WorldWideScience

Sample records for two-dimensional potts model

  1. Multiple Potts Models Coupled to Two-Dimensional Quantum Gravity

    CERN Document Server

    Baillie, C F

    1992-01-01

    We perform Monte Carlo simulations using the Wolff cluster algorithm of {\\it multiple} $q=2,3,4$ state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the $c>1$ region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for $c>1$. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for $c>1$.

  2. Multiple Potts models coupled to two-dimensional quantum gravity

    Science.gov (United States)

    Baillie, C. F.; Johnston, D. A.

    1992-07-01

    We perform Monte Carlo simulations using the Wolff cluster algorithm of multiple q=2, 3, 4 state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the c>1 region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for c>1. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for c>1.

  3. Potts models coupled to two-dimensional quantum gravity

    Science.gov (United States)

    Baillie, Clive F.

    We perform Monte Carlo simulations using the Wolff cluster algorithm of the q=2 (Ising), 3 and 4 Potts models on dynamical phi-cubed graphs of spherical topology with up to 5000 nodes. We find that the measured critical exponents are in reasonable agreement with those from the exact solution of the Ising model and with those calculated from KPZ scaling for q=3,4 where no exact solution is available.

  4. Duality and Fisher zeros in the two-dimensional Potts model on a square lattice.

    Science.gov (United States)

    Astorino, Marco; Canfora, Fabrizio

    2010-05-01

    A phenomenological approach to the ferromagnetic two-dimensional (2D) Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the q-state Potts model. The duality symmetry of the 2D Potts model together with the known results on its critical exponent α allows us to fix consistently the details of the proposed expression for the free energy. The agreement of the analytic ansatz with numerical data in the q=3 case is very good at high and low temperatures as well as at the critical point. It is shown that the q>4 cases naturally fit into the same scheme and that one should also expect a good agreement with numerical data. The limiting q=4 case is shortly discussed.

  5. Interfacial adsorption in two-dimensional pure and random-bond Potts models

    Science.gov (United States)

    Fytas, Nikolaos G.; Theodorakis, Panagiotis E.; Malakis, Anastasios

    2017-03-01

    We use Monte Carlo simulations to study the finite-size scaling behavior of the interfacial adsorption of the two-dimensional square-lattice q -states Potts model. We consider the pure and random-bond versions of the Potts model for q =3 ,4 ,5 ,8 , and 10, thus probing the interfacial properties at the originally continuous, weak, and strong first-order phase transitions. For the pure systems our results support the early scaling predictions for the size dependence of the interfacial adsorption at both first- and second-order phase transitions. For the disordered systems, the interfacial adsorption at the (disordered induced) continuous transitions is discussed, applying standard scaling arguments and invoking findings for bulk critical properties. The self-averaging properties of the interfacial adsorption are also analyzed by studying the infinite limit-size extrapolation of properly defined signal-to-noise ratios.

  6. Scaling of cluster heterogeneity in the two-dimensional Potts model.

    Science.gov (United States)

    Lv, Jian-Ping; Yang, Xianqing; Deng, Youjin

    2012-08-01

    Cluster heterogeneity, the number of clusters of mutually distinct sizes, has been recently studied for explosive percolation and standard percolation [H. K. Lee et al., Phys. Rev. E 84, 020101(R) (2011); J. D. Noh et al., Phys. Rev. E 84, 010101(R) (2011)]. In this work we study the scaling of various quantities related with cluster heterogeneity in a broader context of two-dimensional q-state Potts model. We predict, via an analytic approach, the critical exponents for most of the measured quantities, and confirm these predications for various q values using extensive Monte Carlo simulations.

  7. Phase diagram of a two-dimensional large- Q Potts model in an external field

    Science.gov (United States)

    Tsai, Shan-Ho; Landau, D. P.

    2009-04-01

    We use a two-dimensional Wang-Landau sampling algorithm to map out the phase diagram of a Q-state Potts model with Q⩽10 in an external field H that couples to one state. Finite-size scaling analyses show that for large Q the first-order phase transition point at H=0 is in fact a triple point at which three first-order phase transition lines meet. One such line is restricted to H=0; another line has H⩽0. The third line, which starts at the H=0 triple point, ends at a critical point (T,H) which needs to be located in a two-dimensional parameter space. The critical field H(Q) is positive and decreases with decreasing Q, which is in qualitative agreement with previous predictions.

  8. Transfer matrix computation of critical polynomials for two-dimensional Potts models

    Science.gov (United States)

    Lykke Jacobsen, Jesper; Scullard, Christian R.

    2013-02-01

    In our previous work [1] we have shown that critical manifolds of the q-state Potts model can be studied by means of a graph polynomial PB(q, v), henceforth referred to as the critical polynomial. This polynomial may be defined on any periodic two-dimensional lattice. It depends on a finite subgraph B, called the basis, and the manner in which B is tiled to construct the lattice. The real roots v = eK - 1 of PB(q, v) either give the exact critical points for the lattice, or provide approximations that, in principle, can be made arbitrarily accurate by increasing the size of B in an appropriate way. In earlier work, PB(q, v) was defined by a contraction-deletion identity, similar to that satisfied by the Tutte polynomial. Here, we give a probabilistic definition of PB(q, v), which facilitates its computation, using the transfer matrix, on much larger B than was previously possible. We present results for the critical polynomial on the (4, 82), kagome, and (3, 122) lattices for bases of up to respectively 96, 162, and 243 edges, compared to the limit of 36 edges with contraction-deletion. We discuss in detail the role of the symmetries and the embedding of B. The critical temperatures vc obtained for ferromagnetic (v > 0) Potts models are at least as precise as the best available results from Monte Carlo simulations or series expansions. For instance, with q = 3 we obtain vc(4, 82) = 3.742 489 (4), vc(kagome) = 1.876 459 7 (2), and vc(3, 122) = 5.033 078 49 (4), the precision being comparable or superior to the best simulation results. More generally, we trace the critical manifolds in the real (q, v) plane and discuss the intricate structure of the phase diagram in the antiferromagnetic (v < 0) region.

  9. Backbone exponents of the two-dimensional q-state Potts model: a Monte Carlo investigation.

    Science.gov (United States)

    Deng, Youjin; Blöte, Henk W J; Nienhuis, Bernard

    2004-02-01

    We determine the backbone exponent X(b) of several critical and tricritical q-state Potts models in two dimensions. The critical systems include the bond percolation, the Ising, the q=2-sqrt[3], 3, and 4 state Potts, and the Baxter-Wu model, and the tricritical ones include the q=1 Potts model and the Blume-Capel model. For this purpose, we formulate several efficient Monte Carlo methods and sample the probability P2 of a pair of points connected via at least two independent paths. Finite-size-scaling analysis of P2 yields X(b) as 0.3566(2), 0.2696(3), 0.2105(3), and 0.127(4) for the critical q=2-sqrt[3], 1,2, 3, and 4 state Potts model, respectively. At tricriticality, we obtain X(b)=0.0520(3) and 0.0753(6) for the q=1 and 2 Potts model, respectively. For the critical q-->0 Potts model it is derived that X(b)=3/4. From a scaling argument, we find that, at tricriticality, X(b) reduces to the magnetic exponent, as confirmed by the numerical results.

  10. Finite-time scaling via linear driving: application to the two-dimensional Potts model.

    Science.gov (United States)

    Huang, Xianzhi; Gong, Shurong; Zhong, Fan; Fan, Shuangli

    2010-04-01

    We apply finite-time scaling to the q-state Potts model with q=3 and 4 on two-dimensional lattices to determine its critical properties. This consists in applying to the model a linearly varying external field that couples to one of its q states to manipulate its dynamics in the vicinity of its criticality and that drives the system out of equilibrium and thus produces hysteresis and in defining an order parameter other than the usual one and a nonequilibrium susceptibility to extract coercive fields. From the finite-time scaling of the order parameter, the coercivity, and the hysteresis area and its derivative, we are able to determine systematically both static and dynamic critical exponents as well as the critical temperature. The static critical exponents obtained in general and the magnetic exponent delta in particular agree reasonably with the conjectured ones. The dynamic critical exponents obtained appear to confirm the proposed dynamic weak universality but unlikely to agree with recent short-time dynamic results for q=4. Our results also suggest an alternative way to characterize the weak universality.

  11. a Numerical Test of Kpz Scaling:. Potts Models Coupled to Two-Dimensional Quantum Gravity

    Science.gov (United States)

    Baillie, C. F.; Johnston, D. A.

    We perform Monte-Carlo simulations using the Wolff cluster algorithm of the q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of spherical topology with up to 5000 nodes. We find that the measured critical exponents are in reasonable agreement with those from the exact solution of the Ising model and with those calculated from KPZ scaling for q=3, 4 where no exact solution is available. Using Binder’s cumulant we find that the q=10 Potts model displays a first order phase transition on a dynamical graph, as it does on a fixed lattice. We also examine the internal geometry of the graphs generated in the simulation, finding a linear relationship between ring length probabilities and the central charge of the Potts model.

  12. A Numerical Test of KPZ Scaling Potts Models Coupled to Two-Dimensional Quantum Gravity

    CERN Document Server

    Baillie, C F

    1992-01-01

    We perform Monte Carlo simulations using the Wolff cluster algorithm of the q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of spherical topology with up to 5000 nodes. We find that the measured critical exponents are in reasonable agreement with those from the exact solution of the Ising model and with those calculated from KPZ scaling for q=3,4 where no exact solution is available. Using Binder's cumulant we find that the q=10 Potts model displays a first order phase transition on a dynamical graph, as it does on a fixed lattice. We also examine the internal geometry of the graphs generated in the simulation, finding a linear relationship between ring length probabilities and the central charge of the Potts model

  13. Evaporation-condensation transition of the two-dimensional Potts model in the microcanonical ensemble

    KAUST Repository

    Nogawa, Tomoaki

    2011-12-05

    The evaporation-condensation transition of the Potts model on a square lattice is numerically investigated by the Wang-Landau sampling method. An intrinsically system-size-dependent discrete transition between supersaturation state and phase-separation state is observed in the microcanonical ensemble by changing constrained internal energy. We calculate the microcanonical temperature, as a derivative of microcanonical entropy, and condensation ratio, and perform a finite-size scaling of them to indicate the clear tendency of numerical data to converge to the infinite-size limit predicted by phenomenological theory for the isotherm lattice gas model. © 2011 American Physical Society.

  14. Evaporation-condensation transition of the two-dimensional Potts model in the microcanonical ensemble.

    Science.gov (United States)

    Nogawa, Tomoaki; Ito, Nobuyasu; Watanabe, Hiroshi

    2011-12-01

    The evaporation-condensation transition of the Potts model on a square lattice is numerically investigated by the Wang-Landau sampling method. An intrinsically system-size-dependent discrete transition between supersaturation state and phase-separation state is observed in the microcanonical ensemble by changing constrained internal energy. We calculate the microcanonical temperature, as a derivative of microcanonical entropy, and condensation ratio, and perform a finite-size scaling of them to indicate the clear tendency of numerical data to converge to the infinite-size limit predicted by phenomenological theory for the isotherm lattice gas model.

  15. Trigonometrical sums connected with the chiral Potts model, Verlinde dimension formula, two-dimensional resistor network, and number theory

    Energy Technology Data Exchange (ETDEWEB)

    Chair, Noureddine, E-mail: n.chair@ju.edu.jo

    2014-02-15

    We have recently developed methods for obtaining exact two-point resistance of the complete graph minus N edges. We use these methods to obtain closed formulas of certain trigonometrical sums that arise in connection with one-dimensional lattice, in proving Scott’s conjecture on permanent of Cauchy matrix, and in the perturbative chiral Potts model. The generalized trigonometrical sums of the chiral Potts model are shown to satisfy recursion formulas that are transparent and direct, and differ from those of Gervois and Mehta. By making a change of variables in these recursion formulas, the dimension of the space of conformal blocks of SU(2) and SO(3) WZW models may be computed recursively. Our methods are then extended to compute the corner-to-corner resistance, and the Kirchhoff index of the first non-trivial two-dimensional resistor network, 2×N. Finally, we obtain new closed formulas for variant of trigonometrical sums, some of which appear in connection with number theory. -- Highlights: • Alternative derivation of certain trigonometrical sums of the chiral Potts model are given. • Generalization of these trigonometrical sums satisfy recursion formulas. • The dimension of the space of conformal blocks may be computed from these recursions. • Exact corner-to-corner resistance, the Kirchhoff index of 2×N are given.

  16. Curvature-driven coarsening in the two-dimensional Potts model.

    Science.gov (United States)

    Loureiro, Marcos P O; Arenzon, Jeferson J; Cugliandolo, Leticia F; Sicilia, Alberto

    2010-02-01

    We study the geometric properties of polymixtures after a sudden quench in temperature. We mimic these systems with the q -states Potts model on a square lattice with and without weak quenched disorder, and their evolution with Monte Carlo simulations with nonconserved order parameter. We analyze the distribution of hull-enclosed areas for different initial conditions and compare our results with recent exact and numerical findings for q=2 (Ising) case. Our results demonstrate the memory of the presence or absence of long-range correlations in the initial state during the coarsening regime and exhibit superuniversality properties.

  17. Degenerate ground states and multiple bifurcations in a two-dimensional q-state quantum Potts model.

    Science.gov (United States)

    Dai, Yan-Wei; Cho, Sam Young; Batchelor, Murray T; Zhou, Huan-Qiang

    2014-06-01

    We numerically investigate the two-dimensional q-state quantum Potts model on the infinite square lattice by using the infinite projected entangled-pair state (iPEPS) algorithm. We show that the quantum fidelity, defined as an overlap measurement between an arbitrary reference state and the iPEPS ground state of the system, can detect q-fold degenerate ground states for the Z_{q} broken-symmetry phase. Accordingly, a multiple bifurcation of the quantum ground-state fidelity is shown to occur as the transverse magnetic field varies from the symmetry phase to the broken-symmetry phase, which means that a multiple-bifurcation point corresponds to a critical point. A (dis)continuous behavior of quantum fidelity at phase transition points characterizes a (dis)continuous phase transition. Similar to the characteristic behavior of the quantum fidelity, the magnetizations, as order parameters, obtained from the degenerate ground states exhibit multiple bifurcation at critical points. Each order parameter is also explicitly demonstrated to transform under the Z_{q} subgroup of the symmetry group of the Hamiltonian. We find that the q-state quantum Potts model on the square lattice undergoes a discontinuous (first-order) phase transition for q=3 and q=4 and a continuous phase transition for q=2 (the two-dimensional quantum transverse Ising model).

  18. Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions

    Energy Technology Data Exchange (ETDEWEB)

    Babaev, A. B., E-mail: b-albert78@mail.ru; Magomedov, M. A.; Murtazaev, A. K. [Russian Academy of Sciences, Amirkhanov Institute of Physics, Dagestan Scientific Center (Russian Federation); Kassan-Ogly, F. A.; Proshkin, A. I. [Russian Academy of Sciences, Institute of Metal Physics, Ural Branch (Russian Federation)

    2016-02-15

    Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J{sub 1} and J{sub 2}, respectively. PTs in these models are analyzed for the ratio r = J{sub 2}/J{sub 1} of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J{sub 1} < 0 and J{sub 2} < 0 exhibits a first-order PT in the range of 0 ⩽ r < 0.2, whereas, in the interval 0.2 ⩽ r ⩽ 1.0, frustrations arise in the system. At the same time, for J{sub 1} > 0 and J{sub 2} < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ⩽ |r| ⩽ 1/3, the model exhibits a second-order PT.

  19. Size reduction of the transfer matrix of two-dimensional Ising and Potts models

    Directory of Open Access Journals (Sweden)

    M. Ghaemi

    2003-12-01

    Full Text Available  A new algebraic method is developed to reduce the size of the transfer matrix of Ising and three-state Potts ferromagnets on strips of width r sites of square and triangular lattices. This size reduction has been set up in such a way that the maximum eigenvalues of both the reduced and the original transfer matrices became exactly the same. In this method we write the original transfer matrix in a special blocked form in such a way that the sums of row elements of a block of the original transfer matrix be the same. The reduced matrix is obtained by replacing each block of the original transfer matrix with the sum of the elements of one of its rows. Our method results in significant matrix size reduction which is a crucial factor in determining the maximum eigenvalue.

  20. Multi-GPU-based Swendsen-Wang multi-cluster algorithm for the simulation of two-dimensional q-state Potts model

    CERN Document Server

    Komura, Yukihiro

    2012-01-01

    We present the multiple GPU computing with the common unified device architecture (CUDA) for the Swendsen-Wang multi-cluster algorithm of two-dimensional (2D) q-state Potts model. Extending our algorithm for single GPU computing [Comp. Phys. Comm. 183 (2012) 1155], we realize the GPU computation of the Swendsen-Wang multi-cluster algorithm for multiple GPUs. We implement our code on the large-scale open science supercomputer TSUBAME 2.0, and test the performance and the scalability of the simulation of the 2D Potts model. The performance on Tesla M2050 using 256 GPUs is obtained as 37.3 spin flips per a nano second for the q=2 Potts model (Ising model) at the critical temperature with the linear system size L=65536.

  1. Griffiths phase and critical behavior of the two-dimensional Potts models with long-range correlated disorder.

    Science.gov (United States)

    Chatelain, Christophe

    2014-03-01

    The q-state Potts model with long-range correlated disorder is studied by means of large-scale Monte Carlo simulations for q=2, 4, 8, and 16. Evidence is given of the existence of a Griffiths phase, where the thermodynamic quantities display an algebraic finite-size scaling, in a finite range of temperatures. The critical exponents are shown to depend on both the temperature and the exponent of the algebraic decay of disorder correlations, but not on the number of states of the Potts model. The mechanism leading to the violation of hyperscaling relations is observed in the entire Griffiths phase.

  2. Influence of aperiodic modulations on first-order transitions: Numerical study of the two-dimensional Potts model

    Science.gov (United States)

    Girardi, D.; Branco, N. S.

    2011-06-01

    We study the Potts model on a rectangular lattice with aperiodic modulations in its interactions along one direction. Numerical results are obtained using the Wolff algorithm and for many lattice sizes, allowing for a finite-size scaling analyses to be carried out. Three different self-dual aperiodic sequences are employed, which leads to more precise results, since the exact critical temperature is known. We analyze two models, with 6 and 15 number of states: both present first-order transitions on their uniform versions. We show that the Harris-Luck criterion, originally introduced in the study of continuous transitions, is obeyed also for first-order ones. Also, we show that the new universality class that emerges for relevant aperiodic modulations depends on the number of states of the Potts model, as obtained elsewhere for random disorder, and on the aperiodic sequence. We determine the occurrence of log-periodic behavior, as expected for models with aperiodic modulated interactions.

  3. Influence of aperiodic modulations on first-order transitions: numerical study of the two-dimensional Potts model.

    Science.gov (United States)

    Girardi, D; Branco, N S

    2011-06-01

    We study the Potts model on a rectangular lattice with aperiodic modulations in its interactions along one direction. Numerical results are obtained using the Wolff algorithm and for many lattice sizes, allowing for a finite-size scaling analyses to be carried out. Three different self-dual aperiodic sequences are employed, which leads to more precise results, since the exact critical temperature is known. We analyze two models, with 6 and 15 number of states: both present first-order transitions on their uniform versions. We show that the Harris-Luck criterion, originally introduced in the study of continuous transitions, is obeyed also for first-order ones. Also, we show that the new universality class that emerges for relevant aperiodic modulations depends on the number of states of the Potts model, as obtained elsewhere for random disorder, and on the aperiodic sequence. We determine the occurrence of log-periodic behavior, as expected for models with aperiodic modulated interactions.

  4. Dynamic Critical Exponents of Three-Dimensional Ising Models and Two-Dimensional Three-States Potts Models

    Science.gov (United States)

    Murase, Yohsuke; Ito, Nobuyasu

    2008-01-01

    Values of dynamic critical exponents are numerically estimated for various models with the nonequilibrium relaxation method to test the dynamic universality hypothesis. The dynamics used here are single-spin update with Metropolis-type transition probabities. The estimated values of nonequilibrium relaxation exponent of magnetization λm (=β/zν) of Ising models on bcc and fcc lattices are estimated to be 0.251(3) and 0.252(3), respectively, which are consistent with the value of the model on simple-cubic lattice, 0.250(2). The dynamic critical exponents of three-states Potts models on square, honeycomb and triangular lattices are also estimated to be 2.193(5), 2.198(4), and 2.199(3), respectively. They are consistent within the error bars. It is also confirmed that Ising models with regularly modulated coupling constants on square lattice have the same dynamic critical exponents with the uniformly ferromagnetic Ising model.

  5. Dilute Potts model in two dimensions.

    Science.gov (United States)

    Qian, Xiaofeng; Deng, Youjin; Blöte, Henk W J

    2005-11-01

    We study the two-dimensional dilute q-state Potts model by means of transfer-matrix and Monte Carlo methods. Using the random-cluster representation, we include noninteger values of q. We locate phase transitions in the three-dimensional parameter space of q, the Potts coupling K>0, and the chemical potential of the vacancies. The critical plane is found to contain a line of fixed points that divides into a critical branch and a tricritical one, just as predicted by the renormalization scenario formulated by Nienhuis et al for the dilute Potts model. The universal properties along the line of fixed points agree with the theoretical predictions. We also determine the density of the vacancies along these branches. For q=2-squareroot of 2 we obtain the phase diagram in a three-dimensional parameter space that also includes a coupling V> or = 0 between the vacancies. For q=2, the latter space contains the Blume-Capel model as a special case. We include a determination of the tricritical point of this model, as well as an analysis of percolation clusters constructed on tricritical Potts configurations for noninteger q. This percolation study is based on Monte Carlo algorithms that include local updates flipping between Potts sites and vacancies. The bond updates are performed locally for and by means of a cluster algorithm for q>1. The updates for q>1 use a number of operations per site independent of the system size.

  6. Partial order of frustrated Potts model

    Energy Technology Data Exchange (ETDEWEB)

    Igarashi, Ryo [CCSE, Japan Atomic Energy Agency, Higashi-Ueno, Taito, Tokyo 110-0015 (Japan); Ogata, Masao, E-mail: igarashi.ryo@jaea.go.j [Deaprtment of Physics, University of Tokyo, Hongo, Bunkyo, Tokyo 133-0033 (Japan)

    2010-01-01

    We investigate a 4-state ferromagnetic Potts model with a special type of geometrical frustration on a three dimensional diamond lattice. We find that the model undergoes unconventional phase transition; half of the spins in the system order in a two dimensional hexagonal-sheet-like structure while the remaining half of the spins stay disordered. The ordered sheets and the disordered sheets stack one after another. We obtain fairly large residual entropy using the Wang-Landau Monte Carlo simulation.

  7. Dynamical behavior of the Niedermayer algorithm applied to Potts models

    OpenAIRE

    Girardi, D.; Penna, T. J. P.; Branco, N. S.

    2012-01-01

    In this work we make a numerical study of the dynamic universality class of the Niedermayer algorithm applied to the two-dimensional Potts model with 2, 3, and 4 states. This algorithm updates clusters of spins and has a free parameter, $E_0$, which controls the size of these clusters, such that $E_0=1$ is the Metropolis algorithm and $E_0=0$ regains the Wolff algorithm, for the Potts model. For $-1

  8. The XY model coupled to two-dimensional quantum gravity

    Science.gov (United States)

    Baillie, C. F.; Johnston, D. A.

    1992-09-01

    We perform Monte Carlo simulations using the Wolff cluster algorithm of the XY model on both fixed and dynamical phi-cubed graphs (i.e. without and with coupling to two-dimensional quantum gravity). We compare the numerical results with the theoretical expectation that the phase transition remains of KT type when the XY model is coupled to gravity. We also examine whether the universality we discovered in our earlier work on various Potts models with the same value of the central charge, c, carries over to the XY model, which has c=1.

  9. The XY Model Coupled to Two-Dimensional Quantum Gravity

    CERN Document Server

    Baillie, C F; 10.1016/0370-2693(92)91037-A

    2009-01-01

    We perform Monte Carlo simulations using the Wolff cluster algorithm of the XY model on both fixed and dynamical phi-cubed graphs (i.e. without and with coupling to two-dimensional quantum gravity). We compare the numerical results with the theoretical expectation that the phase transition remains of KT type when the XY model is coupled to gravity. We also examine whether the universality we discovered in our earlier work on various Potts models with the same value of the central charge, $c$, carries over to the XY model, which has $c=1$.

  10. Chromatic polynomials, Potts models and all that

    Science.gov (United States)

    Sokal, Alan D.

    2000-04-01

    The q-state Potts model can be defined on an arbitrary finite graph, and its partition function encodes much important information about that graph, including its chromatic polynomial, flow polynomial and reliability polynomial. The complex zeros of the Potts partition function are of interest both to statistical mechanicians and to combinatorists. I give a pedagogical introduction to all these problems, and then sketch two recent results: (a) Construction of a countable family of planar graphs whose chromatic zeros are dense in the whole complex q-plane except possibly for the disc | q-1|chromatic polynomial (or antiferromagnetic Potts-model partition function) in terms of the graph's maximum degree.

  11. Monte Carlo Simulation of the Potts Model on a Dodecagonal Quasiperiodic Structure

    Institute of Scientific and Technical Information of China (English)

    WEN Zhang-Bin; HOU Zhi-Lin; FU Xiu-Jun

    2011-01-01

    By means of a Monte Carlo simulation, we study the three-state Potts model on a two-dimensional quasiperiodic structure based on a dodecagonal cluster covering pattern. The critical temperature and exponents are obtained from finite-size scaling analysis. It is shown that the Potts model on the quasiperiodic lattice belongs to the same universal class as those on periodic ones.%@@ By means of a Monte Carlo simulation, we study the three-state Potts model on a two-dimensional quasiperiodic structure based on a dodecagonal cluster covering pattern.The critical temperature and exponents are obtained from finite-size scaling analysis.It is shown that the Potts model on the quasiperiodic lattice belongs to the same universal class as those on periodic ones.

  12. Equivalent-neighbor Potts models in two dimensions

    Science.gov (United States)

    Qian, Xiaofeng; Deng, Youjin; Liu, Yuhai; Guo, Wenan; Blöte, Henk W. J.

    2016-11-01

    We investigate the two-dimensional q =3 and 4 Potts models with a variable interaction range by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges as expressed by the number z of equivalent neighbors. For not-too-large z , the transitions fit well in the universality classes of the short-range Potts models. However, at longer ranges, the transitions become discontinuous. For q =3 we locate a tricritical point separating the continuous and discontinuous transitions near z =80 , and a critical fixed point between z =8 and 12. For q =4 the transition becomes discontinuous for z >16 . The scaling behavior of the q =4 model with z =16 approximates that of the q =4 merged critical-tricritical fixed point predicted by the renormalization scenario.

  13. Shaken, but not stirred - Potts model coupled to quantum gravity

    CERN Document Server

    Ambjørn, Jan; Loll, R; Pushkina, I

    2008-01-01

    We investigate the critical behaviour of both matter and geometry of the three-state Potts model coupled to two-dimensional Lorentzian quantum gravity in the framework of causal dynamical triangulations. Contrary to what general arguments of the effects of disorder suggest, we find strong numerical evidence that the critical exponents of the matter are not changed under the influence of quantum fluctuations in the geometry, compared to their values on fixed, regular lattices. This lends further support to previous findings that quantum gravity models based on causal dynamical triangulations are in many ways better behaved than their Euclidean counterparts.

  14. Glass transitions in the cellular Potts model

    Science.gov (United States)

    Chiang, M.; Marenduzzo, D.

    2016-10-01

    We study the dynamical transition between a fluid-like and a solid-like phase in a confluent cell monolayer, by using the cellular Potts model and computer simulations. We map out the phase diagram as a function of interfacial tension and of cell motility. While in the fluid phase there is normal diffusion, in the solid phase we observe sub-diffusion, very slow relaxation, and ageing, thereby strongly suggesting that this phase is glassy. Our results complement previous theoretical work within the vertex model and show that the cellular Potts model can account for the experimentally observed glassy dynamics of some biological tissues.

  15. The Potts model and the Tutte polynomial

    Science.gov (United States)

    Welsh, D. J. A.; Merino, C.

    2000-03-01

    This is an invited survey on the relation between the partition function of the Potts model and the Tutte polynomial. On the assumption that the Potts model is more familiar we have concentrated on the latter and its interpretations. In particular we highlight the connections with Abelian sandpiles, counting problems on random graphs, error correcting codes, and the Ehrhart polynomial of a zonotope. Where possible we use the mean field and square lattice as illustrations. We also discuss in some detail the complexity issues involved.

  16. Critical properties of random Potts models

    Science.gov (United States)

    Kinzel, Wolfgang; Domany, Eytan

    1981-04-01

    The critical properties of Potts models with random bonds are considered in two dimensions. A position-space renormalization-group procedure, based on the Migdal-Kadanoff method, is developed. While all previous position-space calculations satisfied the Harris criterion and the resulting scaling relation only approximately, we found conditions under which these relations are exactly satisfied, and constructed our renormalization-group procedure accordingly. Numerical results for phase diagrams and thermodynamic functions for various random-bond Potts models are presented. In addition, some exact results obtained using a duality transformation, as well as an heuristic derivation of scaling properties that correspond to the percolation problem are given.

  17. Dynamical behavior of the Niedermayer algorithm applied to Potts models

    Science.gov (United States)

    Girardi, D.; Penna, T. J. P.; Branco, N. S.

    2012-08-01

    In this work, we make a numerical study of the dynamic universality class of the Niedermayer algorithm applied to the two-dimensional Potts model with 2, 3, and 4 states. This algorithm updates clusters of spins and has a free parameter, E0, which controls the size of these clusters, such that E0=1 is the Metropolis algorithm and E0=0 regains the Wolff algorithm, for the Potts model. For -1clusters of equal spins can be formed: we show that the mean size of the clusters of (possibly) turned spins initially grows with the linear size of the lattice, L, but eventually saturates at a given lattice size L˜, which depends on E0. For L≥L˜, the Niedermayer algorithm is in the same dynamic universality class of the Metropolis one, i.e, they have the same dynamic exponent. For E0>0, spins in different states may be added to the cluster but the dynamic behavior is less efficient than for the Wolff algorithm (E0=0). Therefore, our results show that the Wolff algorithm is the best choice for Potts models, when compared to the Niedermayer's generalization.

  18. Complete analyticity of the 2D Potts model above the critical temperature

    NARCIS (Netherlands)

    Enter, Aernout C.D. van; Fernández, Roberto; Schonmann, Roberto H.; Shlosman, Senya B.

    1997-01-01

    We investigate the complete analyticity (CA) of the two-dimensional q-state Potts model for large values of q. We are able to prove it for every temperature T > Tcr(q), provided we restrict ourselves to nice subsets, their niceness depending on the temperature T. Contrary to this restricted complete

  19. Dynamic exponents for potts model cluster algorithms

    Science.gov (United States)

    Coddington, Paul D.; Baillie, Clive F.

    We have studied the Swendsen-Wang and Wolff cluster update algorithms for the Ising model in 2, 3 and 4 dimensions. The data indicate simple relations between the specific heat and the Wolff autocorrelations, and between the magnetization and the Swendsen-Wang autocorrelations. This implies that the dynamic critical exponents are related to the static exponents of the Ising model. We also investigate the possibility of similar relationships for the Q-state Potts model.

  20. Potts and percolation models on bowtie lattices.

    Science.gov (United States)

    Ding, Chengxiang; Wang, Yancheng; Li, Yang

    2012-08-01

    We give the exact critical frontier of the Potts model on bowtie lattices. For the case of q = 1, the critical frontier yields the thresholds of bond percolation on these lattices, which are exactly consistent with the results given by Ziff et al. [J. Phys. A 39, 15083 (2006)]. For the q = 2 Potts model on a bowtie A lattice, the critical point is in agreement with that of the Ising model on this lattice, which has been exactly solved. Furthermore, we do extensive Monte Carlo simulations of the Potts model on a bowtie A lattice with noninteger q. Our numerical results, which are accurate up to seven significant digits, are consistent with the theoretical predictions. We also simulate the site percolation on a bowtie A lattice, and the threshold is s(c) = 0.5479148(7). In the simulations of bond percolation and site percolation, we find that the shape-dependent properties of the percolation model on a bowtie A lattice are somewhat different from those of an isotropic lattice, which may be caused by the anisotropy of the lattice.

  1. Potts q-color field theory and scaling random cluster model

    CERN Document Server

    Delfino, Gesualdo

    2011-01-01

    We study structural properties of the q-color Potts field theory which, for real values of q, describes the scaling limit of the random cluster model. We show that the number of independent n-point Potts spin correlators coincides with that of independent n-point cluster connectivities and is given by generalized Bell numbers. Only a subset of these spin correlators enters the determination of the Potts magnetic properties for q integer. The structure of the operator product expansion of the spin fields for generic q is also identified. For the two-dimensional case, we analyze the duality relation between spin and kink field correlators, both for the bulk and boundary cases, obtaining in particular a sum rule for the kink-kink elastic scattering amplitudes.

  2. Phase transition and surface sublimation of a mobile Potts model.

    Science.gov (United States)

    Bailly-Reyre, A; Diep, H T; Kaufman, M

    2015-10-01

    We study in this paper the phase transition in a mobile Potts model by the use of Monte Carlo simulation. The mobile Potts model is related to a diluted Potts model, which is also studied here by a mean-field approximation. We consider a lattice where each site is either vacant or occupied by a q-state Potts spin. The Potts spin can move from one site to a nearby vacant site. In order to study the surface sublimation, we consider a system of Potts spins contained in a recipient with a concentration c defined as the ratio of the number of Potts spins N(s) to the total number of lattice sites N(L)=N(x)×N(y)×N(z). Taking into account the attractive interaction between the nearest-neighboring Potts spins, we study the phase transitions as functions of various physical parameters such as the temperature, the shape of the recipient, and the spin concentration. We show that as the temperature increases, surface spins are detached from the solid phase to form a gas in the empty space. Surface order parameters indicate different behaviors depending on the distance to the surface. At high temperatures, if the concentration is high enough, the interior spins undergo a first-order phase transition to an orientationally disordered phase. The mean-field results are shown as functions of temperature, pressure, and chemical potential, which confirm in particular the first-order character of the transition.

  3. Antiferromagnetic Potts model on the Erdos-Renyi random graph

    CERN Document Server

    Contucci, Pierluig; Giardina', Cristian; Starr, Shannon

    2011-01-01

    We study the antiferromagnetic Potts model on the Erdos-Renyi random graph. By identifying a suitable interpolation structure and proving an extended variational principle we show that the replica symmetric solution is an upper bound for the limiting pressure which can be recovered in the framework of Derrida-Ruelle probability cascades. A comparison theorem with a mixed model made of a mean field Potts-antiferromagnet plus a Potts-Sherrington-Kirkpatrick model allows to show that the replica symmetric solution is exact at high temperatures.

  4. Phase Transition Properties of 3D Potts Models

    CERN Document Server

    Bazavov, Alexei; Dubey, Santosh

    2008-01-01

    Using multicanonical Metropolis simulations we estimate phase transition properties of 3D Potts models for q=4 to 10: The transition temperatures, latent heats, entropy gaps, normalized entropies at the disordered and ordered endpoints, interfacial tensions, and spinodal endpoints.

  5. Graphical representations of Ising and Potts models

    CERN Document Server

    Björnberg, Jakob E

    2010-01-01

    We study graphical representations for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960's. The second model is the space-time percolation process, which is closely related to the contact model for the spread of disease. We consider a `space-time' random-cluster model and explore a range of useful probabilistic techniques for studying it. The space-time Potts model emerges as a natural generalization of the quantum Ising model. The basic properties of the phase transitions in these models are treated, such as the fact that there is at most one unbounded FK-cluster, and the resulting lower bound on the critical value in $\\ZZ$. We also develop an alternative graphical representation of the quantum Ising model, called the random-parity representation. This representation is based on the random-current representation of the classical Ising model, and allows us to study in much great...

  6. Krypton on graphite and the striped helical Potts model

    Science.gov (United States)

    Halpin-Healy, Timothy; Kardar, Mehran

    1985-02-01

    A generalization of the helical Potts model, with two species of domain wall due to explicit triaxial helical symmetry breaking, is studied via position-space renormalization-group methods and is discovered to exhibit striped, as well as hexagonal, phases. The disordering transition of the commensurate ferromagnetic phase belongs to the symmetric Potts universality class. No evidence is found for a chiral melting transition. Commensurate-incommensurate phase diagrams for oversaturated krypton on graphite are constructed.

  7. Emergent O(n ) symmetry in a series of three-dimensional Potts models

    Science.gov (United States)

    Ding, Chengxiang; Blöte, Henk W. J.; Deng, Youjin

    2016-09-01

    We study the q -state Potts model on a simple cubic lattice with ferromagnetic interactions in one lattice direction, and antiferromagnetic interactions in the other two directions. As the temperature T decreases, the system undergoes a second-order phase transition that fits in the universality class of the three-dimensional O (n ) model with n =q -1 . This conclusion is based on the estimated critical exponents, and histograms of the order parameter. At even smaller T we find, for q =4 and 5, a first-order transition to a phase with a different type of long-range order. This long-range order dissolves at T =0 , and the system effectively reduces to a disordered two-dimensional Potts antiferromagnet. These results are obtained by means of Monte Carlo simulations and finite-size scaling.

  8. Investigation of the thermodynamic properties and phase transitions in a strongly diluted three-vertex antiferromagnetic Potts model by the Monte Carlo method

    Science.gov (United States)

    Murtazaev, A. K.; Babaev, A. B.; Ataeva, G. Ya.

    2017-01-01

    The thermodynamic properties and phase transitions in a two-dimensional strongly diluted threevertex antiferromagnetic Potts model on a triangular lattice have been investigated using the Monte Carlo method. The systems with linear dimensions of L × L = N, where L = 18-48, have been considered. It has been shown using the method of fourth-order Binder cumulants that, upon the introduction of nonmagnetic impurities into the spin system described by the two-dimensional antiferromagnetic Potts model, the firstorder phase transition changes to a second-order phase transition.

  9. Remarks on Khovanov Homology and the Potts Model

    CERN Document Server

    Kauffman, Louis H

    2009-01-01

    This paper is about Khovanov homology and its relationships with statistical mechanics models such as the Ising model and the Potts model. The paper gives a relatively self-contained introduction to Khovanov homology, and also to a reformulation of the Potts model in terms of a bracket state sum expansion on a knot diagram K(G) related to a planar graph G via the medial construction. We consider the original Khovanov homology and also the homology defined by Stosic via the dichromatic polynomial, and examine those values of the Potts model where the partition function can be expressed in terms of homological Euler characteristics. These points occur at imaginary temperature, and consequences of this phenomenon will be studied in subsequent work. This paper is dedicated to Oleg Viro on his 60-th birthday.

  10. Extending models for two-dimensional constraints

    DEFF Research Database (Denmark)

    Forchhammer, Søren

    2009-01-01

    Random fields in two dimensions may be specified on 2 times 2 elements such that the probabilities of finite configurations and the entropy may be calculated explicitly. The Pickard random field is one example where probability of a new (non-boundary) element is conditioned on three previous...... elements. To extend the concept we consider extending such a field such that a vector or block of elements is conditioned on a larger set of previous elements. Given a stationary model defined on 2 times 2 elements, iterative scaling is used to define the extended model. The extended model may be used...

  11. Spontaneous Magnetization of the Integrable Chiral Potts Model

    CERN Document Server

    Au-Yang, Helen

    2010-01-01

    We show how $Z$-invariance in the chiral Potts model provides a strategy to calculate the pair correlation in the general integrable chiral Potts model using only the superintegrable eigenvectors. When the distance between the two spins in the correlation function becomes infinite it becomes the square of the order parameter. In this way, we show that the spontaneous magnetization can be expressed in terms of the inner products of the eigenvectors of the $N$ asymptotically degenerate maximum eigenvalues. Using our previous results on these eigenvectors, we are able to obtain the order parameter as a sum almost identical to the one given by Baxter. This gives the known spontaneous magnetization of the chiral Potts model by an entirely different approach.

  12. Spontaneous magnetization of the integrable chiral Potts model

    Energy Technology Data Exchange (ETDEWEB)

    Au-Yang, Helen; Perk, Jacques H H, E-mail: helenperk@yahoo.com, E-mail: perk@okstate.edu [Department of Physics, Oklahoma State University, 145 Physical Sciences, Stillwater, OK 74078-3072 (United States)

    2011-11-04

    We show how Z-invariance in the chiral Potts model provides a strategy to calculate the pair correlation in the general integrable chiral Potts model using only the superintegrable eigenvectors. When the distance between the two spins in the correlation function becomes infinite it becomes the square of the order parameter. In this way, we show that the spontaneous magnetization can be expressed in terms of the inner products of the eigenvectors of the N asymptotically degenerate maximum eigenvalues. Using our previous results on these eigenvectors, we are able to obtain the order parameter as a sum almost identical to the one given by Baxter. This gives the known spontaneous magnetization of the chiral Potts model by an entirely different approach. (paper)

  13. On the Potts Model Partition Function in an External Field

    Science.gov (United States)

    McDonald, Leslie M.; Moffatt, Iain

    2012-03-01

    We study the partition function of the Potts model in an external (magnetic) field, and its connections with the zero-field Potts model partition function. Using a deletion-contraction formulation for the partition function Z for this model, we show that it can be expanded in terms of the zero-field partition function. We also show that Z can be written as a sum over the spanning trees, and the spanning forests, of a graph G. Our results extend to Z the well-known spanning tree expansion for the zero-field partition function that arises though its connections with the Tutte polynomial.

  14. Cellular Potts modeling of complex multicellular behaviors in tissue morphogenesis

    NARCIS (Netherlands)

    T. Hirashima (Tsuyoshi); E.G. Rens (Lisanne); R.M.H. Merks (Roeland)

    2017-01-01

    textabstractMathematical modeling is an essential approach for the understanding of complex multicellular behaviors in tissue morphogenesis. Here, we review the cellular Potts model (CPM; also known as the Glazier-Graner-Hogeweg model), an effective computational modeling framework. We discuss its

  15. Influence of frustrations on the thermodynamic properties of the low-dimensional Potts model studied by computer simulation

    Science.gov (United States)

    Babaev, A. B.; Murtazaev, A. K.; Suleimanov, E. M.; Rizvanova, T. R.

    2016-10-01

    Influence of disorder in the form of frustration on the thermodynamic behavior of a two-dimensional three-vertex Potts model has been studied by the Monte Carlo method, taking into account the nearest and next-nearest neighbors. Systems with linear sizes of L × L = N ( L = 9-48) on a triangular lattice have been considered. It has been shown that in the case of J 1 > 0 and J 2 model undergoes a phase transition outside this region.

  16. Approximating the partition function of the ferromagnetic Potts model

    CERN Document Server

    Goldberg, Leslie Ann

    2010-01-01

    We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic q-state Potts model when q>2. Specifically we show that the partition function is hard for the complexity class #RHPi_1 under approximation-preserving reducibility. Thus, it is as hard to approximate the partition function as it is to find approximate solutions to a wide range of counting problems, including that of determining the number of independent sets in a bipartite graph. Our proof exploits the second order phase transition of the "random cluster" model, which is a probability distribution on graphs that is closely related to the q-state Potts

  17. Potts Flux Tube Model at Nonzero Chemical Potential

    CERN Document Server

    Condella, J; Condella, Jac; Tar, Carleton De

    2000-01-01

    We model the deconfinement phase transition in quantum chromodynamics at nonzero baryon number density and large quark mass by extending the flux tube model (three-state, three-dimensional Potts model) to nonzero chemical potential. In a direct numerical simulation we confirm mean-field-theory predictions that the deconfinement transition does not occur in a baryon-rich environment.

  18. Two-dimensional lattice Boltzmann model for magnetohydrodynamics.

    Science.gov (United States)

    Schaffenberger, Werner; Hanslmeier, Arnold

    2002-10-01

    We present a lattice Boltzmann model for the simulation of two-dimensional magnetohydro dynamic (MHD) flows. The model is an extension of a hydrodynamic lattice Boltzman model with 9 velocities on a square lattice resulting in a model with 17 velocities. Earlier lattice Boltzmann models for two-dimensional MHD used a bidirectional streaming rule. However, the use of such a bidirectional streaming rule is not necessary. In our model, the standard streaming rule is used, allowing smaller viscosities. To control the viscosity and the resistivity independently, a matrix collision operator is used. The model is then applied to the Hartmann flow, giving reasonable results.

  19. The three-state antiferromagnetic Potts model: scaling laws

    Energy Technology Data Exchange (ETDEWEB)

    Gottlob, A.P. [Kaiserslautern Univ. (Germany); Hasenbusch, M. [Cambridge Univ. (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics (DAMTP)

    1995-04-01

    We present the results of a Monte Carlo study of the three-dimensional anti-ferromagnetic three-state Potts model. We computed the correlation length, the magnetic susceptibility and the specific heat for various coupling parameters in the high temperature phase of the model. From the scaling behaviour of these quantities we determine estimates for the critical temperature and critical exponents. ((orig.)).

  20. F-Susy And The Three States Potts Model

    CERN Document Server

    Sedra, M B

    2009-01-01

    In view of its several involvements in various physical and mathematical contexts, 2D-fractional supersymmetry (F-susy) is once again considered in this work. We are, for instance, interested to study the three states Potts model $(k = 3)$ which represents with the tricritical Ising model $(k = 2)$ the two leading examples of more general spin $1/k$ fractional supersymmetric theories.

  1. Cumulants of the three-state Potts model and of nonequilibrium models with C{sub 3v} symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Tome, Tania [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, SP (Brazil); Petri, Alberto [Istituto di Acustica O M Corbino, Consiglio Nazionale delle Ricerche, Via del Fosso del Cavaliere, Rome (Italy)

    2002-07-05

    The critical behaviour of two-dimensional stochastic lattice gas models with C{sub 3v} symmetry is analysed. We study the cumulants of the order parameter for the three-state (equilibrium) Potts model and for two irreversible models whose dynamic rules are invariant under the symmetry operations of the point group C{sub 3v}. By means of extensive numerical analysis of the phase transition we show that irreversibility does not affect the critical behaviour of the systems. In particular, we find that the Binder reduced fourth-order cumulant takes a universal value U* which is the same for the three-state Potts model and for the irreversible models. The same universal behaviour is observed for the reduced third-order cumulant. (author)

  2. Free energies of the Potts model on a Cayley tree

    Science.gov (United States)

    Rozikov, U. A.; Rakhmatullaev, M. M.

    2017-01-01

    For the Potts model on the Cayley tree, we obtain some explicit formulas for the free energies and entropies in the case of vector-valued boundary conditions. These formulas include translation-invariant, periodic, and Dobrushin-like boundary conditions and also those corresponding to weakly periodic Gibbs measures.

  3. Saddle-point approach to the gauge Potts model

    Energy Technology Data Exchange (ETDEWEB)

    Camarata, C.; Epele, L.N.; Fanchiotti, H.; Garcia Canal, C.A.

    1984-07-02

    The q-state gauge Potts model in d dimensions is studied via saddle-point techniques. Corrections to the mean-field results, due to gaussian fluctuations, are computed. Results for the free energy, the critical coupling and the latent heat are presented. The limit q->infinite is discussed.

  4. Dynamical phase transitions in the two-dimensional ANNNI model

    Energy Technology Data Exchange (ETDEWEB)

    Barber, M.N.; Derrida, B.

