion, 35:1661, 1995 to study the wave particle interaction. In conventional quasilinear theory, the sea of overlapping modes evolve with time as the particle distribution function self consistently undergo diffusion in phase space. The line broadened quasilinear model is an extension to the conventional theory in a way that allows treatment of isolated modes as well as overlapping modes by broadening the resonant line in phase space. This makes it possible to treat the evolution of modes self consistently from onset to saturation in either case. We describe here the model denoted by LBQ2D which is an extension of the proposed one dimensional line broadened quasilinear model to the case of TAEs interacting with energetic particles in two dimensional phase space, energy as well as canonical angular momentum. We study the saturation of isolated modes in various regimes and present the analytical derivation and numerical results. Finally, we present, using ITER parameters, the case where multiple modes overlap and describe the techniques used for the numerical treatment.
A case study of fluid flow in fractured rock mass based on 2-D DFN modeling
Han, Jisu; Noh, Young-Hwan; Um, Jeong-Gi; Choi, Yosoon
2014-05-01
A two dimensional steady-state fluid flow through fractured rock mass of an abandoned copper mine in Korea is addressed based on discrete fracture network modeling. An injection well and three observation wells were installed at the field site to monitor the variations of total heads induced by injection of fresh water. A series of packer tests were performed to estimate the rock mass permeability. First, the two dimensional stochastic fracture network model was built and validated for a granitic rock mass using the geometrical and statistical data obtained from surface exposures and borehole logs. This validated fracture network model was combined with the fracture data observed on boreholes to generate a stochastic-deterministic fracture network system. Estimated apertures for each of the fracture sets using permeability data obtained from borehole packer tests were discussed next. Finally, a systematic procedure for fluid flow modeling in fractured rock mass in two dimensional domain was presented to estimate the conductance, flow quantity and nodal head in 2-D conceptual linear pipe channel network. The results obtained in this study clearly show that fracture geometry parameters (orientation, density and size) play an important role in the hydraulic behavior of fractured rock masses.
Distributed and coupled 2D electro-thermal model of power semiconductor devices
Belkacem, Ghania; Lefebvre, Stéphane; Joubert, Pierre-Yves; Bouarroudj-Berkani, Mounira; Labrousse, Denis; Rostaing, Gilles
2014-05-01
The development of power electronics in the field of transportations (automotive, aeronautics) requires the use of power semiconductor devices providing protection and diagnostic functions. In the case of series protections power semiconductor devices which provide protection may operate in shortcircuit and act as a current limiting device. This mode of operations is very constraining due to the large dissipation of power. In these particular conditions of operation, electro-thermal models of power semiconductor devices are of key importance in order to optimize their thermal design and increase their reliability. The development of such an electro-thermal model for power MOSFET transistors based on the coupling between two computation softwares (Matlab and Cast3M) is described in this paper. The 2D electro-thermal model is able to predict (i) the temperature distribution on chip surface well as in the volume under short-circuit operations, (ii) the effect of the temperature on the distribution of the current flowing within the die and (iii) the effects of the ageing of the metallization layer on the current density and the temperature. In this paper, the electrical and thermal models are described as well as the implemented coupling scheme.
Aespoe Pillar Stability Experiment. Final 2D coupled thermo-mechanical modelling
A site scale Pillar Stability Experiment is planned in the Aespoe Hard Rock Laboratory. One of the experiment's aims is to demonstrate the possibilities of predicting spalling in the fractured rock mass. In order to investigate the probability and conditions for spalling in the pillar 'prior to experiment' numerical simulations have been undertaken. This report presents the results obtained from 2D coupled thermo-mechanical numerical simulations that have been done with the Finite Element based programme JobFem. The 2D numerical simulations were conducted at two different depth levels, 0.5 and 1.5 m below tunnel floor. The in situ stresses have been confirmed with convergence measurements during the excavation of the tunnel. After updating the mechanical and thermal properties of the rock mass the final simulations have been undertaken. According to the modelling results the temperature in the pillar will increase from the initial 15.2 deg up to 58 deg after 120 days of heating. Based on these numerical simulations and on the thermal induced stresses the total stresses are expected to exceed 210 MPa at the border of the pillar for the level at 0.5 m below tunnel floor and might reach 180-182 MPa for the level at 1.5 m below tunnel floor. The stresses are slightly higher at the border of the confined hole. Upon these results and according to the rock mechanical properties the Crack Initiation Stress is exceeded at the border of the pillar already after the excavation phase. These results also illustrate that the Crack Damage Stress is exceeded only for the level at 0.5 m below tunnel floor and after at least 80 days of heating. The interpretation of the results shows that the required level of stress for spalling can be reached in the pillar
A New 2D-Advection-Diffusion Model Simulating Trace Gas Distributions in the Lowermost Stratosphere
Hegglin, M. I.; Brunner, D.; Peter, T.; Wirth, V.; Fischer, H.; Hoor, P.
2004-12-01
Tracer distributions in the lowermost stratosphere are affected by both, transport (advective and non-advective) and in situ sources and sinks. They influence ozone photochemistry, radiative forcing, and heating budgets. In-situ measurements of long-lived species during eight measurement campaigns revealed relatively simple behavior of the tracers in the lowermost stratosphere when represented in an equivalent-latitude versus potential temperature framework. We here present a new 2D-advection-diffusion model that simulates the main transport pathways influencing the tracer distributions in the lowermost stratosphere. The model includes slow diabatic descent of aged stratospheric air and vertical and/or horizontal diffusion across the tropopause and within the lowermost stratosphere. The diffusion coefficients used in the model represent the combined effects of different processes with the potential of mixing tropospheric air into the lowermost stratosphere such as breaking Rossby and gravity waves, deep convection penetrating the tropopause, turbulent diffusion, radiatively driven upwelling etc. They were specified by matching model simulations to observed distributions of long-lived trace gases such as CO and N2O obtained during the project SPURT. The seasonally conducted campaigns allow us to study the seasonal dependency of the diffusion coefficients. Despite its simplicity the model yields a surprisingly good description of the small scale features of the measurements and in particular of the observed tracer gradients at the tropopause. The correlation coefficients between modeled and measured trace gas distributions were up to 0.95. Moreover, mixing across isentropes appears to be more important than mixing across surfaces of constant equivalent latitude (or PV). With the aid of the model, the distribution of the fraction of tropospheric air in the lowermost stratosphere can be determined.
Transectional heat transfer in thermoregulating bigeye tuna (Thunnus obesus) - a 2D heat flux model.
Boye, Jess; Musyl, Michael; Brill, Richard; Malte, Hans
2009-11-01
We developed a 2D heat flux model to elucidate routes and rates of heat transfer within bigeye tuna Thunnus obesus Lowe 1839 in both steady-state and time-dependent settings. In modeling the former situation, we adjusted the efficiencies of heat conservation in the red and the white muscle so as to make the output of the model agree as closely as possible with observed cross-sectional isotherms. In modeling the latter situation, we applied the heat exchanger efficiencies from the steady-state model to predict the distribution of temperature and heat fluxes in bigeye tuna during their extensive daily vertical excursions. The simulations yielded a close match to the data recorded in free-swimming fish and strongly point to the importance of the heat-producing and heat-conserving properties of the white muscle. The best correspondence between model output and observed data was obtained when the countercurrent heat exchangers in the blood flow pathways to the red and white muscle retained 99% and 96% (respectively) of the heat produced in these tissues. Our model confirms that the ability of bigeye tuna to maintain elevated muscle temperatures during their extensive daily vertical movements depends on their ability to rapidly modulate heating and cooling rates. This study shows that the differential cooling and heating rates could be fully accounted for by a mechanism where blood flow to the swimming muscles is either exclusively through the heat exchangers or completely shunted around them, depending on the ambient temperature relative to the body temperature. Our results therefore strongly suggest that such a mechanism is involved in the extensive physiological thermoregulatory abilities of endothermic bigeye tuna. PMID:19880733
The effect of dominant three-body interaction to the hard-core boson Hubbard model is studied on a two-dimensional square lattice. In terms of the quantum Monte Carlo method, a ρ = 2/3 solid phase is shown explicitly with the coexistence of a charge-density wave and a bond-order wave appearing due to the presence of the dominant three-body interaction. For the strong three-body interaction, the ρ = 2/3 solid phase appears between superfluid phases and shrinks as the strength of the three-body interaction decreases, forming a lobe structure in the phase diagram. For weak three-body interactions, the superfluid phase exists for the whole range of hard-core densities except the full filled case, where the system is a Mott insulator. Our results may be realized in cold-atom experiments.
Liang, Ying; Guo, Huaiming
2012-09-01
The effect of dominant three-body interaction to the hard-core boson Hubbard model is studied on a two-dimensional square lattice. In terms of the quantum Monte Carlo method, a ρ = 2/3 solid phase is shown explicitly with the coexistence of a charge-density wave and a bond-order wave appearing due to the presence of the dominant three-body interaction. For the strong three-body interaction, the ρ = 2/3 solid phase appears between superfluid phases and shrinks as the strength of the three-body interaction decreases, forming a lobe structure in the phase diagram. For weak three-body interactions, the superfluid phase exists for the whole range of hard-core densities except the full filled case, where the system is a Mott insulator. Our results may be realized in cold-atom experiments.
Simulation of abrasive flow machining process for 2D and 3D mixture models
Dash, Rupalika; Maity, Kalipada
2015-12-01
Improvement of surface finish and material removal has been quite a challenge in a finishing operation such as abrasive flow machining (AFM). Factors that affect the surface finish and material removal are media viscosity, extrusion pressure, piston velocity, and particle size in abrasive flow machining process. Performing experiments for all the parameters and accurately obtaining an optimized parameter in a short time are difficult to accomplish because the operation requires a precise finish. Computational fluid dynamics (CFD) simulation was employed to accurately determine optimum parameters. In the current work, a 2D model was designed, and the flow analysis, force calculation, and material removal prediction were performed and compared with the available experimental data. Another 3D model for a swaging die finishing using AFM was simulated at different viscosities of the media to study the effects on the controlling parameters. A CFD simulation was performed by using commercially available ANSYS FLUENT. Two phases were considered for the flow analysis, and multiphase mixture model was taken into account. The fluid was considered to be a
2d Affine XY-Spin Model/4d Gauge Theory Duality and Deconfinement
Anber, Mohamed M.; Poppitz, Erich; /Toronto U.; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept. /San Francisco State U.
2012-08-16
We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2) = Z{sub 2} gauge theories, compactified on a small spatial circle R{sup 1,2} x S{sup 1}, and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R{sup 2} x T{sup 2}. Similarly, thermal gauge theories of higher rank are dual to new families of 'affine' XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU(N{sub c}) gauge theories with n{sub f} {ge} 1 adjoint Weyl fermions.