    1988-06-01

    We study the phase diagram of the two-dimensional anisotropic next-nearest neighbor Ising (ANNNI) model by comparing the time evolution of two distinct spin configurations submitted to the same thermal noise. We clearly se several dynamical transitions between ferromagnetic, paramagnetic, antiphase, and floating phases. These dynamical transitions seem to occur rather close to the transition lines determined previously in the literature.

  5. Two-dimensional effects in nonlinear Kronig-Penney models

    DEFF Research Database (Denmark)

    Gaididei, Yuri Borisovich; Christiansen, Peter Leth; Rasmussen, Kim

    1997-01-01

    An analysis of two-dimensional (2D) effects in the nonlinear Kronig-Penney model is presented. We establish an effective one-dimensional description of the 2D effects, resulting in a set of pseudodifferential equations. The stationary states of the 2D system and their stability is studied...

  6. Two-dimensional model of elastically coupled molecular motors

    Institute of Scientific and Technical Information of China (English)

    Zhang Hong-Wei; Wen Shu-Tang; Chen Gai-Rong; Li Yu-Xiao; Cao Zhong-Xing; Li Wei

    2012-01-01

    A flashing ratchet model of a two-headed molecular motor in a two-dimensional potential is proposed to simulate the hand-over-hand motion of kinesins.Extensive Langevin simulations of the model are performed.We discuss the dependences of motion and efficiency on the model parameters,including the external force and the temperature.A good qualitative agreement with the expected behavior is observed.

  7. Towards a two dimensional model of surface piezoelectricity

    OpenAIRE

    Monge Víllora, Oscar

    2016-01-01

    We want to understand the behaviour of flexoelectricity and surface piezoelectricity and distinguish them in order to go deep into the controversies of the filed. This motivate the construction of a model of continuum flexoelectric theory. The model proposed is a two-dimensional model that integrates the electromechanical equations that include the elastic, dielectric, piezoelectric and flexoelectric effect on a rectangular sample. As the flexoelectric and the surface piezoelectric effects ap...

  8. Application of nested sampling in statistical physics: the Potts model

    CERN Document Server

    Pfeifenberger, Manuel J

    2016-01-01

    We present a systematic benchmark study of the nested sampling algorithm on the basis of the Potts model. This model exhibits a first order phase transition for $q>4$ at the critical temperature. The numerical evaluation of the partition function and thermodynamic observables, which involves high dimensional sums of sharply structured multi-modal density functions, represents a major challenge to most standard numerical techniques, such as Markov Chain Monte Carlo. Nested sampling, on the other hand, is particularly suited for such problems. In this paper we will employ both, nested sampling and thermodynamic integration to evaluate the partition function of the Potts model. In both cases individual moves are based on Swendsen-Wang updates. A autocorrelation time analysis of both algorithms shows that the severe slowing down of thermodynamic integration around the critical temperature does not occur in nested sampling. In addition we show, how thermodynamic variables can be computed with high accuracy from th...

  9. Lung Cancer Pathological Image Analysis Using a Hidden Potts Model

    Directory of Open Access Journals (Sweden)

    Qianyun Li

    2017-06-01

    Full Text Available Nowadays, many biological data are acquired via images. In this article, we study the pathological images scanned from 205 patients with lung cancer with the goal to find out the relationship between the survival time and the spatial distribution of different types of cells, including lymphocyte, stroma, and tumor cells. Toward this goal, we model the spatial distribution of different types of cells using a modified Potts model for which the parameters represent interactions between different types of cells and estimate the parameters of the Potts model using the double Metropolis-Hastings algorithm. The double Metropolis-Hastings algorithm allows us to simulate samples approximately from a distribution with an intractable normalizing constant. Our numerical results indicate that the spatial interaction between the lymphocyte and tumor cells is significantly associated with the patient’s survival time, and it can be used together with the cell count information to predict the survival of the patients.

  10. Lung Cancer Pathological Image Analysis Using a Hidden Potts Model.

    Science.gov (United States)

    Li, Qianyun; Yi, Faliu; Wang, Tao; Xiao, Guanghua; Liang, Faming

    2017-01-01

    Nowadays, many biological data are acquired via images. In this article, we study the pathological images scanned from 205 patients with lung cancer with the goal to find out the relationship between the survival time and the spatial distribution of different types of cells, including lymphocyte, stroma, and tumor cells. Toward this goal, we model the spatial distribution of different types of cells using a modified Potts model for which the parameters represent interactions between different types of cells and estimate the parameters of the Potts model using the double Metropolis-Hastings algorithm. The double Metropolis-Hastings algorithm allows us to simulate samples approximately from a distribution with an intractable normalizing constant. Our numerical results indicate that the spatial interaction between the lymphocyte and tumor cells is significantly associated with the patient's survival time, and it can be used together with the cell count information to predict the survival of the patients.

  11. Minor magnetization loops in two-dimensional dipolar Ising model

    Energy Technology Data Exchange (ETDEWEB)

    Sarjala, M. [Aalto University, Department of Applied Physics, P.O. Box 14100, FI-00076 Aalto (Finland); Seppaelae, E.T., E-mail: eira.seppala@nokia.co [Nokia Research Center, Itaemerenkatu 11-13, FI-00180 Helsinki (Finland); Alava, M.J., E-mail: mikko.alava@tkk.f [Aalto University, Department of Applied Physics, P.O. Box 14100, FI-00076 Aalto (Finland)

    2011-05-15

    The two-dimensional dipolar Ising model is investigated for the relaxation and dynamics of minor magnetization loops. Monte Carlo simulations show that in a stripe phase an exponential decrease can be found for the magnetization maxima of the loops, M{approx}exp(-{alpha}N{sub l}) where N{sub l} is the number of loops. We discuss the limits of this behavior and its relation to the equilibrium phase diagram of the model.

  12. Potts model partition functions on two families of fractal lattices

    Science.gov (United States)

    Gong, Helin; Jin, Xian'an

    2014-11-01

    The partition function of q-state Potts model, or equivalently the Tutte polynomial, is computationally intractable for regular lattices. The purpose of this paper is to compute partition functions of q-state Potts model on two families of fractal lattices. Based on their self-similar structures and by applying the subgraph-decomposition method, we divide their Tutte polynomials into two summands, and for each summand we obtain a recursive formula involving the other summand. As a result, the number of spanning trees and their asymptotic growth constants, and a lower bound of the number of connected spanning subgraphs or acyclic root-connected orientations for each of such two lattices are obtained.

  13. Functional connectivity mapping using the ferromagnetic Potts spin model.

    Science.gov (United States)

    Stanberry, Larissa; Murua, Alejandro; Cordes, Dietmar

    2008-04-01

    An unsupervised stochastic clustering method based on the ferromagnetic Potts spin model is introduced as a powerful tool to determine functionally connected regions. The method provides an intuitively simple approach to clustering and makes no assumptions of the number of clusters in the data or their underlying distribution. The performance of the method and its dependence on the intrinsic parameters (size of the neighborhood, form of the interaction term, etc.) is investigated on the simulated data and real fMRI data acquired during a conventional periodic finger tapping task. The merits of incorporating Euclidean information into the connectivity analysis are discussed. The ability of the Potts model clustering to uncover the hidden structure in the complex data is demonstrated through its application to the resting-state data to determine functional connectivity networks of the anterior and posterior cingulate cortices for the group of nine healthy male subjects. (c) 2007 Wiley-Liss, Inc.

  14. The Potts model on a Bethe lattice with nonmagnetic impurities

    Energy Technology Data Exchange (ETDEWEB)

    Semkin, S. V., E-mail: li15@rambler.ru; Smagin, V. P. [Vladivistok State University of Economics and Service (VSUES) (Russian Federation)

    2015-10-15

    We have obtained a solution for the Potts model on a Bethe lattice with mobile nonmagnetic impurities. A method is proposed for constructing a “pseudochaotic” impurity distribution by a vanishing correlation in the arrangement of impurity atoms for the nearest sites. For a pseudochaotic impurity distribution, we obtained the phase-transition temperature, magnetization, and spontaneous magnetization jumps at the phase-transition temperature.

  15. q-state Potts model on the Apollonian network.

    Science.gov (United States)

    Araújo, Nuno A M; Andrade, Roberto F S; Herrmann, Hans J

    2010-10-01

    The q-state Potts model is studied on the Apollonian network with Monte Carlo simulations and the transfer matrix method. The spontaneous magnetization, correlation length, entropy, and specific heat are analyzed as a function of temperature for different number of states, q. Different scaling functions in temperature and q are proposed. A quantitative agreement is found between results from both methods. No critical behavior is observed in the thermodynamic limit for any number of states.

  16. Academic Meeting Scheduling Using an Antiferromagnetic Potts Model

    Science.gov (United States)

    Kudo, Kazue

    2017-07-01

    Scheduling parallel sessions of an academic meeting is a complicated task. If each presentation is assigned to an appropriate session, an antiferromagnetic Potts model can be used for semi-automatic timetabling. The timetabling method proposed here is based on graph coloring and includes additional constraints to be considered in a practical situation. We examine the feasibility of semi-automatic timetabling in some practical examples.

  17. Local resolution-limit-free Potts model for community detection.

    Science.gov (United States)

    Ronhovde, Peter; Nussinov, Zohar

    2010-04-01

    We report on an exceptionally accurate spin-glass-type Potts model for community detection. With a simple algorithm, we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of noise. It is also competitive with the best currently available algorithms in terms of speed and size of solvable systems. We find that the computational demand often exhibits superlinear scaling O(L1.3) where L is the number of edges in the system, and we have applied the algorithm to synthetic systems as large as 40 x 10(6) nodes and over 1 x 10(9) edges. A previous stumbling block encountered by popular community detection methods is the so-called "resolution limit." Being a "local" measure of community structure, our Potts model is free from this resolution-limit effect, and it further remains a local measure on weighted and directed graphs. We also address the mitigation of resolution-limit effects for two other popular Potts models.

  18. COMPUTER SIMULATION OF ANTIFERROMAGNETIC STRUCTURES DESCRIBED BY THE THREE-VERTEX ANTIFERROMAGNETIC POTTS MODEL

    National Research Council Canada - National Science Library

    Yarash K. Abuev; Albert B. Babaev; Pharkhat E. Esetov

    2017-01-01

    Objectives A computer simulation of the antiferromagnetic structures described by the three-vertex Potts model on a triangular lattice is performed, taking into account the antiferromagnetic exchange...

  19. A two-dimensional analytical model of petroleum vapor intrusion

    Science.gov (United States)

    Yao, Yijun; Verginelli, Iason; Suuberg, Eric M.

    2016-02-01

    In this study we present an analytical solution of a two-dimensional petroleum vapor intrusion model, which incorporates a steady-state diffusion-dominated vapor transport in a homogeneous soil and piecewise first-order aerobic biodegradation limited by oxygen availability. This new model can help practitioners to easily generate two-dimensional soil gas concentration profiles for both hydrocarbons and oxygen and estimate hydrocarbon indoor air concentrations as a function of site-specific conditions such as source strength and depth, reaction rate constant, soil characteristics and building features. The soil gas concentration profiles generated by this new model are shown in good agreement with three-dimensional numerical simulations and two-dimensional measured soil gas data from a field study. This implies that for cases involving diffusion dominated soil gas transport, steady state conditions and homogenous source and soil, this analytical model can be used as a fast and easy-to-use risk screening tool by replicating the results of 3-D numerical simulations but with much less computational effort.

  20. Phase Transitions in Two-Dimensional Traffic Flow Models

    CERN Document Server

    Cuesta, J A; Molera, J M; Cuesta, José A; Martinez, Froilán C; Molera, Juan M

    1993-01-01

    Abstract: We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a jammed state, with a critical point. The jammed phase presents new transitions corresponding to structural transformations of the jam. We discuss their relevance in the infinite size limit.

  1. Phase Transitions in Two-Dimensional Traffic Flow Models

    CERN Document Server

    Cuesta, José A; Molera, Juan M; Escuela, Angel Sánchez; 10.1103/PhysRevE.48.R4175

    2009-01-01

    We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a jammed state, with a critical point. The jammed phase presents new transitions corresponding to structural transformations of the jam. We discuss their relevance in the infinite size limit.

  2. Dynamics of cell shape and forces on micropatterned substrates predicted by a cellular Potts model.

    Science.gov (United States)

    Albert, Philipp J; Schwarz, Ulrich S

    2014-06-03

    Micropatterned substrates are often used to standardize cell experiments and to quantitatively study the relation between cell shape and function. Moreover, they are increasingly used in combination with traction force microscopy on soft elastic substrates. To predict the dynamics and steady states of cell shape and forces without any a priori knowledge of how the cell will spread on a given micropattern, here we extend earlier formulations of the two-dimensional cellular Potts model. The third dimension is treated as an area reservoir for spreading. To account for local contour reinforcement by peripheral bundles, we augment the cellular Potts model by elements of the tension-elasticity model. We first parameterize our model and show that it accounts for momentum conservation. We then demonstrate that it is in good agreement with experimental data for shape, spreading dynamics, and traction force patterns of cells on micropatterned substrates. We finally predict shapes and forces for micropatterns that have not yet been experimentally studied. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

  3. Cellular Potts modeling of complex multicellular behaviors in tissue morphogenesis.

    Science.gov (United States)

    Hirashima, Tsuyoshi; Rens, Elisabeth G; Merks, Roeland M H

    2017-06-01

    Mathematical modeling is an essential approach for the understanding of complex multicellular behaviors in tissue morphogenesis. Here, we review the cellular Potts model (CPM; also known as the Glazier-Graner-Hogeweg model), an effective computational modeling framework. We discuss its usability for modeling complex developmental phenomena by examining four fundamental examples of tissue morphogenesis: (i) cell sorting, (ii) cyst formation, (iii) tube morphogenesis in kidney development, and (iv) blood vessel formation. The review provides an introduction for biologists for starting simulation analysis using the CPM framework. © 2017 Japanese Society of Developmental Biologists.

  4. Corner wetting transition in the two-dimensional Ising model

    Science.gov (United States)

    Lipowski, Adam

    1998-07-01

    We study the interfacial behavior of the two-dimensional Ising model at the corner of weakened bonds. Monte Carlo simulations results show that the interface is pinned to the corner at a lower temperature than a certain temperature Tcw at which it undergoes a corner wetting transition. The temperature Tcw is substantially lower than the temperature of the ordinary wetting transition with a line of weakened bonds. A solid-on-solid-like model is proposed, which provides a supplementary description of the corner wetting transition.

  5. AN APPROACH IN MODELING TWO-DIMENSIONAL PARTIALLY CAVITATING FLOW

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    An approach of modeling viscosity, unsteady partially cavitating flows around lifting bodies is presented. By employing an one-fluid Navier-Stokers solver, the algorithm is proved to be able to handle two-dimensional laminar cavitating flows at moderate Reynolds number. Based on the state equation of water-vapor mixture, the constructive relations of densities and pressures are established. To numerically simulate the cavity wall, different pseudo transition of density models are presumed. The finite-volume method is adopted and the algorithm can be extended to three-dimensional cavitating flows.

  6. Elastic models of defects in two-dimensional crystals

    Science.gov (United States)

    Kolesnikova, A. L.; Orlova, T. S.; Hussainova, I.; Romanov, A. E.

    2014-12-01

    Elastic models of defects in two-dimensional (2D) crystals are presented in terms of continuum mechanics. The models are based on the classification of defects, which is founded on the dimensionality of the specification region of their self-distortions, i.e., lattice distortions associated with the formation of defects. The elastic field of an infinitesimal dislocation loop in a film is calculated for the first time. The fields of the center of dilatation, dislocation, disclination, and circular inclusion in planar 2D elastic media, namely, nanofilms and graphenes, are considered. Elastic fields of defects in 2D and 3D crystals are compared.

  7. Approaches to verification of two-dimensional water quality models

    Energy Technology Data Exchange (ETDEWEB)

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

    1990-11-01

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

  8. Boundary States of the Potts Model on Random Planar Maps

    CERN Document Server

    Atkin, Max; Wheater, John

    2015-01-01

    We revisit the 3-states Potts model on random planar triangulations as a Hermitian matrix model. As a novelty, we obtain an algebraic curve which encodes the partition function on the disc with both fixed and mixed spin boundary conditions. We investigate the critical behaviour of this model and find scaling exponents consistent with previous literature. We argue that the conformal field theory that describes the double scaling limit is Liouville quantum gravity coupled to the $(A_4,D_4)$ minimal model with extended $\\mathcal{W}_3$-symmetry.

  9. On some classes of two-dimensional local models in discrete two-dimensional monatomic FPU lattice with cubic and quartic potential

    Institute of Scientific and Technical Information of China (English)

    Xu Quan; Tian Qiang

    2009-01-01

    This paper discusses the two-dimensional discrete monatomic Fermi-Pasta-Ulam lattice, by using the method of multiple-scale and the quasi-discreteness approach. By taking into account the interaction between the atoms in the lattice and their nearest neighbours, it obtains some classes of two-dimensional local models as follows: two-dimensional bright and dark discrete soliton trains, two-dimensional bright and dark line discrete breathers, and two-dimensional bright and dark discrete breather.

  10. Two dimensional hydrodynamic modeling of a high latitude braided river

    Science.gov (United States)

    Humphries, E.; Pavelsky, T.; Bates, P. D.

    2014-12-01

    Rivers are a fundamental resource to physical, ecologic and human systems, yet quantification of river flow in high-latitude environments remains limited due to the prevalence of complex morphologies, remote locations and sparse in situ monitoring equipment. Advances in hydrodynamic modeling and remote sensing technology allow us to address questions such as: How well can two-dimensional models simulate a flood wave in a highly 3-dimensional braided river environment, and how does the structure of such a flood wave differ from flow down a similar-sized single-channel river? Here, we use the raster-based hydrodynamic model LISFLOOD-FP to simulate flood waves, discharge, water surface height, and velocity measurements over a ~70 km reach of the Tanana River in Alaska. In order to use LISFLOOD-FP a digital elevation model (DEM) fused with detailed bathymetric data is required. During summer 2013, we surveyed 220,000 bathymetric points along the study reach using an echo sounder system connected to a high-precision GPS unit. The measurements are interpolated to a smooth bathymetric surface, using Topo to Raster interpolation, and combined with an existing five meter DEM (Alaska IfSAR) to create a seamless river terrain model. Flood waves are simulated using varying complexities in model solvers, then compared to gauge records and water logger data to assess major sources of model uncertainty. Velocity and flow direction maps are also assessed and quantified for detailed analysis of braided channel flow. The most accurate model output occurs with using the full two-dimensional model structure, and major inaccuracies appear to be related to DEM quality and roughness values. Future work will intercompare model outputs with extensive ground measurements and new data from AirSWOT, an airborne analog for the Surface Water and Ocean Topography (SWOT) mission, which aims to provide high-resolution measurements of terrestrial and ocean water surface elevations globally.

  11. Surface Ship Shock Modeling and Simulation: Two-Dimensional Analysis

    Directory of Open Access Journals (Sweden)

    Young S. Shin

    1998-01-01

    Full Text Available The modeling and simulation of the response of a surface ship system to underwater explosion requires an understanding of many different subject areas. These include the process of underwater explosion events, shock wave propagation, explosion gas bubble behavior and bubble-pulse loading, bulk and local cavitation, free surface effect, fluid-structure interaction, and structural dynamics. This paper investigates the effects of fluid-structure interaction and cavitation on the response of a surface ship using USA-NASTRAN-CFA code. First, the one-dimensional Bleich-Sandler model is used to validate the approach, and second, the underwater shock response of a two-dimensional mid-section model of a surface ship is predicted with a surrounding fluid model using a constitutive equation of a bilinear fluid which does not allow transmission of negative pressures.

  12. Two-dimensional Numerical Modeling Research on Continent Subduction Dynamics

    Institute of Scientific and Technical Information of China (English)

    WANG Zhimin; XU Bei; ZHOU Yaoqi; XU Hehua; HUANG Shaoying

    2004-01-01

    Continent subduction is one of the hot research problems in geoscience. New models presented here have been set up and two-dimensional numerical modeling research on the possibility of continental subduction has been made with the finite element software, ANSYS, based on documentary evidence and reasonable assumptions that the subduction of oceanic crust has occurred, the subduction of continental crust can take place and the process can be simplified to a discontinuous plane strain theory model. The modeling results show that it is completely possible for continental crust to be subducted to a depth of 120 km under certain circumstances and conditions. At the same time, the simulations of continental subduction under a single dynamical factor have also been made, including the pull force of the subducted oceanic lithosphere, the drag force connected with mantle convection and the push force of the mid-ocean ridge. These experiments show that the drag force connected with mantle convection is critical for continent subduction.

  13. New Correlation Duality Relations for the Planar Potts Model

    Science.gov (United States)

    King, C.; Wu, F. Y.

    2002-05-01

    We introduce a new method to generate duality relations for correlation functions of the Potts model on a planar graph. The method extends previously known results, by allowing the consideration of the correlation function for arbitrarily placed vertices on the graph. We show that generally it is linear combinations of correlation functions, not the individual correlations, that are related by dualities. The method is illustrated in several non-trivial cases, and the relation to earlier results is explained. A graph-theoretical formulation of our results in terms of rooted dichromatic, or Tutte, polynomials is also given.

  14. Critical Interfaces in the Random-Bond Potts Model

    Science.gov (United States)

    Jacobsen, Jesper L.; Le Doussal, Pierre; Picco, Marco; Santachiara, Raoul; Wiese, Kay Jörg

    2009-02-01

    We study geometrical properties of interfaces in the random-temperature q-states Potts model as an example of a conformal field theory weakly perturbed by quenched disorder. Using conformal perturbation theory in q-2 we compute the fractal dimension of Fortuin-Kasteleyn (FK) domain walls. We also compute it numerically both via the Wolff cluster algorithm for q=3 and via transfer-matrix evaluations. We also obtain numerical results for the fractal dimension of spin clusters interfaces for q=3. These are found numerically consistent with the duality κspinκFK=16 as expressed in putative SLE parameters.

  15. A motivic approach to phase transitions in Potts models

    Science.gov (United States)

    Aluffi, Paolo; Marcolli, Matilde

    2013-01-01

    We describe an approach to the study of phase transitions in Potts models based on an estimate of the complexity of the locus of real zeros of the partition function, computed in terms of the classes in the Grothendieck ring of the affine algebraic varieties defined by the vanishing of the multivariate Tutte polynomial. We give completely explicit calculations for the examples of the chains of linked polygons and of the graphs obtained by replacing the polygons with their dual graphs. These are based on a deletion-contraction formula for the Grothendieck classes and on generating functions for splitting and doubling edges.

  16. Study of contact angle hysteresis using the Cellular Potts Model.

    Science.gov (United States)

    Mortazavi, Vahid; D'Souza, Roshan M; Nosonovsky, Michael

    2013-02-28

    We use the Cellular Potts Model (CPM) to study the contact angle (CA) hysteresis in multiphase (solid-liquid-vapour) systems. We simulate a droplet over the tilted patterned surface, and a bubble placed under the surface immersed in liquid. The difference between bubbles and droplets was discussed through their CA hysteresis. Dependency of CA hysteresis on the surface structure and other parameters was also investigated. This analysis allows decoupling of the 1D (pinning of the triple line) and 2D (adhesion hysteresis in the contact area) effects and provides new insight into the nature of CA hysteresis.

  17. Gauge Potts model with generalized action: A Monte Carlo analysis

    Energy Technology Data Exchange (ETDEWEB)

    Fanchiotti, H.; Canal, C.A.G.; Sciutto, S.J.

    1985-08-15

    Results of a Monte Carlo calculation on the q-state gauge Potts model in d dimensions with a generalized action involving planar 1 x 1, plaquette, and 2 x 1, fenetre, loop interactions are reported. For d = 3 and q = 2, first- and second-order phase transitions are detected. The phase diagram for q = 3 presents only first-order phase transitions. For d = 2, a comparison with analytical results is made. Here also, the behavior of the numerical simulation in the vicinity of a second-order transition is analyzed.

  18. Infinitely many states and stochastic symmetry in a Gaussian Potts-Hopfield model

    NARCIS (Netherlands)

    van Enter, ACD; Schaap, HG

    2002-01-01

    We study a Gaussian Potts-Hopfield model. Whereas for Ising spins and two disorder variables per site the chaotic pair scenario is realized, we find that for q-state Potts spins q (q - 1)-tuples occur. Beyond the breaking of a continuous stochastic symmetry, we study the fluctuations and obtain the

  19. Equation of State of the Two-Dimensional Hubbard Model

    Science.gov (United States)

    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.

  20. Parallelizing the Cellular Potts Model on graphics processing units

    Science.gov (United States)

    Tapia, José Juan; D'Souza, Roshan M.

    2011-04-01

    The Cellular Potts Model (CPM) is a lattice based modeling technique used for simulating cellular structures in computational biology. The computational complexity of the model means that current serial implementations restrict the size of simulation to a level well below biological relevance. Parallelization on computing clusters enables scaling the size of the simulation but marginally addresses computational speed due to the limited memory bandwidth between nodes. In this paper we present new data-parallel algorithms and data structures for simulating the Cellular Potts Model on graphics processing units. Our implementations handle most terms in the Hamiltonian, including cell-cell adhesion constraint, cell volume constraint, cell surface area constraint, and cell haptotaxis. We use fine level checkerboards with lock mechanisms using atomic operations to enable consistent updates while maintaining a high level of parallelism. A new data-parallel memory allocation algorithm has been developed to handle cell division. Tests show that our implementation enables simulations of >10 cells with lattice sizes of up to 256 3 on a single graphics card. Benchmarks show that our implementation runs ˜80× faster than serial implementations, and ˜5× faster than previous parallel implementations on computing clusters consisting of 25 nodes. The wide availability and economy of graphics cards mean that our techniques will enable simulation of realistically sized models at a fraction of the time and cost of previous implementations and are expected to greatly broaden the scope of CPM applications.

  1. Anisotropic exchange-interaction model: From the Potts model to the exchange-interaction model

    Science.gov (United States)

    King, T. C.; Chen, H. H.

    1995-04-01

    A spin model called the anisotropic exchange-interaction model is proposed. The Potts model, the exchange-interaction model, and the spin-1/2 anisotropic Heisenberg model are special cases of the proposed model. Thermodynamic properties of the model on the bcc and the fcc lattices are determined by the constant-coupling approximation.

  2. A hybrid parallel framework for the cellular Potts model simulations

    Energy Technology Data Exchange (ETDEWEB)

    Jiang, Yi [Los Alamos National Laboratory; He, Kejing [SOUTH CHINA UNIV; Dong, Shoubin [SOUTH CHINA UNIV

    2009-01-01

    The Cellular Potts Model (CPM) has been widely used for biological simulations. However, most current implementations are either sequential or approximated, which can't be used for large scale complex 3D simulation. In this paper we present a hybrid parallel framework for CPM simulations. The time-consuming POE solving, cell division, and cell reaction operation are distributed to clusters using the Message Passing Interface (MPI). The Monte Carlo lattice update is parallelized on shared-memory SMP system using OpenMP. Because the Monte Carlo lattice update is much faster than the POE solving and SMP systems are more and more common, this hybrid approach achieves good performance and high accuracy at the same time. Based on the parallel Cellular Potts Model, we studied the avascular tumor growth using a multiscale model. The application and performance analysis show that the hybrid parallel framework is quite efficient. The hybrid parallel CPM can be used for the large scale simulation ({approx}10{sup 8} sites) of complex collective behavior of numerous cells ({approx}10{sup 6}).

  3. A two-dimensional mathematical model of percutaneous drug absorption

    Directory of Open Access Journals (Sweden)

    Kubota K

    2004-06-01

    Full Text Available Abstract Background When a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, r. The values of r depend on the amount of diffusion and the normalized skin-capillary clearence. It is defined as the ratio of the steady-state drug concentration at the skin-capillary boundary to that at the skin-surface in one-dimensional models. The present paper studies the effect of the parameter values, when the region of contact of the skin with the drug, is a line segment on the skin surface. Methods Though a simple one-dimensional model is often useful to describe percutaneous drug absorption, it may be better represented by multi-dimensional models. A two-dimensional mathematical model is developed for percutaneous absorption of a drug, which may be used when the diffusion of the drug in the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. This model consists of a linear second-order parabolic equation with appropriate initial conditions and boundary conditions. These boundary conditions are of Dirichlet type, Neumann type or Robin type. A finite-difference method which maintains second-order accuracy in space along the boundary, is developed to solve the parabolic equation. Extrapolation in time is applied to improve the accuracy in time. Solution of the parabolic equation gives the concentration of the drug in the skin at a given time. Results Simulation of the numerical methods described is carried out with various values of the parameter r. The illustrations are given in the form of figures. Conclusion Based on the values of r, conclusions are drawn about (1 the flow rate of the drug, (2 the flux and the cumulative amount of drug eliminated into the receptor cell, (3 the steady-state value of the flux, (4 the time to reach the steady

  4. Coherent two-dimensional spectroscopy of a Fano model

    CERN Document Server

    Poulsen, Felipe; Pullerits, Tõnu; Hansen, Thorsten

    2016-01-01

    The Fano lineshape arises from the interference of two excitation pathways to reach a continuum. Its generality has resulted in a tremendous success in explaining the lineshapes of many one-dimensional spectroscopies - absorption, emission, scattering, conductance, photofragmentation - applied to very varied systems - atoms, molecules, semiconductors and metals. Unravelling a spectroscopy into a second dimension reveals the relationship between states in addition to decongesting the spectra. Femtosecond-resolved two-dimensional electronic spectroscopy (2DES) is a four-wave mixing technique that measures the time-evolution of the populations, and coherences of excited states. It has been applied extensively to the dynamics of photosynthetic units, and more recently to materials with extended band-structures. In this letter, we solve the full time-dependent third-order response, measured in 2DES, of a Fano model and give the new system parameters that become accessible.

  5. Current fluctuations in a two dimensional model of heat conduction

    Science.gov (United States)

    Pérez-Espigares, Carlos; Garrido, Pedro L.; Hurtado, Pablo I.

    2011-03-01

    In this work we study numerically and analytically current fluctuations in the two-dimensional Kipnis-Marchioro-Presutti (KMP) model of heat conduction. For that purpose, we use a recently introduced algorithm which allows the direct evaluation of large deviations functions. We compare our results with predictions based on the Hydrodynamic Fluctuation Theory (HFT) of Bertini and coworkers, finding very good agreement in a wide interval of current fluctuations. We also verify the existence of a well-defined temperature profile associated to a given current fluctuation which depends exclusively on the magnitude of the current vector, not on its orientation. This confirms the recently introduced Isometric Fluctuation Relation (IFR), which results from the time-reversibility of the dynamics, and includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by timereversibility on the statistics of nonequilibrium fluctuations.

  6. Parallel family trees for transfer matrices in the Potts model

    CERN Document Server

    Navarro, Cristobal A; Kahler, Nancy Hitschfeld; Navarro, Gonzalo

    2013-01-01

    The computational cost of transfer matrix methods for the Potts model is directly related to the problem of \\textit{into how many ways can two adjacent blocks of a lattice be connected}. Answering this question leads to the generation of a combinatorial set of lattice configurations. This set defines the \\textit{configuration space} of the problem, and the smaller it is, the faster the transfer matrix method can be. The configuration space of generic transfer matrix methods for strip lattices in the Potts model is in the order of the Catalan numbers, leading to an asymptotic cost of $O(4^m)$ with $m$ being the width of the strip. Transfer matrix methods with a smaller configuration space indeed exist but they make assumptions on the temperature, number of spin states, or restrict the topology of the lattice in order to work. In this paper we propose a general and parallel transfer matrix method, based on family trees, that uses a sub-Catalan configuration space of size $O(3^m)$. The improvement is achieved by...

  7. Mathematical modeling of the neuron morphology using two dimensional images.

    Science.gov (United States)

    Rajković, Katarina; Marić, Dušica L; Milošević, Nebojša T; Jeremic, Sanja; Arsenijević, Valentina Arsić; Rajković, Nemanja

    2016-02-01

    In this study mathematical analyses such as the analysis of area and length, fractal analysis and modified Sholl analysis were applied on two dimensional (2D) images of neurons from adult human dentate nucleus (DN). Using mathematical analyses main morphological properties were obtained including the size of neuron and soma, the length of all dendrites, the density of dendritic arborization, the position of the maximum density and the irregularity of dendrites. Response surface methodology (RSM) was used for modeling the size of neurons and the length of all dendrites. However, the RSM model based on the second-order polynomial equation was only possible to apply to correlate changes in the size of the neuron with other properties of its morphology. Modeling data provided evidence that the size of DN neurons statistically depended on the size of the soma, the density of dendritic arborization and the irregularity of dendrites. The low value of mean relative percent deviation (MRPD) between the experimental data and the predicted neuron size obtained by RSM model showed that model was suitable for modeling the size of DN neurons. Therefore, RSM can be generally used for modeling neuron size from 2D images.

  8. Two-dimensional model for circulating fluidized-bed reactors

    Energy Technology Data Exchange (ETDEWEB)

    Schoenfelder, H.; Kruse, M.; Werther, J. [Technical Univ. Hamburg-Harburg, Hamburg (Germany). Dept. of Chemical Engineering

    1996-07-01

    Circulating fluidized bed reactors are widely used for the combustion of coal in power stations as well as for the cracking of heavy oil in the petroleum industry. A two-dimensional reactor model for circulating fluidized beds (CFB) was studied based on the assumption that at every location within the riser, a descending dense phase and a rising lean phase coexist. Fluid mechanical variables may be calculated from one measured radial solids flux profile (upward and downward). The internal mass-transfer behavior is described on the basis of tracer gas experiments. The CFB reactor model was tested against data from ozone decomposition experiments in a CFB cold flow model (15.6-m height, 0.4-m ID) operated in the ranges 2.5--4.5 m/s and 9--45 kg/(m{sup 2}{center_dot}s) of superficial gas velocity and solids mass flux, respectively. Based on effective reaction rate constants determined from the ozone exit concentration, the model was used to predict the spatial reactant distribution within the reactor. Model predictions agreed well with measurements.

  9. A two-dimensional hydrodynamic model of a tidal estuary

    Science.gov (United States)

    Walters, Roy A.; Cheng, Ralph T.

    1979-01-01

    A finite element model is described which is used in the computation of tidal currents in an estuary. This numerical model is patterned after an existing algorithm and has been carefully tested in rectangular and curve-sided channels with constant and variable depth. One of the common uncertainties in this class of two-dimensional hydrodynamic models is the treatment of the lateral boundary conditions. Special attention is paid specifically to addressing this problem. To maintain continuity within the domain of interest, ‘smooth’ curve-sided elements must be used at all shoreline boundaries. The present model uses triangular, isoparametric elements with quadratic basis functions for the two velocity components and a linear basis function for water surface elevation. An implicit time integration is used and the model is unconditionally stable. The resultant governing equations are nonlinear owing to the advective and the bottom friction terms and are solved iteratively at each time step by the Newton-Raphson method. Model test runs have been made in the southern portion of San Francisco Bay, California (South Bay) as well as in the Bay west of Carquinez Strait. Owing to the complex bathymetry, the hydrodynamic characteristics of the Bay system are dictated by the generally shallow basins which contain deep, relict river channels. Great care must be exercised to ensure that the conservation equations remain locally as well as globally accurate. Simulations have been made over several representative tidal cycles using this finite element model, and the results compare favourably with existing data. In particular, the standing wave in South Bay and the progressive wave in the northern reach are well represented.

  10. An efficient Cellular Potts Model algorithm that forbids cell fragmentation

    Science.gov (United States)

    Durand, Marc; Guesnet, Etienne

    2016-11-01

    The Cellular Potts Model (CPM) is a lattice based modeling technique which is widely used for simulating cellular patterns such as foams or biological tissues. Despite its realism and generality, the standard Monte Carlo algorithm used in the scientific literature to evolve this model preserves connectivity of cells on a limited range of simulation temperature only. We present a new algorithm in which cell fragmentation is forbidden for all simulation temperatures. This allows to significantly enhance realism of the simulated patterns. It also increases the computational efficiency compared with the standard CPM algorithm even at same simulation temperature, thanks to the time spared in not doing unrealistic moves. Moreover, our algorithm restores the detailed balance equation, ensuring that the long-term stage is independent of the chosen acceptance rate and chosen path in the temperature space.

  11. DISCRETE MODELLING OF TWO-DIMENSIONAL LIQUID FOAMS

    Institute of Scientific and Technical Information of China (English)

    Qicheng Sun

    2003-01-01

    Liquid foam is a dense random packing of gas or liquid bubbles in a small amount of immiscible liquid containing surfactants. The liquid within the Plateau borders, although small in volume, causes considerable difficulties to the investigation of the spatial structure and physical properties of foams, and the situation becomes even more complicated as the fluid flows. To solve these problems, a discrete model of two-dimensional liquid foams on the bubble scale is proposed in this work. The bubble surface is represented with finite number of nodes, and the liquid within Plateau borders is discretized into lattice particles. The gas in bubbles is treated as ideal gas at constant temperatures. This model is tested by choosing an arbitrary shape bubble as the initial condition. This then automatically evolves into a circular shape, which indicates that the surface energy minimum routine is obeyed without calling external controlling conditions. Without inserting liquid particle among the bubble channels, periodic ordered and disordered dry foams are both simulated, and the fine foam structures are developed. Wet foams are also simulated by inserting fluid among bubble channels. The calculated coordination number, as a function of liquid fractions, agrees well with the standard values.

  12. Development of two-dimensional hot pool model

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Yong Bum; Hahn, H. D

    2000-05-01

    During a normal reactor scram, the heat generation is reduced almost instantaneously while the coolant flow rate follows the pump coast-down. This mismatch between power and flow results in a situation where the core flow entering the hot pool is at a lower temperature than the temperature of the bulk pool sodium. This temperature difference leads to thermal stratification. Thermal stratification can occur in the hot pool region if the entering coolant is colder than the existing hot pool coolant and the flow momentum is not large enough to overcome the negative buoyancy force. Since the fluid of hot pool enters IHX{sub s}, the temperature distribution of hot pool can alter the overall system response. Hence, it is necessary to predict the pool coolant temperature distribution with sufficient accuracy to determine the inlet temperature conditions for the IHX{sub s} and its contribution to the net buoyancy head. Therefore, in this study two-dimensional hot pool model is developed instead of existing one-dimensional model to predict the hot pool coolant temperature and velocity distribution more accurately and is applied to the SSC-K code.

  13. Glauber Dynamics for the Mean-Field Potts Model

    Science.gov (United States)

    Cuff, P.; Ding, J.; Louidor, O.; Lubetzky, E.; Peres, Y.; Sly, A.

    2012-11-01

    We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with q≥3 states and show that it undergoes a critical slowdown at an inverse-temperature β s ( q) strictly lower than the critical β c ( q) for uniqueness of the thermodynamic limit. The dynamical critical β s ( q) is the spinodal point marking the onset of metastability. We prove that when β β s ( q) the mixing time is exponentially large in n. Furthermore, as β↑ β s with n, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of O( n -2/3) around β s . These results form the first complete analysis of mixing around the critical dynamical temperature—including the critical power law—for a model with a first order phase transition.

  14. Exact Potts model partition functions on ladder graphs

    Science.gov (United States)

    Shrock, Robert

    2000-08-01

    We present exact calculations of the partition function Z of the q-state Potts model and its generalization to real q, for arbitrary temperature on n-vertex ladder graphs, i.e., strips of the square lattice with width Ly=2 and arbitrary length Lx, with free, cyclic, and Möbius longitudinal boundary conditions. These partition functions are equivalent to Tutte/Whitney polynomials for these graphs. The free energy is calculated exactly for the infinite-length limit of these ladder graphs and the thermodynamics is discussed. By comparison with strip graphs of other widths, we analyze how the singularities at the zero-temperature critical point of the ferromagnet on infinite-length, finite-width strips depend on the width. We point out and study the following noncommutativity at certain special values q s: lim n→∞ limq→q s Z 1/n≠ limq→q s limn→∞ Z 1/n. It is shown that the Potts antiferromagnet on both the infinite-length line and ladder graphs with cyclic or Möbius boundary conditions exhibits a phase transition at finite temperature if 0< q<2, but with unphysical properties, including negative specific heat and non-existence, in the low-temperature phase, of an n→∞ limit for thermodynamic functions that is independent of boundary conditions. Considering the full generalization to arbitrary complex q and temperature, we determine the singular locus B in the corresponding C2 space, arising as the accumulation set of partition function zeros as n→∞. In particular, we study the connection with the T=0 limit of the Potts antiferromagnet where B reduces to the accumulation set of chromatic zeros. Certain properties of the complex-temperature phase diagrams are shown to exhibit close connections with those of the model on the square lattice, showing that exact solutions on infinite-length strips provide a way of gaining insight into these complex-temperature phase diagrams.

  15. Modelling wound closure in an epithelial cell sheet using the cellular Potts model.

    Science.gov (United States)

    Noppe, Adrian R; Roberts, Anthony P; Yap, Alpha S; Gomez, Guillermo A; Neufeld, Zoltan

    2015-10-01

    We use a two-dimensional cellular Potts model to represent the behavior of an epithelial cell layer and describe its dynamics in response to a microscopic wound. Using an energy function to describe properties of the cells, we found that the interaction between contractile tension along cell-cell junctions and cell-cell adhesion plays an important role not only in determining the dynamics and morphology of cells in the monolayer, but also in influencing whether or not a wound in the monolayer will close. Our results suggest that, depending on the balance between cell-cell adhesion and junctional tension, mechanics of the monolayer can either correspond to a hard or a soft regime that determines cell morphology and polygonal organization in the monolayer. Moreover, the presence of a wound in a hard regime, where junctional tension is significant, can lead to two results: (1) wound closure or (2) an initial increase and expansion of the wound area towards an equilibrium value. Theoretical approximations and simulations allowed us to determine the thresholds in the values of cell-cell adhesion and initial wound size that allow the system to lead to wound closure. Overall, our results suggest that around the site of injury, changes in the balance between contraction and adhesion determine whether or not non-monotonous wound closure occurs.

  16. The aggregate path coupling method for the Potts model on bipartite graph

    Science.gov (United States)

    Hernández, José C.; Kovchegov, Yevgeniy; Otto, Peter T.

    2017-02-01

    In this paper, we derive the large deviation principle for the Potts model on the complete bipartite graph Kn,n as n increases to infinity. Next, for the Potts model on Kn,n, we provide an extension of the method of aggregate path coupling that was originally developed in the work of Kovchegov, Otto, and Titus [J. Stat. Phys. 144(5), 1009-1027 (2011)] for the mean-field Blume-Capel model and in Kovchegov and Otto [J. Stat. Phys. 161(3), 553-576 (2015)] for a general mean-field setting that included the generalized Curie-Weiss-Potts model analyzed in the work of Jahnel et al. [Markov Process. Relat. Fields 20, 601-632 (2014)]. We use the aggregate path coupling method to identify and determine the threshold value βs separating the rapid and slow mixing regimes for the Glauber dynamics of the Potts model on Kn,n.

  17. Interplay between sign problem and Z_3 symmetry in three-dimensional Potts model

    CERN Document Server

    Hirakida, Takehiro; Takahashi, Junichi; Yahiro, Masanobu

    2016-01-01

    We construct four kinds of Z3-symmetric three-dimentional (3-d) Potts models, each with different number of states at each site on a 3-d lattice, by extending the 3-d three-state Potts model. Comparing the ordinary Potts model with the four Z3-symmetric Potts models, we investigate how Z3 symmetry affects the sign problem and see how the deconfinement transition line changes in the $\\mu-\\kappa$ plane as the number of states increases, where $\\mu$ $(\\kappa)$ plays a role of chemical potential (temperature) in the models. We find that the sign problem is almost cured by imposing Z3 symmetry. This mechanism may happen in Z3-symmetric QCD-like theory. We also show that the deconfinement transition line has stronger $\\mu$-dependence with respect to increasing the number of states.

  18. Interplay between sign problem and Z3 symmetry in three-dimensional Potts models

    Science.gov (United States)

    Hirakida, Takehiro; Kouno, Hiroaki; Takahashi, Junichi; Yahiro, Masanobu

    2016-07-01

    We construct four kinds of Z3 -symmetric three-dimensional (3D) Potts models, each with a different number of states at each site on a 3D lattice, by extending the 3D 3-state Potts model. Comparing the ordinary Potts model with the four Z3-symmetric Potts models, we investigate how Z3 symmetry affects the sign problem and see how the deconfinement transition line changes in the μ -κ plane as the number of states increases, where μ (κ ) plays a role of chemical potential (temperature) in the models. We find that the sign problem is almost cured by imposing Z3 symmetry. This mechanism may happen in Z3-symmetric QCD-like theory. We also show that the deconfinement transition line has stronger μ dependence with respect to increasing the number of states.

  19. Twelve-state Potts model in a magnetic field

    Science.gov (United States)

    Kassan-Ogly, F. A.; Filippov, B. N.; Proshkin, A. I.; Zarubin, A. V.

    2015-02-01

    In this work, we have obtained an exact solution to the one-dimensional modified 12-state Potts model using the Kramers-Wannier transfer matrix with allowance for the exchange interaction between nearest neighbors in an external magnetic field. Analytical expressions have been derived for the heat capacity, magnetization, magnetic susceptibility, magnetic entropy, and magnetocaloric effect as functions of temperature, magnitude and sign of exchange interaction, and the magnitude and direction of the magnetic field. The behavior of all of these parameters has been investigated in detail using numerical methods. The possibility of applying the results obtained to explain the observed magnetic properties of real cubic magnets with a NaCl structure and easy axes oriented along the [110] crystallographic directions has been discussed.

  20. Glauber Dynamics for the mean-field Potts Model

    CERN Document Server

    Cuff, Paul; Louidor, Oren; Lubetzky, Eyal; Peres, Yuval; Sly, Allan

    2012-01-01

    We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with $q\\geq 3$ states and show that it undergoes a critical slowdown at an inverse-temperature $\\beta_s(q)$ strictly lower than the critical $\\beta_c(q)$ for uniqueness of the thermodynamic limit. The dynamical critical $\\beta_s(q)$ is the spinodal point marking the onset of metastability. We prove that when $\\beta\\beta_s(q)$ the mixing time is exponentially large in $n$. Furthermore, as $\\beta \\uparrow \\beta_s$ with $n$, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of $O(n^{-2/3})$ around $\\beta_s$. These results form the first complete analysis of the critical slowdown of a dynamics with a first order phase transition.

  1. Generalized Potts-Models and their Relevance for Gauge Theories

    Directory of Open Access Journals (Sweden)

    Andreas Wipf

    2007-01-01

    Full Text Available We study the Polyakov loop dynamics originating from finite-temperature Yang-Mills theory. The effective actions contain center-symmetric terms involving powers of the Polyakov loop, each with its own coupling. For a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both approaches. The phase diagram exhibits both first and second order transitions between symmetric, ferromagnetic and antiferromagnetic phases with phase boundaries merging at three tricritical points. The critical exponents ν and γ at the continuous transition between symmetric and antiferromagnetic phases are the same as for the 3-state spin Potts model.

  2. Geometrical properties of the Potts model during the coarsening regime.

    Science.gov (United States)

    Loureiro, Marcos P O; Arenzon, Jeferson J; Cugliandolo, Leticia F

    2012-02-01

    We study the dynamic evolution of geometric structures in a polydegenerate system represented by a q-state Potts model with nonconserved order parameter that is quenched from its disordered into its ordered phase. The numerical results obtained with Monte Carlo simulations show a strong relation between the statistical properties of hull perimeters in the initial state and during coarsening: The statistics and morphology of the structures that are larger than the averaged ones are those of the initial state, while the ones of small structures are determined by the curvature-driven dynamic process. We link the hull properties to the ones of the areas they enclose. We analyze the linear von Neumann-Mullins law, both for individual domains and on the average, concluding that its validity, for the later case, is limited to domains with number of sides around 6, while presenting stronger violations in the former case. © 2012 American Physical Society

  3. Structural propensities of kinase family proteins from a Potts model of residue co‐variation

    National Research Council Canada - National Science Library

    Haldane, Allan; Flynn, William F; He, Peng; Vijayan, R.S.K; Levy, Ronald M

    2016-01-01

    ...‐variation of pairs of mutations contained in multiple sequence alignments of protein families can be used to build a Potts Hamiltonian model of the sequence patterns which accurately predicts structural contacts...

  4. Blume-Emery-Griffiths model on three-dimensional lattices: Consequences for the antiferromagnetic Potts model

    Science.gov (United States)

    Lapinskas, Saulius; Rosengren, Anders

    1994-06-01

    Using the cluster-variation method we study the phase diagram of the Blume-Emergy-Griffiths (BEG) model on simple cubic and face-centered cubic lattices. For the simple cubic lattice the main attention is paid to reentrant phenomena and ferrimagnetic phases occurring in a certain range of coupling constants. The results are in close agreement with Monte-Carlo data, available for parts of the phase diagram. Several ferrimagnetic phases are obtained in the vicinity of the line in parameter space, at which the model reduces to the antiferromagnetic three-state Potts model. Our results imply the existence of three phase transitions in the antiferromagnetic Potts model on the simple-cubic lattice. The phase diagrams for the BEG model on the face-centered cubic lattice are obtained in the region of antiquadrupolar ordering. Also the several ordered phases of the antiferromagnetic Potts model on this lattice are discussed.

  5. Two-Dimensional Electronic Spectroscopy of a Model Dimer System

    Directory of Open Access Journals (Sweden)

    Prokhorenko V.I.

    2013-03-01

    Full Text Available Two-dimensional spectra of a dimer were measured to determine the timescale for electronic decoherence at room temperature. Anti-correlated beats in the crosspeaks were observed only during the period corresponding to the measured homogeneous lifetime.

  6. The two-dimensional 4-state Potts model in a magnetic field

    CERN Document Server

    Berche, Bertrand; Shchur, Lev

    2013-01-01

    We present a solution of the non-linear renormalization group equations leading to the dominant and subdominant singular behaviours of physical quantities (free energy density, correlation length, internal energy, specific heat, magnetization, susceptibility and magnetocaloric coefficient) at the critical temperature in a non- vanishing magnetic field. The solutions i) lead to exact cancellation of logarithmic corrections in universal amplitude ratios and ii) prove recently proposed relations among logarithmic exponents.

  7. High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials

    Science.gov (United States)

    >Jesper Lykke Jacobsen,

    2014-04-01

    The critical curves of the q-state Potts model can be determined exactly for regular two-dimensional lattices G that are of the three-terminal type. This comprises the square, triangular, hexagonal and bow-tie lattices. Jacobsen and Scullard have defined a graph polynomial PB(q, v) that gives access to the critical manifold for general lattices. It depends on a finite repeating part of the lattice, called the basis B, and its real roots in the temperature variable v = eK - 1 provide increasingly accurate approximations to the critical manifolds upon increasing the size of B. Using transfer matrix techniques, these authors computed PB(q, v) for large bases (up to 243 edges), obtaining determinations of the ferromagnetic critical point vc > 0 for the (4, 82), kagome, and (3, 122) lattices to a precision (of the order 10-8) slightly superior to that of the best available Monte Carlo simulations. In this paper we describe a more efficient transfer matrix approach to the computation of PB(q, v) that relies on a formulation within the periodic Temperley-Lieb algebra. This makes possible computations for substantially larger bases (up to 882 edges), and the precision on vc is hence taken to the range 10-13. We further show that a large variety of regular lattices can be cast in a form suitable for this approach. This includes all Archimedean lattices, their duals and their medials. For all these lattices we tabulate high-precision estimates of the bond percolation thresholds pc and Potts critical points vc. We also trace and discuss the full Potts critical manifold in the (q, v) plane, paying special attention to the antiferromagnetic region v < 0. Finally, we adapt the technique to site percolation as well, and compute the polynomials PB(p) for certain Archimedean and dual lattices (those having only cubic and quartic vertices), using very large bases (up to 243 vertices). This produces the site percolation thresholds pc to a precision of the order of 10-9.

  8. One-dimensional q-state Potts model with multi-site interactions

    Science.gov (United States)

    Turban, Loïc

    2017-05-01

    A one-dimensional (1D) q-state Potts model with N sites, m-site interaction K in a field H is studied for arbitrary values of m. Exact results for the partition function and the two-point correlation function are obtained at H  =  0. The system in a field is shown to be self-dual. Using a change of Potts variables, it is mapped onto a standard 2D Potts model, with first-neighbour interactions K and H, on a cylinder with helical boundary conditions (BC). The 2D system has a length N/m and a transverse size m. Thus the Potts chain with multi-site interactions is expected to develop a 2D critical singularity along the self-duality line, (eqK-1)(eqH-1)=q , when N/m\\to∞ and m\\to∞ .

  9. Multiscale Model of Colorectal Cancer Using the Cellular Potts Framework.

    Science.gov (United States)

    Osborne, James M

    2015-01-01

    Colorectal cancer (CRC) is one of the major causes of death in the developed world and forms a canonical example of tumorigenesis. CRC arises from a string of mutations of individual cells in the colorectal crypt, making it particularly suited for multiscale multicellular modeling, where mutations of individual cells can be clearly represented and their effects readily tracked. In this paper, we present a multicellular model of the onset of colorectal cancer, utilizing the cellular Potts model (CPM). We use the model to investigate how, through the modification of their mechanical properties, mutant cells colonize the crypt. Moreover, we study the influence of mutations on the shape of cells in the crypt, suggesting possible cell- and tissue-level indicators for identifying early-stage cancerous crypts. Crucially, we discuss the effect that the motility parameters of the model (key factors in the behavior of the CPM) have on the distribution of cells within a homeostatic crypt, resulting in an optimal parameter regime that accurately reflects biological assumptions. In summary, the key results of this paper are 1) how to couple the CPM with processes occurring on other spatial scales, using the example of the crypt to motivate suitable motility parameters; 2) modeling mutant cells with the CPM; 3) and investigating how mutations influence the shape of cells in the crypt.

  10. Nature of phase transitions in Axelrod-like coupled Potts models in two dimensions.

    Science.gov (United States)

    Gandica, Yerali; Chiacchiera, Silvia

    2016-03-01

    We study F coupled q-state Potts models in a two-dimensional square lattice. The interaction between the different layers is attractive to favor a simultaneous alignment in all of them, and its strength is fixed. The nature of the phase transition for zero field is numerically determined for F = 2,3. Using the Lee-Kosterlitz method, we find that it is continuous for F = 2 and q = 2, whereas it is abrupt for higher values of q and/or F. When a continuous or a weakly first-order phase transition takes place, we also analyze the properties of the geometrical clusters. This allows us to determine the fractal dimension D of the incipient infinite cluster and to examine the finite-size scaling of the cluster number density via data collapse. A mean-field approximation of the model, from which some general trends can be determined, is presented too. Finally, since this lattice model has been recently considered as a thermodynamic counterpart of the Axelrod model of social dynamics, we discuss our results in connection with this one.

  11. A Cellular Potts Model simulating cell migration on and in matrix environments.

    Science.gov (United States)

    Scianna, Marco; Preziosi, Luigi; Wolf, Katarina

    2013-02-01

    Cell migration on and through extracellular matrix is fundamental in a wide variety of physiological and pathological phenomena, and is exploited in scaffold-based tissue engineering. Migration is regulated by a number of extracellular matrix- or cell-derived biophysical parameters, such as matrix fiber orientation, pore size, and elasticity, or cell deformation, proteolysis, and adhesion. We here present an extended Cellular Potts Model (CPM) able to qualitatively and quantitatively describe cell migration efficiencies and phenotypes both on two-dimensional substrates and within three-dimensional matrices, close to experimental evidence. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated into nucleus and cytosolic region, while the extracellular matrix is composed of a fibrous mesh and a homogeneous fluid. Our model provides a strong correlation of the directionality of migration with the topological extracellular matrix distribution and a biphasic dependence of migration on the matrix structure, density, adhesion, and stiffness, and, moreover, simulates that cell locomotion in highly constrained fibrillar obstacles requires the deformation of the cell's nucleus and/or the activity of cell-derived proteolysis. In conclusion, we here propose a mathematical modeling approach that serves to characterize cell migration as a biological phenomenon in healthy and diseased tissues and in engineering applications.

  12. A node-based version of the cellular Potts model.

    Science.gov (United States)

    Scianna, Marco; Preziosi, Luigi

    2016-09-01

    The cellular Potts model (CPM) is a lattice-based Monte Carlo method that uses an energetic formalism to describe the phenomenological mechanisms underlying the biophysical problem of interest. We here propose a CPM-derived framework that relies on a node-based representation of cell-scale elements. This feature has relevant consequences on the overall simulation environment. First, our model can be implemented on any given domain, provided a proper discretization (which can be regular or irregular, fixed or time evolving). Then, it allowed an explicit representation of cell membranes, whose displacements realistically result in cell movement. Finally, our node-based approach can be easily interfaced with continuous mechanics or fluid dynamics models. The proposed computational environment is here applied to some simple biological phenomena, such as cell sorting and chemotactic migration, also in order to achieve an analysis of the performance of the underlying algorithm. This work is finally equipped with a critical comparison between the advantages and disadvantages of our model with respect to the traditional CPM and to some similar vertex-based approaches. Copyright © 2016 Elsevier Ltd. All rights reserved.

  13. An extended Cellular Potts Model analyzing a wound healing assay.

    Science.gov (United States)

    Scianna, Marco

    2015-07-01

    A suitable Cellular Potts Model is developed to reproduce and analyze an in vitro wound-healing assay. The proposed approach is able both to quantify the invasive capacity of the overall cell population and to evaluate selected determinants of single cell movement (velocity, directional movement, and final displacement). In this respect, the present CPM allows us to capture differences and correlations in the migratory behavior of cells initially located at different distances from the wound edge. In the case of an undifferentiated extracellular matrix, the model then predicts that a maximal healing can be obtained by a chemically induced increment of cell elasticity and not by a chemically induced downregulation of intercellular adhesive contacts. Moreover, in the case of two-component substrates (formed by a mesh of collagenous-like threads and by a homogeneous medium), CPM simulations show that both fiber number and cell-fiber adhesiveness influence cell speed and wound closure rate in a biphasic fashion. On the contrary, the topology of the fibrous network affects the healing process by mediating the productive directional cell movement. The paper, also equipped with comments on the computational cost of the CPM algorithm, ends with a throughout discussion of the pertinent experimental and theoretical literature. Copyright © 2015 Elsevier Ltd. All rights reserved.

  14. Scale-free random graphs and Potts model

    Indian Academy of Sciences (India)

    D-S Lee; K-I Goh; B Kahng; D Kim

    2005-06-01

    We introduce a simple algorithm that constructs scale-free random graphs efficiently: each vertex has a prescribed weight − (0 < < 1) and an edge can connect vertices and with rate . Corresponding equilibrium ensemble is identified and the problem is solved by the → 1 limit of the -state Potts model with inhomogeneous interactions for all pairs of spins. The number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density. Various critical exponents associated with the percolation transition are also obtained together with finite-size scaling forms. The process of forming the giant cluster is qualitatively different between the cases of > 3 and 2 < < 3, where = 1 + -1 is the degree distribution exponent. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finite shows double peaks.

  15. Verification and Validation Strategy for Implementation of Hybrid Potts-Phase Field Hydride Modeling Capability in MBM

    Energy Technology Data Exchange (ETDEWEB)

    Jason D. Hales; Veena Tikare

    2014-04-01

    The Used Fuel Disposition (UFD) program has initiated a project to develop a hydride formation modeling tool using a hybrid Potts­phase field approach. The Potts model is incorporated in the SPPARKS code from Sandia National Laboratories. The phase field model is provided through MARMOT from Idaho National Laboratory.

  16. A naive matrix-model approach to two-dimensional quantum gravity coupled to matter of arbitrary central charge

    CERN Document Server

    Brézin, E

    1992-01-01

    In the usual matrix-model approach to random discretized two-dimensional manifolds, one introduces n Ising spins on each cell, i.e. a discrete version of 2D quantum gravity coupled to matter with a central charge n/2. The matrix-model consists then of an integral over $2^{n}$ matrices, which we are unable to solve for $n>1$. However for a fixed genus we can expand in the cosmological constant g for arbitrary values of n, and a simple minded analysis of the series yields for n=0,1 and 2 the expected results for the exponent $\\gamma_{string}$ with an amazing precision given the small number of terms that we considered. We then proceed to larger values of n. Simple tests of universality are successfully applied; for instance we obtain the same exponents for n=3 or for one Ising model coupled to a one dimensional target space. The calculations are easily extended to states Potts models, through an integration over $q^{n}$ matrices. We see no sign of the tachyonic instability of the theory, but we have only consid...

  17. The two-dimensional Godunov scheme and what it means for macroscopic pedestrian flow models

    NARCIS (Netherlands)

    Van Wageningen-Kessels, F.L.M.; Daamen, W.; Hoogendoorn, S.P.

    2015-01-01

    An efficient simulation method for two-dimensional continuum pedestrian flow models is introduced. It is a two-dimensional and multi-class extension of the Go-dunov scheme for one-dimensional road traffic flow models introduced in the mid 1990’s. The method can be applied to continuum pedestrian flo

  18. Marginal dimensions of the Potts model with invisible states

    Science.gov (United States)

    Krasnytska, M.; Sarkanych, P.; Berche, B.; Holovatch, Yu; Kenna, R.

    2016-06-01

    We reconsider the mean-field Potts model with q interacting and r non-interacting (invisible) states. The model was recently introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where the Z q -symmetry is spontaneously broken. We analyse the marginal dimensions of the model, i.e., the value of r at which the order of the phase transition changes. In the q = 2 case, we determine that value to be {r}{{c}}=3.65(5); there is a second-order phase transition there when r\\lt {r}{{c}} and a first-order one at r\\gt {r}{{c}}. We also analyse the region 1≤slant q\\lt 2 and show that the change from second to first order there is manifest through a new mechanism involving two marginal values of r. The q = 1 limit gives bond percolation. Above the lower value r c1, the order parameters exhibit discontinuities at temperature \\tilde{t} below a critical value t c. The larger value r c2 marks the point at which the phase transition at t c changes from second to first order. Thus, for {r}{{c}1}\\lt r\\lt {r}{{c}2}, the transition at t c remains second order while at \\tilde{t} the system undergoes a first order phase transition. As r increases further, \\tilde{t} increases, bringing the discontinuity closer to t c. Finally, when r exceeds r c2 \\tilde{t} coincides with t c and the phase transition becomes first order. This new mechanism indicates how the discontinuity characteristic of first order phase transitions emerges.

  19. Minimalistic real-space renormalization of Ising and Potts Models in two dimensions

    Directory of Open Access Journals (Sweden)

    Gary eWillis

    2015-06-01

    Full Text Available We introduce and discuss a real-space renormalization group (RSRG procedure on very small lattices, which in principle does not require any of the usual approximations, e.g. a cut-off in the expansion of the Hamiltonian in powers of the field. The procedure is carried out numerically on very small lattices (4x4 to 2x2 and implemented for the Ising Model and the q=3,4,5 Potts Models. Nevertheless, the resulting estimates of the correlation length exponent and the magnetization exponent are typically within 3% to 7% of the exact values. The 4-state Potts Model generates a third magnetic exponent which seems to be unknown in the literature. A number of questions about the meaning of certain exponents and the procedure itself arise from its use of symmetry principles and its application to the q=5 Potts Model.

  20. On phase transitions of the Potts model with three competing interactions on Cayley tree

    Directory of Open Access Journals (Sweden)

    S. Temir

    2011-06-01

    Full Text Available In the present paper we study a phase transition problem for the Potts model with three competing interactions, the nearest neighbors, the second neighbors and triples of neighbors and non-zero external field on Cayley tree of order two. We prove that for some parameter values of the model there is phase transition. We reduce the problem of describing by limiting Gibbs measures to the problem of solving a system of nonlinear functional equations. We extend the results obtained by Ganikhodjaev and Rozikov [Math. Phys. Anal. Geom., 2009, vol. 12, No. 2, 141-156] on phase transition for the Ising model to the Potts model setting.

  1. Potts model based on a Markov process computation solves the community structure problem effectively.

    Science.gov (United States)

    Li, Hui-Jia; Wang, Yong; Wu, Ling-Yun; Zhang, Junhua; Zhang, Xiang-Sun

    2012-07-01

    The Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of the Potts model. Specifically we model the community structure detection Potts procedure by a Markov process, which has a clear mathematical explanation. Then we show that the local uniform behavior of spin values across multiple timescales in the representation of the Markov variables could naturally reveal the network's hierarchical community structure. In addition, critical topological information regarding multivariate spin configuration could also be inferred from the spectral signatures of the Markov process. Finally an algorithm is developed to determine fuzzy communities based on the optimal number of communities and the stability across multiple timescales. The effectiveness and efficiency of our algorithm are theoretically analyzed as well as experimentally validated.

  2. Potts model based on a Markov process computation solves the community structure problem effectively

    CERN Document Server

    Li, Hui-Jia; Wu, Ling-Yun; Zhang, Junhua; Zhang, Xiang-Sun

    2015-01-01

    Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a new framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of Potts model. Specifically we model the community structure detection Potts procedure by a Markov process, which has a clear mathematical explanation. Then we show that the local uniform behavior of spin values across multiple timescales in the representation of the Markov variables could naturally reveal the network's hierarchical community structure. In addition, critical topological information regarding to multivariate spin configuration could also be inferred from the spectral signatures of the Markov process. Finally an algorithm is developed to determine fuzzy communities based on the optimal number of communities and the stability across multiple timescales. The effectiveness and efficiency of our algorithm are theoretically analyzed as well as experimentally validate...

  3. Potts Model on Maple Leaf Lattice with Pure Three-Site Interaction

    Institute of Scientific and Technical Information of China (English)

    WANG Zhou-Fei; CHEN Li

    2005-01-01

    We use Monte Carlo method to study three-state Potts model on maple leaf lattice with pure three-site interaction. The critical behavior of both ferromagnetic and antiferromagnetic cases is studied. Our results confirm that the critical behavior of the ferromagnetic model is independent of the lattice details and lies in the universality class of the three-state ferromagnetic Potts model. For the antiferromagnetic case the transition is of the first order. We have calculated the energy jump and critical temperature in this area. We find there is a tricritical point separating the first order and second order phases for this system.

  4. A Bayesian non-parametric Potts model with application to pre-surgical FMRI data.

    Science.gov (United States)

    Johnson, Timothy D; Liu, Zhuqing; Bartsch, Andreas J; Nichols, Thomas E

    2013-08-01

    The Potts model has enjoyed much success as a prior model for image segmentation. Given the individual classes in the model, the data are typically modeled as Gaussian random variates or as random variates from some other parametric distribution. In this article, we present a non-parametric Potts model and apply it to a functional magnetic resonance imaging study for the pre-surgical assessment of peritumoral brain activation. In our model, we assume that the Z-score image from a patient can be segmented into activated, deactivated, and null classes, or states. Conditional on the class, or state, the Z-scores are assumed to come from some generic distribution which we model non-parametrically using a mixture of Dirichlet process priors within the Bayesian framework. The posterior distribution of the model parameters is estimated with a Markov chain Monte Carlo algorithm, and Bayesian decision theory is used to make the final classifications. Our Potts prior model includes two parameters, the standard spatial regularization parameter and a parameter that can be interpreted as the a priori probability that each voxel belongs to the null, or background state, conditional on the lack of spatial regularization. We assume that both of these parameters are unknown, and jointly estimate them along with other model parameters. We show through simulation studies that our model performs on par, in terms of posterior expected loss, with parametric Potts models when the parametric model is correctly specified and outperforms parametric models when the parametric model in misspecified.

  5. Super-Potts glass: A disordered model for glass-forming liquids

    Science.gov (United States)

    Angelini, Maria Chiara; Biroli, Giulio

    2014-12-01

    We introduce a disordered system, the super-Potts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take M values and are coupled via pairwise interactions. Its exact solution on a completely connected lattice demonstrates that, for large enough M , it belongs to the class of mean-field systems solved by a one-step replica symmetry breaking ansatz. Numerical simulations by the parallel tempering technique show that in three dimensions it displays a phenomenological behavior similar to the one of glass-forming liquids. The super-Potts glass is therefore a disordered model allowing one to perform extensive and detailed studies of the random first-order transition in finite dimensions. We also discuss its behavior for small values of M , which is similar to the one of spin glasses in a field.

  6. Potts model on directed small-world Voronoi-Delaunay lattices

    Science.gov (United States)

    Marques, R. M.; Lima, F. W. S.; Costa Filho, Raimundo N.

    2016-06-01

    The critical properties of the Potts model with q = 3 and 4 states in two-dimensions on directed small-world Voronoi-Delaunay random lattices with quenched connectivity disorder are investigated. This disordered system is simulated by applying the Monte Carlo update heat bath algorithm. The Potts model on these directed small-world random lattices presents in fact a second-order phase transition with new critical exponents for q = 3 and value of the rewiring probability p = 0.01, but for q = 4 the system exhibits only a first-order phase transition independent of p (0 < p < 1).

  7. Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree

    Science.gov (United States)

    Khakimov, R. M.; Khaydarov, F. Kh.

    2016-11-01

    We study translation-invariant Gibbs measures on a Cayley tree of order k = 3 for the ferromagnetic three-state Potts model. We obtain explicit formulas for translation-invariant Gibbs measures. We also consider periodic Gibbs measures on a Cayley tree of order k for the antiferromagnetic q-state Potts model. Moreover, we improve previously obtained results: we find the exact number of periodic Gibbs measures with the period two on a Cayley tree of order k ≥ 3 that are defined on some invariant sets.

  8. Analytical two-dimensional model of solar cell current-voltage characteristics

    Energy Technology Data Exchange (ETDEWEB)

    Caldararu, F.; Caldararu, M.; Nan, S.; Nicolaescu, D.; Vasile, S. (ICCE, Bucharest (RO). R and D Center for Electron Devices)

    1991-06-01

    This paper describes an analytical two-dimensional model for pn junction solar cell I-V characteristic. In order to solve the two-dimensional equations for the minority carrier concentration the Laplace transformation method is used. The model eliminates Hovel's assumptions concerning a one-dimensional model and provides an I-V characteristic that is simpler than those derived from the one-dimensional model. The method can be extended to any other device with two-dimensional symmetry. (author).

  9. Ordering in Two-Dimensional Ising Models with Competing Interactions

    OpenAIRE

    2004-01-01

    We study the 2D Ising model on a square lattice with additional non-equal diagonal next-nearest neighbor interactions. The cases of classical and quantum (transverse) models are considered. Possible phases and their locations in the space of three Ising couplings are analyzed. In particular, incommensurate phases occurring only at non-equal diagonal couplings, are predicted. We also analyze a spin-pseudospin model comprised of the quantum Ising model coupled to XY spin chains in a particular ...

  10. Equation of state from the Potts-percolation model of a solid.

    Science.gov (United States)

    Kaufman, Miron; Diep, H T

    2011-11-01

    We expand the Potts-percolation model of a solid to include stress and strain. Neighboring atoms are connected by bonds. We set the energy of a bond to be given by the Lennard-Jones potential. If the energy is larger than a threshold the bond is more likely to fail, whereas if the energy is lower than the threshold, the bond is more likely to be alive. In two dimensions we compute the equation of state: stress as a function of interatomic distance and temperature by using renormalization-group and Monte Carlo simulations. The phase diagram, the equation of state, and the isothermal modulus are determined. When the Potts heat capacity is divergent the continuous transition is replaced by a weak first-order transition through the van der Waals loop mechanism. When the Potts transition is first order the stress exhibits a large discontinuity as a function of the interatomic distance.

  11. E and S hysteresis model for two-dimensional magnetic properties

    CERN Document Server

    Soda, N

    2000-01-01

    We define an effective hysteresis model of two-dimensional magnetic properties for the magnetic field analysis. Our hysteresis model is applicable to both alternating and rotating flux conditions. Moreover, we compare the calculated results with the measured ones, and verify the accuracy of this model. We can calculate iron losses in the magnetic materials exactly. As a result, it is shown that the hysteresis model is generally applicable to two-dimensional magnetic properties of some kinds of magnetic materials.

  12. Random matrix theory and higher genus integrability: the quantum chiral Potts model

    Energy Technology Data Exchange (ETDEWEB)

    Angles d' Auriac, J.Ch. [Centre de Recherches sur les Tres Basses Temperatures, BP 166, Grenoble (France)]. E-mail: dauriac@polycnrs-gre.fr; Maillard, J.M.; Viallet, C.M. [LPTHE, Tour 16, Paris (France)]. E-mails: maillard@lpthe.jussieu.fr; viallet@lpthe.jussieu.fr

    2002-06-14

    We perform a random matrix theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L 8. Our analysis gives clear evidence of a Gaussian orthogonal ensemble (GOE) statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore, a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of 'higher genus integrability'. (author)

  13. Two-dimensional MHD model of the Jovian magnetodisk

    Science.gov (United States)

    Kislov, R. A.; Malova, H. V.; Vasko, I. Y.

    2015-09-01

    A self-consistent stationary axially symmetric MHD model of the Jovian magnetodisk is constructed. This model is a generalization of the models of plane current sheets that have been proposed earlier in order to describe the structure of the current sheet in the magnetotail of the Earth [1, 2]. The model takes centrifugal force, which is induced by the corotation electric field, and the azimuthal magnetic field into account. The configurations of the magnetic field lines for the isothermic (plasma temperature assumed to be constant) and the isentropic (plasma entropy assumed to be constant) models of the magnetodisk are determined. The dependence of the thickness of the magnetodisk on the distance to Jupiter is obtained. The thickness of the magnetodisk and the magnetic field distribution in the isothermic and isentropic models are similar. The inclusion of a low background plasma pressure results in a considerable reduction in the thickness of the magnetodisk. This effect may be attributed to the fact that centrifugal force prevails over the pressure gradient at large distances from the planet. The mechanism of unipolar induction and the related large-scale current system are analyzed. The direct and return Birkeland currents are determined in the approximation of a weak azimuthal magnetic field. The modeling results agree with theoretical estimates from other studies and experimental data.

  14. two - dimensional mathematical model of water flow in open ...

    African Journals Online (AJOL)

    ES Obe

    1996-09-01

    Sep 1, 1996 ... simplification of the system of the governing shallow water equations ... For optional design of the ... models. One of the facilities for preliminary appraisal of the ... distribution. ..... indicated for the individual methods, located ...

  15. Potts Model with Invisible Colors : Random-Cluster Representation and Pirogov–Sinai Analysis

    NARCIS (Netherlands)

    Enter, Aernout C.D. van; Iacobelli, Giulio; Taati, Siamak

    We study a recently introduced variant of the ferromagnetic Potts model consisting of a ferromagnetic interaction among q “visible” colors along with the presence of r non-interacting “invisible” colors. We introduce a random-cluster representation for the model, for which we prove the existence of

  16. Mean-field theory of random-site q-state Potts models

    NARCIS (Netherlands)

    van Enter, Aernout; Hemmen, Jan Leonard van; Pospiech, C.

    1988-01-01

    A class of random-site mean-field Potts models is introduced and solved exactly. The bifurcation properties of the resulting mean-field equations are analysed in detail. Particular emphasis is put on the relation between the solutions and the underlying symmetries of the model. It turns out that, in

  17. Two-dimensional biomass combustion modeling of CFB

    Energy Technology Data Exchange (ETDEWEB)

    Afsin Gungor [Nigde University, Nigde (Turkey). Department of Mechanical Engineering, Faculty of Engineering and Architecture

    2008-07-15

    In this study, a 2D model for a CFB biomass combustor has been developed which integrates and simultaneously predicts the hydrodynamics, heat transfer and combustion aspects. Combustor hydrodynamic is modeled taking into account previous work. Simulation model calculates the axial and radial distribution of voidage, velocity, particle size distribution, pressure drop, gas emissions and temperature at each time interval for gas and solid phase both for bottom and upper zones. The model results are compared with and validated against experimental data both for small-size and industrial-size biomass combustors which uses different types of biomass fuels given in the literature. As a result of sensitivity analysis, it is observed that: major portion of the combustion will take place in the upper zone, the air staging could improve combustion, for industrial-size CFB biomass combustors and the decrease of NOx adversely results in high CO emissions as air ratio decreases. Unexpected results concerning the emissions is caused by using data of different sized CFBs and is clearly an indicator of the necessity to compare the model results with various sized CFBs as far as possible. 71 refs., 10 figs., 5 tabs.

  18. Two-dimensional hydrologic modeling to evaluate aquatic habitat conditions

    Science.gov (United States)

    Pamela Edwards; Frederica Wood; Michael Little; Peter Vila; Peter Vila

    2006-01-01

    We describe the modeling and mapping procedures used to examine aquatic habitat conditions and habitat suitability of a small river in north- central West Virginia where fish survival and reproduction in specific reaches are poor. The study includes: (1) surveying cross sections of streambed reaches and measuring discharges and corresponding water-surface elevations,...

  19. Improved actions for the two-dimensional sigma-model

    OpenAIRE

    Caracciolo, Sergio; Montanari, Andrea; Pelissetto, Andrea

    1997-01-01

    For the O(N) sigma-model we studied the improvement program for actions with two- and four-spin interactions. An interesting example is an action which is reflection-positive, on-shell improved, and has all the coupling defined on an elementary plaquette. We show the large N solution and preliminary Monte Carlo results for N=3.

  20. Horizontal mixing coefficients for two-dimensional chemical models calculated from National Meteorological Center Data

    Science.gov (United States)

    Newman, P. A.; Schoeberl, M. R.; Plumb, R. A.

    1986-01-01

    Calculations of the two-dimensional, species-independent mixing coefficients for two-dimensional chemical models for the troposphere and stratosphere are performed using quasi-geostrophic potential vorticity fluxes and gradients from 4 years of National Meteorological Center data for the four seasons in both hemispheres. Results show that the horizontal mixing coefficient values for the winter lower stratosphere are broadly consistent with those currently employed in two-dimensional models, but the horizontal mixing coefficient values in the northern winter upper stratosphere are much larger than those usually used.

  1. Flow Modelling for partially Cavitating Two-dimensional Hydrofoils

    DEFF Research Database (Denmark)

    Krishnaswamy, Paddy

    2001-01-01

    The present work addresses te computational analysis of partial sheet hydrofoil cavitation in two dimensions. Particular attention is given to the method of simulating the flow at the end of the cavity. A fixed-length partially cavitating panel method is used to predict the height of the re...... of the model and comparing the present calculations with numerical results. The flow around the partially cavitating hydrofoil with a re-entrant jet has also been treated with a viscous/inviscid interactive method. The viscous flow model is based on boundary layer theory applied on the compound foil......, consisting of the union of the cavity and the hydrofoil surface. The change in the flow direction in the cavity closure region is seen to have a slightly adverse effect on the viscous pressure distribution. Otherwise, it is seen that the viscous re-entrant jet solution compares favourably with experimental...

  2. Numerical modeling of transient two-dimensional viscoelastic waves

    CERN Document Server

    Lombard, Bruno

    2010-01-01

    This paper deals with the numerical modeling of transient mechanical waves in linear viscoelastic solids. Dissipation mechanisms are described using the Zener model. No time convolutions are required thanks to the introduction of memory variables that satisfy local-in-time differential equations. By appropriately choosing the Zener parameters, it is possible to accurately describe a large range of materials, such as solids with constant quality factors. The evolution equations satisfied by the velocity, the stress, and the memory variables are written in the form of a first-order system of PDEs with a source term. This system is solved by splitting it into two parts: the propagative part is discretized explicitly, using a fourth-order ADER scheme on a Cartesian grid, and the diffusive part is then solved exactly. Jump conditions along the interfaces are discretized by applying an immersed interface method. Numerical experiments of wave propagation in viscoelastic and fluid media show the efficiency of this nu...

  3. Relations between two-dimensional models from dimensional reduction

    Energy Technology Data Exchange (ETDEWEB)

    Amaral, R.L.P.G.; Natividade, C.P. [Universidade Federal Fluminense, Niteroi, RJ (Brazil). Inst. de Fisica

    1998-12-31

    In this work we explore the consequences of dimensional reduction of the 3D Maxwell-Chern-Simons and some related models. A connection between topological mass generation in 3D and mass generation according to the Schwinger mechanism in 2D is obtained. Besides, a series of relationships are established by resorting to dimensional reduction and duality interpolating transformations. Nonabelian generalizations are also pointed out. (author) 10 refs.

  4. Model and observed seismicity represented in a two dimensional space

    Directory of Open Access Journals (Sweden)

    M. Caputo

    1976-06-01

    Full Text Available In recent years theoretical seismology lias introduced
    some formulae relating the magnitude and the seismic moment of earthquakes
    to the size of the fault and the stress drop which generated the
    earthquake.
    In the present paper we introduce a model for the statistics of the
    earthquakes based on these formulae. The model gives formulae which
    show internal consistency and are also confirmed by observations.
    For intermediate magnitudes the formulae reproduce also the trend
    of linearity of the statistics of magnitude and moment observed in all the
    seismic regions of the world. This linear trend changes into a curve with
    increasing slope for large magnitudes and moment.
    When a catalogue of the magnitudes and/or the seismic moment of
    the earthquakes of a seismic region is available, the model allows to estimate
    the maximum magnitude possible in the region.

  5. A Two-Dimensional PEM Fuel Cell Model

    Science.gov (United States)

    Shi, Zhongying; Wang, Xia; Zhang, Zhuqian

    2006-11-01

    Proton Exchange Membrane (PEM) fuel cell is a typical low temperature cell, where hydrogen and air are fed into the porous anodic electrode and cathodic electrode though the gas distributors on the bipolar plates, respectively. Activated by the catalyst on anode side, hydrogen will spilt into protons and electrons. Since only protons will be allowed to pass through the membrane, electrons must go through an external circuit. Electrons and protons meet air on cathode side to produce water and heat catalyzed by the catalyst on the cathode side. Numerical simulations are useful tools to describe the basic transport and electrochemical phenomena of PEM fuel cells. The goal of the present work is to develop 2-D computational models of PEM fuel cells, which take into account fluid flow, multi- species transport, current distribution and electrical potential. The velocity field in free channel described by Navier-Stokes equation and the velocity field in porous media described by Darcy’s Law are coupled along the channel-MEA interface. The governing differential equations are solved over a single computational domain, which consists of two gas channel layers, two gas diffusion layers, two catalyst layers as well as a membrane. The model is solved with commercial software COMSOL Multiphysics 3.2b. Parametric study will be conducted to analyze the effects of various parameters on the performance of PEM fuel cells. The results, including the mass concentration, the polarization curve and the velocity distribution, will be presented.

  6. Renormalization-group theory for cooling first-order phase transitions in Potts models.

    Science.gov (United States)

    Liang, Ning; Zhong, Fan

    2017-03-01

    We develop a dynamic field-theoretic renormalization-group (RG) theory for cooling first-order phase transitions in the Potts model. It is suggested that the well-known imaginary fixed points of the q-state Potts model for q>10/3 in the RG theory are the origin of the dynamic scaling found recently from numerical simulations, apart from logarithmic corrections. This indicates that the real and imaginary fixed points of the Potts model are both physical and control the scalings of the continuous and discontinuous phase transitions, respectively, of the model. Our one-loop results for the scaling exponents are already not far away from the numerical results. Further, the scaling exponents depend on q only slightly, consistent with the numerical results. Therefore, the theory is believed to provide a natural explanation of the dynamic scaling including the scaling exponents and their scaling laws for various observables in the cooling first-order phase transition of the Potts model.

  7. Renormalization-group theory for cooling first-order phase transitions in Potts models

    Science.gov (United States)

    Liang, Ning; Zhong, Fan

    2017-03-01

    We develop a dynamic field-theoretic renormalization-group (RG) theory for cooling first-order phase transitions in the Potts model. It is suggested that the well-known imaginary fixed points of the q -state Potts model for q >10 /3 in the RG theory are the origin of the dynamic scaling found recently from numerical simulations, apart from logarithmic corrections. This indicates that the real and imaginary fixed points of the Potts model are both physical and control the scalings of the continuous and discontinuous phase transitions, respectively, of the model. Our one-loop results for the scaling exponents are already not far away from the numerical results. Further, the scaling exponents depend on q only slightly, consistent with the numerical results. Therefore, the theory is believed to provide a natural explanation of the dynamic scaling including the scaling exponents and their scaling laws for various observables in the cooling first-order phase transition of the Potts model.

  8. On Regularity Criteria for the Two-Dimensional Generalized Liquid Crystal Model

    Directory of Open Access Journals (Sweden)

    Yanan Wang

    2014-01-01

    Full Text Available We establish the regularity criteria for the two-dimensional generalized liquid crystal model. It turns out that the global existence results satisfy our regularity criteria naturally.

  9. Mesh-free Hamiltonian implementation of two dimensional Darwin model

    Science.gov (United States)

    Siddi, Lorenzo; Lapenta, Giovanni; Gibbon, Paul

    2017-08-01

    A new approach to Darwin or magnetoinductive plasma simulation is presented, which combines a mesh-free field solver with a robust time-integration scheme avoiding numerical divergence errors in the solenoidal field components. The mesh-free formulation employs an efficient parallel Barnes-Hut tree algorithm to speed up the computation of fields summed directly from the particles, avoiding the necessity of divergence cleaning procedures typically required by particle-in-cell methods. The time-integration scheme employs a Hamiltonian formulation of the Lorentz force, circumventing the development of violent numerical instabilities associated with time differentiation of the vector potential. It is shown that a semi-implicit scheme converges rapidly and is robust to further numerical instabilities which can develop from a dominant contribution of the vector potential to the canonical momenta. The model is validated by various static and dynamic benchmark tests, including a simulation of the Weibel-like filamentation instability in beam-plasma interactions.

  10. Two dimensional cellular automaton for evacuation modeling: hybrid shuffle update

    CERN Document Server

    Arita, Chikashi; Appert-Rolland, Cécile

    2015-01-01

    We consider a cellular automaton model with a static floor field for pedestrians evacuating a room. After identifying some properties of real pedestrian flows, we discuss various update schemes, and we introduce a new one, the hybrid shuffle update. The properties specific to pedestrians are incorporated in variables associated to particles called phases, that represent their step cycles. The dynamics of the phases gives naturally raise to some friction, and allows to reproduce several features observed in experiments. We study in particular the crossover between a low- and a high-density regime that occurs when the density of pedestrian increases, the dependency of the outflow in the strength of the floor field, and the shape of the queue in front of the exit.

  11. TWO-DIMENSIONAL MODELLING OF ACCIDENTAL FLOOD WAVES PROPAGATION

    Directory of Open Access Journals (Sweden)

    Lorand Catalin STOENESCU

    2011-05-01

    Full Text Available The study presented in this article describes a modern modeling methodology of the propagation of accidental flood waves in case a dam break; this methodology is applied in Romania for the first time for the pilot project „Breaking scenarios of Poiana Uzului dam”. The calculation programs used help us obtain a bidimensional calculation (2D of the propagation of flood waves, taking into consideration the diminishing of the flood wave on a normal direction to the main direction; this diminishing of the flood wave is important in the case of sinuous courses of water or with urban settlements very close to the minor river bed. In the case of Poiana Uzului dam, 2 scenarios were simulated with the help of Ph.D. Eng. Dan Stematiu, plausible scenarios but with very little chances of actually producing. The results were presented as animations with flooded surfaces at certain time steps successively.

  12. Staggered Flux State in Two-Dimensional Hubbard Models

    Science.gov (United States)

    Yokoyama, Hisatoshi; Tamura, Shun; Ogata, Masao

    2016-12-01

    The stability and other properties of a staggered flux (SF) state or a correlated d-density wave state are studied for the Hubbard (t-t'-U) model on extended square lattices, as a low-lying state that competes with the dx2 - y2-wave superconductivity (d-SC) and possibly causes the pseudogap phenomena in underdoped high-Tc cuprates and organic κ-BEDT-TTF salts. In calculations, a variational Monte Carlo method is used. In the trial wave function, a configuration-dependent phase factor, which is vital to treat a current-carrying state for a large U/t, is introduced in addition to ordinary correlation factors. Varying U/t, t'/t, and the doping rate (δ) systematically, we show that the SF state becomes more stable than the normal state (projected Fermi sea) for a strongly correlated (U/t ≳ 5) and underdoped (δ ≲ 0.16) area. The decrease in energy is sizable, particularly in the area where Mott physics prevails and the circular current (order parameter) is strongly suppressed. These features are consistent with those for the t-J model. The effect of the frustration t'/t plays a crucial role in preserving charge homogeneity and appropriately describing the behavior of hole- and electron-doped cuprates and κ-BEDT-TTF salts. We argue that the SF state does not coexist with d-SC and is not a "normal state" from which d-SC arises. We also show that a spin current (flux or nematic) state is never stabilized in the same regime.

  13. Two-Dimensional Coupling Model on Social Deprivation and Its Application

    Science.gov (United States)

    Fu, Yun

    This paper qualitatively describes the deprivation under different coupling situations of two-dimensional indicators and then establishes the two-dimensional coupling model on social deprivation, using the social welfare function approach and Foster-Greer-Thorbecke P α method. Finally, this paper applies the model to evaluate the social deprivation of 31 provinces in China under the coupling state of capita disposable income and housing price.

  14. Critical phenomena in the majority voter model on two-dimensional regular lattices.

    Science.gov (United States)

    Acuña-Lara, Ana L; Sastre, Francisco; Vargas-Arriola, José Raúl

    2014-05-01

    In this work we studied the critical behavior of the critical point as a function of the number of nearest neighbors on two-dimensional regular lattices. We performed numerical simulations on triangular, hexagonal, and bilayer square lattices. Using standard finite-size scaling theory we found that all cases fall in the two-dimensional Ising model universality class, but that the critical point value for the bilayer lattice does not follow the regular tendency that the Ising model shows.

  15. First-Order Transition in Potts Models with "Invisible" States - Rigorous Proofs

    NARCIS (Netherlands)

    van Enter, Aernout C. D.; Iacobelli, Giulio; Taati, Siamak

    2011-01-01

    In some recent papers by Tamura, Tanaka and Kawashima [R. Tamura, S. Tanaka and N. Kawashima, Prog. Theor. Phys. 124 (2010), 381; S. Tanaka, R. Tamura and N. Kawashima, J. Phys.: Conf. Ser. 297 (2011), 012022; S. Tanaka and R. Tamura, arXiv:1012.4254] a class of Potts models with "invisible" states

  16. Gibbs Properties of the Fuzzy Potts Model on Trees and in Mean Field

    NARCIS (Netherlands)

    Häggström, O.; Külske, C.

    2004-01-01

    We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do

  17. Improved lower bounds on the ground-state entropy of the antiferromagnetic Potts model.

    Science.gov (United States)

    Chang, Shu-Chiuan; Shrock, Robert

    2015-05-01

    We present generalized methods for calculating lower bounds on the ground-state entropy per site, S(0), or equivalently, the ground-state degeneracy per site, W=e(S(0)/k(B)), of the antiferromagnetic Potts model. We use these methods to derive improved lower bounds on W for several lattices.

  18. Critical frontier of the Potts and percolation models on triangular-type and kagome-type lattices. II. Numerical analysis.

    Science.gov (United States)

    Ding, Chengxiang; Fu, Zhe; Guo, Wenan; Wu, F Y

    2010-06-01

    In the preceding paper, one of us (F. Y. Wu) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu's result is exact, and for the kagome-type lattices Wu's expression is under a homogeneity assumption. The purpose of the present paper is twofold: First, an essential step in Wu's analysis is the derivation of lattice-dependent constants A,B,C for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Second, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the q -state Potts model and the bond percolation on the 3-12 and kagome-type subnet lattices (n×n):(n×n) , n≤4 , for which the exact solution is not known. Our numerical determination of critical properties such as conformal anomaly and magnetic correlation length verifies that the universality principle holds. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical values are correct within errors of our finite-size analysis, which correspond to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices (1×1):(n×n) for 1≤n≤6 .

  19. Comparison between one-dimensional and two-dimensional models for Josephson junctions of overlap type

    DEFF Research Database (Denmark)

    Eilbeck, J. C; Lomdahl, P.S.; Olsen, O.H.

    1985-01-01

    A two-dimensional model of Josephson junction of overlap type is presented. The energy input is provided through induced magnetic fields modeled by a set of boundary conditions. In the limit of a very narrow junction, this model reduces to the one-dimensional model. Further, an equation derived f...

  20. Nonlinear scaling analysis approach of agent-based Potts financial dynamical model.

    Science.gov (United States)

    Hong, Weijia; Wang, Jun

    2014-12-01

    A financial agent-based price model is developed and investigated by one of statistical physics dynamic systems-the Potts model. Potts model, a generalization of the Ising model to more than two components, is a model of interacting spins on a crystalline lattice which describes the interaction strength among the agents. In this work, we investigate and analyze the correlation behavior of normalized returns of the proposed financial model by the power law classification scheme analysis and the empirical mode decomposition analysis. Moreover, the daily returns of Shanghai Composite Index and Shenzhen Component Index are considered, and the comparison nonlinear analysis of statistical behaviors of returns between the actual data and the simulation data is exhibited.

  1. Two-dimensional analytical models for asymmetric fully depleted double-gate strained silicon MOSFETs

    Institute of Scientific and Technical Information of China (English)

    Liu Hong-Xia; Li Jin; Li Bin; Cao Lei; Yuan Bo

    2011-01-01

    This paper develops the simple and accurate two-dimensional analytical models for new asymmetric double-gate fully depleted strained-Si MOSFET. The models mainly include the analytical equations of the surface potential, surface electric field and threshold voltage, which are derived by solving two dimensional Poisson equation in strained-Si layer.The models are verified by numerical simulation. Besides offering the physical insight into device physics in the model,the new structure also provides the basic designing guidance for further immunity of short channel effect and drain-induced barrier-lowering of CMOS-based devices in nanometre scale.

  2. A Large Deformation Model for the Elastic Moduli of Two-dimensional Cellular Materials

    Institute of Scientific and Technical Information of China (English)

    HU Guoming; WAN Hui; ZHANG Youlin; BAO Wujun

    2006-01-01

    We developed a large deformation model for predicting the elastic moduli of two-dimensional cellular materials. This large deformation model was based on the large deflection of the inclined members of the cells of cellular materials. The deflection of the inclined member, the strain of the representative structure and the elastic moduli of two-dimensional cellular materials were expressed using incomplete elliptic integrals. The experimental results show that these elastic moduli are no longer constant at large deformation, but vary significantly with the strain. A comparison was made between this large deformation model and the small deformation model proposed by Gibson and Ashby.