On the assimilation of SWOT type data into 2D shallow-water models
Frédéric, Couderc; Denis, Dartus; Pierre-André, Garambois; Ronan, Madec; Jérôme, Monnier; Jean-Paul, Villa
2013-04-01
In river hydraulics, assimilation of water level measurements at gauging stations is well controlled, while assimilation of images is still delicate. In the present talk, we address the richness of satellite mapped information to constrain a 2D shallow-water model, but also related difficulties. 2D shallow models may be necessary for small scale modelling in particular for low-water and flood plain flows. Since in both cases, the dynamics of the wet-dry front is essential, one has to elaborate robust and accurate solvers. In this contribution we introduce robust second order, stable finite volume scheme [CoMaMoViDaLa]. Comparisons of real like tests cases with more classical solvers highlight the importance of an accurate flood plain modelling. A preliminary inverse study is presented in a flood plain flow case, [LaMo] [HoLaMoPu]. As a first step, a 0th order data processing model improves observation operator and produces more reliable water level derived from rough measurements [PuRa]. Then, both model and flow behaviours can be better understood thanks to variational sensitivities based on a gradient computation and adjoint equations. It can reveal several difficulties that a model designer has to tackle. Next, a 4D-Var data assimilation algorithm used with spatialized data leads to improved model calibration and potentially leads to identify river discharges. All the algorithms are implemented into DassFlow software (Fortran, MPI, adjoint) [Da]. All these results and experiments (accurate wet-dry front dynamics, sensitivities analysis, identification of discharges and calibration of model) are currently performed in view to use data from the future SWOT mission. [CoMaMoViDaLa] F. Couderc, R. Madec, J. Monnier, J.-P. Vila, D. Dartus, K. Larnier. "Sensitivity analysis and variational data assimilation for geophysical shallow water flows". Submitted. [Da] DassFlow - Data Assimilation for Free Surface Flows. Computational software http
A 2D Mathematical Model for Sediment Transport by Waves and Tidal Currents
LU Yong-jun; ZUO Li-qin; SHAO Xue-jun; WANG Hong-chuan; LI Hao-lin
2005-01-01
In this study, the combined actions of waves and tidal currents in estuarine and coastal areas are considered and a 2D mathematical model for sediment transport by waves and tidal currents has been established in orthogonal curvilinear coordinates. Non-equilibrium transport equations of suspended load and bed load are used in the model. The concept of background concentration is introduced, and the formula of sediment transport capacity of tidal currents for the Oujiang River estuary is obtained. The Dou Guoren formula is employed for the sediment transport capacity of waves. Sediment transport capacity in the form of mud and the intensity of back silting are calculated by use of Luo Zaosen's formula. The calculated tidal stages are in good agreement with the field data, and the calculated velocities and flow directions of 46 vertical lines for 8 cross sections are also in good agreement with the measured data. On such a basis, simulations of back silting after excavation of the waterway with a sand bar under complicated boundary conditions in the navigation channel induced by suspended load, bed load and mud by waves and tidal currents are discussed.
Basic Brackets of a 2D Model for the Hodge Theory Without its Canonical Conjugate Momenta
Kumar, R.; Gupta, S.; Malik, R. P.
2016-01-01
We deduce the canonical brackets for a two (1+1)-dimensional (2D) free Abelian 1-form gauge theory by exploiting the beauty and strength of the continuous symmetries of a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density that respects, in totality, six continuous symmetries. These symmetries entail upon this model to become a field theoretic example of Hodge theory. Taken together, these symmetries enforce the existence of exactly the same canonical brackets amongst the creation and annihilation operators that are found to exist within the standard canonical quantization scheme. These creation and annihilation operators appear in the normal mode expansion of the basic fields of this theory. In other words, we provide an alternative to the canonical method of quantization for our present model of Hodge theory where the continuous internal symmetries play a decisive role. We conjecture that our method of quantization is valid for a class of field theories that are tractable physical examples for the Hodge theory. This statement is true in any arbitrary dimension of spacetime.
PREDICTION OF BLOOD FLOW VELOCITY AND LEAFLET DEFORMATION VIA 2D MITRAL VALVE MODEL
M.A.H. Mohd Adib
2012-06-01
Full Text Available In the mitral valve, regional variations in structure and material properties combine to affect the biomechanics of the entire valve. From previous studies, we know that the mitral valve leaflet tissue is highly extensible. A two-dimensional model of the mitral valve was generated using an Arbitrary Lagrangian-Eulerian (ALE mesh. A simple approximation of the heart geometry was used and the valve dimensions were based on actual measurements made. Valve opening and closure was simulated using contact equations. The objective of this study was to investigate and predict flow and leaflet phenomena via a simple 2D mitral valve model based on the critical parameter of blood. Two stages of mitral valves analysis were investigated: the systolic and diastolic stages. The results show a linear correlation between the mitral valve leaflet rigidity and the volume of backflow. Additionally, the simulation predicted mitral valve leaflet displacement during closure, which agreed with the results of our previous data analysis and the results for blood flow velocity during systole condition through the mitral valve outlet, as reported in the medical literature. In conclusion, these computational techniques are very useful in the study of both degenerative valve disease and failure of prostheses and will be further developed to investigate heart valve failure and subsequent surgical repair.
T-duality without isometry via extended gauge symmetries of 2D sigma models
Chatzistavrakidis, Athanasios; Deser, Andreas; Jonke, Larisa
2016-01-01
Target space duality is one of the most profound properties of string theory. However it customarily requires that the background fields satisfy certain invariance conditions in order to perform it consistently; for instance the vector fields along the directions that T-duality is performed have to generate isometries. In the present paper we examine in detail the possibility to perform T-duality along non-isometric directions. In particular, based on a recent work of Kotov and Strobl, we study gauged 2D sigma models where gauge invariance for an extended set of gauge transformations imposes weaker constraints than in the standard case, notably the corresponding vector fields are not Killing. This formulation enables us to follow a procedure analogous to the derivation of the Buscher rules and obtain two dual models, by integrating out once the Lagrange multipliers and once the gauge fields. We show that this construction indeed works in non-trivial cases by examining an explicit class of examples based on step 2 nilmanifolds.
Basic Brackets of a 2D Model for the Hodge Theory Without its Canonical Conjugate Momenta
Kumar, R.; Gupta, S.; Malik, R. P.
2016-06-01
We deduce the canonical brackets for a two (1+1)-dimensional (2D) free Abelian 1-form gauge theory by exploiting the beauty and strength of the continuous symmetries of a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density that respects, in totality, six continuous symmetries. These symmetries entail upon this model to become a field theoretic example of Hodge theory. Taken together, these symmetries enforce the existence of exactly the same canonical brackets amongst the creation and annihilation operators that are found to exist within the standard canonical quantization scheme. These creation and annihilation operators appear in the normal mode expansion of the basic fields of this theory. In other words, we provide an alternative to the canonical method of quantization for our present model of Hodge theory where the continuous internal symmetries play a decisive role. We conjecture that our method of quantization is valid for a class of field theories that are tractable physical examples for the Hodge theory. This statement is true in any arbitrary dimension of spacetime.
Hammer, Manfred; Honsa, R.; Richter, L.
2003-01-01
Superpositions of two perpendicularly oriented bidirectional eigenmode propagation (BEP) fields, composed of basis modes that satisfy Dirichlet boundary conditions, can establish rigorous semianalytical solutions for problems of 2-D fixed-frequency wave propagation on unbounded, cross-shaped domains
Combining multitracing and 2D-modelling to identify the dynamic of heavy metals during flooding.
Hissler, C.; Hostache, R.; Matgen, P.; Tosheva, Z.; David, E.; Bates, P.; Stille, P.
2012-04-01
to assess the risk of floodplain contamination in heavy metal due to river sediment deposition and to heavy metal partitioning between particulate and dissolved phases. We focus on a multidisciplinary approach combining environmental geochemistry (multitracing) and hydraulic modelling (using TELEMAC-2D). One important single flood event was selected to illustrate this innovative approach. During the entire flood, the river water was sampled every hour in order to collect the particulate and the dissolved fractions. All the tracers were analyzed in both fractions. An important set of hydrological and sedimentological data are used to reach a more efficient calibration of the TELEMAC modelling system. In addition to standard techniques of hydrochemistry, new approaches of in situ suspended sediment transport monitoring will help getting new insights on the hydraulic system behaviour.
Two-dimensional (2-D) pellet-cladding modelling using fem at NRI rex PLC
The method and calculation results of 2-D (r-z) and 2-D (r-φ) contact elasto-thermal solutions of pellet-cladding configuration are presented. Calculations were performed with coupled thermal and mechanical methods with inner sources and appropriate material properties dependent on temperature. Preliminary results of those simulations will be appropriate for advanced Russian TVEL fuel geometry recently delivered to the Dukovany NPP. Validation on experiment will be the subject of further work. (authors)
2D BEM modeling of a singular thermal diffusion free boundary problem with phase change
Nikolayev, Vadim
2016-01-01
We report a 2D Boundary Element Method (BEM) modeling of the thermal diffusion-controlled growth of a vapor bubble attached to a heating surface during saturated pool boiling. The transient heat conduction problem is solved in a liquid that surrounds a bubble with a free boundary and in a semi-infinite solid heater. The heat generated homogeneously in the heater causes evaporation, i. e. the bubble growth. A singularity exists at the point of the triple (liquid-vapor-solid) contact. At high system pressure the bubble is assumed to grow slowly, its shape being defined by the surface tension and the vapor recoil force, a force coming from the liquid evaporating into the bubble. It is shown that at some typical time the dry spot under the bubble begins to grow rapidly under the action of the vapor recoil. Such a bubble can eventually spread into a vapor film that can separate the liquid from the heater, thus triggering the boiling crisis (Critical Heat Flux phenomenon).
Modeling of two-storey precast school building using Ruaumoko 2D program
Hamid, N. H.; Tarmizi, L. H.; Ghani, K. D. [Faculty of Civil Engineering, Universiti Teknologi MARA, 40450 Shah Alam, Selangor (Malaysia)
2015-05-15
The long-distant earthquake loading from Sumatra and Java Island had caused some slight damages to precast and reinforced concrete buildings in West Malaysia such as cracks on wall panels, columns and beams. Subsequently, the safety of existing precast concrete building is needed to be analyzed because these buildings were designed using BS 8110 which did not include the seismic loading in the design. Thus, this paper emphasizes on the seismic performance and dynamic behavior of precast school building constructed in Malaysia under three selected past earthquakes excitations ; El Centro 1940 North-South, El Centro East-West components and San Fernando 1971 using RUAUMOKO 2D program. This program is fully utilized by using prototype precast school model and dynamic non-linear time history analysis. From the results, it can be concluded that two-storey precast school building has experienced severe damage and partial collapse especially at beam-column joint under San Fernando and El Centro North-South Earthquake as its exceeds the allowable inter-storey drift and displacement as specified in Eurocode 8. The San Fernando earthquake has produced a massive destruction to the precast building under viscous damping, ξ = 5% and this building has generated maximum building displacement of 435mm, maximum building drift of 0.68% and maximum bending moment at 8458kNm.
Real-time thermal field theory analyses of 2D Gross-Neveu model
Bang-Rong, Z
2000-01-01
Discrete symmetry breaking and possible restoration at finite temperature $T$ are analysed in 2D Gross-Neveu model by the real-time thermal field theory in the fermion bubble approximation. The dynamical fermion mass $m$ is proven to be scale-independent and this fact indicates the equivalence between the fermion bubble diagram approximation and the mean field approximation used in the auxialiary scalar field approach. Reproducing of the non-zero critical temperature $T_c=0.567 m(0)$, ($m(0)$ is the dynamical fermion mass at T=0), shows the equivalence between the real-time and the imaginary-time thermal field theory in this problem. However, in the real-time formalism, more results including absence of scalar bound state, the equation of criticality curve of chemical potential-temperature and the $\\ln(T_c/T)$ behavior of $m^2$ at $T\\stackrel{<}{\\sim} T_c$ can be easily obtained. The last one indicates the second-order phase transition feature of the symmetry restoration.
Straatsma, Menno; Huthoff, Fredrik
2011-01-01
In The Netherlands, 2D-hydrodynamic simulations are used to evaluate the effect of potential safety measures against river floods. In the investigated scenarios, the floodplains are completely inundated, thus requiring realistic representations of hydraulic roughness of floodplain vegetation. The current study aims at providing better insight into the uncertainty of flood water levels due to uncertain floodplain roughness parameterization. The study focuses on three key elements in the uncertainty of floodplain roughness: (1) classification error of the landcover map, (2), within class variation of vegetation structural characteristics, and (3) mapping scale. To assess the effect of the first error source, new realizations of ecotope maps were made based on the current floodplain ecotope map and an error matrix of the classification. For the second error source, field measurements of vegetation structure were used to obtain uncertainty ranges for each vegetation structural type. The scale error was investigated by reassigning roughness codes on a smaller spatial scale. It is shown that classification accuracy of 69% leads to an uncertainty range of predicted water levels in the order of decimeters. The other error sources are less relevant. The quantification of the uncertainty in water levels can help to make better decisions on suitable flood protection measures. Moreover, the relation between uncertain floodplain roughness and the error bands in water levels may serve as a guideline for the desired accuracy of floodplain characteristics in hydrodynamic models.
A 2D MODELLING OF THERMAL HEAT SINK FOR IMPATT AT HIGH POWER MMW FREQUENCY
Sohom Kumar Mitra
2013-02-01
Full Text Available A very useful method of formulating the Total Thermal Resistance of ordinary mesa structure of DDR IMPATT diode oscillators are presented in this paper. The main aim of this paper is to provide a 2D model for Si and SiC based IMPATT having different heat sinks (Type IIA diamond and copper at high power MMW frequency and study the characteristics of Total thermal resistance versus diode diameter for both the devices. Calculations of Total thermal resistances associated with different DDR IMPATT diodes with different base materials operating at 94 GHz (W-Band are included in this paper using the author’s developed formulation for both type-IIA diamond and copper semi-infinite heat sinks separately. Heat Sinks are designed using both type-IIA diamond and copper for all those diodes to operate near 500 K (which is well below the burn-out temperatures of all those base materials for CW steady state operation. Results are provided in the form of necessary graphs and tables.
Modeling of two-storey precast school building using Ruaumoko 2D program
The long-distant earthquake loading from Sumatra and Java Island had caused some slight damages to precast and reinforced concrete buildings in West Malaysia such as cracks on wall panels, columns and beams. Subsequently, the safety of existing precast concrete building is needed to be analyzed because these buildings were designed using BS 8110 which did not include the seismic loading in the design. Thus, this paper emphasizes on the seismic performance and dynamic behavior of precast school building constructed in Malaysia under three selected past earthquakes excitations ; El Centro 1940 North-South, El Centro East-West components and San Fernando 1971 using RUAUMOKO 2D program. This program is fully utilized by using prototype precast school model and dynamic non-linear time history analysis. From the results, it can be concluded that two-storey precast school building has experienced severe damage and partial collapse especially at beam-column joint under San Fernando and El Centro North-South Earthquake as its exceeds the allowable inter-storey drift and displacement as specified in Eurocode 8. The San Fernando earthquake has produced a massive destruction to the precast building under viscous damping, ξ = 5% and this building has generated maximum building displacement of 435mm, maximum building drift of 0.68% and maximum bending moment at 8458kNm
GPU computing with OpenCL to model 2D elastic wave propagation: exploring memory usage
Iturrarán-Viveros, Ursula; Molero-Armenta, Miguel
2015-01-01
Graphics processing units (GPUs) have become increasingly powerful in recent years. Programs exploring the advantages of this architecture could achieve large performance gains and this is the aim of new initiatives in high performance computing. The objective of this work is to develop an efficient tool to model 2D elastic wave propagation on parallel computing devices. To this end, we implement the elastodynamic finite integration technique, using the industry open standard open computing language (OpenCL) for cross-platform, parallel programming of modern processors, and an open-source toolkit called [Py]OpenCL. The code written with [Py]OpenCL can run on a wide variety of platforms; it can be used on AMD or NVIDIA GPUs as well as classical multicore CPUs, adapting to the underlying architecture. Our main contribution is its implementation with local and global memory and the performance analysis using five different computing devices (including Kepler, one of the fastest and most efficient high performance computing technologies) with various operating systems.
2D and 3D multipactor modeling in dielectric-loaded accelerator structures
Sinitsyn, Oleksandr; Nusinovich, Gregory; Antonsen, Thomas
2010-11-01
Multipactor (MP) is known as the avalanche growth of the number of secondary electrons emitted from a solid surface exposed to an RF electric field under vacuum conditions. MP is a severe problem in modern rf systems and, therefore, theoretical and experimental studies of MP are of great interest to the researchers working in various areas of physics and engineering. In this work we present results of MP studies in dielectric-loaded accelerator (DLA) structures. First, we show simulation results obtained with the use of the 2D self-consistent MP model (O. V. Sinitsyn, et. al., Phys. Plasmas, vol. 16, 073102 (2009)) and compare those to experimental ones obtained during recent extensive studies of DLA structures performed by Argonne National Laboratory, Naval Research Laboratory, SLAC National Accelerator Laboratory and Euclid TechLabs (C. Jing, et al., IEEE Trans. Plasma Sci., vol. 38, pp. 1354-1360 (2010)). Then we present some new results of 3D analysis of MP which include studies of particle trajectories and studies of MP development at the early stage.
D Recording for 2d Delivering - the Employment of 3d Models for Studies and Analyses -
Rizzi, A.; Baratti, G.; Jiménez, B.; Girardi, S.; Remondino, F.
2011-09-01
In the last years, thanks to the advances of surveying sensors and techniques, many heritage sites could be accurately replicated in digital form with very detailed and impressive results. The actual limits are mainly related to hardware capabilities, computation time and low performance of personal computer. Often, the produced models are not visible on a normal computer and the only solution to easily visualized them is offline using rendered videos. This kind of 3D representations is useful for digital conservation, divulgation purposes or virtual tourism where people can visit places otherwise closed for preservation or security reasons. But many more potentialities and possible applications are available using a 3D model. The problem is the ability to handle 3D data as without adequate knowledge this information is reduced to standard 2D data. This article presents some surveying and 3D modeling experiences within the APSAT project ("Ambiente e Paesaggi dei Siti d'Altura Trentini", i.e. Environment and Landscapes of Upland Sites in Trentino). APSAT is a multidisciplinary project funded by the Autonomous Province of Trento (Italy) with the aim documenting, surveying, studying, analysing and preserving mountainous and hill-top heritage sites located in the region. The project focuses on theoretical, methodological and technological aspects of the archaeological investigation of mountain landscape, considered as the product of sequences of settlements, parcelling-outs, communication networks, resources, and symbolic places. The mountain environment preserves better than others the traces of hunting and gathering, breeding, agricultural, metallurgical, symbolic activities characterised by different lengths and environmental impacts, from Prehistory to the Modern Period. Therefore the correct surveying and documentation of this heritage sites and material is very important. Within the project, the 3DOM unit of FBK is delivering all the surveying and 3D material to
1D and 2D urban dam-break flood modelling in Istanbul, Turkey
Ozdemir, Hasan; Neal, Jeffrey; Bates, Paul; Döker, Fatih
2014-05-01
Urban flood events are increasing in frequency and severity as a consequence of several factors such as reduced infiltration capacities due to continued watershed development, increased construction in flood prone areas due to population growth, the possible amplification of rainfall intensity due to climate change, sea level rise which threatens coastal development, and poorly engineered flood control infrastructure (Gallegos et al., 2009). These factors will contribute to increased urban flood risk in the future, and as a result improved modelling of urban flooding according to different causative factor has been identified as a research priority (Gallegos et al., 2009; Ozdemir et al. 2013). The flooding disaster caused by dam failures is always a threat against lives and properties especially in urban environments. Therefore, the prediction of dynamics of dam-break flows plays a vital role in the forecast and evaluation of flooding disasters, and is of long-standing interest for researchers. Flooding occurred on the Ayamama River (Istanbul-Turkey) due to high intensity rainfall and dam-breaching of Ata Pond in 9th September 2009. The settlements, industrial areas and transportation system on the floodplain of the Ayamama River were inundated. Therefore, 32 people were dead and millions of Euros economic loses were occurred. The aim of this study is 1 and 2-Dimensional flood modelling of the Ata Pond breaching using HEC-RAS and LISFLOOD-Roe models and comparison of the model results using the real flood extent. The HEC-RAS model solves the full 1-D Saint Venant equations for unsteady open channel flow whereas LISFLOOD-Roe is the 2-D shallow water model which calculates the flow according to the complete Saint Venant formulation (Villanueva and Wright, 2006; Neal et al., 2011). The model consists a shock capturing Godunov-type scheme based on the Roe Riemann solver (Roe, 1981). 3 m high resolution Digital Surface Model (DSM), natural characteristics of the pond
Facial Sketch Synthesis Using 2D Direct Combined Model-Based Face-Specific Markov Network.
Tu, Ching-Ting; Chan, Yu-Hsien; Chen, Yi-Chung
2016-08-01
A facial sketch synthesis system is proposed, featuring a 2D direct combined model (2DDCM)-based face-specific Markov network. In contrast to the existing facial sketch synthesis systems, the proposed scheme aims to synthesize sketches, which reproduce the unique drawing style of a particular artist, where this drawing style is learned from a data set consisting of a large number of image/sketch pairwise training samples. The synthesis system comprises three modules, namely, a global module, a local module, and an enhancement module. The global module applies a 2DDCM approach to synthesize the global facial geometry and texture of the input image. The detailed texture is then added to the synthesized sketch in a local patch-based manner using a parametric 2DDCM model and a non-parametric Markov random field (MRF) network. Notably, the MRF approach gives the synthesized results an appearance more consistent with the drawing style of the training samples, while the 2DDCM approach enables the synthesis of outcomes with a more derivative style. As a result, the similarity between the synthesized sketches and the input images is greatly improved. Finally, a post-processing operation is performed to enhance the shadowed regions of the synthesized image by adding strong lines or curves to emphasize the lighting conditions. The experimental results confirm that the synthesized facial images are in good qualitative and quantitative agreement with the input images as well as the ground-truth sketches provided by the same artist. The representing power of the proposed framework is demonstrated by synthesizing facial sketches from input images with a wide variety of facial poses, lighting conditions, and races even when such images are not included in the training data set. Moreover, the practical applicability of the proposed framework is demonstrated by means of automatic facial recognition tests. PMID:27244737
Shen, D.; Wang, J.; Cheng, X.; Rui, Y.; Ye, S.
2015-08-01
The rapid progress of lidar technology has made the acquirement and application of high-resolution digital elevation model (DEM) data increasingly popular, especially in regards to the study of floodplain flow. However, high-resolution DEM data pose several disadvantages for floodplain modeling studies; e.g., the data sets contain many redundant interpolation points, large numbers of calculations are required to work with data, and the data do not match the size of the computational mesh. Two-dimensional (2-D) hydraulic modeling, which is a popular method for analyzing floodplain flow, offers highly precise elevation parameterization for computational mesh while ignoring much of the micro-topographic information of the DEM data itself. We offer a flood simulation method that integrates 2-D hydraulic model results and high-resolution DEM data, thus enabling the calculation of flood water levels in DEM grid cells through local inverse distance-weighted interpolation. To get rid of the false inundation areas during interpolation, it employs the run-length encoding method to mark the inundated DEM grid cells and determine the real inundation areas through the run-length boundary tracing technique, which solves the complicated problem of connectivity between DEM grid cells. We constructed a 2-D hydraulic model for the Gongshuangcha detention basin, which is a flood storage area of Dongting Lake in China, by using our integrated method to simulate the floodplain flow. The results demonstrate that this method can solve DEM associated problems efficiently and simulate flooding processes with greater accuracy than simulations only with DEM.
A 2D climate energy balance model coupled with a 3D deep ocean model
J. Ildefonso Diaz
2007-05-01
Full Text Available We study a three dimensional climate model which represents the coupling of the mean surface temperature with the ocean temperature. We prove the existence of a bounded weak solution by a fixed point argument.