  3. Joint Image Reconstruction and Segmentation Using the Potts Model

    CERN Document Server

    Storath, Martin; Frikel, Jürgen; Unser, Michael

    2014-01-01

    We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation from limited data in x-ray and photoacoustic tomography. For instance, our method is able to reconstruct the Shepp-Logan phantom from $7$ angular views only. We demonstrate the practical applicability in an experiment with real PET data.

  4. Nonequilibrium phase transition in a driven Potts model with friction.

    Science.gov (United States)

    Iglói, Ferenc; Pleimling, Michel; Turban, Loïc

    2011-04-01

    We consider magnetic friction between two systems of q-state Potts spins which are moving along their boundaries with a relative constant velocity ν. Due to the interaction between the surface spins there is a permanent energy flow and the system is in a steady state, which is far from equilibrium. The problem is treated analytically in the limit ν=∞ (in one dimension, as well as in two dimensions for large-q values) and for v and q finite by Monte Carlo simulations in two dimensions. Exotic nonequilibrium phase transitions take place, the properties of which depend on the type of phase transition in equilibrium. When this latter transition is of first order, a sequence of second- and first-order nonequilibrium transitions can be observed when the interaction is varied. ©2011 American Physical Society

  5. Quantum search on the two-dimensional lattice using the staggered model with Hamiltonians

    Science.gov (United States)

    Portugal, R.; Fernandes, T. D.

    2017-04-01

    Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk models to provide efficient algorithms from the theoretical side and means to implement quantum walks in laboratories from the practical side. In this paper, we rigorously prove that the recent-proposed staggered quantum walk model provides an efficient quantum search on the two-dimensional lattice, if the reflection operators associated with the graph tessellations are used as Hamiltonians, which is an important theoretical result for validating the staggered model with Hamiltonians. Numerical results show that on the two-dimensional lattice staggered models without Hamiltonians are not as efficient as the one described in this paper and are, in fact, as slow as classical random-walk-based algorithms.

  6. USTIFICATION OF A TWO-DIMENSIONAL NONLINEAR SHELL MODEL OF KOITER'S TYPE

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    A two-dimensional nonlinear shell model"of Koiter's type"has recently been proposed by the first author. It is shown here that, according to two mutually exclusive sets of assumptions bearing on the associated manifold of admissible inextensional displacements, the leading term of a formal asymptotic expansion of the solution of this two-dimensional model, with the thickness as the"small" parameter, satisfies either the two-dimensional equations of a nonlinearly elastic "membrane" shell or those of a nonlinearly elastic "flexural" shell. These conclusions being identical to those recently drawn by B. Miara, then by V. Lods and B. Miara, for the leading term of a formal asymptotic expansion of the solution of the equations of three-dimensional nonlinear elasticity, again with the thickness as the "small" parameter, the nonlinear shell model of Koiter's type considered here is thus justified, at least formally.

  7. Fluctuation complexity of agent-based financial time series model by stochastic Potts system

    Science.gov (United States)

    Hong, Weijia; Wang, Jun

    2015-03-01

    Financial market is a complex evolved dynamic system with high volatilities and noises, and the modeling and analyzing of financial time series are regarded as the rather challenging tasks in financial research. In this work, by applying the Potts dynamic system, a random agent-based financial time series model is developed in an attempt to uncover the empirical laws in finance, where the Potts model is introduced to imitate the trading interactions among the investing agents. Based on the computer simulation in conjunction with the statistical analysis and the nonlinear analysis, we present numerical research to investigate the fluctuation behaviors of the proposed time series model. Furthermore, in order to get a robust conclusion, we consider the daily returns of Shanghai Composite Index and Shenzhen Component Index, and the comparison analysis of return behaviors between the simulation data and the actual data is exhibited.

  8. The exact interface model for wetting in the two-dimensional Ising model

    OpenAIRE

    Upton, P. J.

    2002-01-01

    We use exact methods to derive an interface model from an underlying microscopic model, i.e., the Ising model on a square lattice. At the wetting transition in the two-dimensional Ising model, the long Peierls contour (or interface) gets depinned from the substrate. Using exact transfer-matrix methods, we find that on sufficiently large length scales (i.e., length scales sufficiently larger than the bulk correlation length) the distribution of the long contour is given by a unique probability...

  9. Coupled Simulations of Mechanical Deformation and Microstructural Evolution Using Polycrystal Plasticity and Monte Carlo Potts Models

    Energy Technology Data Exchange (ETDEWEB)

    Battaile, C.C.; Buchheit, T.E.; Holm, E.A.; Neilsen, M.K.; Wellman, G.W.

    1999-01-12

    The microstructural evolution of heavily deformed polycrystalline Cu is simulated by coupling a constitutive model for polycrystal plasticity with the Monte Carlo Potts model for grain growth. The effects of deformation on boundary topology and grain growth kinetics are presented. Heavy deformation leads to dramatic strain-induced boundary migration and subsequent grain fragmentation. Grain growth is accelerated in heavily deformed microstructures. The implications of these results for the thermomechanical fatigue failure of eutectic solder joints are discussed.

  10. Worm algorithms for the 3-state Potts model with magnetic field and chemical potential

    CERN Document Server

    Delgado, Ydalia; Gattringer, Christof

    2012-01-01

    We discuss worm algorithms for the 3-state Potts model with external field and chemical potential. The complex phase problem of this system can be overcome by using a flux representation where the new degrees of freedom are dimer and monomer variables. Working with this representation we discuss two different generalizations of the conventional Prokof'ev-Svistunov algorithm suitable for Monte Carlo simulations of the model at arbitrary chemical potential and evaluate their performance.

  11. Modulated Phase of a Potts Model with Competing Binary Interactions on a Cayley Tree

    Science.gov (United States)

    Ganikhodjaev, N.; Temir, S.; Akin, H.

    2009-11-01

    We study the phase diagram for Potts model on a Cayley tree with competing nearest-neighbor interactions J 1, prolonged next-nearest-neighbor interactions J p and one-level next-nearest-neighbor interactions J o . Vannimenus proved that the phase diagram of Ising model with J o =0 contains a modulated phase, as found for similar models on periodic lattices, but the multicritical Lifshitz point is at zero temperature. Later Mariz et al. generalized this result for Ising model with J o ≠0 and recently Ganikhodjaev et al. proved similar result for the three-state Potts model with J o =0. We consider Potts model with J o ≠0 and show that for some values of J o the multicritical Lifshitz point be at non-zero temperature. We also prove that as soon as the same-level interaction J o is nonzero, the paramagnetic phase found at high temperatures for J o =0 disappears, while Ising model does not obtain such property. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular case, previous work by Ganikhodjaev et al. for J o =0. At vanishing temperature, the phase diagram is fully determined for all values and signs of J 1, J p and J o . At finite temperatures several interesting features are exhibited for typical values of J o / J 1.

  12. Stationary states of the two-dimensional nonlinear Schrödinger model with disorder

    DEFF Research Database (Denmark)

    Gaididei, Yuri Borisovich; Hendriksen, D.; Christiansen, Peter Leth

    1998-01-01

    Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrodinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder. In the discr......Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrodinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder...

  13. A Direct Calculation of Critical Exponents of Two-Dimensional Anisotropic Ising Model

    Institute of Scientific and Technical Information of China (English)

    XIONG Gang; WANG Xiang-Rong

    2006-01-01

    Using an exact solution of the one-dimensional quantum transverse-field Ising model, we calculate the critical exponents of the two-dimensional anisotropic classicalIsing model (IM). We verify that the exponents are the same as those of isotropic classical IM. Our approach provides an alternative means of obtaining and verifying these well-known results.

  14. Two-dimensional quantum compass model in a staggered field: some rigorous results

    Institute of Scientific and Technical Information of China (English)

    He Pei-Song; You Wen-Long; Tian Guang-Shan

    2011-01-01

    We study the properties of the two-dimensional quantum compass model in a staggered field. Using the PerronFr(o)enius theorem and the reflection positivity method, we rigorously determine the low energy spectrum of this model and its global ground state Ψ0. Furthermore, we show that Ψ0 has a directional long-range order.

  15. Modelling and experimental validation of two-dimensional transverse vibrations in a flexible robot link

    DEFF Research Database (Denmark)

    Sørensen, Paul Haase; Baungaard, Jens Rane

    1996-01-01

    A general model for a rotating homogenous flexible robot link is developed. The model describes two-dimensional transverse vibrations induced by the actuator due to misalignment of the actuator axis of rotation relative to the link symmetry axis and due to translational acceleration of the link...

  16. Modeling of the financial market using the two-dimensional anisotropic Ising model

    Science.gov (United States)

    Lima, L. S.

    2017-09-01

    We have used the two-dimensional classical anisotropic Ising model in an external field and with an ion single anisotropy term as a mathematical model for the price dynamics of the financial market. The model presented allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the facts of financial markets. We have obtained the mean price in terms of the strong of the site anisotropy term Δ which reinforces the sensitivity of the agent's sentiment to external news.

  17. Solving the Advection-Diffusion Equations in Biological Contexts using the Cellular Potts Model

    CERN Document Server

    Dan, D; Chen, K; Glazier, J A; Dan, Debasis; Mueller, Chris; Chen, Kun; Glazier, James A.

    2005-01-01

    The Cellular Potts Model (CPM) is a robust, cell-level methodology for simulation of biological tissues and morphogenesis. Both tissue physiology and morphogenesis depend on diffusion of chemical morphogens in the extra-cellular fluid or matrix (ECM). Standard diffusion solvers applied to the cellular potts model use finite difference methods on the underlying CPM lattice. However, these methods produce a diffusing field tied to the underlying lattice, which is inaccurate in many biological situations in which cell or ECM movement causes advection rapid compared to diffusion. Finite difference schemes suffer numerical instabilities solving the resulting advection-diffusion equations. To circumvent these problems we simulate advection-diffusion within the framework of the CPM using off-lattice finite-difference methods. We define a set of generalized fluid particles which detach advection and diffusion from the lattice. Diffusion occurs between neighboring fluid particles by local averaging rules which approxi...

  18. Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant D{sub PQ}

    Energy Technology Data Exchange (ETDEWEB)

    Baxter, R J [Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200 (Australia)

    2010-04-09

    For the Ising model, the calculation of the spontaneous magnetization leads to the problem of evaluating a determinant. Yang did this by calculating the eigenvalues in the large-lattice limit. Montroll, Potts and Ward expressed it as a Toeplitz determinant and used Szego's theorem: this is almost certainly the route originally travelled by Onsager. For the corresponding problem in the superintegrable chiral Potts model, neither approach appears to work: here we show that the determinant D{sub PQ} can be expressed as that of a product of two Cauchy-like matrices. One can then use the elementary exact formula for the Cauchy determinant. One of course regains the known result, originally conjectured in 1989.

  19. Two dimensional black-hole as a topological coset model of c=1 string theory

    CERN Document Server

    Mukhi, S

    1993-01-01

    We show that a special superconformal coset (with $\\hat c =3$) is equivalent to $c=1$ matter coupled to two dimensional gravity. This identification allows a direct computation of the correlation functions of the $c=1$ non-critical string to all genus, and at nonzero cosmological constant, directly from the continuum approach. The results agree with those of the matrix model. Moreover we connect our coset with a twisted version of a Euclidean two dimensional black hole, in which the ghost and matter systems are mixed.

  20. First-order phase transition in $1d$ Potts model with long-range interactions

    OpenAIRE

    Uzelac, K.; Glumac, Z.

    1998-01-01

    The first-order phase transition in the one-dimensional $q$-state Potts model with long-range interactions decaying with distance as $1/r^{1+\\sigma}$ has been studied by Monte Carlo numerical simulations for $0 2$. On the basis of finite-size scaling analysis of interface free energy $\\Delta F_L$, specific heat and Binder's fourth order cumulant, we obtain the first-order transition which occurs for $\\sigma$ below a threshold value $\\sigma_c(q)$.

  1. Julia sets and complex singularities in diamond-like hierarchical Potts models

    Institute of Scientific and Technical Information of China (English)

    QIAO; Jianyong

    2005-01-01

    We study the phase transition of the Potts model on diamond-like hierarchical lattices. It is shown that the set of the complex singularities is the Julia set of a rational mapping. An interesting problem is how are these singularities continued to the complex plane. In this paper, by the method of complex dynamics, we give a complete description about the connectivity of the set of the complex singularities.

  2. Boundary Conditions for Translation-Invariant Gibbs Measures of the Potts Model on Cayley Trees

    Science.gov (United States)

    Gandolfo, D.; Rahmatullaev, M. M.; Rozikov, U. A.

    2017-06-01

    We consider translation-invariant splitting Gibbs measures (TISGMs) for the q-state Potts model on a Cayley tree of order two. Recently a full description of the TISGMs was obtained, and it was shown in particular that at sufficiently low temperatures their number is 2q-1. In this paper for each TISGM μ we explicitly give the set of boundary conditions such that limiting Gibbs measures with respect to these boundary conditions coincide with μ.

  3. The Potts Model on a Bethe Lattice in an External Field

    Science.gov (United States)

    Semkin, S. V.; Smagin, V. P.

    2017-02-01

    A solution for the Potts model with arbitrary number of states on a Bethe lattice in a nonzero external field has been obtained. A line of first-order phase transitions has been constructed in the temperature - external-field plane, terminating at the point of the second-order phase transition. The magnitude of the magnetization jump on the phase-transition lines has been found, as well as some of the critical exponents characterizing this phase transition.

  4. Investigation of the Potts model of a diluted magnet by local field averaging technique

    Science.gov (United States)

    Semkin, S. V.; Smagin, V. P.

    2016-08-01

    Averaging of the local interatomic interaction fields has been applied to the Potts model of a diluted magnet. A self-consistent equation for the magnetization and an equation for the phase transition temperature have been derived. The temperature and magnetic atom density dependences of the spontaneous magnetization have been found for the lattices with the coordination numbers 3 and 4 and various numbers of spin states.

  5. Simple Two-Dimensional Corrections for One-Dimensional Pulse Tube Models

    Science.gov (United States)

    Lee, J. M.; Kittel, P.; Timmerhaus, K. D.; Radebaugh, R.

    2004-01-01

    One-dimensional oscillating flow models are very useful for designing pulse tubes. They are simple to use, not computationally intensive, and the physical relationship between temperature, pressure and mass flow are easy to understand when used in conjunction with phasor diagrams. They do not possess, however, the ability to directly calculate thermal and momentum diffusion in the direction transverse to the oscillating flow. To account for transverse effects, lumped parameter corrections, which are obtained though experiment, must be used. Or two-dimensional solutions of the differential fluid equations must be obtained. A linear two-dimensional solution to the fluid equations has been obtained. The solution provides lumped parameter corrections for one-dimensional models. The model accounts for heat transfer and shear flow between the gas and the tube. The complex Nusselt number and complex shear wall are useful in describing these corrections, with phase relations and amplitudes scaled with the Prandtl and Valensi numbers. The calculated ratio, a, between a two-dimensional solution of the oscillating temperature and velocity and a one-dimensional solution for the same shows a scales linearly with Va for Va less than 30. In this region alpha less than 0.5, that is, the enthalpy flow calculated with a two-dimensional model is 50% of a calculation using a one-dimensional model. For Va greater than 250, alpha = 0.8, showing that diffusion is still important even when it is confined to a thing layer near the tube wall.

  6. On two-dimensionalization of three-dimensional turbulence in shell models

    DEFF Research Database (Denmark)

    Chakraborty, Sagar; Jensen, Mogens Høgh; Sarkar, A.

    2010-01-01

    Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have been studied and reproduced. Within the framework of shell...

  7. A Two-Dimensional Analytic Thermal Model for a High-Speed PMSM Magnet

    CSIR Research Space (South Africa)

    Grobler, AJ

    2015-11-01

    Full Text Available TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 62, NO. 11, NOVEMBER 2015 A Two-Dimensional Analytic Thermal Model for a High-Speed PMSM Magnet Andries J. Groblera, Stanley Robert Holmb, and George van Schoorc a School of Electrical, Electronic...

  8. Proton transport in a membrane protein channel: two-dimensional infrared spectrum modeling.

    NARCIS (Netherlands)

    Liang, C.; Knoester, J.; Jansen, T.L.Th.A.

    2012-01-01

    We model the two-dimensional infrared (2DIR) spectrum of a proton channel to investigate its applicability as a spectroscopy tool to study the proton transport process in biological systems. Proton transport processes in proton channels are involved in numerous fundamental biochemical reactions. How

  9. Solitary excitations in discrete two-dimensional nonlinear Schrodinger models with dispersive dipole-dipole interactions

    DEFF Research Database (Denmark)

    Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.

    1998-01-01

    The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either...

  10. Two-dimensional cellular automaton model of traffic flow with open boundaries

    CERN Document Server

    Tadaki, S I

    1996-01-01

    A two-dimensional cellular automaton model of traffic flow with open boundaries are investigated by computer simulations. The outflow of cars from the system and the average velocity are investigated. The time sequences of the outflow and average velocity have flicker noises in a jamming phase. The low density behavior are discussed with simple jam-free approximation.

  11. A Solvable Model in Two-Dimensional Gravity Coupled to a Nonlinear Matter Field

    Institute of Scientific and Technical Information of China (English)

    YAN Jun; WANG Shun-Jin; TAO Bi-You

    2001-01-01

    The two-dimensional gravity model with a coupling constant k = 4 and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically. These solutions may be used to describe the naked singularity at the origin.``

  12. Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models

    Directory of Open Access Journals (Sweden)

    Xuemei Gao

    2014-01-01

    Full Text Available The aim of this paper is to extend the lattice method proposed by Ritchken and Trevor (1999 for pricing American options with one-dimensional stochastic volatility models to the two-dimensional cases with strangle payoff. This proposed method is compared with the least square Monte-Carlo method via numerical examples.

  13. Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional non-Abelian spin models.

    Science.gov (United States)

    Borisenko, Oleg; Chelnokov, Volodymyr; Cuteri, Francesca; Papa, Alessandro

    2016-07-01

    It is argued that two-dimensional U(N) spin models for any N undergo a Berezinskii-Kosterlitz-Thouless (BKT)-like phase transition, similarly to the famous XY model. This conclusion follows from the Berezinskii-like calculation of the two-point correlation function in U(N) models, approximate renormalization group analysis, and numerical investigations of the U(2) model. It is shown, via Monte Carlo simulations, that the universality class of the U(2) model coincides with that of the XY model. Moreover, preliminary numerical results point out that two-dimensional SU(N) spin models with the fundamental and adjoint terms and N>4 exhibit two phase transitions of BKT type, similarly to Z(N) vector models.

  14. Exact Potts model partition function on strips of the triangular lattice

    Science.gov (United States)

    Chang, Shu-Chiuan; Shrock, Robert

    2000-10-01

    In this paper we present exact calculations of the partition function Z of the q-state Potts model and its generalization to real q, for arbitrary temperature on n-vertex strip graphs, of width Ly=2 and arbitrary length, of the triangular lattice with free, cyclic, and Möbius longitudinal boundary conditions. These partition functions are equivalent to Tutte/Whitney polynomials for these graphs. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. Considering the full generalization to arbitrary complex q and temperature, we determine the singular locus B in the corresponding C2 space, arising as the accumulation set of partition function zeros as n→∞. In particular, we study the connection with the T=0 limit of the Potts antiferromagnet where B reduces to the accumulation set of chromatic zeros. Comparisons are made with our previous exact calculation of Potts model partition functions for the corresponding strips of the square lattice. Our present calculations yield, as special cases, several quantities of graph-theoretic interest.

  15. Eighth-order phase-field-crystal model for two-dimensional crystallization

    OpenAIRE

    Jaatinen, A.; Ala-Nissila, T.

    2010-01-01

    We present a derivation of the recently proposed eighth order phase field crystal model [Jaatinen et al., Phys. Rev. E 80, 031602 (2009)] for the crystallization of a solid from an undercooled melt. The model is used to study the planar growth of a two dimensional hexagonal crystal, and the results are compared against similar results from dynamical density functional theory of Marconi and Tarazona, as well as other phase field crystal models. We find that among the phase field crystal models...

  16. Logarithmic discretization and systematic derivation of shell models in two-dimensional turbulence.

    Science.gov (United States)

    Gürcan, Ö D; Morel, P; Kobayashi, S; Singh, Rameswar; Xu, S; Diamond, P H

    2016-09-01

    A detailed systematic derivation of a logarithmically discretized model for two-dimensional turbulence is given, starting from the basic fluid equations and proceeding with a particular form of discretization of the wave-number space. We show that it is possible to keep all or a subset of the interactions, either local or disparate scale, and recover various limiting forms of shell models used in plasma and geophysical turbulence studies. The method makes no use of the conservation laws even though it respects the underlying conservation properties of the fluid equations. It gives a family of models ranging from shell models with nonlocal interactions to anisotropic shell models depending on the way the shells are constructed. Numerical integration of the model shows that energy and enstrophy equipartition seem to dominate over the dual cascade, which is a common problem of two-dimensional shell models.

  17. GIS-based data model and tools for creating and managing two-dimensional cross sections

    Science.gov (United States)

    Whiteaker, Timothy L.; Jones, Norm; Strassberg, Gil; Lemon, Alan; Gallup, Doug

    2012-02-01

    While modern Geographic Information Systems (GIS) software is robust in handling maps and data in plan view, the software generally falls short when representing features in section view. Further complicating the issue is the fact that geologic cross sections are often drawn by connecting a series of wells together that do not fall along a single straight line. In this case, the x-axis of the cross section represents the distance along the set of individual lines connecting the series of wells, effectively "flattening out" the cross section along this path to create a view of the subsurface with which geologists often work in printed folios. Even 3D-enabled GIS cannot handle this type of cross section. A GIS data model and tools for creating and working with two-dimensional cross sections are presented. The data model and tools create a framework that can be applied using ESRI's ArcGIS software, enabling users to create, edit, manage, and print two-dimensional cross sections from within one of the most well-known GIS software packages. The data model is a component of the arc hydro groundwater data model, which means all two-dimensional cross sections are inherently linked to other features in the hydrogeologic domain, including those represented by xyz coordinates in real world space. Thus, the creation of two-dimensional cross sections can be guided by or completely driven from standard GIS data, and geologic interpretations established on two-dimensional cross sections can be translated back to real world coordinates to create three-dimensional features such as fence diagrams, giving GIS users the capacity to characterize the subsurface environment in a variety of integrated views that was not possible before. A case study for the Sacramento Regional Model in California demonstrates the application of the methodology in support of a regional groundwater management plan.

  18. Model of two-dimensional electron gas formation at ferroelectric interfaces

    Energy Technology Data Exchange (ETDEWEB)

    Aguado-Puente, P.; Bristowe, N. C.; Yin, B.; Shirasawa, R.; Ghosez, Philippe; Littlewood, P. B.; Artacho, Emilio

    2015-07-01

    The formation of a two-dimensional electron gas at oxide interfaces as a consequence of polar discontinuities has generated an enormous amount of activity due to the variety of interesting effects it gives rise to. Here, we study under what circumstances similar processes can also take place underneath ferroelectric thin films. We use a simple Landau model to demonstrate that in the absence of extrinsic screening mechanisms, a monodomain phase can be stabilized in ferroelectric films by means of an electronic reconstruction. Unlike in the LaAlO3/SrTiO3 heterostructure, the emergence with thickness of the free charge at the interface is discontinuous. This prediction is confirmed by performing first-principles simulations of free-standing slabs of PbTiO3. The model is also used to predict the response of the system to an applied electric field, demonstrating that the two-dimensional electron gas can be switched on and off discontinuously and in a nonvolatile fashion. Furthermore, the reversal of the polarization can be used to switch between a two-dimensional electron gas and a two-dimensional hole gas, which should, in principle, have very different transport properties. We discuss the possible formation of polarization domains and how such configuration competes with the spontaneous accumulation of free charge at the interfaces.

  19. Free-energy landscape and nucleation pathway of polymorphic minerals from solution in a Potts lattice-gas model.

    Science.gov (United States)

    Okamoto, Atsushi; Kuwatani, Tatsu; Omori, Toshiaki; Hukushima, Koji

    2015-10-01

    Metastable minerals commonly form during reactions between water and rock. The nucleation mechanism of polymorphic phases from solution are explored here using a two-dimensional Potts model. The model system is composed of a solvent and three polymorphic solid phases. The local state and position of the solid phase are updated by Metropolis dynamics. Below the critical temperature, a large cluster of the least stable solid phase initially forms in the solution before transitioning into more-stable phases following the Ostwald step rule. The free-energy landscape as a function of the modal abundance of each solid phase clearly reveals that before cluster formation, the least stable phase has an energetic advantage because of its low interfacial energy with the solution, and after cluster formation, phase transformation occurs along the valley of the free-energy landscape, which contains several minima for the regions of three phases. Our results indicate that the solid-solid and solid-liquid interfacial energy contribute to the formation of the complex free-energy landscape and nucleation pathways following the Ostwald step rule.

  20. Universality class of the two-dimensional site-diluted Ising model.

    Science.gov (United States)

    Martins, P H L; Plascak, J A

    2007-07-01

    In this work, we evaluate the probability distribution function of the order parameter for the two-dimensional site-diluted Ising model. Extensive Monte Carlo simulations have been performed for different spin concentrations p (0.70universality class of the diluted Ising model seems to be independent of the amount of dilution. Logarithmic corrections of the finite-size critical temperature behavior of the model can also be inferred even for such small lattices.

  1. Measurement of the Equation of State of the Two-Dimensional Hubbard Model

    Science.gov (United States)

    Miller, Luke; Cocchi, Eugenio; Drewes, Jan; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Koehl, Michael

    2016-05-01

    The subtle interplay between kinetic energy, interactions and dimensionality challenges our comprehension of strongly-correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions, 0 constitute benchmarks for state-of-the-art theoretical approaches.

  2. Analysis of Two-Layered Random Interfaces for Two Dimensional Widom-Rowlinson's Model

    Directory of Open Access Journals (Sweden)

    Jun Wang

    2011-01-01

    Full Text Available The statistical behaviors of two-layered random-phase interfaces in two-dimensional Widom-Rowlinson's model are investigated. The phase interfaces separate two coexisting phases of the lattice Widom-Rowlinson model; when the chemical potential μ of the model is large enough, the convergence of the probability distributions which describe the fluctuations of the phase interfaces is studied. In this paper, the backbones of interfaces are introduced in the model, and the corresponding polymer chains and cluster expansions are developed and analyzed for the polymer weights. And the existence of the free energy for two-layered random-phase interfaces of the two-dimensional Widom-Rowlinson model is given.

  3. A two-dimensional analytical model of laminar flame in lycopodium dust particles

    Energy Technology Data Exchange (ETDEWEB)

    Rahbari, Alireza [Shahid Rajaee Teacher Training University, Tehran (Iran, Islamic Republic of); Shakibi, Ashkan [Iran University of Science and Technology, Tehran (Iran, Islamic Republic of); Bidabadi, Mehdi [Combustion Research Laboratory, Narmak, Tehran (Iran, Islamic Republic of)

    2015-09-15

    A two-dimensional analytical model is presented to determine the flame speed and temperature distribution of micro-sized lycopodium dust particles. This model is based on the assumptions that the particle burning rate in the flame front is controlled by the process of oxygen diffusion and the flame structure consists of preheat, reaction and post flame zones. In the first step, the energy conservation equations for fuel-lean condition are expressed in two dimensions, and then these differential equations are solved using the required boundary condition and matching the temperature and heat flux at the interfacial boundaries. Consequently, the obtained flame temperature and flame speed distributions in terms of different particle diameters and equivalence ratio for lean mixture are compared with the corresponding experimental data for lycopodium dust particles. Consequently, it is shown that this two-dimensional model demonstrates better agreement with the experimental results compared to the previous models.

  4. Efficient Monte Carlo Methods for the Potts Model at Low Temperature

    CERN Document Server

    Molkaraie, Mehdi

    2015-01-01

    We consider the problem of estimating the partition function of the ferromagnetic $q$-state Potts model. We propose an importance sampling algorithm in the dual of the normal factor graph representing the model. The algorithm can efficiently compute an estimate of the partition function in a wide range of parameters; in particular, when the coupling parameters of the model are strong (corresponding to models at low temperature) or when the model contains a mixture of strong and weak couplings. We show that, in this setting, the proposed algorithm significantly outperforms the state of the art methods in the primal and in the dual domains.

  5. Canonical quantization of a two-dimensional model with anomalous breaking of gauge invariance

    OpenAIRE

    Girotti, Horacio Oscar; Rothe, Heinz J.; Rothe, Klaus D.

    1986-01-01

    We investigate in detail the operator quantum dynamics of a two-dimensional model exhibiting anomalous breaking of gauge invariance. The equal-time algebra is systematically obtained by using the Dirac-bracket formalism for constrained systems. For certain values of the regularization parameter the system is shown to undergo drastic changes. For the value of the parameter corresponding to the chiral Schwinger model no operator solutions are found to exist.

  6. Striped periodic minimizers of a two-dimensional model for martensitic phase transitions

    CERN Document Server

    Giuliani, Alessandro

    2010-01-01

    In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional:

  7. Tensor renormalization group approach to two-dimensional classical lattice models.

    Science.gov (United States)

    Levin, Michael; Nave, Cody P

    2007-09-21

    We describe a simple real space renormalization group technique for two-dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement. In this sense, the technique can be thought of as a classical analogue of the density matrix renormalization group method. We demonstrate the method - which we call the tensor renormalization group method - by computing the magnetization of the triangular lattice Ising model.

  8. On the geometry of classically integrable two-dimensional non-linear sigma models

    Energy Technology Data Exchange (ETDEWEB)

    Mohammedi, N., E-mail: nouri@lmpt.univ-tours.f [Laboratoire de Mathematiques et Physique Theorique (CNRS - UMR 6083), Universite Francois Rabelais de Tours, Faculte des Sciences et Techniques, Parc de Grandmont, F-37200 Tours (France)

    2010-11-11

    A master equation expressing the zero curvature representation of the equations of motion of a two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. Special attention is paid to those representations possessing a spectral parameter. Furthermore, a closer connection between integrability and T-duality transformations is emphasised. Finally, new integrable non-linear sigma models are found and all their corresponding Lax pairs depend on a spectral parameter.

  9. The gauging of two-dimensional bosonic sigma models on world-sheets with defects

    CERN Document Server

    Gawedzki, Krzysztof; Waldorf, Konrad

    2013-01-01

    We extend our analysis of the gauging of rigid symmetries in bosonic two-dimensional sigma models with Wess-Zumino terms in the action to the case of world-sheets with defects. A structure that permits a non-anomalous coupling of such sigma models to world-sheet gauge fields of arbitrary topology is analysed, together with obstructions to its existence, and the classification of its inequivalent choices.

  10. CSOS models descending from chiral Potts models: degeneracy of the eigenspace and loop algebra

    Science.gov (United States)

    Au-Yang, Helen; Perk, Jacques H. H.

    2016-04-01

    Monodromy matrices of the {{\\boldsymbol{τ }}}2\\phantom{^{\\prime }} model are known to satisfy a Yang-Baxter equation with a six-vertex R-matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this R-matrix. We show the reason why in the superintegrable case the eigenspace is degenerate, but not in the general case. We then show that the eigenspaces of special CSOS models descending from the chiral Potts model are also degenerate. The existence of an L({{sl}}2) quantum loop algebra (or subalgebra) in these models is established by showing that the Serre relations hold for the generators. The highest weight polynomial (or the Drinfeld polynomial) of the representation is obtained by using the method of Baxter for the superintegrable case. As a byproduct, the eigenvalues of all such CSOS models are given explicitly.

  11. Inflection points of microcanonical entropy: Monte Carlo simulation of q state Potts model on a finite square lattice

    Energy Technology Data Exchange (ETDEWEB)

    Praveen, E., E-mail: svmstaya@gmail.com; Satyanarayana, S. V. M., E-mail: svmstaya@gmail.com [Department of Physics, Pondicherry University, Puducherry-605014 (India)

    2014-04-24

    Traditional definition of phase transition involves an infinitely large system in thermodynamic limit. Finite systems such as biological proteins exhibit cooperative behavior similar to phase transitions. We employ recently discovered analysis of inflection points of microcanonical entropy to estimate the transition temperature of the phase transition in q state Potts model on a finite two dimensional square lattice for q=3 (second order) and q=8 (first order). The difference of energy density of states (DOS) Δ ln g(E) = ln g(E+ ΔE) −ln g(E) exhibits a point of inflexion at a value corresponding to inverse transition temperature. This feature is common to systems exhibiting both first as well as second order transitions. While the difference of DOS registers a monotonic variation around the point of inflexion for systems exhibiting second order transition, it has an S-shape with a minimum and maximum around the point of inflexion for the case of first order transition.

  12. Computational energetic model of morphogenesis based on multi-agent Cellular Potts Model.

    Science.gov (United States)

    Tripodi, Sébastien; Ballet, Pascal; Rodin, Vincent

    2010-01-01

    The Cellular Potts Model (CPM) is a cellular automaton (CA), developed by Glazier and Graner in 1992, to model the morphogenesis. In this model, the entities are the cells. It has already been improved in many ways; however, a key point in biological systems, not defined in CPM, is energetic exchange between entities. We integrate this energetic concept inside the CPM. We simulate a cell differentiation inside a growing cell tissue. The results are the emergence of dynamic patterns coming from the consumption and production of energy. A model described by CA is less scalable than one described by a multi-agent system (MAS). We have developed a MAS based on the CPM, where a cell agent is implemented from the cell of CPM together with several behaviours, in particular the consumption and production of energy from the consumption of molecules.

  13. A Novel Machine Learning Strategy Based on Two-Dimensional Numerical Models in Financial Engineering

    Directory of Open Access Journals (Sweden)

    Qingzhen Xu

    2013-01-01

    Full Text Available Machine learning is the most commonly used technique to address larger and more complex tasks by analyzing the most relevant information already present in databases. In order to better predict the future trend of the index, this paper proposes a two-dimensional numerical model for machine learning to simulate major U.S. stock market index and uses a nonlinear implicit finite-difference method to find numerical solutions of the two-dimensional simulation model. The proposed machine learning method uses partial differential equations to predict the stock market and can be extensively used to accelerate large-scale data processing on the history database. The experimental results show that the proposed algorithm reduces the prediction error and improves forecasting precision.

  14. Modeling of the optical properties of a two-dimensional system of small conductive particles.

    Science.gov (United States)

    Kondikov, A. A.; Tonkaev, P. A.; Chaldyshev, V. V.; Vartanyan, T. A.

    2016-08-01

    Software was developed for quick numerical calculations and graphic display of the absorption, reflection and transmittance spectra of two-dimensional systems of small conductive particles. It allowed us to make instant comparison of calculation results and experimental data. A lattice model was used to simulate nearly distributed particles, and the coherent-potential approximation was applied to obtain a solution to the problem of interacting particles. The Delphi programming environment was used.

  15. Spontaneous supersymmetry breaking in the two-dimensional N=1 Wess-Zumino model

    CERN Document Server

    Steinhauer, Kyle

    2014-01-01

    We study the phase diagram of the two-dimensional N=1 Wess-Zumino model on the lattice using Wilson fermions and the fermion loop formulation. We give a complete nonperturbative determination of the ground state structure in the continuum and infinite volume limit. We also present a determination of the particle spectrum in the supersymmetric phase, in the supersymmetry broken phase and across the supersymmetry breaking phase transition. In the supersymmetry broken phase we observe the emergence of the Goldstino particle.

  16. Inflation Cosmological Solutions in Two-Dimensional Brans-Dicke Gravity Model

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The purpose of this paper is to study cosmological properties of two-dimensional Brans-Dicke gravity model. For massless scalar field, the new cosmological solutions are found by integration of field equation, these solutions correspond to the inflation solutions with positive cosmological constant. The result of this paper show that the inflation process of universe is controlled by the classical and quantum effect of the scalar field.

  17. Coexistence of Incommensurate Magnetism and Superconductivity in the Two-Dimensional Hubbard Model.

    Science.gov (United States)

    Yamase, Hiroyuki; Eberlein, Andreas; Metzner, Walter

    2016-03-04

    We analyze the competition of magnetism and superconductivity in the two-dimensional Hubbard model with a moderate interaction strength, including the possibility of incommensurate spiral magnetic order. Using an unbiased renormalization group approach, we compute magnetic and superconducting order parameters in the ground state. In addition to previously established regions of Néel order coexisting with d-wave superconductivity, the calculations reveal further coexistence regions where superconductivity is accompanied by incommensurate magnetic order.

  18. Quantum Monte Carlo simulation of a two-dimensional Majorana lattice model

    Science.gov (United States)

    Hayata, Tomoya; Yamamoto, Arata

    2017-07-01

    We study interacting Majorana fermions in two dimensions as a low-energy effective model of a vortex lattice in two-dimensional time-reversal-invariant topological superconductors. For that purpose, we implement ab initio quantum Monte Carlo simulation to the Majorana fermion system in which the path-integral measure is given by a semipositive Pfaffian. We discuss spontaneous breaking of time-reversal symmetry at finite temperatures.

  19. Sums of Ramdom Matrices and the Potts Model on Random Planar Maps

    CERN Document Server

    Atkin, Max R; Wheater, John F

    2015-01-01

    We compute the partition function of the $q$-states Potts model on a random planar lattice with $p\\leq q$ allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit, generalising a result by Voiculescu for the addition of random matrices to a situation beyond free probability theory. We show that the partition functions with $p$ and $q-p$ colours on the boundary are related algebraically. Finally, we investigate the phase diagram of the model when $0\\leq q\\leq 4$ and comment on the conformal field theory description of the critical points.

  20. Sums of random matrices and the Potts model on random planar maps

    Science.gov (United States)

    Atkin, Max R.; Niedner, Benjamin; Wheater, John F.

    2016-05-01

    We compute the partition function of the q-states Potts model on a random planar lattice with p≤slant q allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit, generalising a result by Voiculescu for the addition of random matrices to a situation beyond free probability theory. We show that the partition functions with p and q - p colours on the boundary are related algebraically. Finally, we investigate the phase diagram of the model when 0≤slant q≤slant 4 and comment on the conformal field theory description of the critical points.

  1. Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state.

    Science.gov (United States)

    Környei, László; Pleimling, Michel; Iglói, Ferenc

    2008-01-01

    The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is generally the same due to self-duality. Here we consider a sudden change in the form of the interaction and study the nonequilibrium critical dynamical properties of the nearest-neighbor model. The relaxation of the magnetization and the decay of the autocorrelation function are found to display a power law behavior with characteristic exponents that depend on the universality class of the initial state.

  2. Modeling two-dimensional water flow and bromide transport in a heterogeneous lignitic mine soil

    Energy Technology Data Exchange (ETDEWEB)

    Buczko, U.; Gerke, H.H. [Brandenburg University of Technology, Cottbus (Germany)

    2006-02-15

    Water and solute fluxes in lignitic mine soils and in many other soils are often highly heterogeneous. Here, heterogeneity reflects dumping-induced inclined structures and embedded heterogeneous distributions of sediment mixtures and of lignitic fragments. Such two-scale heterogeneity effects may be analyzed through the application of two-dimensional models for calculating water and solute fluxes. The objective of this study was to gain more insight to what extent spatial heterogeneity of soil hydraulic parameters contributes to preferential flow at a lignitic mine soil. The simulations pertained to the 'Barenbrucker Hohe' site in Germany where previously water fluxes and applied tracers had been monitored with a cell lysimeter, and from where a soil block had been excavated for detailed two-dimensional characterization of the hydraulic parameters using pedotransfer functions. Based on those previous studies, scenarios with different distributions of hydraulic parameters were simulated. The results show that spatial variability of hydraulic parameters alone can hardly explain the observed flow patterns. The observed preferential flow at the site was probably caused by additional factors such as hydrophobicity, the presence of root channels, anisotropy in the hydraulic conductivity, and heterogeneous root distributions. To study the relative importance of these other factors by applying two-dimensional flow models to such sites, the experimental database must be improved. Single-continuum model approaches may be insufficient for such sites.

  3. Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

    Science.gov (United States)

    Shrock, Robert; Xu, Yan

    2010-12-01

    We present exact results on the partition function of the q-state Potts model on various families of graphs G in a generalized external magnetic field that favors or disfavors spin values in a subset I s ={1,…, s} of the total set of possible spin values, Z( G, q, s, v, w), where v and w are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial Ph( G, q, s, w) that counts the number of colorings of the vertices of G subject to the condition that colors of adjacent vertices are different, with a weighting w that favors or disfavors colors in the interval I s . We derive powerful new upper and lower bounds on Z( G, q, s, v, w) for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for Z( G, q, s, v, w) on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.

  4. Modelling floor heating systems using a validated two-dimensional ground coupled numerical model

    DEFF Research Database (Denmark)

    Weitzmann, Peter; Kragh, Jesper; Roots, Peter

    2005-01-01

    the floor. This model can be used to design energy efficient houses with floor heating focusing on the heat loss through the floor construction and foundation. It is found that it is impor-tant to model the dynamics of the floor heating system to find the correct heat loss to the ground, and further......This paper presents a two-dimensional simulation model of the heat losses and tempera-tures in a slab on grade floor with floor heating which is able to dynamically model the floor heating system. The aim of this work is to be able to model, in detail, the influence from the floor construction...... and foundation on the performance of the floor heating sys-tem. The ground coupled floor heating model is validated against measurements from a single-family house. The simulation model is coupled to a whole-building energy simu-lation model with inclusion of heat losses and heat supply to the room above...

  5. Some exact results on the Potts model partition function in a magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Chang, S-C [Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan (China); Shrock, Robert [C N Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794 (United States)], E-mail: scchang@mail.ncku.edu.tw, E-mail: robert.shrock@stonybrook.edu

    2009-09-25

    We consider the Potts model in a magnetic field on an arbitrary graph G. Using a formula by F Y Wu for the partition function Z of this model as a sum over spanning subgraphs of G, we prove some properties of Z concerning factorization, monotonicity and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context, we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for Z for cyclic strip graphs.

  6. Some exact results on the Potts model partition function in a magnetic field

    Science.gov (United States)

    Chang, Shu-Chiuan; Shrock, Robert

    2009-09-01

    We consider the Potts model in a magnetic field on an arbitrary graph G. Using a formula by F Y Wu for the partition function Z of this model as a sum over spanning subgraphs of G, we prove some properties of Z concerning factorization, monotonicity and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context, we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for Z for cyclic strip graphs.

  7. The early history of the integrable chiral Potts model and the odd-even problem

    Science.gov (United States)

    Perk, Jacques H. H.

    2016-04-01

    In the first part of this paper I shall discuss the round-about way of how the integrable chiral Potts model was discovered about 30 years ago. As there should be more higher-genus models to be discovered, this might be of interest. In the second part I shall discuss some quantum group aspects, especially issues of odd versus even N related to the Serre relations conjecture in our quantum loop subalgebra paper of 5 years ago and how we can make good use of coproducts, also borrowing ideas of Drinfeld, Jimbo, Deguchi, Fabricius, McCoy and Nishino.

  8. Mean-field approximation for the potts model of a diluted magnet in the external field

    Science.gov (United States)

    Semkin, S. V.; Smagin, V. P.

    2016-07-01

    The Potts model of a diluted magnet with an arbitrary number of states placed in the external field has been considered. Phase transitions of this model have been studied in the mean-field approximation, the dependence of the critical temperature on the external field and the density of magnetic atoms has been found, and the magnetic susceptibility has been calculated. An improved mean-field technique has been proposed, which provides more accurate account of the effects associated with nonmagnetic dilution. The influence of dilution on the first-order phase transition curve and the magnetization jump at the phase transition has been studied by this technique.

  9. FUZZY MODEL FOR TWO-DIMENSIONAL RIVER WATER QUALITY SIMULATION UNDER SUDDEN POLLUTANTS DISCHARGED

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    Based on the fuzziness and impreciseness of water environmental system, the fuzzy arithmetic was used to simulate the fuzzy and imprecise relations in modeling river water quality. By defining the parameters of water quality model as symmetrical triangular fuzzy numbers, a two-dimensional fuzzy water quality model for sudden pollutant discharge is established. From the fuzzy model, the pollutant concentrations, corresponding to the specified confidence level of α, can be obtained by means of the α-cut technique and arithmetic operations of triangular fuzzy numbers. Study results reveal that it is feasible in theory and reliable on calculation applying triangular fuzzy numbers to the simulation of river water quality.

  10. Temperature dependence of universal fluctuations in the two-dimensional harmonic XY model.

    Science.gov (United States)

    Palma, G

    2006-04-01

    We compute exact analytical expressions for the skewness and kurtosis in the two-dimensional harmonic XY model. These quantities correspond to the third and fourth normalized moments of the probability density function (PDF) of the magnetization of the model. From their behavior, we conclude that they depend explicitly on the system temperature even in the thermodynamic limit, and hence the PDF itself must depend on it. Our results correct the hypothesis called universal fluctuations, they confirm and extend previous results which showed a T dependence of the PDF, including perturbative expansions within the XY model up to first order in temperature.

  11. Eighth-order phase-field-crystal model for two-dimensional crystallization

    OpenAIRE

    Jaatinen, A.; Ala-Nissilä, Tapio

    2010-01-01

    We present a derivation of the recently proposed eighth-order phase-field crystal model [A. Jaatinen et al., Phys. Rev. E 80, 031602 (2009)] for the crystallization of a solid from an undercooled melt. The model is used to study the planar growth of a two-dimensional hexagonal crystal, and the results are compared against similar results from dynamical density functional theory of Marconi and Tarazona, as well as other phase-field crystal models. We find that among the phase-field crystal mod...

  12. Neimark-Sacker bifurcation of a two-dimensional discrete-time predator-prey model.

    Science.gov (United States)

    Khan, A Q

    2016-01-01

    In this paper, we study the dynamics and bifurcation of a two-dimensional discrete-time predator-prey model in the closed first quadrant [Formula: see text]. The existence and local stability of the unique positive equilibrium of the model are analyzed algebraically. It is shown that the model can undergo a Neimark-Sacker bifurcation in a small neighborhood of the unique positive equilibrium and an invariant circle will appear. Some numerical simulations are presented to illustrate our theocratical results and numerically it is shown that the unique positive equilibrium of the system is globally asymptotically stable.

  13. Two-dimensional modeling of apparent resistivity pseudosections in the Cerro Prieto region

    Energy Technology Data Exchange (ETDEWEB)

    Vega, R.; Martinez, M.

    1981-01-01

    Using a finite-difference program (Dey, 1976) for two-dimensional modeling of apparent resistivity pseudosections obtained by different measuring arrays, four apparent resistivity pseudosections obtained at Cerro Prieto with a Schlumberger array by CFE personnel were modeled (Razo, 1978). Using geologic (Puente and de la Pena, 1978) and lithologic (Diaz, et al., 1981) data from the geothermal region, models were obtained which show clearly that, for the actual resistivity present in the zone, the information contained in the measured pseudosections is primarily due to the near-surface structure and does not show either the presence of the geothermal reservoir or the granitic basement which underlies it.

  14. Functional scale-free networks in the two-dimensional Abelian sandpile model

    Science.gov (United States)

    Zarepour, M.; Niry, M. D.; Valizadeh, A.

    2015-07-01

    Recently, the similarity of the functional network of the brain and the Ising model was investigated by Chialvo [Nat. Phys. 6, 744 (2010), 10.1038/nphys1803]. This similarity supports the idea that the brain is a self-organized critical system. In this study we derive a functional network of the two-dimensional Bak-Tang-Wiesenfeld sandpile model as a self-organized critical model, and compare its characteristics with those of the functional network of the brain, obtained from functional magnetic resonance imaging.