Croissant, Thomas; Lague, Dimitri; Davy, Philippe; Steer, Philippe
2016-04-01
In active mountain ranges, large earthquakes (Mw > 5-6) trigger numerous landslides that impact river dynamics. These landslides bring local and sudden sediment piles that will be eroded and transported along the river network causing downstream changes in river geometry, transport capacity and erosion efficiency. The progressive removal of landslide materials has implications for downstream hazards management and also for understanding landscape dynamics at the timescale of the seismic cycle. The export time of landslide-derived sediments after large-magnitude earthquakes has been studied from suspended load measurements but a full understanding of the total process, including the coupling between sediment transfer and channel geometry change, still remains an issue. Note that the transport of small sediment pulses has been studied in the context of river restoration, but the magnitude of sediment pulses generated by landslides may make the problem different. Here, we study the export of large volumes (>106 m3) of sediments with the 2D hydro-morphodynamic model, Eros. This model uses a new hydrodynamic module that resolves a reduced form of the Saint-Venant equations with a particle method. It is coupled with a sediment transport and lateral and vertical erosion model. Eros accounts for the complex retroactions between sediment transport and fluvial geometry, with a stochastic description of the floods experienced by the river. Moreover, it is able to reproduce several features deemed necessary to study the evacuation of large sediment pulses, such as river regime modification (single-thread to multi-thread), river avulsion and aggradation, floods and bank erosion. Using a synthetic and simple topography we first present how granulometry, landslide volume and geometry, channel slope and flood frequency influence 1) the dominance of pulse advection vs. diffusion during its evacuation, 2) the pulse export time and 3) the remaining volume of sediment in the catchment
Modelling thermal stratification in the North Sea: Application of a 2-D potential energy model
Nielsen, Morten Holtegaard; St. John, Michael
2001-01-01
dynamics we have developed and tested a potential energy model of thermal stratification based on the energy equation (for turbulence). The energy equation relates the temporal and spatial changes of turbulent kinetic energy (TKE), the production of TKE and the dissipation of TKE to the change of potential...... forced with wind, dew point temperature from Ekofisk oilfield in the central North Sea, and tidal current and atmospheric radiation. The model is used to simulate the seasonal cycle of stratification in the central North Sea in the years 1988, 1989 and 1990 and is compared to density profiles in these...... years available from the ICES hydrographic database. We find that the model is able to simulate variations in thermal stratification including the seasonal onset and breakdown of stratification, the thermocline depth, and the effects of discrete wind and cooling events. For the years 1988–1990 we find...
Axial turbomachine modelling with a quasi-2-D approach. Application to gas cooled reactor transients
Full text of publication follows: In the frame of the international forum GenIV, CEA has selected two innovative concepts of High Temperature gas cooled Reactor. The first has a fast neutron spectrum, a robust refractory fuel and a direct cycle conversion. The second is a very high temperature reactor with a thermal neutron spectrum. Both concepts make use of technology derived from High Temperature Gas Reactor. Thermal hydraulic performances are a key issue for the design. For transient conditions and decay heat removal situations, the thermal hydraulic performance must remain as high as possible. In this context, all the transient situations, the incidental and accidental scenarios must be evaluated by a validated system code able to correctly describe, in particular, the thermal-hydraulics of the whole plant. With this type of reactor a special emphasis must be laid on turbomachinery modelling. A first step was to compute a HTGR concept using the steady-state characteristics of each element of the turbomachinery with the computer code CATHARE. In a hypothetical transient event (a 10 inches cold duct break of primary loop which causes a rapid depressurization and a decrease of the core mass flow rate) the results seem of great interest (as a forced convection was maintained by the compressors during the entire transient) but not sufficiently justified in the frame of 0D modelling of turbomachinery. A more precise description of the turbomachinery has been developed based on a quasi-two dimensional approach. Although this type of flow analysis is a simplification of a complex three dimensional system, it is able to describe the behaviour of a compressor or a turbine with a better understanding than the models based on component characteristics. This approach consists in the solving of 2D radially averaged Navier-Stokes equations with the hypothesis of circumferentially uniform flow. The assumption of quasi-steady behaviour is made: source terms for the lift and
2D condensation model for the inner Solar Nebula: an enstatite-rich environment
Pignatale, F. C.; Liffman, Kurt; Maddison, Sarah T.; Brooks, Geoffrey
2016-04-01
Infrared observations provide the dust composition in the protoplanetary discs surface layers, but cannot probe the dust chemistry in the mid-plane, where planet formation occurs. Meteorites show that dynamics was important in determining the dust distribution in the Solar Nebula and needs to be considered if we are to understand the global chemistry in discs. 1D radial condensation sequences can only simulate one disc layer at a time and cannot describe the global chemistry or the complexity of meteorites. To address these limitations, we compute for the first time the 2D distribution of condensates in the inner Solar Nebula using a thermodynamic equilibrium model, and derive time-scales for vertical settling and radial migration of dust. We find two enstatite-rich zones within 1 AU from the young Sun: a band ˜0.1 AU thick in the upper optically-thin layer of the disc interior to 0.8 AU, and in the optically-thick disc mid-plane out to ˜0.4 AU. The two enstatite-rich zones support recent evidence that Mercury and enstatite chondrites (ECs) shared a bulk material with similar composition. Our results are also consistent with infrared observation of protoplanetary disc which show emission of enstatite-rich dust in the inner surface of discs. The resulting chemistry and dynamics suggests that the formation of the bulk material of ECs occurred in the inner surface layer of the disc, within 0.4 AU. We also propose a simple alternative scenario in which gas fractionation and vertical settling of the condensates lead to an enstatite-chondritic bulk material.
Combined global 2D-local 3D modeling of the industrial Czochralski silicon crystal growth process
Jung, T.; Seebeck, J.; Friedrich, J.
2013-04-01
A global, axisymmetric thermal model of a Czochralski furnace is coupled to an external, local, 3D, time-dependent flow model of the melt via the inclusion of turbulent heat fluxes, extracted from the 3D melt model, into the 2D furnace model. Boundary conditions of the 3D model are updated using results from the 2D model. In the 3D model the boundary layers are resolved by aggressive mesh refinement towards the walls, and the Large Eddy Simulation approach is used to model the turbulent flow in the melt volume on a relatively coarse mesh to minimize calculation times. It is shown that by using this approach it is possible to reproduce fairly good results from Direct Numerical Simulations obtained on much finer meshes, as well as experimental results for interface shape and oxygen concentration in the case of growth of silicon crystals with 210 mm diameter for photovoltaics by the Czochralski method.
The space-scale cube: An integrated model for 2D polygonal areas and scale
Meijers, B.M.; Van Oosterom, P.J.M.
2011-01-01
This paper introduces the concept of a space-scale partition, which we term the space-scale cube – analogous with the space-time cube (first introduced by Hägerstrand, 1970). We take the view of ‘map generalization is extrusion of 2D data into the third dimension’ (as introduced by Vermeij et al., 2
A new approach for assimilation of 2D radar precipitation in a high-resolution NWP model
Korsholm, Ulrik Smith; Petersen, Claus; Sass, Bent Hansen;
2015-01-01
A new approach for assimilation of 2D precipitation in numerical weather prediction models is presented and tested in a case with convective, heavy precipitation. In the scheme a nudging term is added to the horizontal velocity divergence tendency equation. In case of underproduction of precipita...
Kowit Boonrawd; Chatchai Jothityangkoon
2015-01-01
A coupling of a 1-D flood routing model and quasi 2-D floodplain inundation model is applied for mapping spacetime flood extent. The routing model is formulated based on a non-linear storage-discharge relationship which is converted from an observed and synthetic rating curve. To draw the rating curve, required parameters for each reaches are estimated from hydraulic properties, floodplain geometry and vegetation and building cover of compound channels. The shape of the floodplain...
Bandrowski, D.; Lai, Y.; Bradley, N.; Gaeuman, D. A.; Murauskas, J.; Som, N. A.; Martin, A.; Goodman, D.; Alvarez, J.
2014-12-01
In the field of river restoration sciences there is a growing need for analytical modeling tools and quantitative processes to help identify and prioritize project sites. 2D hydraulic models have become more common in recent years and with the availability of robust data sets and computing technology, it is now possible to evaluate large river systems at the reach scale. The Trinity River Restoration Program is now analyzing a 40 mile segment of the Trinity River to determine priority and implementation sequencing for its Phase II rehabilitation projects. A comprehensive approach and quantitative tool has recently been developed to analyze this complex river system referred to as: 2D-Hydrodynamic Based Logic Modeling (2D-HBLM). This tool utilizes various hydraulic output parameters combined with biological, ecological, and physical metrics at user-defined spatial scales. These metrics and their associated algorithms are the underpinnings of the 2D-HBLM habitat module used to evaluate geomorphic characteristics, riverine processes, and habitat complexity. The habitat metrics are further integrated into a comprehensive Logic Model framework to perform statistical analyses to assess project prioritization. The Logic Model will analyze various potential project sites by evaluating connectivity using principal component methods. The 2D-HBLM tool will help inform management and decision makers by using a quantitative process to optimize desired response variables with balancing important limiting factors in determining the highest priority locations within the river corridor to implement restoration projects. Effective river restoration prioritization starts with well-crafted goals that identify the biological objectives, address underlying causes of habitat change, and recognizes that social, economic, and land use limiting factors may constrain restoration options (Bechie et. al. 2008). Applying natural resources management actions, like restoration prioritization, is
Novel Method Fusing (2D) 2 LDA with Multichannel Model for Face Recognition
Xia Liu∗; Yang Cao; Yu Cao; Bo Wang
2015-01-01
A fusion method of Gabor features and (2D)2LDA for face feature extraction is proposed in this paper. Gabor filters are utilized to extract multi⁃direction and multi⁃scale features from facial image to employ its robust performance for illumination, expressional variability and other factors. The extracted features have the defect of high dimension and redundancy data. (2D)2LDA is implemented to reduce the dimension of Gabor features and select effective feature data. Finally, the nearest neighbor classifier is used to classify characteristics and complete face recognition. The experiments are implemented by using ORL database and Yale database respectively. The experimental results show that the proposed method significantly reduces the dimension of Gabor features and decrease the influence of other factors. The proposed method acquires excellent recognition accuracy and has light architectures as well.
Information on the gauge principle from an N=1/2, D=2 supersymmetric model
The gauge principle does not only work to generate interactions. It potentially yields an abundance of gauge-potential fields transforming under the same local symmetry group. In order to show evidences of this property this work gauge-covariantizes an N = 1/2, D = 2 supersymmetric theory. Then, by relaxing the so-called conventional constraint, a second gauge-potential field naturally emerges. (author)
Driven microswimmers on a 2D substrate: A stochastic towed sled model
Marchegiani, Giampiero; Marchesoni, Fabio
2015-11-01
We investigate, both numerically and analytically, the diffusion properties of a stochastic sled sliding on a substrate, subject to a constant towing force. The problem is motivated by the growing interest in controlling transport of artificial microswimmers in 2D geometries at low Reynolds numbers. We simulated both symmetric and asymmetric towed sleds. Remarkable properties of their mobilities and diffusion constants include sidewise drifts and excess diffusion peaks. We interpret our numerical findings by making use of stochastic approximation techniques.
Driven microswimmers on a 2D substrate: A stochastic towed sled model
We investigate, both numerically and analytically, the diffusion properties of a stochastic sled sliding on a substrate, subject to a constant towing force. The problem is motivated by the growing interest in controlling transport of artificial microswimmers in 2D geometries at low Reynolds numbers. We simulated both symmetric and asymmetric towed sleds. Remarkable properties of their mobilities and diffusion constants include sidewise drifts and excess diffusion peaks. We interpret our numerical findings by making use of stochastic approximation techniques
A 2D Mechanistic Model of Breast Ductal Carcinoma in Situ (DCIS) Morphology and Progression
Norton, Kerri-Ann; Wininger, Michael; Bhanot, Gyan; Ganesan, Shridar; Barnard, Nicola; Shinbrot, Troy
2009-01-01
Ductal carcinoma in situ (DCIS) of the breast is a non-invasive tumor in which cells proliferate abnormally, but remain confined within a duct. Although four distinguishable DCIS morphologies are recognized, the mechanisms that generate these different morphological classes remain unclear, and consequently the prognostic strength of DCIS classification is not strong. To improve the understanding of the relation between morphology and time course, we have developed a 2D in silico particle mode...
The antiferromagnetic ground state of the half-filled Hubbard model with the doubly degenerate orbital has been studied by using the slave-boson mean-field theory, which was previously proposed by the present author. Numerical calculations for the simple cubic model have shown that the metal-insulator transition does not take place except at the vanishing interaction point, in strong contrast with its paramagnetic solution. The energy gap in the density of states of the antiferromagnetic insulator is much reduced by the effect of electron correlation. The exchange interaction J plays an important role in the antiferromagnetism: although for J=0 the sublattice magnetic moment m in our theory is fairly smaller than mHFA obtained in the Hartree-Fock approximation, m for J/U>0.2 (U is the Coulomb interaction) is increased to become comparable to mHFA. Surprisingly, the antiferromagnetic state is easily destroyed if a small, negative exchange interaction (J/U<-0.05) is introduced. copyright 1997 The American Physical Society
In order to explore a possibility of superfluidity in confined strongly-correlated fermion systems, e.g., nano-scale cuprate High-Tc superconductors and atomic Fermi gases loaded on optical lattice, we implement an exact diagonalization code for their mathematical model, i.e., a trapped Hubbard model on the Earth Simulator. We compare two diagonalization algorithms, the traditional Lanczos method and a new algorithm, the preconditioned conjugate gradient (PCG) method, and find that when using the PCG the total CPU time can be reduced to 1/3 - 1/5 compared to the former one since the convergence can be dramatically improved by choosing a good preconditioner and the communication overhead is much more efficiently concealed in the PCG method. Consequently, such a performance improvement enables us to do systematic studies for several parameters. Numerical simulation results reveal that an unconventional type of pairing specific to the confined system, which may cause superfluidity, develops under a strong repulsive interaction. (author)
Numerical Simulations of High-Frequency Respiratory Flows in 2D and 3D Lung Bifurcation Models
Chen, Zixi; Parameswaran, Shamini; Hu, Yingying; He, Zhaoming; Raj, Rishi; Parameswaran, Siva
2014-07-01
To better understand the human pulmonary system and optimize the high-frequency oscillatory ventilation (HFOV) design, numerical simulations were conducted under normal breathing frequency and HFOV condition using a CFD code Ansys Fluent and its user-defined C programs. 2D and 3D double bifurcating lung models were created, and the geometry corresponds to fifth to seventh generations of airways with the dimensions based on the Weibel's pulmonary model. Computations were carried out for different Reynolds numbers (Re = 400 and 1000) and Womersley numbers (α = 4 and 16) to study the air flow fields, gas transportation, and wall shear stresses in the lung airways. Flow structure was compared with experimental results. Both 2D and 3D numerical models successfully reproduced many results observed in the experiment. The oxygen concentration distribution in the lung model was investigated to analyze the influence of flow oscillation on gas transport inside the lung model.
Statistical coronary motion models for 2D+t/3D registration of X-ray coronary angiography and CTA
Baka, N.; Metz, C.T.; Schultz, C.;
2013-01-01
Accurate alignment of intra-operative X-ray coronary angiography (XA) and pre-operative cardiac CT angiography (CTA) may improve procedural success rates of minimally invasive coronary interventions for patients with chronic total occlusions. It was previously shown that incorporating patient...... motion models to provide constraints for the 2D+t/3D registration. We propose a methodology for building statistical motion models of the coronary arteries from a training population of 4D CTA datasets. We compare the 2D+t/3D registration performance of the proposed statistical models with other motion...... estimates, including the patient specific motion extracted from 4D CTA, the mean motion of a population, the predicted motion based on the cardiac shape. The coronary motion models, constructed on a training set of 150 patients, had a generalization accuracy of 1mm root mean square point-to-point distance...
Sato, Toshihiro; Tsunetsugu, Hirokazu
2016-08-01
We numerically study optical conductivity σ (ω ) near the "antiferromagnetic" phase transition in the square-lattice Hubbard model at half filling. We use a cluster dynamical mean field theory and calculate conductivity including vertex corrections and, to this end, we have reformulated the vertex corrections in the antiferromagnetic phase. We find that the vertex corrections change various important details in temperature and ω dependencies of conductivity in the square lattice, and this contrasts sharply the case of the Mott transition in the frustrated triangular lattice. Generally, the vertex corrections enhance variations in the ω dependence, and sharpen the Drude peak and a high-ω incoherent peak in the paramagnetic phase. They also enhance the dip in σ (ω ) at ω =0 in the antiferromagnetic phase. Therefore, the dc conductivity is enhanced in the paramagnetic phase and suppressed in the antiferromagnetic phase, but this change occurs slightly below the transition temperature. We also find a temperature region above the transition temperature in which the dc conductivity shows an insulating behavior but σ (ω ) retains the Drude peak, and this region is stabilized by the vertex corrections. We also investigate which fluctuations are important in the vertex corrections and analyze momentum dependence of the vertex function in detail.
Finite-temperature T > 0 transport properties of integrable and nonintegrable one-dimensional (1D) many-particle quantum systems are rather different, showing ballistic and diffusive behavior, respectively. The repulsive 1D Hubbard model is a prominent example of an integrable correlated system. For electronic densities n ≠ 1 (and spin densities m ≠ 0) it is an ideal charge (and spin) conductor, with ballistic charge (and spin) transport for T ⩾ 0. In spite of the fact that it is solvable by the Bethe ansatz, at n = 1 (and m = 0) its T > 0 charge (and spin) transport properties are an issue that remains poorly understood. Here we combine this solution with symmetry and the explicit calculation of current-operator matrix elements between energy eigenstates to show that for on-site repulsion U > 0 and at n = 1 the charge stiffness Dη(T) vanishes for T > 0 in the thermodynamic limit. A similar behavior is found by such methods for the spin stiffness Ds(T) for U > 0 and T > 0, which vanishes at m = 0. This absence of finite temperature n = 1 ballistic charge transport and m = 0 ballistic spin transport are exact results that clarify long-standing open problems. (paper)
Rigorous 2D Model for Study of Pulsed and Monochromatic Waves Propagation Near the Earth’s Surface
Sautbekov, Seil S.; Yuriy K. Sirenko; Nataliya P. Yashina; Aleksey A. Vertiy
2014-01-01
A model problem considered in the paper allows solving rather complex 2D problems of the electromagnetic wave propagation with a required accuracy using conventional personal computers. The problems are of great importance for the theory and practical applications. The association of FDTD schemes with exact absorbing conditions makes up the basis for constructing models of the kind. This approach reduces the original open initial boundary value problems to the equivalent closed problems which...
Harman Ajiwibowo
2011-01-01
The effectiveness of a breakwater can be measured by quantifying the transmission coefficient (KT). The smaller the coefficient, the better the performance of the breakwater. A physical modeling on the proposed breakwater was conducted to identify the coefficient of Perforated Skirt Breakwater (PSB). The PSB model was tested in 2-D wave flume at Ocean Wave Research Laboratory FTSL ITB, to obtain the effectiveness of PSB for short-period waves (prototype periods, Tp= 4 second and smaller). The...
Simulating floods : On the application of a 2D-hydraulic model for flood hazard and risk assessment
Alkema, D.
2007-01-01
Over the last decades, river floods in Europe seem to occur more frequently and are causing more and more economic and emotional damage. Understanding the processes causing flooding and the development of simulation models to evaluate countermeasures to control that damage are important issues. This study deals with the application of a 2D hydraulic flood propagation model for flood hazard and risk assessment. It focuses on two components: 1) how well does it predict the spatial-dynamic chara...
A. Caserta; L. Malagnini; A. Rovelli; Marra, F
1995-01-01
The geological information collected in the last years by the Istituto Nazionale di Geofisica for the city of Rome is used to construct 1- and 2-D models of the nearsurface structure. These models are the basis for the numerical generation of synthetic accelerograms which can simulate the horizontal ground motion (SH waves) produced in the different areas of the city by a large (M ? 7) potential earthquake 100 km away in Central Apennines. The proposed methodology yields earthquake engineerin...
Modeling of Nitrate Leaching from a Potato Field using HYDRUS-2D
Shekofteh, Hosein; Afyuni, Majid; Hajabbasi, Mohammad Ali;
2013-01-01
applied to simulate nitrate leaching from a drip-irrigated sandy agricultural soil for varying emitter discharges and various amounts of fertilizer. It was found that for small emitter discharge values free drainage increased significantly with increase in discharge, whereas the increase was leveled out......Excessive use of nitrogen (N) fertilizers is likely to be responsible for the increasing nitrate in groundwater. Thus, appropriate water and nutrient management is required to minimize groundwater pollution and to maximize the nutrient-use efficiency. In this study HYDRUS-2D software package was...... fertilizer amount, nitrate leaching from a potato field can be minimized even in a sandy soil....
Diego A. Garzón-Alvarado; CARLOS GALEANO; JUAN MANTILLA
2012-01-01
Este articulo presenta distintas pruebas numéricas en dominios que presenta variación de parámetros, de forma espacial, de la ecuación de reacción- difusión en el espacio de Turing. Las pruebas son desarrolladas en cuadrados de lado unitario 2D en el cual se realizan subdivisiones (subdominios). En cada subdomminio se ingresan parámetros que corresponden a los diferentes números de onda, por lo tanto presentan un medio heterogéneo. Cada número de onda fue predicho mediante la teoría lineal de...
Phase fluctuations and BCS-LP crossover in 2D short coherence length superconductors
We study the effects of phase fluctuations in 2D short-coherence length superconductors on the basis of the extended Hubbard model with intersite attraction. In the Kosterlitz-Thouless scenario the critical temperatures for anisotropic pairings were determined and compared with the ones of BCS Hartree-Fock approximation. The Uemura-type plots, i.e. the critical temperature vs. zero temperature phase stiffness, were obtained for extended s-wave and dx2-y2 wave pairings. We also discuss the crossover from BCS to local pair superconductivity for d-wave pairing. (author)
LI Haifeng; HU Zunhe; LIU Jingtai
2016-01-01
To facilitate scene understanding and robot navigation in large scale urban environment, a two-layer enhanced geometric map (EGMap) is designed using videos from a monocular onboard camera. The 2D layer of EGMap consists of a 2D building boundary map from top-down view and a 2D road map, which can support localization and advanced map-matching when compared with standard polyline-based maps. The 3D layer includes features such as 3D road model, and building facades with coplanar 3D vertical and horizontal line segments, which can provide the 3D metric features to localize the vehicles and flying-robots in 3D space. Starting from the 2D building boundary and road map, EGMap is initially constructed using feature fusion with geometric constraints under a line feature-based simultaneous localization and mapping (SLAM) framework iteratively and progressively. Then, a local bundle adjustment algorithm is proposed to jointly refine the camera localizations and EGMap features. Furthermore, the issues of uncertainty, memory use, time efficiency and obstacle effect in EGMap construction are discussed and analyzed. Physical experiments show that EGMap can be successfully constructed in large scale urban environment and the construction method is demonstrated to be very accurate and robust.
Spin-spin critical point correlation functions for the 2D random bond Ising and Potts models
Dotsenko, V S; Pujol, P; Vladimir Dotsenko; Marco Picco; Pierre Pujol
1994-01-01
We compute the combined two and three loop order correction to the spin-spin correlation functions for the 2D Ising and q-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group approach for the perturbation series around the conformal field theories representing the pure models. We obtain corrections for the correlations functions which produce crossover in the amplitude but don't change the critical exponent in the case of the Ising model and which produce a shift in the critical exponent, due to randomness, in the case of the Potts model. Comparison with numerical data is discussed briefly.