  15. Boundary magnetization of a two-dimensional Ising model with inhomogeneous nearest-neighbor interactions

    Science.gov (United States)

    Pelizzola, Alessandro

    1994-11-01

    An explicit formula for the boundary magnetization of a two-dimensional Ising model with a strip of inhomogeneous interactions is obtained by means of a transfer matrix mean-field method introduced by Lipowski and Suzuki. There is clear numerical evidence that the formula is exact By taking the limit where the width of the strip approaches infinity and the interactions have well defined bulk limits, I arrive at the boundary magnetization for a model which includes the Hilhorst-van Leeuwen model. The rich critical behavior of the latter magnetization is thereby rederived with little effort.

  16. Two-dimensional Thermal Modeling of Lithium-ion Battery Cell Based on Electrothermal Impedance Spectroscopy

    DEFF Research Database (Denmark)

    Swierczynski, Maciej Jozef; Stroe, Daniel Loan; Knap, Vaclav

    2016-01-01

    Thermal modeling of lithium-ion batteries is gaining its importance together with increasing power density and compact design of the modern battery systems in order to assure battery safety and long lifetime. Thermal models of lithium-ion batteries are usually either expensive to develop...... and accurate or equivalent thermal circuit based with moderate accuracy and without spatial temperature distribution. This work presents initial results that can be used as a fundament for the cost-efficient development of the two-dimensional thermal model of lithium-ion battery based on multipoint...

  17. Interface tension of the 3d 4-state Potts model using the Wang-Landau algorithm

    CERN Document Server

    Hietanen, A

    2011-01-01

    We study the interface tension of the 4-state Potts model in three dimensions using the Wang- Landau algorithm. The interface tension is given by the ratio of the partition function with a twisted boundary condition in one direction and periodic boundary conditions in all other directions over the partition function with periodic boundary conditions in all directions. With the Wang-Landau algorithm we can explicitly calculate both partition functions and obtain the result for all temperatures. We find solid numerical evidence for perfect wetting. Our algorithm is tested by calculating thermodynamic quantities at the phase transition point.

  18. Metastability of Non-reversible, Mean-Field Potts Model with Three Spins

    Science.gov (United States)

    Landim, C.; Seo, I.

    2016-11-01

    We examine a non-reversible, mean-field Potts model with three spins on a set with N\\uparrow ∞ points. Without an external field, there are three critical temperatures and five different metastable regimes. The analysis can be extended by a perturbative argument to the case of small external fields, and it can be carried out in the case where the external field is in the direction or in the opposite direction to one of the values of the spins. Numerical computations permit to identify other phenomena which are not present in the previous situations.

  19. Universality and massive excitations in 3d 3-state Potts model

    CERN Document Server

    Falcone, R; Gravina, M; Papa, A

    2007-01-01

    The mass spectrum of the 3d 3-state Potts model is considered in the broken phase (a) near the second order Ising critical point in the temperature-magnetic field plane and (b) near the weakly first order transition point at zero magnetic field. In the case (a), the mass spectrum is compared with the prediction from universality of mass ratios in the 3d Ising class; in the case (b) a mass ratio is determined to be compared with the corresponding one in the spectrum of screening masses of the (3+1)d SU(3) pure gauge theory at finite temperature in the deconfined phase near the transition.

  20. Locally self-similar phase diagram of the disordered Potts model on the hierarchical lattice.

    Science.gov (United States)

    Anglès d'Auriac, J-Ch; Iglói, Ferenc

    2013-02-01

    We study the critical behavior of the random q-state Potts model in the large-q limit on the diamond hierarchical lattice with an effective dimensionality d(eff)>2. By varying the temperature and the strength of the frustration the system has a phase transition line between the paramagnetic and the ferromagnetic phases which is controlled by four different fixed points. According to our renormalization group study the phase boundary in the vicinity of the multicritical point is self-similar; it is well represented by a logarithmic spiral. We expect an infinite number of reentrances in the thermodynamic limit; consequently one cannot define standard thermodynamic phases in this region.

  1. Ground-State Transition in a Two-Dimensional Frenkel-Kontorova Model

    Institute of Scientific and Technical Information of China (English)

    YUAN Xiao-Ping; ZHENG Zhi-Gang

    2011-01-01

    The ground state of a generalized Frenkel-Kontorova model with a transversaJ degree of freedom is studied. When the coupling strength, K, and the frequency of & single-Atom vibration in the transversaJ direction, ωou are increased, the ground state of the model undergoes a transition from a two-dimensional configuration to a one-dimensional one. This transition can manifest in different ways. Furthermore, we find that the prerequisite of a two-dimensionai ground state is θ≠1//q.%The ground state of a generalized Frenkel-Kontorova model with a transversal degree of freedom is studied.When the coupling strength,K,and the frequency of a single-atom vibration in the transversal direction,ωoy,are increased,the ground state of the model undergoes a transition from a two-dimensional configuration to a one-dimensional one.This transition can manifest in different ways.Furthermore,we find that the prerequisite of a two-dimensional ground state is θ ≠ 1/q.In recent years,the Frenkel-Kontorova (FK) model has been applied to a variety of physical systems,such as adsorbed monolayers,[1,2] Josephsonjunction arrays,[3-5] tribology[6-8] and charge-density waves.[9,10] Experimental and large-scale simulation data at the nanoscale have become available,and more complicated FK-type models have been investigated using simulations of molecular dynamics.[11

  2. Two-dimensional, isothermal, multi-component model for a polymer electrolyte membrane fuel cell

    Energy Technology Data Exchange (ETDEWEB)

    Mahinpey, N.; Jagannathan, A.; Idem, R. [Regina Univ., SK (Canada). Faculty of Engineering

    2007-07-01

    A fuel cell is an electrochemical energy conversion device which is more efficient than an internal combustion engine in converting fuel to power. Numerous fuel cell models have been developed by a number of authors accounting for the various physical processes. Earlier models were restricted to being one dimensional, steady-state, and isothermal while more recent two-dimensional models had several limitations. This paper presented the results of a study that developed a two-dimensional computational fluid dynamics model of a polymer electrolyte membrane fuel cell using a finite element method to solve a multi-component transport model coupled with flow in porous media, charge balance, electrochemical kinetics, and rigorous water balance in the membrane. The mass transport, momentum transport, and electrochemical processes occurring in the membrane electrolyte and catalyst layers were modeled. The local equilibrium was assumed at the interfaces and the model was combined with the kinetics and was analytically solved for the anodic and cathodic current using an agglomerate spherical catalyst pellet. The paper compared the modeling results with previously published experimental data. The study investigated the effects of channel and bipolar plate shoulder size, porosity of the electrodes, temperature, relative humidity and current densities on the cell performance. It was concluded that smaller sized channels and bipolar plate shoulders were required to obtain higher current densities, although larger channels were satisfactory at moderate current densities. 13 refs., 5 figs.

  3. Monte Carlo renormalization-group investigation of the two-dimensional O(4) sigma model

    Science.gov (United States)

    Heller, Urs M.

    1988-01-01

    An improved Monte Carlo renormalization-group method is used to determine the beta function of the two-dimensional O(4) sigma model. While for (inverse) couplings beta = greater than about 2.2 agreement is obtained with asymptotic scaling according to asymptotic freedom, deviations from it are obtained at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating 'scaling' according to the full beta function. These results contradict recent claims that the model has a critical point at finite coupling.

  4. Thermal metal in network models of a disordered two-dimensional superconductor

    Science.gov (United States)

    Chalker, J. T.; Read, N.; Kagalovsky, V.; Horovitz, B.; Avishai, Y.; Ludwig, A. W.

    2002-01-01

    We study the symmetry class for localization which arises from models of noninteracting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotation invariance. Two-dimensional systems in this category, which is known as class D, can display phases with three different types of quasiparticle dynamics: metallic, localized, or with a quantized (thermal) Hall conductance. Correspondingly, they can show a variety of delocalization transitions. We illustrate this behavior by investigating numerically the phase diagrams of network models with the appropriate symmetry and show the appearance of the metallic phase.

  5. Digital hardware implementation of a stochastic two-dimensional neuron model.

    Science.gov (United States)

    Grassia, F; Kohno, T; Levi, T

    2017-02-22

    This study explores the feasibility of stochastic neuron simulation in digital systems (FPGA), which realizes an implementation of a two-dimensional neuron model. The stochasticity is added by a source of current noise in the silicon neuron using an Ornstein-Uhlenbeck process. This approach uses digital computation to emulate individual neuron behavior using fixed point arithmetic operation. The neuron model's computations are performed in arithmetic pipelines. It was designed in VHDL language and simulated prior to mapping in the FPGA. The experimental results confirmed the validity of the developed stochastic FPGA implementation, which makes the implementation of the silicon neuron more biologically plausible for future hybrid experiments.

  6. Two-dimensional model of intrinsic magnetic flux losses in helical flux compression generators

    CERN Document Server

    Haurylavets, V V

    2012-01-01

    Helical Flux Compression Generators (HFCG) are used for generation of mega-amper current and high magnetic fields. We propose the two dimensional HFCG filament model based on the new description of the stator and armature contact point. The model developed enables one to quantitatively describe the intrinsic magnetic flux losses and predict the results of experiments with various types of HFCGs. We present the effective resistance calculations based on the non-linear magnetic diffusion effect describing HFCG performance under the strong conductor heating by currents.

  7. Monte Carlo renormalization-group investigation of the two-dimensional O(4) sigma model

    Science.gov (United States)

    Heller, Urs M.

    1988-01-01

    An improved Monte Carlo renormalization-group method is used to determine the beta function of the two-dimensional O(4) sigma model. While for (inverse) couplings beta = greater than about 2.2 agreement is obtained with asymptotic scaling according to asymptotic freedom, deviations from it are obtained at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating 'scaling' according to the full beta function. These results contradict recent claims that the model has a critical point at finite coupling.

  8. Two-Dimensional Wang-Landau Sampling of AN Asymmetric Ising Model

    Science.gov (United States)

    Tsai, Shan-Ho; Wang, Fugao; Landau, D. P.

    We study the critical endpoint behavior of an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. We use a two-dimensional Wang-Landau sampling method to determine the density of states for this model. An accurate density of states allowed us to map out the phase diagram accurately and observe a clear divergence of the curvature of the spectator phase boundary and of the derivative of the magnetization coexistence diameter near the critical endpoint, in agreement with previous theoretical predictions.

  9. Nanolithographic Fabrication and Heterogeneous Reaction Studies ofTwo-Dimensional Platinum Model Catalyst Systems

    Energy Technology Data Exchange (ETDEWEB)

    Contreras, Anthony Marshall [Univ. of California, Berkeley, CA (United States)

    2006-05-20

    In order to better understand the fundamental components that govern catalytic activity, two-dimensional model platinum nanocatalyst arrays have been designed and fabricated. These catalysts arrays are meant to model the interplay of the metal and support important to industrial heterogeneous catalytic reactions. Photolithography and sub-lithographic techniques such as electron beam lithography, size reduction lithography and nanoimprint lithography have been employed to create these platinum nanoarrays. Both in-situ and ex-situ surface science techniques and catalytic reaction measurements were used to correlate the structural parameters of the system to catalytic activity.

  10. Precision of meshfree methods and application to forward modeling of two-dimensional electromagnetic sources

    Science.gov (United States)

    Li, Jun-Jie; Yan, Jia-Bin; Huang, Xiang-Yu

    2015-12-01

    Meshfree method offers high accuracy and computational capability and constructs the shape function without relying on predefined elements. We comparatively analyze the global weak form meshfree methods, such as element-free Galerkin method (EFGM), the point interpolation method (PIM), and the radial point interpolation method (RPIM). Taking two dimensional Poisson equation as an example, we discuss the support-domain dimensionless size, the field nodes, and background element settings with respect to their effect on calculation accuracy of the meshfree method. RPIM and EFGM are applied to controlled-source two-dimensional electromagnetic modeling with fixed shape parameters. The accuracy of boundary conditions imposed directly and by a penalty function are discussed in the case of forward modeling of two-dimensional magnetotellurics in a homogeneous medium model. The coupling algorithm of EFG-PIM and EFG-RPIM are generated by integrating the PIM or RPIM and EFGM. The results of the numerical modeling suggest the following. First, the proposed meshfree method and corresponding coupled methods are well-suited for electromagnetic numerical modeling. The accuracy of the algorithm is the highest when the support-domain dimensionless size is 1.0 and the distribution of field nodes is consistent with the nodes of background elements. Second, the accuracy of PIM and RPIM are lower than that of EFGM for the Poisson equation but higher than EFGM for the homogeneous medium MT response. Third, RPIM overcomes the matrix inversion problem of PIM and has a wider selection of support-domain dimensionless sizes as compared to RPIM.

  11. Comprehensive two-dimensional river ice model based on boundary-fitted coordinate transformation method

    Directory of Open Access Journals (Sweden)

    Ze-yu MAO

    2014-01-01

    Full Text Available River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.

  12. Numerical study of Potts models with aperiodic modulations: influence on first-order transitions

    Science.gov (United States)

    Branco, Nilton; Girardi, Daniel

    2012-02-01

    We perform a numerical study of Potts models on a rectangular lattice with aperiodic interactions along one spatial direction. The number of states q is such that the transition is a first-order one for the uniform model. The Wolff algorithm is employed, for many lattice sizes, allowing for a finite-size scaling analyses to be carried out. Three different self-dual aperiodic sequences are employed, such that the exact critical temperature is known: this leads to precise results for the exponents. We analyze models with q=6 and 15 and show that the Harris-Luck criterion, originally introduced in the study of continuous transitions, is obeyed also for first-order ones. The new universality class that emerges for relevant aperiodic modulations depends on the number of states of the Potts model, as obtained elsewhere for random disorder, and on the aperiodic sequence. We determine the occurrence of log-periodic behavior, as expected for models with aperiodic modulated interactions.

  13. Retention modelling of polychlorinated biphenyls in comprehensive two-dimensional gas chromatography.

    Science.gov (United States)

    D'Archivio, Angelo Antonio; Incani, Angela; Ruggieri, Fabrizio

    2011-01-01

    In this paper, we use a quantitative structure-retention relationship (QSRR) method to predict the retention times of polychlorinated biphenyls (PCBs) in comprehensive two-dimensional gas chromatography (GC×GC). We analyse the GC×GC retention data taken from the literature by comparing predictive capability of different regression methods. The various models are generated using 70 out of 209 PCB congeners in the calibration stage, while their predictive performance is evaluated on the remaining 139 compounds. The two-dimensional chromatogram is initially estimated by separately modelling retention times of PCBs in the first and in the second column ((1) t (R) and (2) t (R), respectively). In particular, multilinear regression (MLR) combined with genetic algorithm (GA) variable selection is performed to extract two small subsets of predictors for (1) t (R) and (2) t (R) from a large set of theoretical molecular descriptors provided by the popular software Dragon, which after removal of highly correlated or almost constant variables consists of 237 structure-related quantities. Based on GA-MLR analysis, a four-dimensional and a five-dimensional relationship modelling (1) t (R) and (2) t (R), respectively, are identified. Single-response partial least square (PLS-1) regression is alternatively applied to independently model (1) t (R) and (2) t (R) without the need for preliminary GA variable selection. Further, we explore the possibility of predicting the two-dimensional chromatogram of PCBs in a single calibration procedure by using a two-response PLS (PLS-2) model or a feed-forward artificial neural network (ANN) with two output neurons. In the first case, regression is carried out on the full set of 237 descriptors, while the variables previously selected by GA-MLR are initially considered as ANN inputs and subjected to a sensitivity analysis to remove the redundant ones. Results show PLS-1 regression exhibits a noticeably better descriptive and predictive

  14. Confinement in the q-state Potts model: an RG-TCSA study

    Energy Technology Data Exchange (ETDEWEB)

    Lencsés, M. [MTA-BME “Momentum” Statistical Field Theory Research Group, 1111 Budapest, Budafoki út 8 (Hungary); Department of Theoretical Physics, Eötvös University, 1117 Budapest, Pázmány Péter sétány 1/A (Hungary); Takács, G. [MTA-BME “Momentum” Statistical Field Theory Research Group, 1111 Budapest, Budafoki út 8 (Hungary); Department of Theoretical Physics, Budapest University of Technology and Economics, 1111 Budapest, Budafoki út 8 (Hungary)

    2015-09-22

    In the ferromagnetic phase of the q-state Potts model, switching on an external magnetic field induces confinement of the domain wall excitations. For the Ising model (q=2) the spectrum consists of kink-antikink states which are the analogues of mesonic states in QCD, while for q=3, depending on the sign of the field, the spectrum may also contain three-kink bound states which are the analogues of the baryons. In recent years the resulting “hadron” spectrum was described using several different approaches, such as quantum mechanics in the confining linear potential, WKB methods and also the Bethe-Salpeter equation. Here we compare the available predictions to numerical results from renormalization group improved truncated conformal space approach (RG-TCSA). While mesonic states in the Ising model have already been considered in a different truncated Hamiltonian approach, this is the first time that a precision numerical study is performed for the 3-state Potts model. We find that the semiclassical approach provides a very accurate description for the mesonic spectrum in all the parameter regime for weak magnetic field, while the low-energy expansion from the Bethe-Salpeter equation is only valid for very weak fields where it gives a slight improvement over the semiclassical results. In addition, we confirm the validity of the recent predictions for the baryon spectrum obtained from solving the quantum mechanical three-body problem.

  15. Confinement in the q-state Potts model: an RG-TCSA study

    CERN Document Server

    Lencses, M

    2015-01-01

    In the ferromagnetic phase of the q-state Potts model, switching on an external magnetic field induces confinement of the domain wall excitations. For the Ising model (q = 2) the spectrum consists of kink-antikink states which are the analogues of mesonic states in QCD, while for q = 3, depending on the sign of the field, the spectrum may also contain three-kink bound states which are the analogues of the baryons. In recent years the resulting "hadron" spectrum was described using several different approaches, such as quantum mechanics in the confining linear potential, WKB methods and also the Bethe-Salpeter equation. Here we compare the available predictions to numerical results from renormalization group improved truncated conformal space approach (RG-TCSA). While mesonic states in the Ising model have already been considered in a different truncated Hamiltonian approach, this is the first time that a precision numerical study is performed for the 3-state Potts model. We find that the semiclassical approac...

  16. A two-dimensional CA model for traffic flow with car origin and destination

    Science.gov (United States)

    In-nami, Junji; Toyoki, Hiroyasu

    2007-05-01

    Dynamic phase transitions in a two-dimensional traffic flow model defined on a decorated square-lattice are studied numerically. The square-lattice point and the decorated site denote intersections and roads, respectively. In the present model, a car has a finite deterministic path between the origin and the destination, which is assigned to the car from the beginning. In this new model, we found a new phase between the free-flow phase and the frozen-jam phase that is absent from previous models. The new model is characterized by the persistence of a macroscopic cluster. Furthermore, the behavior in this macroscopic cluster phase is classified into three regions characterized by the shape of the cluster. The boundary of the three regions is phenomenologically estimated. When the trip length is short and the car density is high, both ends of the belt-like cluster connect to each other through the periodic boundary with some probability. This type of cluster is classified topologically as a string on a two-dimensional torus.

  17. Two-dimensional habitat modeling in the Yellowstone/Upper Missouri River system

    Science.gov (United States)

    Waddle, T. J.; Bovee, K.D.; Bowen, Z.H.

    1997-01-01

    This study is being conducted to provide the aquatic biology component of a decision support system being developed by the U.S. Bureau of Reclamation. In an attempt to capture the habitat needs of Great Plains fish communities we are looking beyond previous habitat modeling methods. Traditional habitat modeling approaches have relied on one-dimensional hydraulic models and lumped compositional habitat metrics to describe aquatic habitat. A broader range of habitat descriptors is available when both composition and configuration of habitats is considered. Habitat metrics that consider both composition and configuration can be adapted from terrestrial biology. These metrics are most conveniently accessed with spatially explicit descriptors of the physical variables driving habitat composition. Two-dimensional hydrodynamic models have advanced to the point that they may provide the spatially explicit description of physical parameters needed to address this problem. This paper reports progress to date on applying two-dimensional hydraulic and habitat models on the Yellowstone and Missouri Rivers and uses examples from the Yellowstone River to illustrate the configurational metrics as a new tool for assessing riverine habitats.

  18. Numerical model for the shear rheology of two-dimensional wet foams with deformable bubbles.

    Science.gov (United States)

    Kähärä, T; Tallinen, T; Timonen, J

    2014-09-01

    Shearing of two-dimensional wet foam is simulated using an introduced numerical model, and results are compared to those of experiments. This model features realistically deformable bubbles, which distinguishes it from previously used models for wet foam. The internal bubble dynamics and their contact interactions are also separated in the model, making it possible to investigate the effects of the related microscale properties of the model on the macroscale phenomena. Validity of model assumptions was proved here by agreement between the simulated and measured Herschel-Bulkley rheology, and shear-induced relaxation times. This model also suggests a relationship between the shear stress and normal stress as well as between the average degree of bubble deformation and applied shear stress. It can also be used to analyze suspensions of bubbles and solid particles, an extension not considered in this work.

  19. Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model

    Science.gov (United States)

    Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; Neupert, Titus; Maciejko, Joseph

    2016-08-01

    We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1 /2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d -density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state—protected by time-reversal and reflection symmetries—cannot be connected adiabatically to a free-fermion topological phase.

  20. Critical manifold of the Potts model: exact results and homogeneity approximation.

    Science.gov (United States)

    Wu, F Y; Guo, Wenan

    2012-08-01

    The q-state Potts model has stood at the frontier of research in statistical mechanics for many years. In the absence of a closed-form solution, much of the past effort has focused on locating its critical manifold, trajectory in the parameter (q,e(J)) space where J is the reduced interaction, along which the free energy is singular. However, except in isolated cases, antiferromagnetic (AF) models with JPotts model with AF interactions focusing on obtaining its critical manifold in exact and/or closed-form expressions. We first reexamine the known critical frontiers in light of AF interactions. For the square lattice we confirm the Potts self-dual point to be the sole critical frontier for J>0. We also locate its critical frontier for J0. More generally we consider the centered-triangle (CT) and Union-Jack (UJ) lattices consisting of mixed J and K interactions, and deduce critical manifolds under homogeneity hypotheses. For K = 0 the CT lattice is the diced lattice, and we determine its critical manifold for all J and find q(c) = 3.32472. For K = 0 the UJ lattice is the square lattice and from this we deduce both the J > 0 and J < 0 critical manifolds and q(c) = 3. Our theoretical predictions are compared with recent numerical results.

  1. Resonance and Rectification in a Two-Dimensional Frenkel-Kontorova Model with Triangular Symmetry

    Institute of Scientific and Technical Information of China (English)

    YANG Yang; WANG Cang-Long; DUAN Wen-Shan; CHEN Jian-Min

    2011-01-01

    The mode-locking phenomena in the dc- and ac-driven overdamped two-dimensional Frenkel-Kontorova model with triangular symmetric structures are studied. The obtained results show that the transverse velocitylongitudinal velocity(vy) can occur when n is an odd number. It is also found in our simulations that the critical depinning force oscillates with the amplitude of ac-driven force, i.e., the system is dominated by the ac-driven force. The oscillatory behavior is strongly determined by the initial phase of ac force.

  2. p-wave superconductivity in a two-dimensional generalized Hubbard model

    Energy Technology Data Exchange (ETDEWEB)

    Millan, J. Samuel [Instituto de Investigaciones en Materiales, Universidad Nacional Autonoma de Mexico (UNAM), Apartado Postal 70-360, 04510, Mexico D.F. (Mexico); Facultad de Ingenieria, UNACAR, 24180, Cd. de Carmen, Campeche (Mexico); Perez, Luis A. [Instituto de Fisica, UNAM, Apartado Postal 20-364, 01000, Mexico D.F. (Mexico); Wang Chumin [Instituto de Investigaciones en Materiales, Universidad Nacional Autonoma de Mexico (UNAM), Apartado Postal 70-360, 04510, Mexico D.F. (Mexico)]. E-mail: chumin@servidor.unam.mx

    2005-02-21

    In this Letter, we consider a two-dimensional Hubbard model that includes a second-neighbor correlated hopping interaction, and we find a triplet p-wave superconducting ground state within the BCS formalism. A small distortion of the square-lattice right angles is introduced in order to break the degeneracy of kx+/-ky oriented p-wave pairing states. For the strong coupling limit, analytical results are obtained. An analysis of the superconducting critical temperature reveals the existence of an optimal electron density and the gap ratio exhibits a non-BCS behavior. Finally, the particular case of strontium ruthenate is examined.

  3. Topological Invariants of Edge States for Periodic Two-Dimensional Models

    Energy Technology Data Exchange (ETDEWEB)

    Avila, Julio Cesar; Schulz-Baldes, Hermann, E-mail: schuba@mi.uni-erlangen.de; Villegas-Blas, Carlos [Instituto de Matematicas, UNAM (Mexico)

    2013-06-15

    Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define topological invariants by considering the associated Bott-Maslov indices which can be easily calculated numerically. For time-reversal symmetric systems in the symplectic universality class this leads to a Z{sub 2} -invariant for the edge states. It is shown that the edge state invariants are related to Chern numbers of the bulk systems and also to (spin) edge currents, in the spirit of the theory of topological insulators.

  4. Existence of a line of critical points in a two-dimensional Lebwohl Lasher model

    Energy Technology Data Exchange (ETDEWEB)

    Shabnam, Sabana [Department of Physics, Lady Brabourne College, Kolkata 700017 (India); DasGupta, Sudeshna, E-mail: sudeshna.dasgupta10@gmail.com [Department of Physics, Lady Brabourne College, Kolkata 700017 (India); Roy, Soumen Kumar [Department of Physics, Jadavpur University, Kolkata 700032 (India)

    2016-02-15

    Controversy regarding transitions in systems with global symmetry group O(3) has attracted the attention of researchers and the detailed nature of this transition is still not well understood. As an example of such a system in this paper we have studied a two-dimensional Lebwohl Lasher model, using the Wolff cluster algorithm. Though we have not been able to reach any definitive conclusions regarding the order present in the system, from finite size scaling analysis, hyperscaling relations and the behavior of the correlation function we have obtained strong indications regarding the presence of quasi-long range order and the existence of a line of critical points in our system.

  5. Existence of a line of critical points in a two-dimensional Lebwohl Lasher model

    Science.gov (United States)

    Shabnam, Sabana; DasGupta, Sudeshna; Roy, Soumen Kumar

    2016-02-01

    Controversy regarding transitions in systems with global symmetry group O(3) has attracted the attention of researchers and the detailed nature of this transition is still not well understood. As an example of such a system in this paper we have studied a two-dimensional Lebwohl Lasher model, using the Wolff cluster algorithm. Though we have not been able to reach any definitive conclusions regarding the order present in the system, from finite size scaling analysis, hyperscaling relations and the behavior of the correlation function we have obtained strong indications regarding the presence of quasi-long range order and the existence of a line of critical points in our system.

  6. Topological invariants of edge states for periodic two-dimensional models

    CERN Document Server

    Avila, Julio Cesar; Villegas-Blas, Carlos

    2012-01-01

    Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define topological invariants by considering the associated Bott-Maslov indices which can be easily calculated numerically. For time-reversal symmetric systems in the symplectic universality class this leads to a Z_2-invariant for the edge states. It is shown that the edge state invariants are related to Chern numbers of the bulk systems and also to (spin) edge currents, in the spirit of the theory of topological insulators.

  7. The Model for Two-dimensional Layout Optimization Problem with Performance Constraints and Its Optimality Function

    Institute of Scientific and Technical Information of China (English)

    Xu Zhang; En-min Feng

    2004-01-01

    This paper studies the two-dimensional layout optimization problem.An optimization model with performance constraints is presented.The layout problem is partitioned intofinite subproblems in terms of graph theory,in such a way of that each subproblem overcomes its on-o inature optimal variable.A minimax problem is constructed that is locally equivalent to each subproblem.By using this minimax problem,we present the optimality function for every subproblem and prove that the first order necessary optimality condition is satisfied at a point if and only if this point is a zero of optimality function.

  8. Heteroepitaxial growth modes with dislocations in a two-dimensional elastic lattice model

    Science.gov (United States)

    Katsuno, Hiroyasu; Uwaha, Makio; Saito, Yukio

    2008-11-01

    We study equilibrium shapes of adsorbate crystals by allowing a possibility of dislocations on an elastic substrate in a two-dimensional lattice model. The ground state energy is calculated numerically with the use of an elastic lattice Green's function. From the equilibrium shapes determined for various coverages, we infer the growth mode. As the misfit parameter increases, the growth mode changes from the Frank-van der Merwe (FM) to the Stranski-Krastanov (SK), further to the FM with dislocations for a parameter range of ordinary semiconductor materials. Conceivable growth modes such as the SK with dislocations appear in a parameter range between the SK and the FM with dislocations.

  9. Scaling and universality in the two-dimensional Ising model with a magnetic field.

    Science.gov (United States)

    Mangazeev, Vladimir V; Dudalev, Michael Yu; Bazhanov, Vladimir V; Batchelor, Murray T

    2010-06-01

    The scaling function of the two-dimensional Ising model on the square and triangular lattices is obtained numerically via Baxter's variational corner transfer-matrix approach. The use of Aharony-Fisher nonlinear scaling variables allowed us to perform calculations sufficiently away from the critical point and to confirm all predictions of the scaling and universality hypotheses. Our results are in excellent agreement with quantum field theory calculations of Fonseca and Zamolodchikov as well as with many previously known exact and numerical calculations, including susceptibility results by Barouch, McCoy, Tracy, and Wu.

  10. Two-dimensional airflow modeling underpredicts the wind velocity over dunes.

    Science.gov (United States)

    Michelsen, Britt; Strobl, Severin; Parteli, Eric J R; Pöschel, Thorsten

    2015-11-17

    We investigate the average turbulent wind field over a barchan dune by means of Computational Fluid Dynamics. We find that the fractional speed-up ratio of the wind velocity over the three-dimensional barchan shape differs from the one obtained from two-dimensional calculations of the airflow over the longitudinal cut along the dune's symmetry axis - that is, over the equivalent transverse dune of same size. This finding suggests that the modeling of the airflow over the central slice of barchan dunes is insufficient for the purpose of the quantitative description of barchan dune dynamics as three-dimensional flow effects cannot be neglected.

  11. Two-dimensional airflow modeling underpredicts the wind velocity over dunes

    OpenAIRE

    Britt Michelsen; Severin Strobl; Parteli, Eric J. R.; Thorsten Pöschel

    2015-01-01

    We investigate the average turbulent wind field over a barchan dune by means of Computational Fluid Dynamics. We find that the fractional speed-up ratio of the wind velocity over the three-dimensional barchan shape differs from the one obtained from two-dimensional calculations of the airflow over the longitudinal cut along the dune’s symmetry axis — that is, over the equivalent transverse dune of same size. This finding suggests that the modeling of the airflow over the central slice of barc...

  12. Hamiltonian dynamics of the two-dimensional lattice {phi}{sup 4} model

    Energy Technology Data Exchange (ETDEWEB)

    Caiani, Lando [Scuola Internazionale Superiore di Studi Avanzati (SISSA/ISAS), Trieste (Italy); Casetti, Lapo [Istituto Nazionale di Fisica della Materia (INFM), Unita di Ricerca del Politecnico di Torino, Dipartimento di Fisica, Politecnico di Torino, Turin (Italy); Pettini, Marco [Osservatorio Astrofisico di Arcetri, Florence (Italy)

    1998-04-17

    The Hamiltonian dynamics of the classical {phi}{sup 4} model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the presence of the continuous phase transition at a finite energy density and are consistent both qualitatively and quantitatively with the predictions of equilibrium statistical mechanics. The Hamiltonian microscopic dynamics also exhibits critical slowing down close to the transition. Moreover, the relationship between chaos and the phase transition is considered, and interpreted in the light of a geometrization of dynamics. (author)

  13. The Mott metal-insulator transition in half-filled two-dimensional Hubbard models

    Directory of Open Access Journals (Sweden)

    Peyman Sahebsara

    2008-06-01

    Full Text Available We study the Mott transition in the two dimensional Hubbard model by using the variational cluster approximation. The transition potential obtained is roughly Uc ≈ 2 and 6 for square and triangular lattices, respectively. A comparison between results of this approximation and other quantum cluster methods is presented. Our zero-temperature calculation at strong coupling show that the transition on the triangular and square lattices occur at lower values of compared with other numerical techniques such as DMFT, CDMFT, and DCA. We also study the thermodynamic limit by an extrapolation to infinite size.

  14. Phase Diagram of the Two-Dimensional Ising Model with Dipolar Interaction

    Institute of Scientific and Technical Information of China (English)

    SUN Gang; CHU Qian-Jin

    2001-01-01

    We treat the two-dimensional Ising model with the dipolar interaction by the numerical calculation under the restriction that the spin configurations are distributed with a 4 × 4 period. The phase diagram with respect to temperature and dipolar interaction strength is constructed. Most characters of the phase diagram are consistent with those obtained in the references by the Monte Carlo simulation, except that we find a new rectangle phase, which is ordered in the spin structure with the 1 × 2 rectangle.

  15. Nonlinear kinetic modeling and simulations of Raman scattering in a two-dimensional geometry

    Directory of Open Access Journals (Sweden)

    Bénisti Didier

    2013-11-01

    Full Text Available In this paper, we present our nonlinear kinetic modeling of stimulated Raman scattering (SRS by the means of envelope equations, whose coefficients have been derived using a mixture of perturbative and adiabatic calculations. First examples of the numerical resolution of these envelope equations in a two-dimensional homogeneous plasma are given, and the results are compared against those of particle-in-cell (PIC simulations. These preliminary comparisons are encouraging since our envelope code provides threshold intensities consistent with those of PIC simulations while requiring computational resources reduced by 4 to 5 orders of magnitude compared to full-kinetic codes.

  16. An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows

    Energy Technology Data Exchange (ETDEWEB)

    Snider, D.M. [SAIC, Albuquerque, NM (United States); O`Rourke, P.J. [Los Alamos National Lab., NM (United States); Andrews, M.J. [Texas A and M Univ., College Station, TX (United States). Dept. of Mechanical Engineering

    1997-06-01

    A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.

  17. Nebular Spectra of SN 1998bw Revisited: Detailed Study by One and Two Dimensional Models

    CERN Document Server

    Maeda, K; Mazzali, P A; Deng, J

    2006-01-01

    Refined one- and two-dimensional models for the nebular spectra of the hyper-energetic Type Ic supernova (SN) 1998bw, associated with the gamma-ray burst GRB980425, from 125 to 376 days after B-band maximum are presented. One dimensional, spherically symmetric spectrum synthesis calculations show that reproducing features in the observed spectra, i.e., the sharply peaked [OI] 6300\\AA doublet and MgI] 4570\\AA emission, and the broad [FeII] blend around 5200\\AA, requires the existence of a high-density O-rich core expanding at low velocities ($\\lsim 8,000$ km s$^{-1}$) and of Fe-rich material moving faster than the O-rich material. Synthetic spectra at late phases from aspherical (bipolar) explosion models are also computed with a two-dimensional spectrum synthesis code. The above features are naturally explained by the aspherical model if the explosion is viewed from a direction close to the axis of symmetry ($\\sim 30^{\\rm o}$), since the aspherical model yields a high-density O-rich region confined along the ...

  18. Solution of the Complex Action Problem in the Potts Model for Dense QCD

    CERN Document Server

    Alford, M; Cox, J; Wiese, U J

    2001-01-01

    Monte Carlo simulations of lattice QCD at non-zero baryon chemical potential $\\mu$ suffer from the notorious complex action problem. We consider QCD with static quarks coupled to a large chemical potential. This leaves us with an SU(3) Yang-Mills theory with a complex action containing the Polyakov loop. Close to the deconfinement phase transition the qualitative features of this theory, in particular its Z(3) symmetry properties, are captured by the 3-d 3-state Potts model. We solve the complex action problem in the Potts model by using a cluster algorithm. The improved estimator for the $\\mu$-dependent part of the Boltzmann factor is real and positive and is used for importance sampling. We localize the critical endpoint of the first order deconfinement phase transition line and find consistency with universal 3-d Ising behavior. We also calculate the static quark-quark, quark-anti-quark, and anti-quark-anti-quark potentials which show screening as expected for a system with non-zero baryon density.

  19. Structural propensities of kinase family proteins from a Potts model of residue co-variation.

    Science.gov (United States)

    Haldane, Allan; Flynn, William F; He, Peng; Vijayan, R S K; Levy, Ronald M

    2016-08-01

    Understanding the conformational propensities of proteins is key to solving many problems in structural biology and biophysics. The co-variation of pairs of mutations contained in multiple sequence alignments of protein families can be used to build a Potts Hamiltonian model of the sequence patterns which accurately predicts structural contacts. This observation paves the way to develop deeper connections between evolutionary fitness landscapes of entire protein families and the corresponding free energy landscapes which determine the conformational propensities of individual proteins. Using statistical energies determined from the Potts model and an alignment of 2896 PDB structures, we predict the propensity for particular kinase family proteins to assume a "DFG-out" conformation implicated in the susceptibility of some kinases to type-II inhibitors, and validate the predictions by comparison with the observed structural propensities of the corresponding proteins and experimental binding affinity data. We decompose the statistical energies to investigate which interactions contribute the most to the conformational preference for particular sequences and the corresponding proteins. We find that interactions involving the activation loop and the C-helix and HRD motif are primarily responsible for stabilizing the DFG-in state. This work illustrates how structural free energy landscapes and fitness landscapes of proteins can be used in an integrated way, and in the context of kinase family proteins, can potentially impact therapeutic design strategies. © 2016 The Protein Society.

  20. Measuring and modeling two-dimensional irrigation infiltration under film-mulched furrows

    Institute of Scientific and Technical Information of China (English)

    YongYong Zhang; PuTe Wu; XiNing Zhao; WenZhi Zhao

    2016-01-01

    Furrow irrigation with film-mulched agricultural beds is being promoted in the arid region of northwest China because it improves water utilization. Two-dimensional infiltration patterns under film-mulched furrows can provide guidelines and criteria for irrigation design and operation. Our objective was to investigate soil water dynamics during ponding irrigation infiltration of mulched furrows in a cross-sectional ridge-furrow configuration, using laboratory experiments and math-ematical simulations. Six experimental treatments, with two soil types (silt loam and sandy loam), were investigated to monitor the wetting patterns and soil water distribution in a cuboid soil chamber. Irrigation of mulched furrows clearly increased water lateral infiltration on ridge shoulders and ridges, due to enhancement of capillary driving force. Increases to both initial soil water content (SWC) and irrigation water level resulted in increased wetted soil volume. Empirical regression equations accurately estimated the wetted lateral distance (Rl) and downward distance (Rd) with elapsed time in a variably wetted soil medium. Optimization of model parameters followed by the Inverse approach resulted in satisfactory agreement between observed and predicted cumulative infiltration and SWC. On the basis of model calibration, HYDRUS-2D model can accurately simulate two-dimensional soil water dynamics under irrigation of mulched furrows. There were significant differences in wetting patterns between unmulched and mulched furrow irrigation using HYDRUS-2D simulation. The Rd under the mulched furrows was 32.14%less than the unmulched furrows. Therefore, film-mulched furrows are recommended in a furrow irrigation system.

  1. A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows

    CERN Document Server

    Mininni, P D; Pouquet, A G

    2004-01-01

    We explore some consequences of the ``alpha model,'' also called the ``Lagrangian-averaged'' model, for two-dimensional incompressible magnetohydrodynamic (MHD) turbulence. This model is an extension of the smoothing procedure in fluid dynamics which filters velocity fields locally while leaving their associated vorticities unsmoothed, and has proved useful for high Reynolds number turbulence computations. We consider several known effects (selective decay, dynamic alignment, inverse cascades, and the probability distribution functions of fluctuating turbulent quantities) in magnetofluid turbulence and compare the results of numerical solutions of the primitive MHD equations with their alpha-model counterparts' performance for the same flows, in regimes where available resolution is adequate to explore both. The hope is to justify the use of the alpha model in regimes that lie outside currently available resolution, as will be the case in particular in three-dimensional geometry or for magnetic Prandtl number...

  2. An evaluation of the role of eddy diffusion in stratospheric interactive two-dimensional models

    Science.gov (United States)

    Schneider, Hans R.; Ko, Malcolm K. W.; Sze, Nien Dak; Shi, Guang-Yu; Wang, Wei-Chyung

    1989-01-01

    An interactive two-dimensional model of the stratosphere, consisting of a primitive equation dynamics module, a simplified HO(x) ozone model, and a full radiative transfer scheme, is used to study the effect of eddy diffusion in the model. Consideration is given to the effects of nonlocal forcing from dissipation in the model troposphere and frictional drag at mesospheric levels, mechanical damping in the stratosphere itself, and potential vorticity flux due to large scale waves. It is found that the ozone distributions generated with the model are very sensitive to the choice of values for the friction and the eddy diffusion coefficients. It is shown that reasonable latitudinal gradients of ozone may be obtained by using small values for the mechanical damping for the mid- and high-latitude stratopsphere.

  3. Two dimensional, two fluid model for sodium boiling in LMFBR fuel assemblies

    Energy Technology Data Exchange (ETDEWEB)

    Granziera, M.R.; Kazimi, M.S.

    1980-05-01

    A two dimensional numerical model for the simulation of sodium boiling transient was developed using the two fluid set of conservation equations. A semiimplicit numerical differencing scheme capable of handling the problems associated with the ill-posedness implied by the complex characteristic roots of the two fluid problems was used, which took advantage of the dumping effect of the exchange terms. Of particular interest in the development of the model was the identification of the numerical problems caused by the strong disparity between the axial and radial dimensions of fuel assemblies. A solution to this problem was found which uses the particular geometry of fuel assemblies to accelerate the convergence of the iterative technique used in the model. Three sodium boiling experiments were simulated with the model, with good agreement between the experimental results and the model predictions.

  4. One- and two-dimensional Stirling machine simulation using experimentally generated reversing flow turbuulence models

    Energy Technology Data Exchange (ETDEWEB)

    Goldberg, L.F. [Univ. of Minnesota, Minneapolis, MN (United States)

    1990-08-01

    The activities described in this report do not constitute a continuum but rather a series of linked smaller investigations in the general area of one- and two-dimensional Stirling machine simulation. The initial impetus for these investigations was the development and construction of the Mechanical Engineering Test Rig (METR) under a grant awarded by NASA to Dr. Terry Simon at the Department of Mechanical Engineering, University of Minnesota. The purpose of the METR is to provide experimental data on oscillating turbulent flows in Stirling machine working fluid flow path components (heater, cooler, regenerator, etc.) with particular emphasis on laminar/turbulent flow transitions. Hence, the initial goals for the grant awarded by NASA were, broadly, to provide computer simulation backup for the design of the METR and to analyze the results produced. This was envisaged in two phases: First, to apply an existing one-dimensional Stirling machine simulation code to the METR and second, to adapt a two-dimensional fluid mechanics code which had been developed for simulating high Rayleigh number buoyant cavity flows to the METR. The key aspect of this latter component was the development of an appropriate turbulence model suitable for generalized application to Stirling simulation. A final-step was then to apply the two-dimensional code to an existing Stirling machine for which adequate experimental data exist. The work described herein was carried out over a period of three years on a part-time basis. Forty percent of the first year`s funding was provided as a match to the NASA funds by the Underground Space Center, University of Minnesota, which also made its computing facilities available to the project at no charge.

  5. Multi-scale modeling in morphogenesis: a critical analysis of the cellular Potts model.

    Science.gov (United States)

    Voss-Böhme, Anja

    2012-01-01

    Cellular Potts models (CPMs) are used as a modeling framework to elucidate mechanisms of biological development. They allow a spatial resolution below the cellular scale and are applied particularly when problems are studied where multiple spatial and temporal scales are involved. Despite the increasing usage of CPMs in theoretical biology, this model class has received little attention from mathematical theory. To narrow this gap, the CPMs are subjected to a theoretical study here. It is asked to which extent the updating rules establish an appropriate dynamical model of intercellular interactions and what the principal behavior at different time scales characterizes. It is shown that the longtime behavior of a CPM is degenerate in the sense that the cells consecutively die out, independent of the specific interdependence structure that characterizes the model. While CPMs are naturally defined on finite, spatially bounded lattices, possible extensions to spatially unbounded systems are explored to assess to which extent spatio-temporal limit procedures can be applied to describe the emergent behavior at the tissue scale. To elucidate the mechanistic structure of CPMs, the model class is integrated into a general multiscale framework. It is shown that the central role of the surface fluctuations, which subsume several cellular and intercellular factors, entails substantial limitations for a CPM's exploitation both as a mechanistic and as a phenomenological model.

  6. Multi-scale modeling in morphogenesis: a critical analysis of the cellular Potts model.

    Directory of Open Access Journals (Sweden)

    Anja Voss-Böhme

    Full Text Available Cellular Potts models (CPMs are used as a modeling framework to elucidate mechanisms of biological development. They allow a spatial resolution below the cellular scale and are applied particularly when problems are studied where multiple spatial and temporal scales are involved. Despite the increasing usage of CPMs in theoretical biology, this model class has received little attention from mathematical theory. To narrow this gap, the CPMs are subjected to a theoretical study here. It is asked to which extent the updating rules establish an appropriate dynamical model of intercellular interactions and what the principal behavior at different time scales characterizes. It is shown that the longtime behavior of a CPM is degenerate in the sense that the cells consecutively die out, independent of the specific interdependence structure that characterizes the model. While CPMs are naturally defined on finite, spatially bounded lattices, possible extensions to spatially unbounded systems are explored to assess to which extent spatio-temporal limit procedures can be applied to describe the emergent behavior at the tissue scale. To elucidate the mechanistic structure of CPMs, the model class is integrated into a general multiscale framework. It is shown that the central role of the surface fluctuations, which subsume several cellular and intercellular factors, entails substantial limitations for a CPM's exploitation both as a mechanistic and as a phenomenological model.

  7. Remarks on Two-Dimensional Power Correction in Soft Wall Model

    Institute of Scientific and Technical Information of China (English)

    HUANG Tao; ZUO Fen

    2008-01-01

    We present a direct derivation of the two-point correlation function of the vector current in the soft wall model by using the AdS/CFT dictionary. The resulting correlator is exactly the same as the one previously obtained from dispersion relation with the same spectral function as in this model. The coeffcient C2 of the two-dimensional power correction is found to be C2 = -c/2 with c the slope of the Regge trajectory, rather than C2 = -c/3 derived from the strategy of the first quantized string theory. Taking the slope of the p trajectory c ≈ 0.9 CeV2 as input, we then obtain C2 ≈ -0.45 GeV2. The gluon condensate is found to be (αsG2) ≈ 0.064 GeV4, which is almost identical to the QCD sum rule estimation. By comparing these two equivalent derivation of the correlator of scalar glueball operator, we demonstrate that the two-dimensionai correction cannot be eliminated by including the non-leading solution in the bulk-to-boundary propagator, as carried out by Colangelo et al.[arXiv:0711.4747].In other words, the two-dimensional correction does exist in the scalar glueball case. Also it is manifest by using the dispersion relation that the minus sign of gluon condensate and violation of the low energy theorem are related to the subtraction scheme.