SU-E-T-05: A 2D EPID Transit Dosimetry Model Based On An Empirical Quadratic Formalism
Tan, Y [University of Glasgow, Glasgow, Scotland (United Kingdom); National University Cancer Institute (Singapore); Metwaly, M; Glegg, M [Beatson West of Scotland Cancer Centre, Glasgow, Scotland (United Kingdom); Baggarley, S [National University Cancer Institute (Singapore); Elliott, A [University of Glasgow, Glasgow, Scotland (United Kingdom)
2014-06-01
Purpose: To describe a 2D electronic portal imaging device (EPID) transit dosimetry model, based on an empirical quadratic formalism, that can predict either EPID or in-phantom dose distribution for comparisons with EPID captured image or treatment planning system (TPS) dose respectively. Methods: A quadratic equation can be used to relate the reduction in intensity of an exit beam to the equivalent path length of the attenuator. The calibration involved deriving coefficients from a set of dose planes measured for homogeneous phantoms with known thicknesses under reference conditions. In this study, calibration dose planes were measured with EPID and ionisation chamber (IC) in water for the same reference beam (6MV, 100mu, 20×20cm{sup 2}) and set of thicknesses (0–30cm). Since the same calibration conditions were used, the EPID and IC measurements can be related through the quadratic equation. Consequently, EPID transit dose can be predicted from TPS exported dose planes and in-phantom dose can be predicted using EPID distribution captured during treatment as an input. The model was tested with 4 open fields, 6 wedge fields, and 7 IMRT fields on homogeneous and heterogeneous phantoms. Comparisons were done using 2D absolute gamma (3%/3mm) and results were validated against measurements with a commercial 2D array device. Results: The gamma pass rates for comparisons between EPID measured and predicted ranged from 93.6% to 100.0% for all fields and phantoms tested. Results from this study agreed with 2D array measurements to within 3.1%. Meanwhile, comparisons in-phantom between TPS computed and predicted ranged from 91.6% to 100.0%. Validation with 2D array device was not possible for inphantom comparisons. Conclusion: A 2D EPID transit dosimetry model for treatment verification was described and proven to be accurate. The model has the advantage of being generic and allows comparisons at the EPID plane as well as multiple planes in-phantom.
Small-amplitude 2D patterns with nontrivial symmetry in a simple nonlinear field model
Quasiperiodic (QP) small-amplitude patterns are studied in a scalar field theory with quadratic nonlinearity. QP solutions of the class in interest are found as a projection of strictly periodic solutions of an associated 4D problem onto an 'irrationally oriented' 2D subspace. The periodic solutions of the 4D problem are constructed using a version of the method of asymptotic expansions. The analysis reveals complex patterns. In particular, there exists a one-parametric QP pattern with strict 12-fold symmetry, which contains infinitely many local patches with approximate 5-fold symmetry. In limit cases, the complex patterns transform into a simple pattern: a close pack of hexagonal cells. In certain resonance cases there exist patterns consisting of alternating pieces of close cell packs with either hexagonal or quadrangular symmetry. The relation between the 12-fold and 5-fold approximate symmetries is discussed. (author)
Symmetric and skew-symmetric weight functions in perturbation models of 2D interfacial cracks
Piccolroaz, A; Movchan, A B
2008-01-01
In this paper we address the vector problem of a 2D interfacial crack loaded by a general asymmetric distribution of forces acting on its faces. It is shown that the general integral formula for the evaluation of stress intensity factors, as well as high-order terms, requires both symmetric and skew-symmetric weight function matrices. The symmetric weight function matrix is obtained via the solution of a Wiener-Hopf functional equation, whereas the derivation of the skew-symmetric weight function matrix requires the construction of the corresponding full field singular solution. The weight function matrices are then used in the perturbation analysis of a crack advancing quasi-statically along the interface between two dissimilar media. A general and rigorous asymptotic procedure is developed to compute the perturbations of stress intensity factors as well as high-order terms.
2-D fluid dynamics models for laser driven fusion on IBM 3090 vector multiprocessors
Fluid-dynamics codes for laser fusion are complex research codes, consisting of many distinct modules and embodying a variety of numerical methods. They are therefore good candidates for testing general purpose advanced computer architectures and the related software. In this paper, after a brief outline of the basic concepts of laser fusion, the implementation of the 2-D laser fusion fluid code DUED on the IBM 3090 VF vector multiprocessors is discussed. Emphasis is put on parallelization, performed by means of IBM Parallel FORTRAN (PF). It is shown how different modules have been optimized by using different features of PF: i) modules based on depth-2 nested loops exploit automatic parallelization; ii) laser light ray tracing is partitioned by scheduling parallel ICCG algorithm (executed in parallel by appropiately synchronized parallel subroutines). Performance results are given for separate modules of the code, as well as for typical complete runs
MATHEMATICAL MODEL FOR 2-D TIDAL FLOW AND WATER QUALITY WITH ORTHOGONAL CURVILINEAR COORDINATES
Liu Yu-ling; Wei Wen-li; Shen Yong-ming
2003-01-01
This paper presents a numerical method forsimulating the 2-D tidal flow and water quality with the or-thogonal curvilinear coordinates. In order to overcome thecomputational difficulties in natural rivers, such as the com-plicated boundary figures, the great disparity between lengthand width of computational domain, etc. , orthogonal bounda-ry-fitted grid was used. The irregular domain in physical planewas transformed into a rectangular domain in a transformedplane, and the depth-averaged momentum equations and massequation were given and discretized based on the alternatingdirection implicit finite difference scheme in curvilinear coordi-nates. The application of the presented method was illustratedby an example of analyzing the Yangtze River in the vicinity ofNanjing city. A fair agreement between the measured data andcomputed results demonstrates the validity of the developedmethod.
I. Kalisperakis; Stentoumis, Ch.; L. Grammatikopoulos; K. Karantzalos
2015-01-01
The indirect estimation of leaf area index (LAI) in large spatial scales is crucial for several environmental and agricultural applications. To this end, in this paper, we compare and evaluate LAI estimation in vineyards from different UAV imaging datasets. In particular, canopy levels were estimated from i.e., (i) hyperspectral data, (ii) 2D RGB orthophotomosaics and (iii) 3D crop surface models. The computed canopy levels have been used to establish relationships with the measured ...
Albrecht, Marc; Mila, Frederic
1995-01-01
We study the competition between magnetic order and valence bond order in a two dimensional (2D) frustrated Heisenberg model introduced some time ago by Shastry and Sutherland ({\\sc B. Sriram Shastry} and {\\sc Bill Sutherland}, {\\em Physica} 108{\\bf B},1069 (1981) ) for which a configuration of dimers is known to be the ground state in a certain range of parameters. Using exact diagonalisation of small clusters, linear spin wave theory and Schwinger boson mean field theory, we show that the t...
Pedersen, Henrik; Ólafsdóttir, Hildur; Darkner, Sune; Lyksborg, Mark; Larsen, Rasmus
2009-01-01
This paper introduces a novel approach to modelling of volumetric cardiac magnetic resonance imaging (MRI) with simultaneous resolution of cardiac and respiratory motion. The major challenge is that the inherent slow nature of MRI prevents obtaining real-time volumetric images of the heart with sufficient spatial and temporal resolution. To overcome this problem our method predicts pixel intensities in multiple 2D slices, acquired with high spatial and temporal resolution, and subsequently as...
Operto, S.; VIRIEUX, J; Ribodetti, Alessandra; Anderson, J E
2009-01-01
A 2D finite-difference, frequency-domain method was developed for modeling viscoacoustic seismic waves in transversely isotropic media with a tilted symmetry axis. The medium is parameterized by the P-wave velocity on the symmetry axis, the density, the attenuation factor, Thomsen's anisotropic parameters delta and epsilon, and the tilt angle. The finite-difference discretization relies on a parsimonious mixed-grid approach that designs accurate yet spatially compact stencils. The system of l...
Limin Wang; Weiwei Dong
2012-01-01
This paper develops the optimal fault-tolerant guaranteed cost control scheme for a batch process with actuator failures. Based on an equivalent two-dimensional Fornasini-Marchsini (2D-FM) model description of a batch process, the relevant concepts of the fault-tolerant guaranteed cost control are introduced. The robust iterative learning reliable guaranteed cost controller (ILRGCC), which includes a robust extended feedback control for ensuring the performances over time and an iterative lea...
Ute Weckmann; A. Jung; T. Branch; Oliver Ritter
2007-01-01
Two of the Earth´s largest geophysical anomalies, the Beattie Magnetic Anomaly (BMA) and the Southern Cape Conductive Belt (SCCB) extend across the southern African continent for more than 1000 km in an east-west direction. Based on previous electrical and magnetometer array measurements it is believed that both anomalies have a common crustal source with a width of 50 km represented by serpentinized palaeo-oceanic srust. New two-dimensional (2D) electrical conductivity models along a profile...
Toward IMRT 2D dose modeling using artificial neural networks: A feasibility study
Purpose: To investigate the feasibility of artificial neural networks (ANN) to reconstruct dose maps for intensity modulated radiation treatment (IMRT) fields compared with those of the treatment planning system (TPS). Methods: An artificial feed forward neural network and the back-propagation learning algorithm have been used to replicate dose calculations of IMRT fields obtained from PINNACLE3 v9.0. The ANN was trained with fluence and dose maps of IMRT fields for 6 MV x-rays, which were obtained from the amorphous silicon (a-Si) electronic portal imaging device of Novalis TX. Those fluence distributions were imported to the TPS and the dose maps were calculated on the horizontal midpoint plane of a water equivalent homogeneous cylindrical virtual phantom. Each exported 2D dose distribution from the TPS was classified into two clusters of high and low dose regions, respectively, based on the K-means algorithm and the Euclidian metric in the fluence-dose domain. The data of each cluster were divided into two sets for the training and validation phase of the ANN, respectively. After the completion of the ANN training phase, 2D dose maps were reconstructed by the ANN and isodose distributions were created. The dose maps reconstructed by ANN were evaluated and compared with the TPS, where the mean absolute deviation of the dose and the γ-index were used. Results: A good agreement between the doses calculated from the TPS and the trained ANN was achieved. In particular, an average relative dosimetric difference of 4.6% and an average γ-index passing rate of 93% were obtained for low dose regions, and a dosimetric difference of 2.3% and an average γ-index passing rate of 97% for high dose region. Conclusions: An artificial neural network has been developed to convert fluence maps to corresponding dose maps. The feasibility and potential of an artificial neural network to replicate complex convolution kernels in the TPS for IMRT dose calculations have been
Toward IMRT 2D dose modeling using artificial neural networks: A feasibility study
Kalantzis, Georgios; Vasquez-Quino, Luis A.; Zalman, Travis; Pratx, Guillem; Lei, Yu [Radiation Oncology Department, University of Texas, Health Science Center San Antonio, Texas 78229 and Radiation Oncology Department, Stanford University School of Medicine, Stanford, California 94305 (United States); Radiation Oncology Department, University of Texas, Health Science Center San Antonio, Texas 78229 (United States); Radiation Oncology Department, Stanford University School of Medicine, Stanford, California 94305 (United States); Radiation Oncology Department, University of Texas, Health Science Center San Antonio, Texas 78229 (United States)
2011-10-15
Purpose: To investigate the feasibility of artificial neural networks (ANN) to reconstruct dose maps for intensity modulated radiation treatment (IMRT) fields compared with those of the treatment planning system (TPS). Methods: An artificial feed forward neural network and the back-propagation learning algorithm have been used to replicate dose calculations of IMRT fields obtained from PINNACLE{sup 3} v9.0. The ANN was trained with fluence and dose maps of IMRT fields for 6 MV x-rays, which were obtained from the amorphous silicon (a-Si) electronic portal imaging device of Novalis TX. Those fluence distributions were imported to the TPS and the dose maps were calculated on the horizontal midpoint plane of a water equivalent homogeneous cylindrical virtual phantom. Each exported 2D dose distribution from the TPS was classified into two clusters of high and low dose regions, respectively, based on the K-means algorithm and the Euclidian metric in the fluence-dose domain. The data of each cluster were divided into two sets for the training and validation phase of the ANN, respectively. After the completion of the ANN training phase, 2D dose maps were reconstructed by the ANN and isodose distributions were created. The dose maps reconstructed by ANN were evaluated and compared with the TPS, where the mean absolute deviation of the dose and the {gamma}-index were used. Results: A good agreement between the doses calculated from the TPS and the trained ANN was achieved. In particular, an average relative dosimetric difference of 4.6% and an average {gamma}-index passing rate of 93% were obtained for low dose regions, and a dosimetric difference of 2.3% and an average {gamma}-index passing rate of 97% for high dose region. Conclusions: An artificial neural network has been developed to convert fluence maps to corresponding dose maps. The feasibility and potential of an artificial neural network to replicate complex convolution kernels in the TPS for IMRT dose calculations
Purpose: [123I]Epidepride is a radio-tracer with very high affinity for dopamine D2/D3 receptors in brain. The importance of alteration in dopamine D2/D3 receptor binding condition has been wildly verified in schizophrenia. In the present study we set up a rat schizophrenia model by chronic injection of a non-competitive NMDA receptor antagonist, MK-801, to examine if [123I]epidepride could be used to evaluate the alterations of dopamine D2/D3 receptor binding condition in specific brain regions. Method: Rats were given repeated injection of MK-801 (dissolved in saline, 0.3 mg/kg) or saline for 1 month. Afterwards, total distance traveled (cm) and social interaction changes were recorded. Radiochemical purity of [123I]epidepride was analyzed by Radio-Thin-Layer Chromatography (chloroform: methanol, 9:1, v/v) and [123I]epidepride neuroimages were obtained by ex vivo autoradiography and small animal SPECT/CT. Data obtained were then analyzed to determine the changes of specific binding ratio. Result: Chronic MK-801 treatment for a month caused significantly increased local motor activity and induced an inhibition of social interaction. As shown in [123I]epidepride ex vivo autoradiographs, MK-801 induced a decrease of specific binding ratio in the striatum (24.01%), hypothalamus (35.43%), midbrain (41.73%) and substantia nigra (37.93%). In addition, [123I]epidepride small animal SPECT/CT neuroimaging was performed in the striatum and midbrain. There were statistically significant decreases in specific binding ratio in both the striatum (P 123I]epidepride is a useful radio-tracer to reveal the alterations of dopamine D2/D3 receptor binding in a rat schizophrenia model and is also helpful to evaluate therapeutic effects of schizophrenia in the future.
Rigorous 2D Model for Study of Pulsed and Monochromatic Waves Propagation Near the Earth’s Surface
Seil S. Sautbekov
2014-01-01
Full Text Available A model problem considered in the paper allows solving rather complex 2D problems of the electromagnetic wave propagation with a required accuracy using conventional personal computers. The problems are of great importance for the theory and practical applications. The association of FDTD schemes with exact absorbing conditions makes up the basis for constructing models of the kind. This approach reduces the original open initial boundary value problems to the equivalent closed problems which can be solved numerically using the standard grid methods.
Autovino, Dario; Negm, Amro; Rallo, Giovanni; Provenzano, Giuseppe
2016-04-01
In Mediterranean countries characterized by limited water resources for agricultural and societal sectors, irrigation management plays a major role to improve water use efficiency at farm scale, mainly where irrigation systems are correctly designed to guarantee a suitable application efficiency and the uniform water distribution throughout the field. In the last two decades, physically-based agro-hydrological models have been developed to simulate mass and energy exchange processes in the soil-plant-atmosphere (SPA) system. Mechanistic models like HYDRUS 2D/3D (Šimunek et al., 2011) have been proposed to simulate all the components of water balance, including actual crop transpiration fluxes estimated according to a soil potential-dependent sink term. Even though the suitability of these models to simulate the temporal dynamics of soil and crop water status has been reported in the literature for different horticultural crops, a few researches have been considering arboreal crops where the higher gradients of root water uptake are the combination between the localized irrigation supply and the three dimensional root system distribution. The main objective of the paper was to assess the performance of HYDRUS-2D model to evaluate soil water contents and transpiration fluxes of an olive orchard irrigated with two different water distribution systems. Experiments were carried out in Castelvetrano (Sicily) during irrigation seasons 2011 and 2012, in a commercial farm specialized in the production of table olives (Olea europaea L., var. Nocellara del Belice), representing the typical variety of the surrounding area. During the first season, irrigation water was provided by a single lateral placed along the plant row with four emitters per plant (ordinary irrigation), whereas during the second season a grid of emitters laid on the soil was installed in order to irrigate the whole soil surface around the selected trees. The model performance was assessed based on the
The aim of this paper is to determine electric and physical properties by 2D modelling of glow discharge low pressure in continuous regime maintained by term constant source. This electric discharge is confined in reactor plan-parallel geometry. This reactor is filled by Argon monatomic gas. Our continuum model the order two is composed the first three moments the Boltzmann's equations coupled with Poisson's equation by self consistent method. These transport equations are discretized by the finite volumes method. The equations system is resolved by a new technique, it is about the N-BEE explicit scheme using the time splitting method.
Local Mass Transfer Coefficient for Idealized 2D Urban Street Canyon Models
Leung, Ka Kit; Liu, Chun-Ho
2011-09-01
Human activities in urban areas is one of the major sources of anthropogenic releases in the atmospheric boundary layer (ABL). The mechanism of urban morphology for the heat and mass transfer in built environment is thus an attractive topic in the research community. In this paper, a series of laboratory measurements is conducted to elucidate the mass transfer from hypothetical urban roughness constructed by idealized 2D street canyons. The experiments are carried out in the wind tunnel in the University of Hong Kong. The urban ABL structure inside the wind tunnel is controlled by placing small cubic Styrofoam blocks upstream of the test section. The street canyons are fabricated by movable rectangular acrylic blocks so that different building height to street width (aspect) ratios are examined. The height of building blocks is kept minimum to make sure that the urban ABL over the street canyons is high enough for fully developed turbulent flows. The prevailing wind is normal to the street axis, demonstrating the scenario of least pollutant removal from the street canyons to the urban ABL. The sample street canyon is covered by soaked filter papers to represent uniform mass concentrations on the building facades and ground surface. The wet bulb temperature of the filter papers is continuously monitored to ensure saturated conditions. Their weight before and after an experiment is used to measure the amount of water evaporated. Preliminary results illustrate the local mass transfer coefficient distribution for aspect ratios 1/4, 1/2, 1, and 2, which are comparable with those available in literuatre.
In order to design and define appropriate dimensions for a supercritical oxidation reactor, a comparative 2D and 3D simulation of the fluid dynamics and heat transfer during an oxidation process has been performed. The solver used is a commercial code, Fluent 6.2 (R). The turbulent flow field in the reactor, created by the stirrer, is taken into account with a k-omega model and a swirl imposed to the fluid. In the 3D case the rotation of the stirrer can be modelled using the sliding mesh model and the moving reference frame model. This work allows comparing 2D and 3D velocity and heat transfer calculations. The predicted values (mainly species concentrations and temperature profiles) are of the same order in both cases. The reactivity of the system is taken into account with a classical Eddy Dissipation Concept combustion model. Comparisons with experimental temperature measurements validate the ability of the CFD modelling to simulate the supercritical water oxidation reactive medium. Results indicate that the flow can be considered as plug flow-like and that heat transfer is strongly enhanced by the stirring. (authors)
2D MHD and 1D HD models of a solar flare -- a comprehensive comparison of the results
Falewicz, R; Murawski, K; Srivastava, A K
2015-01-01
Without any doubt solar flaring loops possess a multi-thread internal structure that is poorly resolved and there are no means to observe heating episodes and thermodynamic evolution of the individual threads. These limitations cause fundamental problems in numerical modelling of flaring loops, such as selection of a structure and a number of threads, and an implementation of a proper model of the energy deposition process. A set of 1D hydrodynamic and 2D magnetohydrodynamic models of a flaring loop are developed to compare energy redistribution and plasma dynamics in the course of a prototypical solar flare. Basic parameters of the modeled loop are set according to the progenitor M1.8 flare recorded in the AR10126 on September 20, 2002 between 09:21 UT and 09:50 UT. The non-ideal 1D models include thermal conduction and radiative losses of the optically thin plasma as energy loss mechanisms, while the non-ideal 2D models take into account viscosity and thermal conduction as energy loss mechanisms only. The 2...
A New Material Model for 2D FE Analysis of Adhesively Bonded Composite Joints
Zhao, Libin; Wang, Yana; TianLiang QIN; Zhang, Jianyu
2014-01-01
Effective and convenient stress analysis techniques play important roles in the analysis and design of adhesively bonded composite joints. A new material model is presented at the level of composite ply according to the orthotropic elastic mechanics theory and plane strain assumption. The model proposed has the potential to reserve nature properties of laminates with ply-to-ply modeling. The equivalent engineering constants in the model are obtained only by the material properties of unidirec...
Kowit Boonrawd
2015-04-01
Full Text Available A coupling of a 1-D flood routing model and quasi 2-D floodplain inundation model is applied for mapping spacetime flood extent. The routing model is formulated based on a non-linear storage-discharge relationship which is converted from an observed and synthetic rating curve. To draw the rating curve, required parameters for each reaches are estimated from hydraulic properties, floodplain geometry and vegetation and building cover of compound channels. The shape of the floodplain is defined by using fitting exercise based on the reverse approach between past and simulated inundation flood extent, to solve the current problem of inadequate topographic input data for floodplain. Mapping of daily flood can be generated relying on flat water levels. The quasi 2-D raster model is tested and applied to generate more realistic water surface and is used to estimate flood extent. The model is applied to the floodplains of Chiang Mai, north of Thailand and used to estimate a time series of hourly flood maps. Extending from daily to hourly flood extent, mapping development provides more details of flood inundation extent and depth.
Purpose: In external beam radiation therapy of pelvic sites, patient setup errors can be quantified by registering 2D projection radiographs acquired during treatment to a 3D planning computed tomograph (CT). We present a 2D-3D registration framework based on a statistical model of the intensity values in the two imaging modalities. Methods: The model assumes that intensity values in projection radiographs are independently but not identically distributed due to the nonstationary nature of photon counting noise. Two probability distributions are considered for the intensity values: Poisson and Gaussian. Using maximum likelihood estimation, two similarity measures, maximum likelihood with a Poisson (MLP) and maximum likelihood with Gaussian (MLG), distribution are derived. Further, we investigate the merit of the model-based registration approach for data obtained with current imaging equipment and doses by comparing the performance of the similarity measures derived to that of the Pearson correlation coefficient (ICC) on accurately collected data of an anthropomorphic phantom of the pelvis and on patient data. Results: Registration accuracy was similar for all three similarity measures and surpassed current clinical requirements of 3 mm for pelvic sites. For pose determination experiments with a kilovoltage (kV) cone-beam CT (CBCT) and kV projection radiographs of the phantom in the anterior-posterior (AP) view, registration accuracies were 0.42 mm (MLP), 0.29 mm (MLG), and 0.29 mm (ICC). For kV CBCT and megavoltage (MV) AP portal images of the same phantom, registration accuracies were 1.15 mm (MLP), 0.90 mm (MLG), and 0.69 mm (ICC). Registration of a kV CT and MV AP portal images of a patient was successful in all instances. Conclusions: The results indicate that high registration accuracy is achievable with multiple methods including methods that are based on a statistical model of a 3D CT and 2D projection images.
A microscopic nuclear collective rotation-vibration model: 2D submodel
Gulshani, Parviz
2016-01-01
The previous microscopic collective rotation-vibration model is improved to include interaction between collective oscillations in a pair of spatial directions, and to remove many of the previous-model approximations. As in the previous model, the nuclear Schrodinger equation (instead of the Hamiltonian) is canonically transformed to obtain a Schrodinger equation for collective rotation and vibration of a nucleus coupled to an intrinsic motion, with the related constraints imposed on the wave...
New urban area flood model: a comparison with MIKE11-quasi2d
Sole, A.; Zuccaro, G.
2005-01-01
Recent hydrogeological events have increased both public interest and that of the Scientific Community in a more accurate study of flooding in urban areas. The present project proposes a new model which offers an optimal integration of two models, one for flood wave propagation in riverbeds and the other for flooding in urban areas. We consider it necessary to not only treat the modelling of the outflow in riverbeds and outside riverbeds.together but to integrate them thoroughly. We simulate...