  8. A two dimensional thermal network model for a photovoltaic solar wall

    Energy Technology Data Exchange (ETDEWEB)

    Dehra, Himanshu [1-140 Avenue Windsor, Lachine, Quebec (Canada)

    2009-11-15

    A two dimensional thermal network model is proposed to predict the temperature distribution for a section of photovoltaic solar wall installed in an outdoor room laboratory in Concordia University, Montreal, Canada. The photovoltaic solar wall is constructed with a pair of glass coated photovoltaic modules and a polystyrene filled plywood board as back panel. The active solar ventilation through a photovoltaic solar wall is achieved with an exhaust fan fixed in the outdoor room laboratory. The steady state thermal network nodal equations are developed for conjugate heat exchange and heat transport for a section of a photovoltaic solar wall. The matrix solution procedure is adopted for formulation of conductance and heat source matrices for obtaining numerical solution of one dimensional heat conduction and heat transport equations by performing two dimensional thermal network analyses. The temperature distribution is predicted by the model with measurement data obtained from the section of a photovoltaic solar wall. The effect of conduction heat flow and multi-node radiation heat exchange between composite surfaces is useful for predicting a ventilation rate through a solar ventilation system. (author)

  9. Dual geometric worm algorithm for two-dimensional discrete classical lattice models

    Science.gov (United States)

    Hitchcock, Peter; Sørensen, Erik S.; Alet, Fabien

    2004-07-01

    We present a dual geometrical worm algorithm for two-dimensional Ising models. The existence of such dual algorithms was first pointed out by Prokof’ev and Svistunov [N. Prokof’ev and B. Svistunov, Phys. Rev. Lett. 87, 160601 (2001)]. The algorithm is defined on the dual lattice and is formulated in terms of bond variables and can therefore be generalized to other two-dimensional models that can be formulated in terms of bond variables. We also discuss two related algorithms formulated on the direct lattice, applicable in any dimension. These latter algorithms turn out to be less efficient but of considerable intrinsic interest. We show how such algorithms quite generally can be “directed” by minimizing the probability for the worms to erase themselves. Explicit proofs of detailed balance are given for all the algorithms. In terms of computational efficiency the dual geometrical worm algorithm is comparable to well known cluster algorithms such as the Swendsen-Wang and Wolff algorithms, however, it is quite different in structure and allows for a very simple and efficient implementation. The dual algorithm also allows for a very elegant way of calculating the domain wall free energy.

  10. Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model

    Science.gov (United States)

    Ehlers, G.; White, S. R.; Noack, R. M.

    2017-03-01

    The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid-real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at n =0.875 filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both U /t =4.0 and 8.0 . We find that the strength of the charge ordering depends on U /t and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.

  11. Development and validation of a two-dimensional fast-response flood estimation model

    Energy Technology Data Exchange (ETDEWEB)

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

    2009-01-01

    A finite difference formulation of the shallow water equations using an upwind differencing method was developed maintaining computational efficiency and accuracy such that it can be used as a fast-response flood estimation tool. The model was validated using both laboratory controlled experiments and an actual dam breach. Through the laboratory experiments, the model was shown to give good estimations of depth and velocity when compared to the measured data, as well as when compared to a more complex two-dimensional model. Additionally, the model was compared to high water mark data obtained from the failure of the Taum Sauk dam. The simulated inundation extent agreed well with the observed extent, with the most notable differences resulting from the inability to model sediment transport. The results of these validation studies complex two-dimensional model. Additionally, the model was compared to high water mark data obtained from the failure of the Taum Sauk dam. The simulated inundation extent agreed well with the observed extent, with the most notable differences resulting from the inability to model sediment transport. The results of these validation studies show that a relatively numerical scheme used to solve the complete shallow water equations can be used to accurately estimate flood inundation. Future work will focus on further reducing the computation time needed to provide flood inundation estimates for fast-response analyses. This will be accomplished through the efficient use of multi-core, multi-processor computers coupled with an efficient domain-tracking algorithm, as well as an understanding of the impacts of grid resolution on model results.

  12. Research of MPPT for photovoltaic generation based on two-dimensional cloud model

    Science.gov (United States)

    Liu, Shuping; Fan, Wei

    2013-03-01

    The cloud model is a mathematical representation to fuzziness and randomness in linguistic concepts. It represents a qualitative concept with expected value Ex, entropy En and hyper entropy He, and integrates the fuzziness and randomness of a linguistic concept in a unified way. This model is a new method for transformation between qualitative and quantitative in the knowledge. This paper is introduced MPPT (maximum power point tracking, MPPT) controller based two- dimensional cloud model through analysis of auto-optimization MPPT control of photovoltaic power system and combining theory of cloud model. Simulation result shows that the cloud controller is simple and easy, directly perceived through the senses, and has strong robustness, better control performance.

  13. Eighth-order phase-field-crystal model for two-dimensional crystallization

    Science.gov (United States)

    Jaatinen, A.; Ala-Nissila, T.

    2010-12-01

    We present a derivation of the recently proposed eighth-order phase-field crystal model [A. Jaatinen , Phys. Rev. E 80, 031602 (2009)10.1103/PhysRevE.80.031602] for the crystallization of a solid from an undercooled melt. The model is used to study the planar growth of a two-dimensional hexagonal crystal, and the results are compared against similar results from dynamical density functional theory of Marconi and Tarazona, as well as other phase-field crystal models. We find that among the phase-field crystal models studied, the eighth-order fitting scheme gives results in good agreement with the density functional theory for both static and dynamic properties, suggesting it is an accurate and computationally efficient approximation to the density functional theory.

  14. A two-dimensional analytical model for short channel junctionless double-gate MOSFETs

    Science.gov (United States)

    Jiang, Chunsheng; Liang, Renrong; Wang, Jing; Xu, Jun

    2015-05-01

    A physics-based analytical model of electrostatic potential for short-channel junctionless double-gate MOSFETs (JLDGMTs) operated in the subthreshold regime is proposed, in which the full two-dimensional (2-D) Poisson's equation is solved in channel region by a method of series expansion similar to Green's function. The expression of the proposed electrostatic potential is completely rigorous and explicit. Based on this expression, analytical models of threshold voltage, subthreshold swing, and subthreshold drain current for JLDGMTs were derived. Subthreshold behavior was studied in detail by changing different device parameters and bias conditions, including doping concentration, channel thickness, gate length, gate oxide thickness, drain voltage, and gate voltage. Results predicted by all the analytical models agree well with numerical solutions from the 2-D simulator. These analytical models can be used to investigate the operating mechanisms of nanoscale JLDGMTs and to optimize their device performance.

  15. Two-dimensional modeling of electrochemical and transport phenomena in the porous structures of a PEMFC

    Energy Technology Data Exchange (ETDEWEB)

    Sahraoui, Melik [Institut Preparatoire aux Etudes d' Ingenieurs de Tunis (IPEIT) (Tunisia); Kharrat, Chafik; Halouani, Kamel [UR: Micro-Electro-Thermal Systems (METS-ENIS), Industrial Energy Systems Group, Institut Preparatoire aux Etudes d' Ingenieurs de Sfax (IPEIS), University of Sfax, B.P: 1172, 3018 Sfax (Tunisia)

    2009-04-15

    A two-dimensional CFD model of PEM fuel cell is developed by taking into account the electrochemical, mass and heat transfer phenomena occurring in all of its regions simultaneously. The catalyst layers and membrane are each considered as distinct regions with finite thickness and calculated properties such as permeability, local protonic conductivity, and local dissolved water diffusion. This finite thickness model enables to model accurately the protonic current in these regions with higher accuracy than using an infinitesimal interface. In addition, this model takes into account the effect of osmotic drag in the membrane and catalyst layers. General boundary conditions are implemented in a way taking into consideration any given species concentration at the fuel cell inlet, such as water vapor which is a very important parameter in determining the efficiency of fuel cells. Other operating parameters such as temperature, pressure and porosity of the porous structure are also investigated to characterize their effect on the fuel cell efficiency. (author)

  16. Simple Screened Hydrogen Model of Excitons in Two-Dimensional Materials

    DEFF Research Database (Denmark)

    Olsen, Thomas; Latini, Simone; Rasmussen, Filip Anselm;

    2016-01-01

    We present a generalized hydrogen model for the binding energies (EB) and radii of excitons in two-dimensional (2D) materials that sheds light on the fundamental differences between excitons in two and three dimensions. In contrast to the well-known hydrogen model of three-dimensional (3D) excitons...... the recently observed linear scaling of exciton binding energies with band gap. It is also shown that the model accurately reproduces the nonhydrogenic Rydberg series in WS2 and can account for screening from the environment....... that only depends on the excitonic mass and the 2D polarizability α. The model is shown to produce accurate results for 51 transition metal dichalcogenides. Remarkably, over a wide range of polarizabilities the binding energy becomes independent of the mass and we obtain E2DB≈3/(4πα), which explains...

  17. Two-dimensional mathematical model of a reciprocating room-temperature Active Magnetic Regenerator

    DEFF Research Database (Denmark)

    Petersen, Thomas Frank; Pryds, Nini; Smith, Anders;

    2008-01-01

    heat exchanger. The model simulates the different steps of the AMR refrigeration cycle and evaluates the performance in terms of refrigeration capacity and temperature span between the two heat exchangers. The model was used to perform an analysis of an AMR with a regenerator made of gadolinium...... and water as the heat transfer fluid. The results show that the AMR is able to obtain a no-load temperature span of 10.9 K in a 1 T magnetic field with a corresponding work input of 93.0 kJ m−3 of gadolinium per cycle. The model shows significant temperature differences between the regenerator and the heat...... transfer fluid during the AMR cycle. This indicates that it is necessary to use two-dimensional models when a parallel-plate regenerator geometry is used....

  18. Evidence for an unconventional universality class from a two-dimensional dimerized quantum heisenberg model.

    Science.gov (United States)

    Wenzel, Sandro; Bogacz, Leszek; Janke, Wolfhard

    2008-09-19

    The two-dimensional J-J' dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio alpha=J'/J. The critical point of the order-disorder quantum phase transition in the J-J' model is determined as alpha_c=2.5196(2) by finite-size scaling for up to approximately 10 000 quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the J-J' model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.

  19. Finite Element Model for Failure Study of Two-Dimensional Triaxially Braided Composite

    Science.gov (United States)

    Li, Xuetao; Binienda, Wieslaw K.; Goldberg, Robert K.

    2010-01-01

    A new three-dimensional finite element model of two-dimensional triaxially braided composites is presented in this paper. This meso-scale modeling technique is used to examine and predict the deformation and damage observed in tests of straight sided specimens. A unit cell based approach is used to take into account the braiding architecture as well as the mechanical properties of the fiber tows, the matrix and the fiber tow-matrix interface. A 0 deg / plus or minus 60 deg. braiding configuration has been investigated by conducting static finite element analyses. Failure initiation and progressive degradation has been simulated in the fiber tows by use of the Hashin failure criteria and a damage evolution law. The fiber tow-matrix interface was modeled by using a cohesive zone approach to capture any fiber-matrix debonding. By comparing the analytical results to those obtained experimentally, the applicability of the developed model was assessed and the failure process was investigated.

  20. More on two-dimensional O (N ) models with N =(0 ,1 ) supersymmetry

    Science.gov (United States)

    Peterson, Adam J.; Kurianovych, Evgeniy; Shifman, Mikhail

    2016-03-01

    We study the behavior of two-dimensional supersymmetric connections of n copies of O (N ) models with an N =(0 ,1 ) heterotic deformation generated by a right-moving fermion. We develop the model in analogy with the connected N =(0 ,2 ) C P (N -1 ) models for the case of a single connecting fermionic superfield. We calculate the effective potential in the large-N limit and determine the vacuum field configurations. Similarly to other supersymmetry (SUSY) connected models we find that SUSY is unbroken under certain conditions despite the vanishing of the Witten index. Specifically, this preservation of SUSY occurs when we have an even number n of O (N ) families. As in previous cases we show that this result follows from a Zn symmetry under a particular exchange of the O (N ) families. This leads to a definition of a modified Witten index, which guarantees the preservation of SUSY in this case.

  1. Two dimensional solids and liquids influenced by small and large substrate potential

    DEFF Research Database (Denmark)

    Vives, E.; Lindgård, Per-Anker

    1991-01-01

    A general, continuous model for two dimensional solids and liquids on a substrate is studied by means of Monte Carlo simulation. The results can be applied to the case of adsorbed atoms or molecules on surfaces as well as intercalated compounds. We have focused on the study of the melting...... experiments, in particular for weak potentials and large atomic mean square displacements. New results for large potentials are also presented and possible relations to the Potts lattice gas description studied....

  2. Two-dimensional models as testing ground for principles and concepts of local quantum physics

    Science.gov (United States)

    Schroer, Bert

    2006-02-01

    In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g., chiral models, factorizing models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work, I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: (1) a modular interpretation of the chiral model Diff( S)-covariance with a close connection to the recently formulated local covariance principle for QFT in curved spacetime and (2) a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational chiral theories. The SL (2, Z) modular Verlinde relation is a special case of this thermal duality and (within the family of rational models) the matrix S appearing in the thermal duality relation becomes identified with the statistics character matrix S. The relevant angular "Euclideanization" is done in the setting of the Tomita-Takesaki modular formalism of operator algebras. I find it appropriate to dedicate this work to the memory of J.A. Swieca with whom I shared the interest in two-dimensional models as a testing ground for QFT for more than one decade. This is a significantly extended version of an "Encyclopedia of Mathematical Physics" contribution hep-th/0502125.

  3. Two-dimensional models as testing ground for principles and concepts of local quantum physics

    Energy Technology Data Exchange (ETDEWEB)

    Schroer, Bert [FU Berlin (Germany). Institut fuer Theoretische Physik

    2005-04-15

    In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g. chiral models, factoring models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: (1) a modular interpretation of the chiral model Diff(S)-covariance with a close connection to the recently formulated local covariance principle for QFT in curved spacetime and (2) a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational chiral theories. The SL(2,Z) modular Verlinde relation is a special case of this thermal duality and (within the family of rational models) the matrix S appearing in the thermal duality relation becomes identified with the statistics character matrix S. The relevant angular 'Euclideanization' is done in the setting of the Tomita-Takesaki modular formalism of operator algebras. I find it appropriate to dedicate this work to the memory of J. A. Swieca with whom I shared the interest in two-dimensional models as a testing ground for QFT for more than one decade. This is a significantly extended version of an 'Encyclopedia of Mathematical Physics' contribution hep-th/0502125. (author)

  4. Tricritical point for the three-dimensional disordered Potts model ( q = 3) on a simple cubic lattice

    Science.gov (United States)

    Babaev, A. B.; Murtazaev, A. K.

    2017-03-01

    Slightly diluted magnetic systems described by the disordered three-dimensional Potts model with the number of spin states q = 3 are studied in the case of a simple cubic lattice. The position of the tricritical point in the phase diagram is determined using the histogram Monte Carlo technique.

  5. Two-dimensional models of early-type fast rotating stars: the ESTER project

    CERN Document Server

    Rieutord, Michel

    2015-01-01

    In this talk I present the latest results of the ESTER project that has taken up the challenge of building two dimensional (axisymmetric) models of stars rotating at any rotation rate. In particular, I focus on main sequence massive and intermediate mass stars. I show what should be expected in such stars as far as the differential rotation and the associated meridional circulation are concerned, notably the emergence of a Stewartson layer along the tangent cylinder of the core. I also indicate what may be inferred about the evolution of an intermediate-mass star at constant angular momentum and how Be stars may form. I finally give some comparisons between models and observations of the gravity darkening on some nearby fast rotators as it has been derived from interferometric observations. In passing, I also discuss how 2D models can help to recover the fundamental parameters of a star.

  6. Improved modeling and numerics to solve two-dimensional elliptic fluid flow and heat transfer problems

    Science.gov (United States)

    Chan, B. C.

    1986-05-01

    A basic, limited scope, fast-running computer model is presented for the solution of two-dimensional, transient, thermally-coupled fluid flow problems. This model is to be the module in the SSC (an LMFBR thermal-hydraulic systems code) for predicting complex flow behavior, as occurs in the upper plenum of the loop-type design or in the sodium pool of the pool-type design. The nonlinear Navier-Stokes equations and the two-equation (two-variable) transport model of turbulence are reduced to a set of linear algebraic equations in an implicit finite difference scheme, based on the control volume approach. These equations are solved iteratively in a line-by-line procedure using the tri-diagonal matrix algorithm. The results of calculational examplers are shown in the computer-generated plots.

  7. Hydrodynamics for a model of a confined quasi-two-dimensional granular gas.

    Science.gov (United States)

    Brey, J Javier; Buzón, V; Maynar, P; García de Soria, M I

    2015-05-01

    The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and momentum fluxes are calculated to Navier-Stokes order, and the associated transport coefficients are explicitly determined as functions of the coefficient of normal restitution and the velocity parameter involved in the definition of the model. Also an Euler transport term contributing to the energy transport equation is considered. This term arises from the gradient expansion of the rate of change of the temperature due to the inelasticity of collisions, and it vanishes for elastic systems. The hydrodynamic equations are particularized for the relevant case of a system in the homogeneous steady state. The relationship with previous works is analyzed.

  8. Present status of two-dimensional ESTER models: Application to Be stars

    CERN Document Server

    Rieutord, M

    2013-01-01

    ESTER two-dimensional models solve the steady state structure of fast rotating early-type stars including the large scale flows associated with the baroclinicity of the radiative zones. Models are compared successfully to the fundamental parameters of the two main components of the triple system $\\delta$ Velorum that have been derived from interferometric and orbit measurements. Testing the models on the Be star Achernar ($\\alpha$ Eri), we cannot reproduce the data and conclude that this star has left the main sequence and is likely crossing the Herzsprung gap. Computing main sequence evolution of fast rotating stars at constant angular momentum shows that their criticality increases with time suggesting that the Be phenomenon and the ensuing mass ejections is the result of evolution.

  9. An extended two-dimensional mathematical model of vertical ring furnaces

    Science.gov (United States)

    Peter, S.; Charette, A.; Bui, R. T.; Tomsett, A.; Potocnik, V.

    1996-04-01

    An extended two-dimensional (2-D+) mathematical model of vertical anode baking furnaces has been developed. The work was motivated by the fact that a previous 2-D model was unable to predict the nonuniform baking in the transverse direction, i.e., perpendicular to the longitudinal axis of the furnace. The modeling strategy based on dividing each section in four zones (underlid, pit, underpit, head wall and fire shaft zones) and introducing two symmetry planes in the exterior pits is explained. The basic heat-transfer relations used are also detailed. Selected results shown include draught and oxygen concentration profiles in the flue, gas and anode temperature distributions and fuel consumption in the back fire ramp. Simulation and experimental results are compared.

  10. A two-dimensional model for the study of interpersonal attraction.

    Science.gov (United States)

    Montoya, R Matthew; Horton, Robert S

    2014-02-01

    We describe a model for understanding interpersonal attraction in which attraction can be understood as a product of the initial evaluations we make about others. The model posits that targets are evaluated on two basic dimensions, capacity and willingness, such that affective and behavioral attraction result from evaluations of (a) a target's capacity to facilitate the perceiver's goals/needs and (b) a target's potential willingness to facilitate those goals/needs. The plausibility of the two-dimensional model of attraction is evaluated vis-à-vis the extant literature on various attraction phenomena including the reciprocity of liking effect, pratfall effect, matching hypothesis, arousal effects, and similarity effect. We conclude that considerable evidence across a wide range of phenomena supports the idea that interpersonal attraction is principally determined by inferences about the target's capacity and willingness.

  11. Statistical mechanics of two-dimensional foams: Physical foundations of the model.

    Science.gov (United States)

    Durand, Marc

    2015-12-01

    In a recent series of papers, a statistical model that accounts for correlations between topological and geometrical properties of a two-dimensional shuffled foam has been proposed and compared with experimental and numerical data. Here, the various assumptions on which the model is based are exposed and justified: the equiprobability hypothesis of the foam configurations is argued. The range of correlations between bubbles is discussed, and the mean-field approximation that is used in the model is detailed. The two self-consistency equations associated with this mean-field description can be interpreted as the conservation laws of number of sides and bubble curvature, respectively. Finally, the use of a "Grand-Canonical" description, in which the foam constitutes a reservoir of sides and curvature, is justified.

  12. Two-dimensional numerical modeling of the longitudinal and lateral channel deformations in alluvial rivers

    Institute of Scientific and Technical Information of China (English)

    XIA Junqiang; WANG Guangqian; WU Baosheng

    2004-01-01

    Two kinds of bank erosion mechanisms were analyzed, including fluvial and non-fluvial controlled mechanisms, and mechanical methods of simulating the erosion processes of cohesive, non-cohesive and composite riverbanks were improved. Then a two-dimensional numerical model of the channel deformation was developed, consisting of a 2D flow and sediment transport submodel and bank-erosion submodels of different soil riverbanks. In the model, a new technique for updating the bank geometry during the bed evolution was presented, which combines closely two kinds of submodels. The proposed model is capable of not only predicting the processes of flood routing and longitudinal channel deformation in natural rivers, but also simulating the processes of lateral channel deformation, especially the processes of lateral erosion and failure of cohesive, non-cohesive and composite riverbanks.

  13. Two-dimensional modeling of volatile organic compounds adsorption onto beaded activated carbon.

    Science.gov (United States)

    Tefera, Dereje Tamiru; Jahandar Lashaki, Masoud; Fayaz, Mohammadreza; Hashisho, Zaher; Philips, John H; Anderson, James E; Nichols, Mark

    2013-10-15

    A two-dimensional heterogeneous computational fluid dynamics model was developed and validated to study the mass, heat, and momentum transport in a fixed-bed cylindrical adsorber during the adsorption of volatile organic compounds (VOCs) from a gas stream onto a fixed bed of beaded activated carbon (BAC). Experimental validation tests revealed that the model predicted the breakthrough curves for the studied VOCs (acetone, benzene, toluene, and 1,2,4-trimethylbenzene) as well as the pressure drop and temperature during benzene adsorption with a mean relative absolute error of 2.6, 11.8, and 0.8%, respectively. Effects of varying adsorption process variables such as carrier gas temperature, superficial velocity, VOC loading, particle size, and channelling were investigated. The results obtained from this study are encouraging because they show that the model was able to accurately simulate the transport processes in an adsorber and can potentially be used for enhancing absorber design and operation.

  14. Two-Dimensional ARMA Modeling for Breast Cancer Detection and Classification

    CERN Document Server

    Bouaynaya, Nidhal; Schonfeld, Dan

    2009-01-01

    We propose a new model-based computer-aided diagnosis (CAD) system for tumor detection and classification (cancerous v.s. benign) in breast images. Specifically, we show that (x-ray, ultrasound and MRI) images can be accurately modeled by two-dimensional autoregressive-moving average (ARMA) random fields. We derive a two-stage Yule-Walker Least-Squares estimates of the model parameters, which are subsequently used as the basis for statistical inference and biophysical interpretation of the breast image. We use a k-means classifier to segment the breast image into three regions: healthy tissue, benign tumor, and cancerous tumor. Our simulation results on ultrasound breast images illustrate the power of the proposed approach.

  15. Two-dimensional mathematical model of a packed bed dryer and experimentation

    Energy Technology Data Exchange (ETDEWEB)

    Basirat-Tabrizi, H.; Saffar-Avval, M.; Assarie, M.R. [Amirkabir University of Technology, Tehran (Iran). Dept. of Mechanical Engineering

    2002-04-01

    A comprehensive heat and mass transfer model, based on the Eulerian two fluid model (TFM), developed for a packed-bed-drying process. The temperature and moisture content in a particle was considered with the conjugate effects between the gas and particles in a packed bed. Numerical study of the model was carried out on two-dimensional, axi-symmetrical cylindrical coordinates in order to investigate the effects of the different parameters such as particle size, variation of inlet gas temperature on the moisture content, and temperature of solid and gas outlet. For experimental observations, an experimental apparatus was designed and utilized. The theoretical results were then compared to the experimental data, which indicated good agreement. (author)

  16. Synchronizability of Small-World Networks Generated from a Two-Dimensional Kleinberg Model

    Directory of Open Access Journals (Sweden)

    Yi Zhao

    2013-01-01

    Full Text Available This paper investigates the synchronizability of small-world networks generated from a two-dimensional Kleinberg model, which is more general than NW small-world network. The three parameters of the Kleinberg model, namely, the distance of neighbors, the number of edge-adding, and the edge-adding probability, are analyzed for their impacts on its synchronizability and average path length. It can be deduced that the synchronizability becomes stronger as the edge-adding probability increases, and the increasing edge-adding probability could make the average path length of the Kleinberg small-world network go smaller. Moreover, larger distance among neighbors and more edges to be added could play positive roles in enhancing the synchronizability of the Kleinberg model. The lorentz oscillators are employed to verify the conclusions numerically.

  17. Test of quantum thermalization in the two-dimensional transverse-field Ising model

    Science.gov (United States)

    Blaß, Benjamin; Rieger, Heiko

    2016-12-01

    We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems.

  18. Two-dimensional modeling of the back amorphous-crystalline silicon heterojunction (BACH) photovoltaic device

    Science.gov (United States)

    Chowdhury, Zahidur R.; Chutinan, Alongkarn; Gougam, Adel B.; Kherani, Nazir P.; Zukotynski, Stefan

    2010-06-01

    Back Amorphous-Crystalline Silicon Heterojunction (BACH)1 solar cell can be fabricated using low temperature processes while integrating high efficiency features of heterojunction silicon solar cells and back-contact homojunction solar cells. This article presents a two-dimensional modeling study of the BACH cell concept. A parametric study of the BACH cell has been carried out using Sentaurus after benchmarking the software. A detailed model describing the optical generation is defined. Solar cell efficiency of 24.4% is obtained for AM 1.5 global spectrum with VOC of greater than 720 mV and JSC exceeding 40 mA/cm2, considering realistic surface passivation quality and other dominant recombination processes.

  19. Finite element model to study two dimensional unsteady state calcium distribution in cardiac myocytes

    Directory of Open Access Journals (Sweden)

    Kunal Pathak

    2016-09-01

    Full Text Available The calcium signaling plays a crucial role in expansion and contraction of cardiac myocytes. This calcium signaling is achieved by calcium diffusion, buffering mechanisms and influx in cardiac myocytes. The various calcium distribution patterns required for achieving calcium signaling in myocytes are still not well understood. In this paper an attempt has been made to develop a model of calcium distribution in myocytes incorporating diffusion of calcium, point source and excess buffer approximation. The model has been developed for a two dimensional unsteady state case. Appropriate boundary conditions and initial condition have been framed. The finite element method has been employed to obtain the solution. The numerical results have been used to study the effect of buffers and source amplitude on calcium distribution in myocytes.

  20. Thermodynamics of the two-dimensional XY model from functional renormalization

    CERN Document Server

    Jakubczyk, Pawel

    2016-01-01

    We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the non-universal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on $\\phi^4$-type truncations. Our computation indicates that such an approximation is insufficient in the high-$T$ phase and a correct analysis of the specific heat profile requires account of an infinite number of interaction vertices.

  1. Identification of the heat transfer coefficient in the two-dimensional model of binary alloy solidification

    Science.gov (United States)

    Hetmaniok, Edyta; Hristov, Jordan; Słota, Damian; Zielonka, Adam

    2017-05-01

    The paper presents the procedure for solving the inverse problem for the binary alloy solidification in a two-dimensional space. This is a continuation of some previous works of the authors investigating a similar problem but in the one-dimensional domain. Goal of the problem consists in identification of the heat transfer coefficient on boundary of the region and in reconstruction of the temperature distribution inside the considered region in case when the temperature measurements in selected points of the alloy are known. Mathematical model of the problem is based on the heat conduction equation with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependance on the concentration of the alloy component. For describing this concentration the Scheil model is used. Investigated procedure involves also the parallelized Ant Colony Optimization algorithm applied for minimizing a functional expressing the error of approximate solution.

  2. Two-dimensional water quality modeling of Town Creek embayment on Guntersville Reservoir

    Energy Technology Data Exchange (ETDEWEB)

    Bender, M.D.; Shiao, Ming C.; Hauser, G.E. (Tennessee Valley Authority, Norris, TN (USA). Engineering Lab.); Butkus, S.R. (Tennessee Valley Authority, Norris, TN (USA). Water Quality Dept.)

    1990-09-01

    TVA investigated water quality of Town Creek embayment using a branched two-dimensional model of Guntersville Reservoir. Simulation results were compared in terms of algal biomass, nutrient concentrations, and volume of embayment with depleted dissolved oxygen. Stratification and flushing play a significant role in the embayment water quality. Storms introduce large loadings of organics, nutrients, and suspended solids. Dissolved oxygen depletion is most severe after storms followed by low flow that fails to flush the embayment. Embayment water quality responses to potential animal waste and erosion controls were explored. Modeling indicated animal waste controls were much more cost-effective than erosion controls. Erosion controls will decrease embayment suspended solids and thereby increase algal biomass due to greater light penetration. 29 refs., 16 figs., 4 tabs.

  3. Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis

    CERN Document Server

    Benzekry, Sebastien

    2010-01-01

    Angiogenesis is a key process in the tumoral growth which allows the cancerous tissue to impact on its vasculature in order to improve the nutrient's supply and the metastatic process. In this paper, we introduce a model for the density of metastasis which takes into account for this feature. It is a two dimensional structured equation with a vanishing velocity field and a source term on the boundary. We present here the mathematical analysis of the model, namely the well-posedness of the equation and the asymptotic behavior of the solutions, whose natural regularity led us to investigate some basic properties of the space $\\Wd(\\Om)=\\{V\\in L^1;\\;\\div(GV)\\in L^1\\}$, where $G$ is the velocity field of the equation.

  4. A Two-Dimensional Cloud Model for Condition Assessment of HVDC Converter Transformers

    Directory of Open Access Journals (Sweden)

    Linjie Zhao

    2012-01-01

    Full Text Available Converter transformers are the key and the most important components in high voltage direct current (HVDC power transmission systems. Statistics show that the failure rate of HVDC converter transformers is approximately twice of that of transformers in AC power systems. This paper presents an approach integrated with a two-dimensional cloud model and an entropy-based weight model to evaluate the condition of HVDC converter transformers. The integrated approach can describe the complexity of HVDC converter transformers and achieve an effective assessment of their condition. Data from electrical testing, DGA, oil testing, and visual inspection were chosen to form the double-level assessment index system. Analysis results show that the integrated approach is capable of providing a relevant and effective assessment which in turn, provides valuable information for the maintenance of HVDC converter transformers.

  5. A meron cluster solution for the sign problem of the two-dimensional O(3) model

    CERN Document Server

    Brechtefeld, F

    2002-01-01

    The two-dimensional O(3) model at a vacuum angle theta=pi is investigated. This model has a severe sign problem. By a Wolff cluster algorithm an integer or half-integer topological charge is assigned to each cluster. The meron clusters (clusters with half-integer topological charge) are used to construct an improved estimator for the correlation function of two spins at theta=pi. Only configurations with 0 and 2 merons contribute to this correlation function. An algorithm, that generates configurations with only 0 and 2 merons, is constructed and numerical simulations at theta=pi are performed. The numerical results indicate the presence of long range correlations at theta=pi.

  6. Quantum Phase Transition in the Two-Dimensional Random Transverse-Field Ising Model

    Science.gov (United States)

    Pich, C.; Young, A. P.

    1998-03-01

    We study the quantum phase transition in the random transverse-field Ising model by Monte Carlo simulations. In one-dimension it has been established that this system has the following striking behavior: (i) the dynamical exponent is infinite, and (ii) the exponents for the divergence of the average and typical correlation lengths are different. An important issue is whether this behavior is special to one-dimension or whether similar behavior persists in higher dimensions. Here we attempt to answer this question by studies of the two-dimensional model. Our simulations use the Wolff cluster algorithm and the results are analyzed by anisotropic finite size scaling, paying particular attention to the Binder ratio of moments of the order parameter distribution and the distribution of the spin-spin correlation functions for various distances.

  7. Two-dimensional modeling of stepped planing hulls with open and pressurized air cavities

    Directory of Open Access Journals (Sweden)

    Konstantin I. Matveev

    2012-06-01

    Full Text Available A method of hydrodynamic discrete sources is applied for two-dimensional modeling of stepped planing surfaces. The water surface deformations, wetted hull lengths, and pressure distribution are calculated at given hull attitude and Froude number. Pressurized air cavities that improve hydrodynamic performance can also be modeled with the current method. Presented results include validation examples, parametric calculations of a single-step hull, effect of trim tabs, and performance of an infinite series of periodic stepped surfaces. It is shown that transverse steps can lead to higher lift-drag ratio, although at reduced lift capability, in comparison with a stepless hull. Performance of a multi-step configuration is sensitive to the wave pattern between hulls, which depends on Froude number and relative hull spacing.

  8. Velocity selection at large undercooling in a two-dimensional nonlocal model of solidification

    Science.gov (United States)

    Barbieri, Angelo

    1987-01-01

    The formation of needle-crystal dendrites from an undercooled melt is investigated analytically, applying the method of Caroli et al. (1986) to Langer's (1980) symmetric two-dimensional nonlocal model of solidification with finite anisotropy in the limit of large undercooling. A solution based on the WKB approximation is obtained, and a saddle-point evaluation is performed. It is shown that needle-crystal solutions exist only if the capillary anisotropy is nonzero, in which case a particular value of the growth velocity can be selected. This finding and the expression for the dependence of the selected velocity on the singular perturbation parameter and the strength of the anisotropy are found to be in complete agreement with the results of a boundary-layer model (Langer and Hong, 1986).

  9. Thermodynamics of the two-dimensional XY model from functional renormalization.

    Science.gov (United States)

    Jakubczyk, P; Eberlein, A

    2016-06-01

    We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the nonuniversal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific-heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on ϕ^{4}-type truncations. Our computation indicates that such an approximation is insufficient in the high-T phase and a correct analysis of the specific-heat profile requires account of an infinite number of interaction vertices.

  10. Averaged model for probabilistic coalescence avalanches in two-dimensional emulsions: Insights into uncertainty propagation

    Science.gov (United States)

    Danny Raj, M.; Rengaswamy, R.

    2017-03-01

    A two-dimensional concentrated emulsion exhibits spontaneous rapid destabilization through an avalanche of coalescence events which propagate through the assembly stochastically. We propose a deterministic model to explain the average dynamics of the avalanching process. The dynamics of the avalanche phenomenon is studied as a function of a composite parameter, the decay time ratio, which characterizes the ratio of the propensity of coalescence to cease propagation to that of propagation. When this ratio is small, the avalanche grows autocatalytically to destabilize the emulsion. Using a scaling analysis, we unravel the relation between a local characteristic of the system and a global system wide effect. The anisotropic nature of local coalescence results in a system size dependent transition from nonautocatalytic to autocatalytic behavior. By incorporating uncertainty into the parameters in the model, several possible realizations of the coalescence avalanche are generated. The results are compared with the Monte Carlo simulations to derive insights into how the uncertainty propagates in the system.

  11. Phase diagram of the two-dimensional O(3) model from dual lattice simulations

    CERN Document Server

    Bruckmann, Falk; Kloiber, Thomas; Sulejmanpasic, Tin

    2016-01-01

    We have simulated the asymptotically free two-dimensional O(3) model at nonzero chemical potential using the model's dual representation. We first demonstrate how the latter solves the sign (complex action) problem. The system displays a crossover at nonzero temperature, while at zero temperature it undergoes a quantum phase transition when mu reaches the particle mass (generated dynamically similar to QCD). The density follows a square root behavior universal for repulsive bosons in one spatial dimension. We have also measured the spin stiffness, known to be sensitive to the spatial correlation length, using different scaling trajectories to zero temperature and infinite size. It points to a dynamical critical exponent z=2. Comparisons to thermodynamic Bethe ansaetze are shown as well.

  12. Numerical simulations of blast wave characteristics with a two-dimensional axisymmetric room model

    Science.gov (United States)

    Sugiyama, Y.; Homae, T.; Wakabayashi, K.; Matsumura, T.; Nakayama, Y.

    2017-01-01

    This paper numerically visualizes explosion phenomena in order to discuss blast wave characteristics with a two-dimensional axisymmetric room model. After the shock wave exits via an opening, the blast wave propagates into open space. In the present study, a parametric study was conducted to determine the blast wave characteristics from the room exit by changing the room shape and the mass of the high explosive. Our results show that the blast wave characteristics can be correctly estimated using a scaling factor proposed in the present paper that includes the above parameters. We conducted normalization of the peak overpressure curve using the shock overpressure at the exit and the length scale of the room volume. In the case where the scaling factor has the same value, the normalized peak overpressure curve does not depend on the calculation conditions, and the scaling factor describes the blast wave characteristics emerging from the current room model.

  13. Eigenvectors of an Arbitrary Onsager Sector in Superintegrable $\\tau^{(2)}$-model and Chiral Potts Model

    CERN Document Server

    Roan, Shi-shyr

    2010-01-01

    We study the eigenvector problem in homogeneous superintegrable chiral Potts model (CPM) by the symmetry principal. Using duality and degeneracy symmetries of $\\tau^{(2)}$-model, we construct the complete eigenvectors in superintegrable CPM for an arbitrary Onsager sector. By duality in CPM, the Bethe state and the Fabricius-McCoy current for a sector in $\\tau^{(2)}$-model are constructed by employing algebraic-Bethe-ansatz techniques on its equivalent XXZ chain. The algebra-generators for the $sl_2$-loop-algebra symmetry of a $\\tau^{(2)}$-sector are determined by the Fabricius-McCoy current. Together with the loop-algebra and Onsager-algebra symmetries, we obtain the local-vector representation of $\\tau^{(2)}$- and CPM-eigenvectors. In this paper we also present the complete and precise constraints of quantum numbers for $\\tau^{(2)}$-sectors. By examining the relationship between solutions of Bethe equations, a new reflective symmetry, besides the duality relation, is found in the superintegrable $\\tau^{(2)}...

  14. Grain coarsening in two-dimensional phase-field models with an orientation field

    Science.gov (United States)

    Korbuly, Bálint; Pusztai, Tamás; Henry, Hervé; Plapp, Mathis; Apel, Markus; Gránásy, László

    2017-05-01

    In the literature, contradictory results have been published regarding the form of the limiting (long-time) grain size distribution (LGSD) that characterizes the late stage grain coarsening in two-dimensional and quasi-two-dimensional polycrystalline systems. While experiments and the phase-field crystal (PFC) model (a simple dynamical density functional theory) indicate a log-normal distribution, other works including theoretical studies based on conventional phase-field simulations that rely on coarse grained fields, like the multi-phase-field (MPF) and orientation field (OF) models, yield significantly different distributions. In a recent work, we have shown that the coarse grained phase-field models (whether MPF or OF) yield very similar limiting size distributions that seem to differ from the theoretical predictions. Herein, we revisit this problem, and demonstrate in the case of OF models [R. Kobayashi, J. A. Warren, and W. C. Carter, Physica D 140, 141 (2000), 10.1016/S0167-2789(00)00023-3; H. Henry, J. Mellenthin, and M. Plapp, Phys. Rev. B 86, 054117 (2012), 10.1103/PhysRevB.86.054117] that an insufficient resolution of the small angle grain boundaries leads to a log-normal distribution close to those seen in the experiments and the molecular scale PFC simulations. Our paper indicates, furthermore, that the LGSD is critically sensitive to the details of the evaluation process, and raises the possibility that the differences among the LGSD results from different sources may originate from differences in the detection of small angle grain boundaries.

  15. Confining vacua and Q-state Potts models with Q<1

    CERN Document Server

    Gliozzi, F

    2007-01-01

    In most Yang-Mills models the vacuum where magnetic monopoles condense coincides with that where center vortices percolate, thus it is not clear which of these two properties is most directly involved in producing confinement. It is pointed out that there is a class of 3D gauge models, which can be though of as duals of Q-state Potts models with Q < 1, where the magnetic monopole condensation is a necessary but not sufficient condition for percolation of center vortices. A set of numerical tests at Q=1/10 shows that there is a vacuum in which the magnetic monopole condensate does not yield confinement, in the sense that large Wilson loops obey a perimeter law. In such a vacuum the center vortices form a dilute gas of loops. At stronger coupling there is also a truly confining vacuum where both confining mechanisms are present.

  16. The role of extracellular matrix in glioma invasion: a cellular Potts model approach.

    Science.gov (United States)

    Rubenstein, Brenda M; Kaufman, Laura J

    2008-12-15

    In this work, a cellular Potts model based on the differential adhesion hypothesis is employed to analyze the relative importance of select cell-cell and cell-extracellular matrix (ECM) contacts in glioma invasion. To perform these simulations, three types of cells and two ECM components are included. The inclusion of explicit ECM with an inhomogeneous fibrous component and a homogeneously dispersed afibrous component allows exploration of the importance of relative energies of cell-cell and cell-ECM contacts in a variety of environments relevant to in vitro and in vivo experimental investigations of glioma invasion. Simulations performed here focus chiefly on reproducing findings of in vitro experiments on glioma spheroids embedded in collagen I gels. For a given range and set ordering of energies associated with key cell-cell and cell-ECM interactions, our model qualitatively reproduces the dispersed glioma invasion patterns found for most glioma cell lines embedded as spheroids in collagen I gels of moderate concentration. In our model, we find that invasion is maximized at intermediate collagen concentrations, as occurs experimentally. This effect is seen more strongly in model gels composed of short collagen fibers than in those composed of long fibers, which retain significant connectivity even at low density. Additional simulations in aligned model matrices further elucidate how matrix structure dictates invasive patterns. Finally, simulations that allow invading cells to both dissolve and deposit ECM components demonstrate how Q-Potts models may be elaborated to allow active cell alteration of their surroundings. The model employed here provides a quantitative framework with which to bound the relative values of cell-cell and cell-ECM interactions and investigate how varying the magnitude and type of these interactions, as well as ECM structure, could potentially curtail glioma invasion.

  17. Review of simplified Pseudo-two-Dimensional models of lithium-ion batteries

    Science.gov (United States)

    Jokar, Ali; Rajabloo, Barzin; Désilets, Martin; Lacroix, Marcel

    2016-09-01

    Over the last decade, many efforts have been deployed to develop models for the prediction, the control, the optimization and the parameter estimation of Lithium-ion (Li-ion) batteries. It appears that the most successful electrochemical-based model for Li-ion battery is the Pseudo-two-Dimensional model (P2D). Due to the fact that the governing equations are complex, this model cannot be used in real-time applications like Battery Management Systems (BMSs). To remedy the situation, several investigations have been carried out to simplify the P2D model. Mathematical and physical techniques are employed to reduce the order of magnitude of the P2D governing equations. The present paper is a review of the studies on the modeling of Li-ion batteries with simplified P2D models. The assumptions on which these models rest are stated, the calculation methods are examined, the advantages and the drawbacks of the models are discussed and their applications are presented. Suggestions for overcoming the shortcomings of the models are made. Challenges and future directions in the modeling of Li-ion batteries are also discussed.

  18. Application of Corner Transfer Matrix Renormalization Group Method to the Correlation Function of a Two-Dimensional Ising Model

    Institute of Scientific and Technical Information of China (English)

    何春山; 李志兵

    2003-01-01

    The correlation function of a two-dimensionalIsing model is calculated by the corner transfer matrix renormalization group method.We obtain the critical exponent η= 0.2496 with few computer resources.

  19. Acid-mediated tumour cell invasion: a discrete modelling approach using the extended Potts model.

    Science.gov (United States)

    Al-Husari, Maymona; Webb, Steven D

    2013-08-01

    Acidic extracellular pH has been shown to play a crucial part in the invasive and metastatic cascade of some tumours. In this study, we examine the effect of extracellular acidity on tumour invasion focusing, in particular, on cellular adhesion, proteolytic enzyme activity and cellular proliferation. Our numerical simulations using a cellular Potts model show that, under acidic extracellular pH, changes in cell-matrix adhesion strength has a comparable effect on tumour invasiveness as the increase in proteolytic enzyme activity. We also show that tumour cells cultured under physiological pH tend to be large and the tumours develop a "diffuse" morphology compared to those cultured at acidic pH, which display protruding "fingers" at the advancing front. A key model prediction is the observation that the main effect on invasion from culturing cells at low extracellular pH stems from changes in the intercellular and cell-matrix adhesion strengths and proteolytic enzyme secretion rate. However, we show that the effects of proteolysis needs to be significant as low to moderate changes only has nominal effects on cell invasiveness. We find that the low pH e effects on cell size and proliferation rate have much lower influence on cell invasiveness.

  20. Continuous and discrete modeling of the decay of two-dimensional nanostructures

    Energy Technology Data Exchange (ETDEWEB)

    Castez, Marcos F; Albano, Ezequiel V [Instituto de Investigaciones FisicoquImicas Teoricas y Aplicadas (INIFTA), CCT La Plata, Casilla de Correo 16, Sucursal 4, (1900) La Plata, UNLP, CONICET (Argentina)

    2009-07-01

    In this work we review some recent research on the surface diffusion-mediated decay of two-dimensional nanostructures. These results include both a continuous, vectorial model and a discrete kinetic Monte Carlo approach. Predictions from the standard linear continuous theory of surface-diffusion-driven interface decay are contrasted with simulational results both from kinetic and morphological points of view. In particular, we focused our attention on high-aspect-ratio nanostructures, where strong deviations from linear theory take place, including nonexponential amplitude decay and the emergence of several interesting nanostructures such as overhangs developing, nanoislands and nanovoids formation, loss of convexity, nanostructures-pinch off and nanostructures-break off, etc. (topical review)

  1. Drude Weight,Optical Conductivity of Two-Dimensional Hubbard Model at Half Filling

    Institute of Scientific and Technical Information of China (English)

    XU Lei; ZHANG Jun

    2008-01-01

    We study the Drude weight D and optical conductivity of the two-dimensional (2D) Hubbard model at half filling with staggered magnetic flux (SMF).When SMF being introduced,the hopping integrals are modulated by the magnetic flux.The optical sum rule,which is related to the mean kinetic energy of band electrons,is evaluated for this 2D Hubbard Hamiltonian.Our present result gives the dependence of the kinetic energy,D and the optical conductivity on SMF and U.At half filling D vanishes exponentially with system size.We also find in the frequency dependence of the optical conductivity,there is &function peak at ω≈2|m|U and the incoherent excitations begin to present themselves extended to a higher energy region.

  2. Superconducting phase and pairing fluctuations in the half-filled two-dimensional Hubbard model.

    Science.gov (United States)

    Sentef, Michael; Werner, Philipp; Gull, Emanuel; Kampf, Arno P

    2011-09-16

    The two-dimensional Hubbard model exhibits superconductivity with d-wave symmetry even at half-filling in the presence of a next-nearest neighbor hopping. Using plaquette cluster dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, we reveal the non-Fermi liquid character of the metallic phase in proximity to the superconducting state. Specifically, the low-frequency scattering rate for momenta near (π, 0) varies nonmonotonically at low temperatures, and the dc conductivity is T linear at elevated temperatures with an upturn upon cooling. Evidence is provided that pairing fluctuations dominate the normal-conducting state even considerably above the superconducting transition temperature.

  3. A two-dimensional volatility basis set – Part 3: Prognostic modeling and NOx dependence

    Directory of Open Access Journals (Sweden)

    W. K. Chuang

    2015-06-01

    Full Text Available When NOx is introduced to organic emissions, aerosol production is sometimes, but not always, reduced. Under certain conditions, these interactions will instead increase aerosol concentrations. We expanded the two-dimensional volatility basis set (2-D-VBS to include the effects of NOx on aerosol formation. This includes the formation of organonitrates, where the addition of a nitrate group contributes to a decrease of 2.5 orders of magnitude in volatility. With this refinement, we model outputs from experimental results, such as the atomic N : C ratio, organonitrate mass, and nitrate fragments in AMS measurements. We also discuss the mathematical methods underlying the implementation of the 2-D-VBS and provide the complete code in the Supplemental material. A developer version is available on Bitbucket, an online community repository.