吴修广; 沈永明; 郑永红
2004-01-01
A numerical model for shallow water flow has been developed based on the unsteady Reynolds-averaged NavierStokes equations with the hydrodynamic pressure instead of hydrostatic pressure assumption. The equations are transformed into the σ-coordinate system and the eddy viscosity is calculated with the standard k - e turbulence model. The control volume method is used to discrete the equations, and the boundary conditions at the bed for shallow water models only include vertical diffusion terms expressed with wall functions. And the semi-implicit method for pressure linked equation arithmetic is adopted to solve the equations. The model is applied to the 2D vertical plane flow of a curent over two steep-sided trenches for which experiment data are available for comparison and good agreement is obtained. And the model is used to predicting the flow in a channel with a steep-sided submerged breakwater at the bottom, and the streamline is drawn.
Filipović, Vilim; Romić, Davor; Romić, Marija; Matijević, Lana; Mallmann, Fábio J. K.; Robinson, David A.
2016-04-01
Growing vegetables commercially requires intensive management and involves high irrigation demands and input of agrochemicals. Plastic mulch application in combination with drip irrigation is a common agricultural management technique practiced due to variety of benefits to the crop, mostly vegetable biomass production. However, the use of these techniques can result in various impacts on water and nutrient distribution in underlying soil and consequently affect nutrient leaching towards groundwater resources. The aim of this work is to estimate the effect of plastic mulch cover in combination with drip irrigation on water and nitrate dynamics in soil using HYDRUS-2D model. The field site was located in Croatian costal karst area on a Gleysol (WRB). The experiment was designed according to the split-plot design in three repetitions and was divided into plots with plastic mulch cover (MULCH) and control plots with bare soil (CONT). Each of these plots received applications of three levels of nitrogen fertilizer: 70, 140, and 210 kg per ha. All plots were equipped with drip irrigation and cropped with bell pepper (Capsicum annuum L. cv. Bianca F1). Lysimeters were installed at 90 cm depth in all plots and were used for monitoring the water and nitrate outflow. HYDRUS-2D was used for modeling the water and nitrogen outflow in the MULCH and CONT plots, implementing the proper boundary conditions. HYDRUS-2D simulated results showed good fitting to the field site observed data in both cumulative water and nitrate outflow, with high level of agreement. Water flow simulations produced model efficiency of 0.84 for CONT and 0.56 for MULCH plots, while nitrate simulations showed model efficiency ranging from 0.67 to 0.83 and from 0.70 to 0.93, respectively. Additional simulations were performed with the absence of the lysimeter, revealing faster transport of nitrates below drip line in the CONT plots, mostly because of the increased surface area subjected to precipitation
2-D Model Test Study of the Breakwater at Porto de Dande , Angola
Andersen, Thomas Lykke; Ramirez, Jorge Robert Rodriguez; Burcharth, Hans F.
This report deals with a two-dimensional model test study of the new breakwater at Porto de Dande, Angola. One cross-section was tested for stability and overtopping in various sea conditions. The length scale used for the model tests was 1:32. Unless otherwise specified all values given in this ...
Numerical study of the classical 2D discrete frustrated phi(4) model
Savkin, V.; Rubtsov, A.N.; Janssen, T.
2004-01-01
The two-dimensional discrete frustrated phi(4) model is studied by Monte Carlo simulations for two sets of the parameters of the model. Two phase transitions and a floating-incommensurate phase are observed for the case of stronger frustration. The phase transition from the floating-fluid phase to t
Activated sludge models ASM1, ASM2, ASM2d and ASM3
Henze, Mogens; Gujer, W.; Mino, T.; van Loosdrecht, M.C.M.
sludge processes has become a common part of the design and operation of wastewater treatment plants. Today models are being used in design, control, teaching and research.ContentsASM3: Introduction, Comparison of ASM1 and ASM3, ASM3: Definition of compounds in the model, ASM3: Definition of processes in...
The critical points of the multimatrix model as the theories of 2-d W-gravity
We further explore the connections between the generalized KdV hierarchy, the multimatrix model and Wn-gravity. We show that the Lax-pair formulation of the generalized KdV hierarchy is nothing but the Hamiltonian equations of W-gravity. Thus we demonstrate that the multicritical points of the multimatrix model are W-gravity theories. 16 refs
Li, Yunfeng; Pizlo, Zygmunt; Steinman, Robert M
2009-05-01
Human beings perceive 3D shapes veridically, but the underlying mechanisms remain unknown. The problem of producing veridical shape percepts is computationally difficult because the 3D shapes have to be recovered from 2D retinal images. This paper describes a new model, based on a regularization approach, that does this very well. It uses a new simplicity principle composed of four shape constraints: viz., symmetry, planarity, maximum compactness and minimum surface. Maximum compactness and minimum surface have never been used before. The model was tested with random symmetrical polyhedra. It recovered their 3D shapes from a single randomly-chosen 2D image. Neither learning, nor depth perception, was required. The effectiveness of the maximum compactness and the minimum surface constraints were measured by how well the aspect ratio of the 3D shapes was recovered. These constraints were effective; they recovered the aspect ratio of the 3D shapes very well. Aspect ratios recovered by the model were compared to aspect ratios adjusted by four human observers. They also adjusted aspect ratios very well. In those rare cases, in which the human observers showed large errors in adjusted aspect ratios, their errors were very similar to the errors made by the model. PMID:18621410
Simulation of Ultra-Small MOSFETs Using a 2-D Quantum-Corrected Drift-Diffusion Model
Biegal, Bryan A.; Rafferty, Connor S.; Yu, Zhiping; Ancona, Mario G.; Dutton, Robert W.; Saini, Subhash (Technical Monitor)
1998-01-01
The continued down-scaling of electronic devices, in particular the commercially dominant MOSFET, will force a fundamental change in the process of new electronics technology development in the next five to ten years. The cost of developing new technology generations is soaring along with the price of new fabrication facilities, even as competitive pressure intensifies to bring this new technology to market faster than ever before. To reduce cost and time to market, device simulation must become a more fundamental, indeed dominant, part of the technology development cycle. In order to produce these benefits, simulation accuracy must improve markedly. At the same time, device physics will become more complex, with the rapid increase in various small-geometry and quantum effects. This work describes both an approach to device simulator development and a physical model which advance the effort to meet the tremendous electronic device simulation challenge described above. The device simulation approach is to specify the physical model at a high level to a general-purpose (but highly efficient) partial differential equation solver (in this case PROPHET, developed by Lucent Technologies), which then simulates the model in 1-D, 2-D, or 3-D for a specified device and test regime. This approach allows for the rapid investigation of a wide range of device models and effects, which is certainly essential for device simulation to catch up with, and then stay ahead of, electronic device technology of the present and future. The physical device model used in this work is the density-gradient (DG) quantum correction to the drift-diffusion model [Ancona, Phys. Rev. B 35(5), 7959 (1987)]. This model adds tunneling and quantum smoothing of carrier density profiles to the drift-diffusion model. We used the DG model in 1-D and 2-D (for the first time) to simulate both bipolar and unipolar devices. Simulations of heavily-doped, short-base diodes indicated that the DG quantum
Interface localization in the 2D Ising model with a driven line
We study the effect of a one-dimensional driving field on the interface between two coexisting phases in a two dimensional model. This is done by considering an Ising model on a cylinder with Glauber dynamics in all sites and additional biased Kawasaki dynamics in the central ring. Based on the exact solution of the two-dimensional Ising model, we are able to compute the phase diagram of the driven model within a special limit of fast drive and slow spin flips in the central ring. The model is found to exhibit two phases where the interface is pinned to the central ring: one in which it fluctuates symmetrically around the central ring and another where it fluctuates asymmetrically. In addition, we find a phase where the interface is centered in the bulk of the system, either below or above the central ring of the cylinder. In the latter case, the symmetry breaking is ‘stronger’ than that found in equilibrium when considering a repulsive potential on the central ring. This equilibrium model is analyzed here by using a restricted solid-on-solid model. (paper)
Application of 2-D sediment model to fluctuating backwater area of Yangtze River
Yong FAN
2009-01-01
Based on the characteristics of backflow,a two-dimensional mathematical model of sediment movement was established.The complexity of the watercourse boundary at the confluence of the main stream and the tributary was dealt with using a boundary-fitting orthogonal coordinate system.The basic equation of the two-dimensional total sediment load model,the numerical calculation format,and key problems associated with using the orthogonal curvilinear coordinate system were discussed.Water and sediment flow in the Chongqing reach of the Yangtze River were simulated.The calculated water level,flow velocity distribution,amount of silting and scouring,and alluvial distribution are found to be in agreement with the measured data,which indicates that the numerical model and calculation method are reasonable.The model can be used for calculation of flow in a relatively complicated river network.
Application of 2-D sediment model to fluctuating backwater area of Yangtze River
Yong FAN
2009-09-01
Full Text Available Based on the characteristics of backflow, a two-dimensional mathematical model of sediment movement was established. The complexity of the watercourse boundary at the confluence of the main stream and the tributary was dealt with using a boundary-fitting orthogonal coordinate system. The basic equation of the two-dimensional total sediment load model, the numerical calculation format, and key problems associated with using the orthogonal curvilinear coordinate system were discussed. Water and sediment flow in the Chongqing reach of the Yangtze River were simulated. The calculated water level, flow velocity distribution, amount of silting and scouring, and alluvial distribution are found to be in agreement with the measured data, which indicates that the numerical model and calculation method are reasonable. The model can be used for calculation of flow in a relatively complicated river network.
A microscopic nuclear collective rotation-vibration model: 2D submodel
Gulshani, Parviz
2016-01-01
The previous microscopic collective rotation-vibration model is improved to include interaction between collective oscillations in a pair of spatial directions, and to remove many of the previous-model approximations. As in the previous model, the nuclear Schrodinger equation (instead of the Hamiltonian) is canonically transformed to obtain a Schrodinger equation for collective rotation and vibration of a nucleus coupled to an intrinsic motion, with the related constraints imposed on the wavefunction (rather than on the particle co-ordinates). The resulting equation is then effectively linearized into three self-consistent, time-reversal invariant, cranking-type equations using a variational method. The relation of the equations to the phenomenological hydrodynamic collective Bohr-Davydov-Faessler-Greiner model is discussed. To facilitate the solution of the equations and enhance physical insight, we consider in this article the collective oscillations in only two space directions. For harmonic oscillator mea...
A 2D analytical cylindrical gate tunnel FET (CG-TFET) model: impact of shortest tunneling distance
Dash, S.; Mishra, G. P.
2015-09-01
A 2D analytical tunnel field-effect transistor (FET) potential model with cylindrical gate (CG-TFET) based on the solution of Laplace’s equation is proposed. The band-to-band tunneling (BTBT) current is derived by the help of lateral electric field and the shortest tunneling distance. However, the analysis is extended to obtain the subthreshold swing (SS) and transfer characteristics of the device. The dependency of drain current, SS and transconductance on gate voltage and shortest tunneling distance is discussed. Also, the effect of scaling the gate oxide thickness and the cylindrical body diameter on the electrical parameters of the device is analyzed.
Large-N limit of the gradient flow in the 2D O(N) nonlinear sigma model
The gradient flow equation in the 2D O(N) nonlinear sigma model with lattice regularization is solved in the leading order of the 1/N expansion. By using this solution, we analytically compute the thermal expectation value of a lattice energy–momentum tensor defined through the gradient flow. The expectation value reproduces thermodynamic quantities obtained by the standard large-N method. This analysis confirms that the above lattice energy–momentum tensor restores the correct normalization automatically in the continuum limit, in a system with a non-perturbative mass gap
Development of a 1D-2D coupled hydrodynamic model for the Øyeren Delta in southern Norway
2011-01-01
In this study a coupled 1D-2D hydrodynamic model, MIKE FLOOD was used to simulate flood inundation extent, water levels and water velocities in the delta region of Lake Øyeren in southern Norway. The objective was to evaluate the improvement gained using a more complex framework. In addition, the credibility of existing flood zone maps made for Lillestrøm by Norges Vassdrag- og Energidirektorat (NVE) in 2005 was assessed. They were based on the assumption that the water levels predicted for F...