  4. Isotropic model of fractional transport in two-dimensional bounded domains.

    Science.gov (United States)

    Kullberg, A; del-Castillo-Negrete, D; Morales, G J; Maggs, J E

    2013-05-01

    A two-dimensional fractional Laplacian operator is derived and used to model nonlocal, nondiffusive transport. This integro-differential operator appears in the long-wavelength, fluid description of quantities undergoing non-Brownian random walks without characteristic length scale. To study bounded domains, a mask function is introduced that modifies the kernel in the fractional Laplacian and removes singularities at the boundary. Green's function solutions to the fractional diffusion equation are presented for the unbounded domain and compared to the one-dimensional Cartesian approximations. A time-implicit numerical integration scheme is presented to study fractional diffusion in a circular disk with azimuthal symmetry. Numerical studies of steady-state reveal temperature profiles in which the heat flux and temperature gradient are in the same direction, i.e., uphill transport. The response to off-axis heating, scaling of confinement time with system size, and propagation of cold pulses are investigated.

  5. Two-dimensional physical habitat modeling of effects of habitat structures on urban stream restoration

    Directory of Open Access Journals (Sweden)

    Dongkyun IM

    2011-12-01

    Full Text Available River corridors, even if highly modified or degraded, still provide important habitats for numerous biological species, and carry high aesthetic and economic values. One of the keys to urban stream restoration is recovery and maintenance of ecological flows sufficient to sustain aquatic ecosystems. In this study, the Hongje Stream in the Seoul metropolitan area of Korea was selected for evaluating a physically-based habitat with and without habitat structures. The potential value of the aquatic habitat was evaluated by a weighted usable area (WUA using River2D, a two-dimensional hydraulic model. The habitat suitability for Zacco platypus in the Hongje Stream was simulated with and without habitat structures. The computed WUA values for the boulder, spur dike, and riffle increased by about 2%, 7%, and 131%, respectively, after their construction. Also, the three habitat structures, especially the riffle, can contribute to increasing hydraulic heterogeneity and enhancing habitat diversity.

  6. Subtlety in the Critical Behavior of the Two Dimensional XY Model

    Science.gov (United States)

    Kim, Jae-Kwon

    1996-03-01

    We study the two dimensional classical XY model using the single cluster Monte Carlo algorithm^1. We present extensive high -temperature -phase bulk data that are extracted based on a novel finite- size- scaling Monte Carlo technique^2. The largest value of the estimated bulk correlation length is 1390 in lattice units. Our data reveal that η=1/4 sets in near criticality. The standard finite-size-scaling analysis of the data close to criticality, however, seems to indicate that η=1/4 is compatible only for a critical temperature (T_c) over the range 0.900 Wolff, Phys. Rev. Lett. 62, 361 (1989) ^2 J.-K. Kim, Euro. Phys. Lett. 28, 211 (1994) Research supported in part by the NSF

  7. Breakdown of the Nagaoka phase in the two-dimensional t-J model

    Science.gov (United States)

    Eisenberg, E.; Berkovits, R.; Huse, David A.; Altshuler, B. L.

    2002-04-01

    In the limit of weak exchange J at low hole concentration δ the ground state of the two-dimensional t-J model is believed to be ferromagnetic. We study the leading instability of this Nagaoka state, which emerges with increasing J. Both exact diagonalization of small clusters, and a semiclassical analytical calculation of larger systems show that above a certain critical value of the exchange, Jcr~tδ2, Nagaoka's state is unstable to phase separation. In a finite-size system a bubble of antiferromagnetic Mott insulator appears in the ground state above this threshold. The size of this bubble depends on δ and scales as a power of the system size N.

  8. Nonlocal Coulomb interaction in the two-dimensional spin-1/2 Falicov–Kimball model

    Indian Academy of Sciences (India)

    S K Bhowmick; N K Ghosh

    2012-02-01

    The two-dimensional (2D) extended Falicov–Kimball model has been studied to observe the role of nonlocal Coulomb interaction (nc) using an exact diagonalization technique. The f-state occupation ($n^f$), the f–d intersite correlation function (fd), the specific heat (), entropy () and the specific heat coefficient () have been examined. Nonlocal Coulomb interaction-induced discontinuous insulator-to-metal transition occurs at a critical f-level energy. More ordered state is obtained with the increase of nc. In the specific heat curves, two-peak structure as well as a singlepeak structure appears. At low-temperature region, a sharp rise in the specific heat coefficient is observed. The peak value of shifts to the higher temperature region with nc.

  9. Pairing in the two-dimensional Hubbard model: An exact diagonalization study

    Science.gov (United States)

    Lin, H. Q.; Hirsch, J. E.; Scalapino, D. J.

    1988-05-01

    We have studied the pair susceptibilities for all possible pair wave functions that fit on a two-dimensional (2D) eight-site Hubbard cluster by exact diagonalization of the Hamiltonian. Band fillings corresponding to four and six electrons were studied (two or four holes in the half-filled band) for a wide range of Hubbard interaction strengths and temperatures. Our results show that all pairing susceptibilities are suppressed by the Hubbard repulsion. We have also carried out perturbation-theory calculations which show that the leading-order U2 contributions to the d-wave pair susceptibility suppresses d-wave pairing over a significant temperature range. These results are consistent with recent Monte Carlo results and provide further evidence suggesting that the 2D Hubbard model does not exhibit superconductivity.

  10. Critical Casimir force scaling functions of the two-dimensional Ising model for various boundary conditions

    CERN Document Server

    Hobrecht, Hendrik

    2016-01-01

    We present a systematic method to calculate the scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function $Z$ on an $L\\times M$ square lattice, wrapped around a torus with aspect ratio $\\rho=L/M$. By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a $2\\times2$ transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films $\\rho\\to 0$. Additionally, for the cylinder at criticality our result confirms the predictions...

  11. Reexamination of the long-range Potts model: a multicanonical approach.

    Science.gov (United States)

    Reynal, S; Diep, H T

    2004-02-01

    We investigate the critical behavior of the one-dimensional q-state Potts model with long-range (LR) interactions 1/r(d+sigma), using a multicanonical algorithm. The recursion scheme initially proposed by Berg is improved so as to make it suitable for a large class of LR models with unequally spaced energy levels. The choice of an efficient predictor and a reliable convergence criterion is discussed. We obtain transition temperatures in the first-order regime which are in far better agreement with mean-field predictions than in previous Monte Carlo studies. By relying on the location of spinodal points and resorting to scaling arguments, we determine the threshold value sigma(c)(q) separating the first- and second-order regimes to two-digit precision within the range 3sigma(c)(q)sigma<1.2, thus lending strong support to Sak's scenario.

  12. Fermat Surface and Group Theory in Symmetry of Rapidity Family in Chiral Potts Model

    CERN Document Server

    Roan, Shi-shyr

    2013-01-01

    The present paper discusses various mathematical aspects about the rapidity symmetry in chiral Potts model (CPM) in the context of algebraic geometry and group theory . We re-analyze the symmetry group of a rapidity curve in $N$-state CPM, explore the universal group structure for all $N$, and further enlarge it to modular symmetries of the complete rapidity family in CPM. As will be shown in the article that all rapidity curves in $N$-state CPM constitute a Fermat hypersurface in $\\PZ^3$ of degree 2N as the natural generalization of the Fermat K3 elliptic surface $(N=2)$, we conduct a thorough algebraic geometry study about the rapidity fibration of Fermat surface and its reduced hyperelliptic fibration via techniques in algebraic surface theory. Symmetries of rapidity family in CPM and hyperelliptic family in $\\tau^{(2)}$-model are exhibited through the geometrical representation of the universal structural group in mathematics.

  13. DISPLAY-2: a two-dimensional shallow layer model for dense gas dispersion including complex features.

    Science.gov (United States)

    Venetsanos, A G; Bartzis, J G; Würtz, J; Papailiou, D D

    2003-04-25

    A two-dimensional shallow layer model has been developed to predict dense gas dispersion, under realistic conditions, including complex features such as two-phase releases, obstacles and inclined ground. The model attempts to predict the time and space evolution of the cloud formed after a release of a two-phase pollutant into the atmosphere. The air-pollutant mixture is assumed ideal. The cloud evolution is described mathematically through the Cartesian, two-dimensional, shallow layer conservation equations for mixture mass, mixture momentum in two horizontal directions, total pollutant mass fraction (vapor and liquid) and mixture internal energy. Liquid mass fraction is obtained assuming phase equilibrium. Account is taken in the conservation equations for liquid slip and eventual liquid rainout through the ground. Entrainment of ambient air is modeled via an entrainment velocity model, which takes into account the effects of ground friction, ground heat transfer and relative motion between cloud and surrounding atmosphere. The model additionally accounts for thin obstacles effects in three ways. First a stepwise description of the obstacle is generated, following the grid cell faces, taking into account the corresponding area blockage. Then obstacle drag on the passing cloud is modeled by adding flow resistance terms in the momentum equations. Finally the effect of extra vorticity generation and entrainment enhancement behind obstacles is modeled by adding locally into the entrainment formula without obstacles, a characteristic velocity scale defined from the obstacle pressure drop and the local cloud height.The present model predictions have been compared against theoretical results for constant volume and constant flux gravity currents. It was found that deviations of the predicted cloud footprint area change with time from the theoretical were acceptably small, if one models the frictional forces between cloud and ambient air, neglecting the Richardson

  14. Assessment of the reliability of reproducing two-dimensional resistivity models using an image processing technique.

    Science.gov (United States)

    Ishola, Kehinde S; Nawawi, Mohd Nm; Abdullah, Khiruddin; Sabri, Ali Idriss Aboubakar; Adiat, Kola Abdulnafiu

    2014-01-01

    This study attempts to combine the results of geophysical images obtained from three commonly used electrode configurations using an image processing technique in order to assess their capabilities to reproduce two-dimensional (2-D) resistivity models. All the inverse resistivity models were processed using the PCI Geomatica software package commonly used for remote sensing data sets. Preprocessing of the 2-D inverse models was carried out to facilitate further processing and statistical analyses. Four Raster layers were created, three of these layers were used for the input images and the fourth layer was used as the output of the combined images. The data sets were merged using basic statistical approach. Interpreted results show that all images resolved and reconstructed the essential features of the models. An assessment of the accuracy of the images for the four geologic models was performed using four criteria: the mean absolute error and mean percentage absolute error, resistivity values of the reconstructed blocks and their displacements from the true models. Generally, the blocks of the images of maximum approach give the least estimated errors. Also, the displacement of the reconstructed blocks from the true blocks is the least and the reconstructed resistivities of the blocks are closer to the true blocks than any other combined used. Thus, it is corroborated that when inverse resistivity models are combined, most reliable and detailed information about the geologic models is obtained than using individual data sets.

  15. Coupled two-dimensional edge plasma and neutral gas modeling of tokamak scrape-off-layers

    Energy Technology Data Exchange (ETDEWEB)

    Maingi, R. [North Carolina State Univ., Raleigh, NC (United States)

    1992-08-01

    The objective of this study is to devise a detailed description of the tokamak scrape-off-layer (SOL), which includes the best available models of both the plasma and neutral species and the strong coupling between the two in many SOL regimes. A good estimate of both particle flux and heat flux profiles at the limiter/divertor target plates is desired. Peak heat flux is one of the limiting factors in determining the survival probability of plasma-facing-components at high power levels. Plate particle flux affects the neutral flux to the pump, which determines the particle exhaust rate. A technique which couples a two-dimensional (2-D) plasma and a 2-D neutral transport code has been developed (coupled code technique), but this procedure requires large amounts of computer time. Relevant physics has been added to an existing two-neutral-species model which takes the SOL plasma/neutral coupling into account in a simple manner (molecular physics model), and this model is compared with the coupled code technique mentioned above. The molecular physics model is benchmarked against experimental data from a divertor tokamak (DIII-D), and a similar model (single-species model) is benchmarked against data from a pump-limiter tokamak (Tore Supra). The models are then used to examine two key issues: free-streaming-limits (ion energy conduction and momentum flux) and the effects of the non-orthogonal geometry of magnetic flux surfaces and target plates on edge plasma parameter profiles.

  16. A Vertical Two-Dimensional Model to Simulate Tidal Hydrodynamics in A Branched Estuary

    Institute of Scientific and Technical Information of China (English)

    LIU Wen-Cheng; WU Chung-Hsing

    2005-01-01

    A vertical (laterally averaged) two-dimensional hydrodynamic model is developed for tides, tidal current, and salinity in a branched estuarine system. The governing equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. An explicit scheme is employed to solve the continuity equations. The momentum and mass balance equations are solved implicitly in the Cartesian coordinate system. The tributaries are governed by the same dynamic equations. A control volume at the junctions is designed to conserve mass and volume transport in the finite difference schemes, based on the physical principle of continuum medium of fluid. Predictions by the developed model are compared with the analytic solutions of steady wind-driven circulatory flow and tidal flow. The model results for the velocities and water surface elevations coincide with analytic results. The model is then applied to the Tanshui River estuarine system. Detailed model calibration and verification have been conducted with measured water surface elevations,tidal current, and salinity distributions. The overall performance of the model is in qualitative agreement with the available field data. The calibrated and verified numerical model has been used to quantify the tidal prism and flushing rate in the Tanshui River-Tahan Stream, Hsintien Stream, and Keelung River.

  17. A Monte Carlo Uncertainty Analysis of Ozone Trend Predictions in a Two Dimensional Model. Revision

    Science.gov (United States)

    Considine, D. B.; Stolarski, R. S.; Hollandsworth, S. M.; Jackman, C. H.; Fleming, E. L.

    1998-01-01

    We use Monte Carlo analysis to estimate the uncertainty in predictions of total O3 trends between 1979 and 1995 made by the Goddard Space Flight Center (GSFC) two-dimensional (2D) model of stratospheric photochemistry and dynamics. The uncertainty is caused by gas-phase chemical reaction rates, photolysis coefficients, and heterogeneous reaction parameters which are model inputs. The uncertainty represents a lower bound to the total model uncertainty assuming the input parameter uncertainties are characterized correctly. Each of the Monte Carlo runs was initialized in 1970 and integrated for 26 model years through the end of 1995. This was repeated 419 times using input parameter sets generated by Latin Hypercube Sampling. The standard deviation (a) of the Monte Carlo ensemble of total 03 trend predictions is used to quantify the model uncertainty. The 34% difference between the model trend in globally and annually averaged total O3 using nominal inputs and atmospheric trends calculated from Nimbus 7 and Meteor 3 total ozone mapping spectrometer (TOMS) version 7 data is less than the 46% calculated 1 (sigma), model uncertainty, so there is no significant difference between the modeled and observed trends. In the northern hemisphere midlatitude spring the modeled and observed total 03 trends differ by more than 1(sigma) but less than 2(sigma), which we refer to as marginal significance. We perform a multiple linear regression analysis of the runs which suggests that only a few of the model reactions contribute significantly to the variance in the model predictions. The lack of significance in these comparisons suggests that they are of questionable use as guides for continuing model development. Large model/measurement differences which are many multiples of the input parameter uncertainty are seen in the meridional gradients of the trend and the peak-to-peak variations in the trends over an annual cycle. These discrepancies unambiguously indicate model formulation

  18. Two Dimensional Mathematical Model of Tumor Angiogenesis: Coupling of Avascular Growth and Vascularization

    Directory of Open Access Journals (Sweden)

    Farideh Hosseini

    2015-09-01

    Full Text Available Introduction As a tumor grows, the demand for oxygen and nutrients increases and it grows further if acquires the ability to induce angiogenesis. In this study, we aimed to present a two-dimensional continuous mathematical model for avascular tumor growth, coupled with a discrete model of angiogenesis. Materials and Methods In the avascular growth model, tumor is considered as a single mass, which uptakes oxygen through diffusion and invades the extracellular matrix (ECM. After the tumor reaches its maximum size in the avascular growth phase, tumor cells may be in three different states (proliferative, quiescent and apoptotic, depending on oxygen availability. Quiescent cells are assumed to secrete tumor angiogenic factors, which diffuse into the surrounding tissue until reaching endothelial cells. The mathematical model for tumor angiogenesis is consisted of a five-point finite difference scheme to simulate the progression of endothelial cells in ECM and their penetration into the tumor. Results The morphology of produced networks was investigated, based on various ECM degradation patterns. The generated capillary networks involved the rules of microvascular branching and anastomosis. Model predictions were in qualitative agreement with experimental observations and might have implications as a supplementary model to facilitate mathematical analyses for anti-cancer therapies. Conclusion Our numerical simulations could facilitate the qualitative comparison between three layers of tumor cells, their TAF-producing abilities and subsequent penetration of micro-vessels in order to determine the dynamics of microvascular branching and anastomosis in ECM and three different parts of the tumor.

  19. Two-dimensional models as testing ground for principles and concepts of local quantum physics

    CERN Document Server

    Schrör, B

    2005-01-01

    In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g. chiral models, factorizing models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) and a modular interpretation of the chiral model Diff(S)-covariance with a close connection to the recently formulated local covariance principle for QFT in curved spacetime. As a special case of the thermal duality, the SL(2,Z) modular Verlinde relation is thus a consequence of the principles of thermal QFT togeth...

  20. Turbulence models and Reynolds analogy for two-dimensional supersonic compression ramp flow

    Science.gov (United States)

    Wang, Chi R.; Bidek, Maleina C.

    1994-01-01

    Results of the application of turbulence models and the Reynolds analogy to the Navier-Stokes computations of Mach 2.9 two-dimensional compression ramp flows are presented. The Baldwin-Lomax eddy viscosity model and the kappa-epsilon turbulence transport equations for the turbulent momentum flux modeling in the Navier-Stokes equations are studied. The Reynolds analogy for the turbulent heat flux modeling in the energy equation was also studied. The Navier-Stokes equations and the energy equation were numerically solved for the flow properties. The Reynolds shear stress, the skin friction factor, and the surface heat transfer rate were calculated and compared with their measurements. It was concluded that with a hybrid kappa-epsilon turbulence model for turbulence modeling, the present computations predicted the skin friction factors of the 8 deg and 16 deg compression ramp flows and with the turbulent Prandtl number Pr(sub t) = 0.93 and the ratio of the turbulent thermal and momentum transport coefficients mu(sub q)/mu(sub t) = 2/Prt, the present computations also predicted the surface heat transfer rates beneath the boundary layer flow of the 16 compression ramp.

  1. Milgrom Relation Models for Spiral Galaxies from Two-Dimensional Velocity Maps

    CERN Document Server

    Barnes, E I; Sellwood, J A; Barnes, Eric I.; Kosowsky, Arthur; Sellwood, Jerry A.

    2007-01-01

    Using two-dimensional velocity maps and I-band photometry, we have created mass models of 40 spiral galaxies using the Milgrom relation (the basis of modified Newtonian dynamics, or MOND) to complement previous work. A Bayesian technique is employed to compare several different dark matter halo models to Milgrom and Newtonian models. Pseudo-isothermal dark matter halos provide the best statistical fits to the data in a majority of cases, while the Milgrom relation generally provides good fits as well. We also find that Milgrom models give mass-to-light ratios that roughly correlate with galaxy color, as predicted by stellar population models. A subsample of galaxies in the Hydra cluster follow a tight relation between mass-to-light and color, but one that is significantly different from relations found in previous studies. Ruling out the Milgrom relation with rotational kinematics is difficult due to systematic uncertainties in the observations as well as underlying model assumptions. We discuss in detail two...

  2. Stable spins in the zero temperature spinodal decomposition of 2D Potts models

    Science.gov (United States)

    Derrida, B.; de Oliveira, P. M. C.; Stauffer, D.

    1996-02-01

    We present the results of zero temperature Monte Carlo simulations of the q-state Potts model on a square lattice with either four or eight neighbors, and for the triangular lattice with six neighbors. In agreement with previous works, we observe that the domain growth process gets blocked for the nearest-neighbor square lattice when q is large enough, whereas for the eight neighbor square lattice and for the triangular lattice no blocking is observed. Our simulations indicate that the number of spins which never flipped from the beginning of the simulation up to time t follows a power law as a function of the energy, even in the case of blocking. The exponent of this power law varies from less than {sol1}/{2} for the Ising case (1 q = 2) to 2 for q → ∞ and seems to be universal. The effect of blocking on this exponent is invisible at least up to q = 7.

  3. Kosterlitz-Thouless and Potts transitions in a generalized XY model.

    Science.gov (United States)

    Canova, Gabriel A; Levin, Yan; Arenzon, Jeferson J

    2014-01-01

    We present extensive numerical simulations of a generalized XY model with nematic-like terms recently proposed by Poderoso et al. [ Phys. Rev. Lett. 106 067202 (2011)]. Using finite size scaling and focusing on the q=3 case, we locate the transitions between the paramagnetic (P), the nematic-like (N), and the ferromagnetic (F) phases. The results are compared with the recently derived lower bounds for the P-N and P-F transitions. While the P-N transition is found to be very close to the lower bound, the P-F transition occurs significantly above the bound. Finally, the transition between the nematic-like and the ferromagnetic phases is found to belong to the three-states Potts universality class.

  4. The three-dimensional, three state Potts model in a negative external field

    CERN Document Server

    Bonati, Claudio

    2010-01-01

    We investigate the critical behaviour of the three-dimensional, three state Potts model in presence of a negative external field $h$, i.e. disfavouring one of the three states. A genuine phase transition is present for all values of $|h|$, corresponding to the spontaneous breaking of a residual $Z_2$ symmetry. The transition is first/second order respectively for small/large values of $|h|$, with a tricritical field $h_{\\rm tric}$ separating the two regimes. We provide, using different and consistent approaches, a precise determination of $h_{\\rm tric}$; we also compare with previous studies and discuss the relevance of our investigation to analogous studies of the QCD phase diagram in presence of an imaginary chemical potential.

  5. A Cellular Potts Model of single cell migration in presence of durotaxis.

    Science.gov (United States)

    Allena, R; Scianna, M; Preziosi, L

    2016-05-01

    Cell migration is a fundamental biological phenomenon during which cells sense their surroundings and respond to different types of signals. In presence of durotaxis, cells preferentially crawl from soft to stiff substrates by reorganizing their cytoskeleton from an isotropic to an anisotropic distribution of actin filaments. In the present paper, we propose a Cellular Potts Model to simulate single cell migration over flat substrates with variable stiffness. We have tested five configurations: (i) a substrate including a soft and a stiff region, (ii) a soft substrate including two parallel stiff stripes, (iii) a substrate made of successive stripes with increasing stiffness to create a gradient and (iv) a stiff substrate with four embedded soft squares. For each simulation, we have evaluated the morphology of the cell, the distance covered, the spreading area and the migration speed. We have then compared the numerical results to specific experimental observations showing a consistent agreement. Copyright © 2016 Elsevier Inc. All rights reserved.

  6. Effects of random and deterministic discrete scale invariance on the critical behavior of the Potts model.

    Science.gov (United States)

    Monceau, Pascal

    2012-12-01

    The effects of disorder on the critical behavior of the q-state Potts model in noninteger dimensions are studied by comparison of deterministic and random fractals sharing the same dimensions in the framework of a discrete scale invariance. We carried out intensive Monte Carlo simulations. In the case of a fractal dimension slightly smaller than two d(f) ~/= 1.974636, we give evidence that the disorder structured by discrete scale invariance does not change the first order transition associated with the deterministic case when q = 7. Furthermore the study of the high value q = 14 shows that the transition is a second order one both for deterministic and random scale invariance, but that their behavior belongs to different university classes.

  7. Nucleation near the eutectic point in a Potts-lattice gas model.

    Science.gov (United States)

    Agarwal, Vishal; Peters, Baron

    2014-02-28

    We use the Potts-lattice gas model to study nucleation at and near the eutectic composition. We use rare-event methods to compute the free energy landscape for the competing nucleation products, and short trajectories at the barrier top to obtain prefactors. We introduce a procedure to tune the frequency of semigrand Monte Carlo moves so that the dynamics of a small closed system roughly resemble those of an infinite system. The non-dimensionalized nucleation rates follow trends as predicted by the classical nucleation theory. Finally, we develop corrections that convert free energy surfaces from closed (canonical) simulations into free energy surfaces from open (semigrand) simulations. The new corrections extend earlier corrections to now address situations like nucleation at the eutectic point where two products nucleate competitively.

  8. A two-dimensional CFD model of a refrigerated display case

    Energy Technology Data Exchange (ETDEWEB)

    Stribling, D.; Tassou, S.A. [Brunel Univ., Uxbridge (United Kingdom). Dept. of Mechanical Engineering; Marriott, D. [Safeway Stores plc, Middlesex (United Kingdom)

    1997-12-31

    The discomfort caused by the cold air overspill from vertical refrigerated display cases in supermarkets is widely accepted as being a problem to customers. This, together with the adverse effect on case performance caused by heat and moisture transfer across the air curtain, suggests that there may be room for improvement in the design and fundamental operation of these display fixtures. This paper presents a two-dimensional computational fluid dynamics (CFD) model of a vertical dairy display case that could be used in the design and optimization of such equipment. Comparisons are also made with experimentally obtained values of velocity and temperature measured around the case in order to assess the accuracy and viability of such a model. Parameters of the computer model, such as the size of the calculation grid, the turbulence model, and the discretization scheme, were also varied to determine their effect on the converged solution, and these results are presented. The CFD model showed good qualitative agreement with measured values and requires only fine tuning to make it quantitatively accurate.

  9. Effect of a levee setback on aquatic resources using two-dimensional flow and bioenergetics models

    Science.gov (United States)

    Black, Robert W.; Czuba, Christiana R.; Magirl, Christopher S.; McCarthy, Sarah; Berge, Hans; Comanor, Kyle

    2016-04-05

    Watershed restoration is the focus of many resource managers and can include a multitude of restoration actions each with specific restoration objectives. For the White River flowing through the cities of Pacific and Sumner, Washington, a levee setback has been proposed to reconnect the river with its historical floodplain to help reduce flood risks, as well as provide increased habitat for federally listed species of salmonids. The study presented here documents the use of a modeling framework that integrates two-dimensional hydraulic modeling with process-based bioenergetics modeling for predicting how changes in flow from reconnecting the river with its floodplain affects invertebrate drift density and the net rate of energy intake of juvenile salmonids. Modeling results were calculated for flows of 25.9 and 49.3 cubic meters per second during the spring, summer, and fall. Predicted hypothetical future mean velocities and depths were significantly lower and more variable when compared to current conditions. The abundance of low energetic cost and positive growth locations for salmonids were predicted to increase significantly in the study reach following floodplain reconnection, particularly during the summer. This modeling framework presents a viable approach for evaluating the potential fisheries benefits of reconnecting a river to its historical floodplain that integrates our understanding of hydraulic, geomorphology, and organismal biology.

  10. A two-dimensional model of the methane cycle in a sedimentary accretionary wedge

    Directory of Open Access Journals (Sweden)

    D. E. Archer

    2012-08-01

    Full Text Available A two-dimensional model of sediment column geophysics and geochemistry has been adapted to the problem of an accretionary wedge formation, patterned after the margin of the Juan de Fuca plate as it subducts under the North American plate. Much of the model description is given in a companion paper about the application of the model to an idealized passive margin setting; here we build on that formulation to simulate the impact of the sediment deformation, as it approaches the subduction zone, on the methane cycle. The active margin configuration of the model shares sensitivities with the passive margin configuration, in that sensitivities to organic carbon deposition and respiration kinetics, and to vertical bubble transport and redissolution in the sediment, are stronger than the sensitivity to ocean temperature. The active margin simulation shows a complex sensitivity of hydrate inventory to plate subduction velocity, with results depending strongly on the geothermal heat flux. In low heat-flux conditions, the model produces a larger inventory of hydrate per meter of coastline in the passive margin than active margin configurations. However, the local hydrate concentrations, as pore volume saturation, are higher in the active setting than in the passive, as generally observed in the field.

  11. TWO-DIMENSIONAL CELLULAR AUTOMATON MODEL FOR THE EVOLUTION OF ACTIVE REGION CORONAL PLASMAS

    Energy Technology Data Exchange (ETDEWEB)

    López Fuentes, Marcelo [Instituto de Astronomía y Física del Espacio, CONICET-UBA, CC. 67, Suc. 28, 1428 Buenos Aires (Argentina); Klimchuk, James A., E-mail: lopezf@iafe.uba.ar [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States)

    2015-02-01

    We study a two-dimensional cellular automaton (CA) model for the evolution of coronal loop plasmas. The model is based on the idea that coronal loops are made of elementary magnetic strands that are tangled and stressed by the displacement of their footpoints by photospheric motions. The magnetic stress accumulated between neighbor strands is released in sudden reconnection events or nanoflares that heat the plasma. We combine the CA model with the Enthalpy Based Thermal Evolution of Loops model to compute the response of the plasma to the heating events. Using the known response of the X-Ray Telescope on board Hinode, we also obtain synthetic data. The model obeys easy-to-understand scaling laws relating the output (nanoflare energy, temperature, density, intensity) to the input parameters (field strength, strand length, critical misalignment angle). The nanoflares have a power-law distribution with a universal slope of –2.5, independent of the input parameters. The repetition frequency of nanoflares, expressed in terms of the plasma cooling time, increases with strand length. We discuss the implications of our results for the problem of heating and evolution of active region coronal plasmas.

  12. Two-Dimensional Depth-Averaged Beach Evolution Modeling: Case Study of the Kizilirmak River Mouth, Turkey

    DEFF Research Database (Denmark)

    Baykal, Cüneyt; Ergin, Ayşen; Güler, Işikhan

    2014-01-01

    transformation model, a two-dimensional depth-averaged numerical waveinduced circulation model, a sediment transport model, and a bottom evolution model. To validate and verify the numerical model, it is applied to several cases of laboratory experiments. Later, the model is applied to a shoreline change problem...

  13. One- and two-dimensional modelling of overland flow in semiarid shrubland, Jornada basin, New Mexico

    Science.gov (United States)

    Howes, David A.; Abrahams, Athol D.; Pitman, E. Bruce

    2006-03-01

    Two distributed parameter models, a one-dimensional (1D) model and a two-dimensional (2D) model, are developed to simulate overland flow in two small semiarid shrubland watersheds in the Jornada basin, southern New Mexico. The models are event-based and represent each watershed by an array of 1-m2 cells, in which the cell size is approximately equal to the average area of the shrubs.Each model uses only six parameters, for which values are obtained from field surveys and rainfall simulation experiments. In the 1D model, flow volumes through a fixed network are computed by a simple finite-difference solution to the 1D kinematic wave equation. In the 2D model, flow directions and volumes are computed by a second-order predictor-corrector finite-difference solution to the 2D kinematic wave equation, in which flow routing is implicit and may vary in response to flow conditions.The models are compared in terms of the runoff hydrograph and the spatial distribution of runoff. The simulation results suggest that both the 1D and the 2D models have much to offer as tools for the large-scale study of overland flow. Because it is based on a fixed flow network, the 1D model is better suited to the study of runoff due to individual rainfall events, whereas the 2D model may, with further development, be used to study both runoff and erosion during multiple rainfall events in which the dynamic nature of the terrain becomes an important consideration.

  14. Two-dimensional finite elements model for boron management in agroforestry sites.

    Science.gov (United States)

    Tayfur, Gokmen; Tanji, Kenneth K; Baba, Alper

    2010-01-01

    Agroforesty systems, which are recommended as a management option to lower the shallow groundwater level and to reuse saline subsurface drainage waters from the tile-drained croplands in the drainage-impacted areas of Jan Joaquin Valley of California, have resulted in excessive boron buildup in the soil root zone. To assess the efficacy of the long-term impacts of soil boron buildup in agroforesty systems, a mathematical model was developed to simulate non-conservative boron transport. The developed dynamic two-dimensional finite element model simulates water flow and boron transport in saturated-unsaturated soil system, including boron sorption and boron uptake by root-water extraction processes. The simulation of two different observed field data sets by the developed model is satisfactory, with mean absolute error of 1.5 mg/L and relative error of 6.5%. Application of the model to three different soils shows that boron adsorption is higher in silt loam soil than that in sandy loam and clay loam soils. This result agrees with the laboratory experimental observations. The results of the sensitivity analysis indicate that boron uptake by root-water extraction process influences the boron concentration distribution along the root zone. Also, absorption coefficient and maximum adsorptive capacity of a soil for boron are found to be sensitive parameters.

  15. Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model

    Science.gov (United States)

    Panajotov, Krassimir; Clerc, Marcel G.; Tlidi, Mustapha

    2017-06-01

    Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height. Contribution to the Topical Issue "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

  16. Two-Dimensional Core-Collapse Supernova Models with Multi-Dimensional Transport

    CERN Document Server

    Dolence, Joshua C; Zhang, Weiqun

    2014-01-01

    We present new two-dimensional (2D) axisymmetric neutrino radiation/hydrodynamic models of core-collapse supernova (CCSN) cores. We use the CASTRO code, which incorporates truly multi-dimensional, multi-group, flux-limited diffusion (MGFLD) neutrino transport, including all relevant $\\mathcal{O}(v/c)$ terms. Our main motivation for carrying out this study is to compare with recent 2D models produced by other groups who have obtained explosions for some progenitor stars and with recent 2D VULCAN results that did not incorporate $\\mathcal{O}(v/c)$ terms. We follow the evolution of 12, 15, 20, and 25 solar-mass progenitors to approximately 600 milliseconds after bounce and do not obtain an explosion in any of these models. Though the reason for the qualitative disagreement among the groups engaged in CCSN modeling remains unclear, we speculate that the simplifying ``ray-by-ray' approach employed by all other groups may be compromising their results. We show that ``ray-by-ray' calculations greatly exaggerate the ...

  17. Nonequilibrium critical dynamics of two dimensional interacting monomer-dimer model: non-Ising criticality

    Science.gov (United States)

    Nam, Keekwon; Kim, Bongsoo; Jong Lee, Sung

    2014-08-01

    We investigate the nonequilibrium relaxation dynamics of an interacting monomer-dimer model with nearest neighbor repulsion on a square lattice, which possesses two symmetric absorbing states. The model is known to exhibit two nearby continuous transitions: the Z2 symmetry-breaking order-disorder transition and the absorbing transition with directed percolation criticality. We performed a more detailed analysis of our extensive simulations on bigger lattice systems which reaffirms that the symmetry-breaking transition exhibits a non-Ising critical behavior with β ≃ 0.149(2) and η ≃ 0.30(1) that are distinct from those values of a pure two dimensional Ising model. Finite size scaling of dimer density near the symmetry breaking transition gives logarithmic scaling (α = 0.0) which is consistent with the hyperscaling relation but the corresponding exponent of νB ≃ 1.37(2) exhibits a conspicuous deviation from the pure Ising value of 1. The value of dynamic critical exponent z, however, is found to be close to that of the kinetic Ising model as 1/z ≃ 0.466(5) from the relaxation of staggered magnetization (and also similar but slightly smaller values from coarsening).

  18. Ca2+ movement in smooth muscle cells studied with one- and two-dimensional diffusion models.

    Science.gov (United States)

    Kargacin, G; Fay, F S

    1991-11-01

    Although many of the processes involved in the regulation of Ca2+ in smooth muscle have been studied separately, it is still not well known how they are integrated into an overall regulatory system. To examine this question and to study the time course and spatial distribution of Ca2+ in cells after activation, one- and two-dimensional diffusion models of the cell that included the major processes thought to be involved in Ca regulation were developed. The models included terms describing Ca influx, buffering, plasma membrane extrusion, and release and reuptake by the sarcoplasmic reticulum. When possible these processes were described with known parameters. Simulations with the models indicated that the sarcoplasmic reticulum Ca pump is probably primarily responsible for the removal of cytoplasmic Ca2+ after cell activation. The plasma membrane Ca-ATPase and Na/Ca exchange appeared more likely to be involved in the long term regulation of Ca2+. Pumping processes in general had little influence on the rate of rise of Ca transients. The models also showed that spatial inhomogeneities in Ca2+ probably occur in cells during the spread of the Ca signal following activation and during the subsequent return of Ca2+ to its resting level.

  19. Re-orientation transition in molecular thin films: Potts model with dipolar interaction.

    Science.gov (United States)

    Hoang, Danh-Tai; Kasperski, Maciej; Puszkarski, Henryk; Diep, H T

    2013-02-06

    We study the low-temperature behavior and the phase transition of a thin film by Monte Carlo simulation. The thin film has a simple cubic lattice structure where each site is occupied by a Potts parameter which indicates the molecular orientation of the site. We take only three molecular orientations in this paper, which correspond to the three-state Potts model. The Hamiltonian of the system includes (i) the exchange interaction J(ij) between nearest-neighbor sites i and j, (ii) the long-range dipolar interaction of amplitude D truncated at a cutoff distance r(c), and (iii) a single-ion perpendicular anisotropy of amplitude A. We allow J(ij) = J(s) between surface spins, and J(ij) = J otherwise. We show that the ground state depends on the ratio D/A and r(c). For a single layer, for a given A, there is a critical value D(c) below (above) which the ground-state (GS) configuration of molecular axes is perpendicular (parallel) to the film surface. When the temperature T is increased, a re-orientation transition occurs near D(c): the low-T in-plane ordering undergoes a transition to the perpendicular ordering at a finite T, below the transition to the paramagnetic phase. The same phenomenon is observed in the case of a film with a thickness. Comparison with the Fe/Gd experiment is given. We show that the surface phase transition can occur below or above the bulk transition depending on the ratio J(s)/J. Surface and bulk order parameters as well as other physical quantities are shown and discussed.

  20. Capillary wave approach to order-order fluid interfaces in the 3D three-state Potts model

    CERN Document Server

    Provero, P

    1994-01-01

    The physics of fluid interfaces between domains of different magnetization in the ordered phase of the 3D three-state Potts model is studied by means of a Monte Carlo simulation. It is shown that finite--size effects in the interface free energy are well described by the capillary wave model at two loop order, supporting the idea of the universality of this description of fluid interfaces in 3D statistical models.

  1. Two Dimensional Analytical Modeling for SOI and SON MOSFET and Their Performance Comparison

    Directory of Open Access Journals (Sweden)

    Saptarsi Ghosh

    2011-01-01

    Full Text Available During last few decade continuous device performance improvements have been achieved through a combination of device scaling, new device structures and material property improvement to its fundamental limits. Conventional silicon (bulk CMOS technology can’t overcome the fundamental physical limitations belong to sub-micro or nanometer region which leads to alternative device technology like Silicon-on-Insulator (SOI technology and its recent innovative modification Silicon-On-Nothing (SON MOSFET. Analytical simulation is very important to understand the relative performance of those devices under different structural and operational parameter variations. For present analytical simulation asymmetric structure of Silicon-On-Insulator (SOI MOSFET and Silicon-On-Nothing (SON MOSFET are considered. The proposed structure of SON MOSFET is similar to that of the SOI MOSFET with the only exception being the oxide layer here is substituted with air which has much lower permittivity than Silicon-dioxide. Variation of threshold voltage against effective channel lengths is compared for both the structures. From our simulation it is observed that the proposed SON model has lower drain to source current (IDS than SOI model. In our modeling based on solution of two dimensional Poisson’s equation short channel effects such as DIBL and fringing field effects are also taken into account. SON is found to provide better suppression of SCE s than SOI. The results predicted by our analytical simulation hold good agreement with experimental results.

  2. A New Paradigm of Modeling Two-Dimensional Overland Watershed Water Quality

    Science.gov (United States)

    Zhang, F.; Yeh, G. G.

    2003-12-01

    This paper presents the development of sediment and reactive chemical transport under non-isotherm condition in two-dimensional overland watershed system. Through decomposition of reaction network via Gauss-Jordan column reduction, (a) redundant fast reactions and irrelevant kinetic reactions are removed from the system; (b) fast reactions and slow reactions can be decoupled; (c) species reaction equations are transformed into two sets: equilibrium species mass action equations and kinetic-variable reaction equations. This enable our model to include as many types of reactions as possible, choose kinetic-variables instead of chemical species as primary dependent variables, and simplify the reaction terms in transport equations. In our model two options are provided to solve the advection-dispersion transport equation: Lagrangian-Eulerian approach, and Finite Element Method in Conservative Form, and three options to deal with the reaction term: Fully-implicit, Predictor-corrector, and Operator-splitting methods. The production-consumption rate of chemical species is determined by reaction-based formulations. One example problem is employed to demonstrate the design capability of the model and the robustness of the numerical simulations.

  3. Phase diagram and correlation functions of the two-dimensional dissipative quantum XY model

    Science.gov (United States)

    Hou, Changtao; Varma, Chandra M.

    2016-11-01

    The two-dimensional quantum XY model, with a Caldeira-Leggett form of dissipation, is applicable to the quantum-critical properties of diverse experimental systems, ranging from superconductor to insulator transitions, ferromagnetic and antiferromagnetic transitions in metals, to the loop-current order transition in cuprates. We solve the reexpression of this model in terms of orthogonal topological excitations, vortices, and a variety of instantons, by renormalization group methods. The calculations explain the extraordinary properties of the model discovered in Monte Carlo calculations: the product form of the quantum-critical fluctuations in space and time, a spatial correlation length proportional to the logarithm of the temporal correlation length near the transition from a disordered to a fully ordered state, and the occurrence of a phase with spatial order without temporal order. They are intimately related to the flow of the metric of time in relation to the metric of space, i.e., of the dynamical critical exponent z . These properties appear to be essential in understanding the strange metallic phase found in a variety of quantum-critical transitions as well as the accompanying high-temperature superconductivity.

  4. Efficient two-dimensional magnetotellurics modelling using implicitly restarted Lanczos method

    Indian Academy of Sciences (India)

    Krishna Kumar; Pravin K Gupta; Sri Niwas

    2011-08-01

    This paper presents an efficient algorithm, FDA2DMT (Free Decay Analysis for 2D Magnetotellurics (MT)), based on eigenmode approach to solve the relevant partial differential equation, for forward computation of two-dimensional (2D) responses. The main advantage of this approach lies in the fact that only a small subset of eigenvalues and corresponding eigenvectors are required for satisfactory results. This small subset (pre-specified number) of eigenmodes are obtained using shift and invert implementation of Implicitly Restarted Lanczos Method (IRLM). It has been established by experimentation that only 15–20% smallest eigenvalue and corresponding eigenvectors are sufficient to secure the acceptable accuracy. Once the single frequency response is computed using eigenmode approach, the responses for subsequent frequencies can be obtained in negligible time. Experiment design results for validation of FDA2DMT are presented by considering two synthetic models from COMMEMI report, Brewitt-Taylor and Weaver (1976) model and a field data based model from Garhwal Himalaya.

  5. Evolution of desertification in a two-dimensional energy balance model coupled with thermodynamics and dynamics

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    The relationship between desert evolution and change in albedo has been investigated quasi-analytically using a zonal mean two-dimensional energy balance model which considers the radiation transmission process due to thermodynamics and bound- ary layer movement caused by kinetics. A climate state including temperature, zonal wind, meridional wind and vertical wind can be simulated according to the current zonal distribution of albedo. Given desert distribution, characterized by the value and distribution of albedo, the response of climate on albedo has been studied to analyze the evolution of desert climate. One significant result is that the simple model can reproduce mean meridional circulation. Another result indicates that climate corresponds to two equilibria. This happens when the junction temperature between vegetation and desert is higher than a certain critical value. As for the first equilibrium, the desert belt is predicted to move southward in the northern hemisphere with the increasing values of albedo, which corresponds to the current trend of climate change. For the second equilibrium, vegetation will expand northward with increasing values of albedo, which would indicate a narrowing of the desert belt. In order to determine if the two equilibria exist, new physical models are needed.

  6. Design considerations for pulsed-flow comprehensive two-dimensional GC: dynamic flow model approach.

    Science.gov (United States)

    Harvey, Paul McA; Shellie, Robert A; Haddad, Paul R

    2010-04-01

    A dynamic flow model, which maps carrier gas pressures and carrier gas flow rates through the first dimension separation column, the modulator sample loop, and the second dimension separation column(s) in a pulsed-flow modulation comprehensive two-dimensional gas chromatography (PFM-GCxGC) system is described. The dynamic flow model assists design of a PFM-GCxGC modulator and leads to rapid determination of pneumatic conditions, timing parameters, and the dimensions of the separation columns and connecting tubing used to construct the PFM-GCxGC system. Three significant innovations are introduced in this manuscript, which were all uncovered by using the dynamic flow model. A symmetric flow path modulator improves baseline stability, appropriate selection of the flow restrictors in the first dimension column assembly provides a generally more stable and robust system, and these restrictors increase the modulation period flexibility of the PFM-GCxGC system. The flexibility of a PFM-GCxGC system resulting from these innovations is illustrated using the same modulation interface to analyze Special Antarctic Blend (SAB) diesel using 3 s and 9 s modulation periods.

  7. Probability-changing cluster algorithm for two-dimensional XY and clock models

    Science.gov (United States)

    Tomita, Yusuke; Okabe, Yutaka

    2002-05-01

    We extend the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm to the study of systems with the vector order parameter. Wolff's idea of the embedded cluster formalism is used for assigning clusters. The Kosterlitz-Thouless (KT) transitions for the two-dimensional (2D) XY and q-state clock models are studied by using the PCC algorithm. Combined with the finite-size scaling analysis based on the KT form of the correlation length, ξ~exp(c/(T/TKT-1)), we determine the KT transition temperature and the decay exponent η as TKT=0.8933(6) and η=0.243(4) for the 2D XY model. We investigate two transitions of the KT type for the 2D q-state clock models with q=6,8,12 and confirm the prediction of η=4/q2 at T1, the low-temperature critical point between the ordered and XY-like phases, systematically.

  8. Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials

    CERN Document Server

    Mihalache, D; Skarka, V; Malomed, B A; Leblond, H; Aleksić, N B; Lederer, F

    2010-01-01

    Complex Ginzburg-Landau (CGL) models of laser media (with the cubic-quintic nonlinearity) do not contain an effective diffusion term, which makes all vortex solitons unstable in these models. Recently, it has been demonstrated that the addition of a two-dimensional periodic potential, which may be induced by a transverse grating in the laser cavity, to the CGL equation stabilizes compound (four-peak) vortices, but the most fundamental "crater-shaped" vortices (CSVs), alias vortex rings, which are, essentially, squeezed into a single cell of the potential, have not been found before in a stable form. In this work we report families of stable compact CSVs with vorticity S=1 in the CGL model with the external potential of two different types: an axisymmetric parabolic trap, and the periodic potential. In both cases, we identify stability region for the CSVs and for the fundamental solitons (S=0). Those CSVs which are unstable in the axisymmetric potential break up into robust dipoles. All the vortices with S=2 a...

  9. Infiltration effects on a two-dimensional molecular dynamics model of landslides

    CERN Document Server

    Martelloni, Gianluca

    2012-01-01

    In this paper we propose a two-dimensional (2D) computational model, based on a molecular dynamics (MD) approach, for deep landslides triggered by rainfall. Our model is based on interacting particles or grains and describes the behavior of a fictitious granular material along a slope consisting of a vertical section, i.e. with a wide thickness. The triggering of the landslide is caused by the passing of two conditions: a threshold speed and a condition on the static friction of the particles, the latter based on the Mohr-Coulomb failure criterion (Coulomb 1776; Mohr 1914). The inter-particle interactions are through a potential that, in the absence of suitable experimental data and due to the arbitrariness of the grain dimension is modeled by means of a potential similar to the Lennard-Jones one (Lennard-Jones 1924), i.e., with an attractive and a repulsive part. For the updating of the particle positions we use a MD method which results to be very suitable to simulate this type of systems (Herrmann and Ludi...

  10. A two-dimensional modeling of solid oxide fuel cell button cells with detailed electrochemistry mechanism

    Science.gov (United States)

    Li, Jingde; Bai, Zhengyu; Croiset, Eric

    2016-11-01

    A two-dimensional model of nickel/yttria-stabilized zirconia (Ni/YSZ) solid oxide fuel cell (SOFC) was developed for a button cell system. The model integrates the detailed catalytic, electrochemical elementary reactions with ionic/electronic conduction and multiple gas transport processes in SOFC. The model is validated using published experimental data for H2-H2O fuel gas under different cell sizes and operating conditions. The distributions of gas/surface phase species concentration and current density were predicted and the effects of operating temperature, fuel gas composition and fuel channel tube design on the cell performance were studied. The results show that the electrochemical reaction processes occurs mainly within a 20 μm distance from the anode/electrolyte interface and that the Ni catalyst surface is covered mainly by H(s). For the chamber channel design, the calculations show that the tube chamber should have a diameter no smaller than the cathode electrode to obtain the best SOFC performance.

  11. Understanding Ground Motion in Las Vegas: Insights from Data Analysis and Two-Dimensional Modeling

    Energy Technology Data Exchange (ETDEWEB)

    Rodgers, A; Tkalcic, H; McCallen, D

    2004-02-05

    Seismic ground motions are amplified in low velocity sedimentary basins relative to adjacent sites on high velocity hard rock. We used historical recordings of NTS nuclear explosions and earthquake recordings in Las Vegas Valley to quantify frequency-dependent basin amplification using Standard Spectral Ratios. We show that amplifications, referred to as site response, can reach a factor of 10 in the frequency band 0.4-2.0 Hz. Band-averaged site response between 0.4-2.0 Hz is strongly correlated with basin depth. However, it is also well known that site response is related to shallow shear-wave velocity structure. We simulated low frequency (f<1Hz) ground motion and site response with two-dimensional elastic finite difference simulations. We demonstrate that physically plausible models of the shallow subsurface, including low velocity sedimentary structure, can predict relative amplification as well as some of the complexity in the observed waveforms. This study demonstrates that site response can be modeled without invoking complex and computationally expensive three-dimensional structural models.

  12. Extended defects in the Potts-percolation model of a solid: renormalization group and Monte Carlo analysis.

    Science.gov (United States)

    Diep, H T; Kaufman, Miron

    2009-09-01

    We extend the model of a 2d solid to include a line of defects. Neighboring atoms on the defect line are connected by springs of different strength and different cohesive energy with respect to the rest of the system. Using the Migdal-Kadanoff renormalization group we show that the elastic energy is an irrelevant field at the bulk critical point. For zero elastic energy this model reduces to the Potts model. By using Monte Carlo simulations of the three- and four-state Potts model on a square lattice with a line of defects, we confirm the renormalization-group prediction that for a defect interaction larger than the bulk interaction the order parameter of the defect line changes discontinuously while the defect energy varies continuously as a function of temperature at the bulk critical temperature.

  13. Verification of the two-dimensional hydrodynamic model based on remote sensing

    Science.gov (United States)

    Sazonov, Alexey; Mikhailukova, Polina; Krylenko, Inna; Frolova, Natalya; Kireeva, Mariya

    2016-04-01

    Mathematical modeling methods are used more and more actively to evaluate possible damage, identify potential flood zone and the influence of individual factors affecting the river during the passage of the flood. Calculations were performed by means of domestic software complex «STREAM-2D» which is based on the numerical solution of two-dimensional St. Venant equations. One of the major challenges in mathematical modeling is the verification of the model. This is usually made using data on water levels from hydrological stations: the smaller the difference of the actual level and the simulated one, the better the quality of the model used. Data from hydrological stations are not always available, so alternative sources of verification, such as remote sensing, are increasingly used. The aim of this work is to develop a method of verification of hydrodynamic model based on a comparison of actual flood zone area, which in turn is determined on the basis of the automated satellite image interpretation methods for different imaging systems and flooded area obtained in the course of the model. The study areas are Lena River, The North Dvina River, Amur River near Blagoveshchensk. We used satellite images made by optical and radar sensors: SPOT-5/HRG, Resurs-F, Radarsat-2. Flooded area were calculated using unsupervised classification (ISODATA and K-mean) for optical images and segmentation for Radarsat-2. Knowing the flow rate and the water level at a given date for the upper and lower limits of the model, respectively, it is possible to calculate flooded area by means of program STREAM-2D and GIS technology. All the existing vector layers with the boundaries of flooding are included in a GIS project for flood area calculation. This study was supported by the Russian Science Foundation, project no. 14-17-00155.

  14. Coexistence in the two-dimensional May-Leonard model with random rates

    Science.gov (United States)

    He, Q.; Mobilia, M.; Täuber, U. C.

    2011-07-01

    We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-) steady state in two-dimensional stochastic May-Leonard models of mobile individuals, allowing for particle exchanges with nearest-neighbors and hopping onto empty sites. We therefore consider a class of four-state three-species cyclic predator-prey models whose total particle number is not conserved. We demonstrate that quenched disorder in either the reaction or in the mobility rates hardly impacts the dynamical evolution, the emergence and structure of spiral patterns, or the mean extinction time in this system. We also show that direct particle pair exchange processes promote the formation of regular spiral structures. Moreover, upon increasing the rates of mobility, we observe a remarkable change in the extinction properties in the May-Leonard system (for small system sizes): (1) as the mobility rate exceeds a threshold that separates a species coexistence (quasi-) steady state from an absorbing state, the mean extinction time as function of system size N crosses over from a functional form ˜ e c N / N (where c is a constant) to a linear dependence; (2) the measured histogram of extinction times displays a corresponding crossover from an (approximately) exponential to a Gaussian distribution. The latter results are found to hold true also when the mobility rates are randomly distributed.

  15. Two-Dimensional Aerodynamic Models of Insect Flight for Robotic Flapping Wing Mechanisms of Maximum Efficiency

    Institute of Scientific and Technical Information of China (English)

    Thien-Tong Nguyen; Doyoung Byun

    2008-01-01

    In the "modified quasi-steady" approach, two-dimensional (2D) aerodynamic models of flapping wing motions are analyzed with focus on different types of wing rotation and different positions of rotation axis to explain the force peak at the end of each half stroke. In this model, an additional velocity of the mid chord position due to rotation is superimposed on the translational relative velocity of air with respect to the wing. This modification produces augmented forces around the end of eachstroke. For each case of the flapping wing motions with various combination of controlled translational and rotational velocities of the wing along inclined stroke planes with thin figure-of-eight trajectory, discussions focus on lift-drag evolution during one stroke cycle and efficiency of types of wing rotation. This "modified quasi-steady" approach provides a systematic analysis of various parameters and their effects on efficiency of flapping wing mechanism. Flapping mechanism with delayed rotation around quarter-chord axis is an efficient one and can be made simple by a passive rotation mechanism so that it can be useful for robotic application.

  16. Experiment and modeling of a two-dimensional piezoelectric energy harvester

    Science.gov (United States)

    Yang, Yaowen; Wu, Hao; Kiong Soh, Chee

    2015-12-01

    Vibration energy harvesting using piezoelectric materials has attracted much research interest in recent years. Numerous efforts have been devoted to improving the efficiency of vibration energy harvesters and broadening their bandwidths. In most reported literature, energy harvesters are designed to harvest energy from vibration source with a specific excitation direction. However, a practical environmental vibration source may include multiple components from different directions. Thus, it is an important concern to design a vibration energy harvester to be adaptive to multiple excitation directions. In this article, a piezoelectric energy harvester with frame configuration is proposed to achieve two-dimensional (2D) vibration energy harvesting. The harvester works in two fundamental modes, i.e., its vertical and horizontal vibration modes. By tuning the structural parameters, the harvester can capture vibration energy from arbitrary directions in a 2D plane. Experimental studies are carried out to prove its feasibility. A finite element model and an equivalent circuit model are built to simulate the system and validate the experiment outcomes. The study of this 2D energy harvester indicates its promising potential in practical vibration scenarios.

  17. Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimension

    Directory of Open Access Journals (Sweden)

    Franceschini Barbara

    2005-02-01

    Full Text Available Abstract Background Modeling the complex development and growth of tumor angiogenesis using mathematics and biological data is a burgeoning area of cancer research. Architectural complexity is the main feature of every anatomical system, including organs, tissues, cells and sub-cellular entities. The vascular system is a complex network whose geometrical characteristics cannot be properly defined using the principles of Euclidean geometry, which is only capable of interpreting regular and smooth objects that are almost impossible to find in Nature. However, fractal geometry is a more powerful means of quantifying the spatial complexity of real objects. Methods This paper introduces the surface fractal dimension (Ds as a numerical index of the two-dimensional (2-D geometrical complexity of tumor vascular networks, and their behavior during computer-simulated changes in vessel density and distribution. Results We show that Ds significantly depends on the number of vessels and their pattern of distribution. This demonstrates that the quantitative evaluation of the 2-D geometrical complexity of tumor vascular systems can be useful not only to measure its complex architecture, but also to model its development and growth. Conclusions Studying the fractal properties of neovascularity induces reflections upon the real significance of the complex form of branched anatomical structures, in an attempt to define more appropriate methods of describing them quantitatively. This knowledge can be used to predict the aggressiveness of malignant tumors and design compounds that can halt the process of angiogenesis and influence tumor growth.

  18. A two-dimensional (azimuthal-axial) particle-in-cell model of a Hall thruster

    Energy Technology Data Exchange (ETDEWEB)

    Coche, P.; Garrigues, L., E-mail: laurent.garrigues@laplace.univ-tlse.fr [LAPLACE (Laboratoire Plasma et Conversion d' Energie), Université de Toulouse, UPS, INPT Toulouse 118, route de Narbonne, F-31062 Toulouse cedex 9 (France); CNRS, LAPLACE, F-31062 Toulouse (France)

    2014-02-15

    We have developed a two-dimensional Particle-In-Cell model in the azimuthal and axial directions of the Hall thruster. A scaling method that consists to work at a lower plasma density to overcome constraints on time-step and grid-spacing is used. Calculations are able to reproduce the breathing mode due to a periodic depletion of neutral atoms without the introduction of a supplementary anomalous mechanism, as in fluid and hybrid models. Results show that during the increase of the discharge current, an electron-cyclotron drift instability (frequency in the range of MHz and wave number on the order of 3000 rad s{sup −1}) is formed in the region of the negative gradient of magnetic field. During the current decrease, an axial electric wave propagates from the channel toward the exhaust (whose frequency is on the order of 400 kHz) leading to a broadening of the ion energy distribution function. A discussion about the influence of the scaling method on the calculation results is also proposed.

  19. Numerical Simulations of an atmospheric pressure discharge using a two dimensional fluid model

    Science.gov (United States)

    Iqbal, Muhammad M.; Turner, Miles M.

    2008-10-01

    We present numerical simulations of a parallel-plate dielectric barrier discharge using a two-dimensional fluid model with symmetric boundary conditions in pure helium and He-N2 gases at atmospheric pressure. The periodic stationary pattern of electrons and molecular helium ions density is shown at different times during one breakdown pulse for the pure helium gas. The temporal behavior of the helium metastables and excimers species density is examined and their influences on the discharge characteristics are exhibited for an APD. The atmospheric pressure discharge modes (APGD and APTD) are affected with small N2 impurities and the discharge mode structures are described under different operating conditions. The uniform and filamentary behavior of the discharge is controlled with the variable relative permittivity of the dielectric barrier material. The influence of nitrogen impurities plays a major role for the production of the filaments in the after glow phase of He-N2 discharge and the filaments are clearly observed with the increased recombination coefficient of nitrogen ions. The creation and annihilation mechanism of filaments is described with the production and destruction of nitrogen ions at different applied voltages and driving frequencies for a complete cycle. The results of the fluid model are validated by comparison with the experimental atmospheric pressure discharge results in He-N2 plasma discharge.

  20. Sensitivity of two-dimensional model predictions of ozone response to stratospheric aircraft: An update

    Energy Technology Data Exchange (ETDEWEB)

    Considine, D.B.; Douglass, A.R.; Jackman, C.H. [Applied Research Corp., Landover, MD (United States)]|[NASA, Goddard Space Flight Center, Greenbelt, MD (United States)

    1995-02-01

    The Goddard Space Flight Center (GSFC) two-dimensional model of stratospheric photochemistry and dynamics has been used to calculate the O3 response to stratospheric aircraft (high-speed civil transport (HSCT)) emissions. The sensitivity of the model O3 response was examined for systematic variations of five parameters and two reaction rates over a wide range, expanding on calculations by various modeling groups for the NASA High Speed Research Program and the World Meteorological Organization. In all, 448 model runs were required to test the effects of variations in the latitude, altitude, and magnetitude of the aircraft emissions perturbation, the background chlorine levels, the background sulfate aerosol surface area densities, and the rates of two key reactions. No deviation from previous conclusions concerning the response of O3 to HSCTs was found in this more exhaustive exploration of parameter space. Maximum O3 depletions occur for high-altitude, low altitude HSCT perturbations. Small increases in global total O3 can occur for low-altitude, high-altitude injections. Decreasing aerosol surface area densities and background chlorine levels increases the sensitivity of model O3 to the HSCT perturbations. The location of the aircraft emissions is the most important determinant of the model response. Response to the location of the HSCT emissions is not changed qualitatively by changes in background chlorine and aerosol loading. The response is also not very sensitive to changes in the rates of the reactions NO + HO2 yields NO2 + OH and HO2 + O3 yields OH + 2O2 over the limits of their respective uncertainties. Finally, levels of lower stratospheric HO(sub x) generally decrease when the HSCT perturbation is included, even though there are large increases in H2O due to the perturbation.

  1. Two-dimensional modeling of a polymer electrolyte membrane fuel cell with long flow channel. Part I. Model development

    OpenAIRE

    2015-01-01

    A two-dimensional single-phase model is developed for the steady-state and transient analysis of polymer electrolyte membrane fuel cells (PEMFC). Based on diluted and concentrated solution theories, viscous flow is introduced into a phenomenological multi-component modeling framework in the membrane. Characteristic variables related to the water uptake are discussed. A ButlereVolmer formulation of the current-overpotential relationship is developed based on an elementary mechanism of elect...

  2. Yang-Lee zeros of the two- and three-state Potts model defined on phi3 Feynman diagrams.

    Science.gov (United States)

    de Albuquerque, Luiz C; Dalmazi, D

    2003-06-01

    We present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q=2 state (Ising) and the q=3 state Potts model defined on phi(3) Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model, an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the q=3 state Potts model, our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations.

  3. Random-field Potts model for the polar domains of lead magnesium niobate and lead scandium tantalate

    Energy Technology Data Exchange (ETDEWEB)

    Qian, H.; Bursill, L.A

    1997-06-01

    A random filed Potts model is used to establish the spatial relationship between the nanoscale distribution of charges chemical defects and nanoscale polar domains for the perovskite-based relaxor materials lead magnesium niobate (PMN) and lead scandium tantalate (PST). The random fields are not set stochastically but are determined initially by the distribution of B-site cations (Mg, Nb) or (Sc, Ta) generated by Monte Carlo NNNI-model simulations for the chemical defects. An appropriate random field Potts model is derived and algorithms developed for a 2D lattice. It is shown that the local fields are strongly correlated with the chemical domain walls and that polar domains as a function of decreasing temperature is simulated for the two cases of PMN and PST. The dynamics of the polar clusters is also discussed. 33 refs., 9 figs.

  4. Continuity of the Phase Transition for Planar Random-Cluster and Potts Models with {1 ≤ q ≤ 4}

    Science.gov (United States)

    Duminil-Copin, Hugo; Sidoravicius, Vladas; Tassion, Vincent

    2017-01-01

    This article studies the planar Potts model and its random-cluster representation. We show that the phase transition of the nearest-neighbor ferromagnetic q-state Potts model on Z^2 is continuous for {q in {2,3,4}}, in the sense that there exists a unique Gibbs state, or equivalently that there is no ordering for the critical Gibbs states with monochromatic boundary conditions. The proof uses the random-cluster model with cluster-weight {q ≥ 1} (note that q is not necessarily an integer) and is based on two ingredients: The fact that the two-point function for the free state decays sub-exponentially fast for cluster-weights {1≤ q≤ 4}, which is derived studying parafermionic observables on a discrete Riemann surface.

  5. Two-dimensional numerical modelling of dissolved and particulate pollutant transport in the Three Gorges Reservoir

    Science.gov (United States)

    Hu, W.; Wang, L.-J.; Chen, H.; Holbach, A.; Zheng, B.-H.; Norra, S.; Westrich, B.

    2012-04-01

    After impoundment of the Three Gorges Reservoir (TGR) in 2003, hydrological regimes of the Yangtze River, upstream and downstream of the Three Gorges Dam, have been changed enormously, leading to significant environmental, ecological and social impacts. Nutrients and pollutants from agriculture, industry and municipalities are of concern due to their impact on the aquatic environment and hence, transport behavior of sediment associated pollutants must be modeled and analyzed to establish a sustainable water reservoir management. As part of the Chinese-German Yangtze-Project [1], two-dimensional numerical model TELEMAC is applied to study the dissolved and particulate pollutant transport at different locations of concern in the TGR. In-situ measurement campaigns for morphology and water quality data using mobile measuring device (MINIBAT) are carried out to provide detailed information for the different water bodies at different time. Additional morphological data are taken from cross-section profiles in the literature, the digital elevation model (DEM) of Shuttle Radar Topography Mission (SRTM) from CGIAR. Daily and hourly water level and discharge, suspended sediment concentration and pollutant loads are obtained from the authorities and extracted from literature. The model describes the spatial-temporal flow field, transport and dispersion of sediment associated pollutants with emphasis on the dynamic interaction and mutual influence of the river Yangtze, its major tributaries and adjacent lagoon-like dead water bodies due to the 30 meter annual reservoir water level fluctuation. Since algae bloom, especially in the tributaries and side arms of the mainstream, is one of the major issues occurred after 2003, the results of the numerical modeling together with the statistical analysis of the MINIBAT measurements are used for the eutrophication status analysis. Acknowledgments The Yangtze-Project is funded by the Federal Ministry of Education and Research (BMBF

  6. Structural phase transition in perovskite metal-formate frameworks: a Potts-type model with dipolar interactions.

    Science.gov (United States)

    Šimėnas, Mantas; Balčiūnas, Sergejus; Ma Combining Cedilla Czka, Mirosław; Banys, Jūras; Tornau, Evaldas E

    2016-07-21

    We propose a combined experimental and numerical study to describe an order-disorder structural phase transition in perovskite-based [(CH3)2NH2][M(HCOO)3] (M = Zn(2+), Mn(2+), Fe(2+), Co(2+) and Ni(2+)) dense metal-organic frameworks (MOFs). The three-fold degenerate orientation of the molecular (CH3)2NH2(+) (DMA(+)) cation implies a selection of the statistical three-state model of the Potts type. It is constructed on a simple cubic lattice where each lattice point can be occupied by a DMA(+) cation in one of the available states. In our model the main interaction is the nearest-neighbor Potts-type interaction, which effectively accounts for the H-bonding between DMA(+) cations and M(HCOO)3(-) cages. The model is modified by accounting for the dipolar interactions which are evaluated for the real monoclinic lattice using density functional theory. We employ the Monte Carlo method to numerically study the model. The calculations are supplemented with the experimental measurements of electric polarization. The obtained results indicate that the three-state Potts model correctly describes the phase transition order in these MOFs, while dipolar interactions are necessary to obtain better agreement with the experimental polarization. We show that in our model with substantial dipolar interactions the ground state changes from uniform to the layers with alternating polarization directions.

  7. Nonequilibrium critical dynamics of the two-dimensional Ashkin-Teller model at the Baxter line

    Science.gov (United States)

    Fernandes, H. A.; da Silva, R.; Caparica, A. A.; de Felício, J. R. Drugowich

    2017-04-01

    We investigate the short-time universal behavior of the two-dimensional Ashkin-Teller model at the Baxter line by performing time-dependent Monte Carlo simulations. First, as preparatory results, we obtain the critical parameters by searching the optimal power-law decay of the magnetization. Thus, the dynamic critical exponents θm and θp, related to the magnetic and electric order parameters, as well as the persistence exponent θg, are estimated using heat-bath Monte Carlo simulations. In addition, we estimate the dynamic exponent z and the static critical exponents β and ν for both order parameters. We propose a refined method to estimate the static exponents that considers two different averages: one that combines an internal average using several seeds with another, which is taken over temporal variations in the power laws. Moreover, we also performed the bootstrapping method for a complementary analysis. Our results show that the ratio β /ν exhibits universal behavior along the critical line corroborating the conjecture for both magnetization and polarization.

  8. A Method for Geometry Optimization in a Simple Model of Two-Dimensional Heat Transfer

    CERN Document Server

    Peng, Xiaohui; Protas, Bartosz

    2013-01-01

    This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations and involving a one-dimensional cooling element represented by a contour on which interface boundary conditions are specified. The problem consists in finding an optimal shape of the cooling element which will ensure that the solution in a given region is close (in the least squares sense) to some prescribed target distribution. We formulate this problem as PDE-constrained optimization and the locally optimal contour shapes are found using a gradient-based descent algorithm in which the Sobolev shape gradients are obtained using methods of the shape-differential calculus. The main novelty of this work is an accurate and efficient approach to the evaluation of the shape gradients based on a boundary-integral formulation which exploits certain analytical properties of the sol...

  9. Non-equilibrium relaxation in a two-dimensional stochastic lattice Lotka-Volterra model

    Science.gov (United States)

    Chen, Sheng; Täuber, Uwe C.

    We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. There are stable states when the predators and prey coexist. If the local prey carrying capacity is finite, there emerges an extinction threshold for the predator population at a critical value of the predation rate. We investigate the non-equilibrium relaxation of the predator density in the vicinity of this critical point. The expected power law dependence between the relaxation time and predation rate is observed (critical slowing down). The numerically determined associated critical exponents are in accord with the directed percolation universality class. Following a sudden predation rate change to its critical value, one observes critical aging for the predator density autocorrelation function with a universal scaling exponent. This aging scaling signature of the absorbing state phase transition emerges at significantly earlier times than stationary critical power laws, and could thus serve as an advanced indicator of the population's proximity to its extinction threshold. This research is supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award DE-FG02-09ER46613.

  10. Critical Casimir force scaling functions of the two-dimensional Ising model at finite aspect ratios

    Science.gov (United States)

    Hobrecht, Hendrik; Hucht, Alfred

    2017-02-01

    We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function Z on an L× M square lattice, wrapped around a torus with aspect ratio ρ =L/M . By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a 2× 2 transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films ρ \\to 0 . Additionally, for the cylinder at criticality our results confirm the predictions from conformal field theory.

  11. Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature

    Science.gov (United States)

    Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.

    2016-05-01

    Progress in describing thermodynamic phase transitions in quantum systems is obtained by noticing that the Gibbs operator e-β H for a two-dimensional (2D) lattice system with a Hamiltonian H can be represented by a three-dimensional tensor network, the third dimension being the imaginary time (inverse temperature) β . Coarse graining the network along β results in a 2D projected entangled-pair operator (PEPO) with a finite bond dimension D . The coarse graining is performed by a tree tensor network of isometries. The isometries are optimized variationally, taking into account full tensor environment, to maximize the accuracy of the PEPO. The algorithm is applied to the isotropic quantum compass model on an infinite square lattice near a symmetry-breaking phase transition at finite temperature. From the linear susceptibility in the symmetric phase and the order parameter in the symmetry-broken phase, the critical temperature is estimated at Tc=0.0606 (4 ) J , where J is the isotropic coupling constant between S =1/2 pseudospins.

  12. Electron-phonon vertex in the two-dimensional one-band Hubbard model

    Science.gov (United States)

    Huang, Z. B.; Hanke, W.; Arrigoni, E.; Scalapino, D. J.

    2003-12-01

    Using quantum Monte Carlo techniques, we study the effects of electronic correlations on the effective electron-phonon (el-ph) coupling in a two-dimensional one-band Hubbard model. We consider a momentum-independent bare ionic el-ph coupling. In the weak- and intermediate-correlation regimes, we find that the on-site Coulomb interaction U acts to effectively suppress the ionic el-ph coupling at all electron and phonon momenta. In this regime, our numerical simulations are in good agreement with the results of perturbation theory to order U2. However, entering the strong-correlation regime, we find that the forward-scattering process stops decreasing and begins to substantially increase as a function of U, leading to an effective el-ph coupling which is peaked in the forward direction. Whereas at weak and intermediate Coulomb interactions, screening is the dominant correlation effect suppressing the el-ph coupling, at larger U values irreducible vertex corrections become more important and give rise to this increase. These vertex corrections depend crucially on the renormalized electronic structure of the strongly correlated system.

  13. Numerical Modeling of Two-Dimensional Temperature Dynamics Across Ice-Wedge Polygons

    Science.gov (United States)

    Garayshin, Viacheslav V.

    The ice wedges on the North Slope of Alaska have been forming for many millennia, when the ground cracked and the cracks were filled with snowmelt water. The infiltrated water then became frozen and turned into ice. When the annual and summer air temperatures become higher, the depth of the active layer increases. A deeper seasonal thawing may cause melting of ice wedges from their tops. Consequently, the ground starts to settle and a trough begins to form above the ice wedge. The forming trough creates a local temperature anomaly in the surrounding ground, and the permafrost located immediately under the trough starts degrading further. Once the trough is formed, the winter snow cover becomes deeper at the trough area further degrading the permafrost. In this thesis we present a computational approach to study the seasonal temperature dynamics of the ground surrounding an ice wedge and ground subsidence associated with ice wedge degradation. A thermo-mechanical model of the ice wedge based on principles of macroscopic thermodynamics and continuum mechanics was developed and will be presented. The model includes heat conduction and quasi-static mechanical equilibrium equations, a visco-elastic rheology for ground deformation, and an empirical formula which relates unfrozen water content to temperature. The complete system is reduced to a computationally convenient set of coupled equations for temperature, ground displacement and ground porosity in a two-dimensional domain. A finite element method and an implicit scheme in time were utilized to construct a non-linear system of equations, which was solved iteratively. The model employs temperature and moisture content data collected from a field experiment at the Next-Generation Ecosystem Experiments (NGEE) sites in Barrow, Alaska. The model describes seasonal dynamics of temperature and the long-term ground motion near the ice wedges and helps to explain destabilization of the ice wedges north of Alaska's Brooks

  14. Three-state Potts model on triangular lattice with nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions

    Science.gov (United States)

    Murtazaev, Akai K.; Babaev, Albert B.; Magomedov, Magomed A.; Kassan-Ogly, Felix A.; Proshkin, Alexey I.

    2016-11-01

    Using Monte Carlo simulations, we investigated phase transitions and frustrations in the three-state Potts model on a triangular lattice with allowance for antiferromagnetic exchange interactions between nearest-neighbors J1 and next-nearest-neighbors J2. The ratio of the next-nearest-neighbor and nearest-neighbor exchange constants r=J2/J1 is chosen within the range of 0≤r≤2. Based on the analysis of the entropy, specific heat, system state density function, and fourth order Binder cumulants, the phase transitions in the Potts model with interactions J1<0 and J2<0 are shown to be found in value ranges of 0≤r<0.2 and 1.25≤r≤2.0. In an intermediate range of 0.2≤r≤1.0 the phase transition fails and the frustrations are revealed.

  15. Corner free energies and boundary effects for Ising, Potts and fully-packed loop models on the square and triangular lattices

    CERN Document Server

    Vernier, Eric

    2011-01-01

    We obtain long series expansions for the bulk, surface and corner free energies for several two-dimensional statistical models, by combining Enting's finite lattice method (FLM) with exact transfer matrix enumerations. The models encompass all integrable curves of the Q-state Potts model on the square and triangular lattices, including the antiferromagnetic transition curves and the Ising model (Q=2) at temperature T, as well as a fully-packed O(n) type loop model on the square lattice. The expansions are around the trivial fixed points at infinite Q, n or 1/T. By using a carefully chosen expansion parameter, q << 1, all expansions turn out to be of the form \\prod_{k=1}^\\infty (1-q^k)^{\\alpha_k + k \\beta_k}, where the coefficients \\alpha_k and \\beta_k are periodic functions of k. Thanks to this periodicity property we can conjecture the form of the expansions to all orders (except in a few cases where the periodicity is too large). These expressions are then valid for all 0 <= q < 1. We analyse in...

  16. Nonlinear sigma model in the case of N x. cap alpha. N rectangular matrices in two-dimensional euclidean space

    Energy Technology Data Exchange (ETDEWEB)

    Chekhov, L.O.

    1985-12-01

    Matrix nonlinear sigma models are discussed and the matrix nonlinear sigma model in the case of N x ..cap alpha..N rectangular matrices is considered. The authors show that in two-dimensional Euclidean space, the model is renormalizable with respect to ..cap alpha.. and 1/N. The fulfillment of the chirality identity is demonstrated in the operator expansion for the renormalized theory.

  17. Phase transitions in the two-dimensional Anisotropic Biquadratic Heisenberg Model

    Energy Technology Data Exchange (ETDEWEB)

    Moura, A.R., E-mail: armoura@infis.ufu.br [Universidade Federal de Uberlândia (Brazil); Pires, A.S.T., E-mail: antpires@fisica.ufmg.br [Universidade Federal de Minas Gerais (Brazil); Pereira, A.R., E-mail: apereira@ufv.br [Universidade Federal de Viçosa (Brazil)

    2014-05-01

    In this paper we study the influence of the single-ion anisotropy in the two-dimensional biquadratic Heisenberg model (ABHM) on the square lattice at zero and finite low temperatures. It is common to represent the bilinear and biquadratic terms by J{sub 1}=Jcosθ and J{sub 2}=Jsinθ, respectively, and the many phases present in the model as a function of θ are well documented. However we have adopted a constant value for the bilinear constant (J{sub 1}=1) and small values of the biquadratic term (|J{sub 2}|D{sub c}, the excited states are gapped and there is no spin long-range order (LRO) even at zero temperature. Using Schwinger bosonic representation and Self-Consistent Harmonic Approximation (SCHA), we have studied the quantum and thermal phase transitions as a function of the bilinear and biquadratic constants. - Highlights: • We study the anisotropic biquadric bilinear Heisenberg model on a square lattice. • We show the quantum phase transition associated with the anisotropic constant. • We obtain a thermal phase transition similar to the BKT transition.

  18. Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models.

    Science.gov (United States)

    Labuhn, Henning; Barredo, Daniel; Ravets, Sylvain; de Léséleuc, Sylvain; Macrì, Tommaso; Lahaye, Thierry; Browaeys, Antoine

    2016-06-30

    Spin models are the prime example of simplified many-body Hamiltonians used to model complex, strongly correlated real-world materials. However, despite the simplified character of such models, their dynamics often cannot be simulated exactly on classical computers when the number of particles exceeds a few tens. For this reason, quantum simulation of spin Hamiltonians using the tools of atomic and molecular physics has become a very active field over the past years, using ultracold atoms or molecules in optical lattices, or trapped ions. All of these approaches have their own strengths and limitations. Here we report an alternative platform for the study of spin systems, using individual atoms trapped in tunable two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100 per cent. When excited to high-energy Rydberg D states, the atoms undergo strong interactions whose anisotropic character opens the way to simulating exotic matter. We illustrate the versatility of our system by studying the dynamics of a quantum Ising-like spin-1/2 system in a transverse field with up to 30 spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects on the dynamics, we find excellent agreement with ab initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D states has a measurable influence. Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.

  19. Two-dimensional thermal modeling of power monolithic microwave integrated circuits (MMIC's)

    Science.gov (United States)

    Fan, Mark S.; Christou, Aris; Pecht, Michael G.

    1992-01-01

    Numerical simulations of the two-dimensional temperature distributions for a typical GaAs MMIC circuit are conducted, aiming at understanding the heat conduction process of the circuit chip and providing temperature information for device reliability analysis. The method used is to solve the two-dimensional heat conduction equation with a control-volume-based finite difference scheme. In particular, the effects of the power dissipation and the ambient temperature are examined, and the criterion for the worst operating environment is discussed in terms of the allowed highest device junction temperature.

  20. Spin transport in the two-dimensional quantum disordered anisotropic Heisenberg model

    Energy Technology Data Exchange (ETDEWEB)

    Lima, L.S. [Departamento de Física e Matemática, Centro Federal de Educação Tecnológica de Minas Gerais, 30510-000 Belo Horizonte, MG (Brazil); Pires, A.S.T.; Costa, B.V. [Departamento de Física ICEx, UFMG, CP 702, 31270-901 Belo Horizonte, MG (Brazil)

    2014-12-15

    We use the self consistent harmonic approximation together with the Linear Response Theory to study the effect of nonmagnetic disorder on spin transport in the quantum diluted two-dimensional anisotropic Heisenberg model with spin S=1 in a square lattice. The model has a BKT transition at zero dilution. We calculate the regular part of the spin conductivity σ{sup reg}(ω) and the Drude weight D{sub S}(T) as a function of the non-magnetic concentration, x. Our calculations show that the spin conductivity drops abruptly to zero at x{sub c}{sup SCHA}≈0.5 indicating that the system changes from an ideal spin conductor state to an insulator. This value is far above the site percolation threshold x{sub c}{sup site}≈0.41. Although the SCHA fails in determining precisely the percolation threshold, both the spin conductivity and the Drude weight show a quite regular behavior inside 0≤x≤x{sub c}{sup SCHA} indicating that the transition stays in the same universality class all along the interval. - Highlights: • The site dilution generates a large influence on regular part of the spin conductivity, σ{sup reg}(ω), and in the Drude weight, D(T). • In a concentration of impurities about x≈0.5, the regular part of the spin conductivity and the Drude weight fall to zero. • In this point we have a change in the state of the system from an ideal spin conductor to a spin insulator.

  1. On the two-dimensional dynamical Ising model in the phase coexistence region

    Science.gov (United States)

    Martinelli, F.

    1994-09-01

    We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of side L, in the absence of an external field and at large inverse temperature β. We first consider the gap in the spectrum of the generator of the dynamics in two different cases: with plus and open boundary conditions. We prove that, when the symmetry under global spin flip is broken by the boundary conditions, the gap is much larger than the case in which the symmetry is present. For this latter we compute exactly the asymptotics of -(1/β L) log(gap) as L→∞ and show that it coincides with the surface tension along one of the coordinate axes. As a consequence we are able to study quite precisely the large deviations in time of the magnetization and to obtain an upper bound on the spin-spin time correlation in the infinite-volume plus phase. Our results establish a connection between the dynamical large deviations and those of the equilibrium Gibbs measure studied by Shlosman in the framework of the rigorous description of the Wulff shape for the Ising model. Finally we show that, in the case of open boundary conditions, it is possible to rescale the time with L in such a way that, as L→∞, the finite-dimensional distributions of the time-rescaled magnetization converge to those of a symmetric continuous-time Markov chain on the two-state space {- m *(β), m *(β)}, m *(β) being the spontaneous magnetization. Our methods rely upon a novel combination of techniques for bounding from below the gap of symmetric Markov chains on complicated graphs, developed by Jerrum and Sinclair in their Markov chain approach to hard computational problems, and the idea of introducing "block Glauber dynamics" instead of the standard single-site dynamics, in order to put in evidence more effectively the effect of the boundary conditions in the approach to equilibrium.

  2. Two-dimensional spectroscopy of molecular excitons in a model dimer system

    Science.gov (United States)

    Halpin, Alexei

    The physics of molecular excitons has been the subject of many recent studies using electronic two-dimensional photon-echo spectroscopy (2DPE), particularly in the context of light harvesting in photosynthesis. Since the spectra for multichromophoric aggregates are congested, particularly so at room temperature, we present a study of a model dimer comprised of identical chromophores with a well defined electronic coupling strength, to provide clear signatures for coherences between vibronic excitons in 2D spectra. We begin by describing the design of a broadband passively phase-stabilized interferometer for collection of 2D spectra, which also allows for the investigation of state preparation in 2D spectroscopy by using shaped excitation pulses. In experiments on the model dimer we observe strong oscillating off-diagonal features in the 2D spectra which are present only before the onset of dephasing, which occurs in less than 100 fs due to strong system-bath coupling. This is in contrast with the parent dye, where low amplitude oscillations associated with Raman active vibrations persist for several ps following excitation. The results of this comparative study indicate that the signals observed earlier in photosynthetic proteins likely reflect vibrational motion in isolated pigments, and not delocalized quantum coherence. While long-lived vibrational coherences are of questionable biological relevance at face value, we conclude with a discussion on initial findings using coherently controlled 2D spectroscopy, where we observe long-lived signatures associated to vibronic coherences at room temperature. These results point to new directions of study using multidimensional spectroscopy to unravel the role of coherence in excitation energy transfer in molecular aggregates in an experimentally direct fashion.

  3. Self Organized Criticality in a two dimensional Cellular Automaton model of a magnetic flux tube with background flow

    CERN Document Server

    Danila, Bogdan; Mocanu, Gabriela

    2015-01-01

    We investigate the transition to Self Organized Criticality in a two-dimensional model of a flux tube with a background flow. The magnetic induction equation, represented by a partial differential equation with a stochastic source term, is discretized and implemented on a two dimensional cellular automaton. The energy released by the automaton during one relaxation event is the magnetic energy. As a result of the simulations we obtain the time evolution of the energy release, of the system control parameter, of the event lifetime distribution and of the event size distribution, respectively, and we establish that a Self Organized Critical state is indeed reached by the system. Moreover, energetic initial impulses in the magnetohydrodynamic flow can lead to one dimensional signatures in the magnetic two dimensional system, once the Self Organized Critical regime is established. The applications of the model for the study of Gamma Ray Bursts is briefly considered, and it is shown that some astrophysical paramet...

  4. Nonlinear sigma-model in the case of rectangular Nx. alpha. N matrices in two-dimensional euclidean space

    Energy Technology Data Exchange (ETDEWEB)

    Chekhov, L.O.

    1985-06-01

    Matrix nonlinear sigma-model is considered in the case of rectangular matrices of the dimension Nx..alpha..N. Renormalizability of the model with respect to ..alpha.. and 1/N is demonstrated for the case of two-dimensional Euclidean space. Validity of the chiral identity is proved in the operator expansion for the renormalized theory.

  5. COMPUTER SIMULATION OF ANTIFERROMAGNETIC STRUCTURES DESCRIBED BY THE THREE-VERTEX ANTIFERROMAGNETIC POTTS MODEL

    Directory of Open Access Journals (Sweden)

    Yarash K. Abuev

    2017-01-01

    Full Text Available Abstract. Objectives A computer simulation of the antiferromagnetic structures described by the three-vertex Potts model on a triangular lattice is performed, taking into account the antiferromagnetic exchange interactions between the nearest J1 and second J2 neighbours. The main goal of the computer simulation was to elucidate the effects of ground state and areas of frustration on the thermodynamic and magnetic properties of antiferromagnetic structures described by the lowdimensional Potts model. Method The computer simulation is based on the Monte Carlo method. This method is implemented using the Metropolis algorithm in combination with the Wolff claster algorithm. The computer simulation was carried out for low-dimensional systems with periodic boundary conditions and linear dimensions L = 24124. Results On the basis of heat capacity and entropy analysis, phase transitions were observed in the considered model to possess exchange interaction parameters J1 <0 and J2 <0 in the variation intervals 0r<0.2 and 1.0

  6. Three-state Potts model on non-local directed small-world lattices

    Science.gov (United States)

    Ferraz, Carlos Handrey Araujo; Lima, José Luiz Sousa

    2017-10-01

    In this paper, we study the non-local directed Small-World (NLDSW) disorder effects in the three-state Potts model as a form to capture the essential features shared by real complex systems where non-locality effects play a important role in the behavior of these systems. Using Monte Carlo techniques and finite-size scaling analysis, we estimate the infinite lattice critical temperatures and the leading critical exponents in this model. In particular, we investigate the first- to second-order phase transition crossover when NLDSW links are inserted. A cluster-flip algorithm was used to reduce the critical slowing down effect in our simulations. We find that for a NLDSW disorder densities p model exhibits a continuous phase transition falling into a new universality class, which continuously depends on the value of p, while for p∗ ⩽ p ⩽ 1 . 0, the model presents a weak first-order phase transition.

  7. Model for ballistic spin-transport in ferromagnet/two-dimensional electron gas/ferromagnet structures

    NARCIS (Netherlands)

    Schapers, T; Nitta, J; Heersche, HB; Takayanagi, H

    2002-01-01

    The spin dependent conductance of a ferromagnet/two-dimensional electron gas ferromagnet structure is theoretically examined in the ballistic transport regime. It is shown that the spin signal can be improved considerably by making use of the spin filtering effect of a barrier at the ferromagnet two

  8. Collapse arresting in an inhomogeneous two-dimensional nonlinear Schrodinger model

    DEFF Research Database (Denmark)

    Schjødt-Eriksen, Jens; Gaididei, Yuri Borisovich; Christiansen, Peter Leth

    2001-01-01

    Collapse of (2 + 1)-dimensional beams in the inhomogeneous two-dimensional cubic nonlinear Schrodinger equation is analyzed numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams that in a homogeneous medium would collapse may...

  9. Structural properties of Potts model partition functions and chromatic polynomials for lattice strips

    Science.gov (United States)

    Chang, Shu-Chiuan; Shrock, Robert

    2001-07-01

    The q-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width Ly and arbitrary length Lx has the form Z(G,q,v)=∑ j=1N Z,G,λ c Z,G,j(λ Z,G,j) L x, where v is a temperature-dependent variable. The special case of the zero-temperature antiferromagnet ( v=-1) is the chromatic polynomial P( G, q). Using coloring and transfer matrix methods, we give general formulas for C X,G=∑ j=1N X,G,λ c X,G,j for X= Z, P on cyclic and Möbius strip graphs of the square and triangular lattice. Combining these with a general expression for the (unique) coefficient cZ, G, j of degree d in q: c (d)=U 2d( q/2) , where Un( x) is the Chebyshev polynomial of the second kind, we determine the number of λZ, G, j's with coefficient c( d) in Z( G, q, v) for these cyclic strips of width Ly to be n Z(L y,d)=(2d+1)(L y+d+1) -1{2L y}/{L y-d } for 0⩽ d⩽ Ly and zero otherwise. For both cyclic and Möbius strips of these lattices, the total number of distinct eigenvalues λZ, G, j is calculated to be N Z,L y,λ = {2L y}/{L y}. Results are also presented for the analogous numbers nP( Ly, d) and NP, Ly, λ for P( G, q). We find that nP( Ly,0)= nP( Ly-1,1)= MLy-1 (Motzkin number), nZ( Ly,0)= CLy (the Catalan number), and give an exact expression for NP, Ly, λ. Our results for NZ, Ly, λ and NP, Ly, λ apply for both the cyclic and Möbius strips of both the square and triangular lattices; we also point out the interesting relations NZ, Ly, λ=2 NDA, tri, Ly and NP, Ly, λ=2 NDA, sq, Ly, where NDA, Λ, n denotes the number of directed lattice animals on the lattice Λ. We find the asymptotic growths NZ, Ly, λ∼ Ly-1/24 Ly and NP, Ly, λ∼ Ly-1/23 Ly as Ly→∞. Some general geometric identities for Potts model partition functions are also presented.

  10. Two-dimensional NMR measurement and point dipole model prediction of paramagnetic shift tensors in solids

    Energy Technology Data Exchange (ETDEWEB)

    Walder, Brennan J.; Davis, Michael C.; Grandinetti, Philip J. [Department of Chemistry, Ohio State University, 100 West 18th Avenue, Columbus, Ohio 43210 (United States); Dey, Krishna K. [Department of Physics, Dr. H. S. Gour University, Sagar, Madhya Pradesh 470003 (India); Baltisberger, Jay H. [Division of Natural Science, Mathematics, and Nursing, Berea College, Berea, Kentucky 40403 (United States)

    2015-01-07

    A new two-dimensional Nuclear Magnetic Resonance (NMR) experiment to separate and correlate the first-order quadrupolar and chemical/paramagnetic shift interactions is described. This experiment, which we call the shifting-d echo experiment, allows a more precise determination of tensor principal components values and their relative orientation. It is designed using the recently introduced symmetry pathway concept. A comparison of the shifting-d experiment with earlier proposed methods is presented and experimentally illustrated in the case of {sup 2}H (I = 1) paramagnetic shift and quadrupolar tensors of CuCl{sub 2}⋅2D{sub 2}O. The benefits of the shifting-d echo experiment over other methods are a factor of two improvement in sensitivity and the suppression of major artifacts. From the 2D lineshape analysis of the shifting-d spectrum, the {sup 2}H quadrupolar coupling parameters are 〈C{sub q}〉 = 118.1 kHz and 〈η{sub q}〉 = 0.88, and the {sup 2}H paramagnetic shift tensor anisotropy parameters are 〈ζ{sub P}〉 = − 152.5 ppm and 〈η{sub P}〉 = 0.91. The orientation of the quadrupolar coupling principal axis system (PAS) relative to the paramagnetic shift anisotropy principal axis system is given by (α,β,γ)=((π)/2 ,(π)/2 ,0). Using a simple ligand hopping model, the tensor parameters in the absence of exchange are estimated. On the basis of this analysis, the instantaneous principal components and orientation of the quadrupolar coupling are found to be in excellent agreement with previous measurements. A new point dipole model for predicting the paramagnetic shift tensor is proposed yielding significantly better agreement than previously used models. In the new model, the dipoles are displaced from nuclei at positions associated with high electron density in the singly occupied molecular orbital predicted from ligand field theory.

  11. PM-PM: PatchMatch with Potts Model for object segmentation and stereo matching.

    Science.gov (United States)

    Xu, Shibiao; Zhang, Feihu; He, Xiaofei; Shen, Xukun; Zhang, Xiaopeng

    2015-07-01

    This paper presents a unified variational formulation for joint object segmentation and stereo matching, which takes both accuracy and efficiency into account. In our approach, depth-map consists of compact objects, each object is represented through three different aspects: 1) the perimeter in image space; 2) the slanted object depth plane; and 3) the planar bias, which is to add an additional level of detail on top of each object plane in order to model depth variations within an object. Compared with traditional high quality solving methods in low level, we use a convex formulation of the multilabel Potts Model with PatchMatch stereo techniques to generate depth-map at each image in object level and show that accurate multiple view reconstruction can be achieved with our formulation by means of induced homography without discretization or staircasing artifacts. Our model is formulated as an energy minimization that is optimized via a fast primal-dual algorithm, which can handle several hundred object depth segments efficiently. Performance evaluations in the Middlebury benchmark data sets show that our method outperforms the traditional integer-valued disparity strategy as well as the original PatchMatch algorithm and its variants in subpixel accurate disparity estimation. The proposed algorithm is also evaluated and shown to produce consistently good results for various real-world data sets (KITTI benchmark data sets and multiview benchmark data sets).

  12. Operator content of the critical Potts model in d dimensions and logarithmic correlations

    Energy Technology Data Exchange (ETDEWEB)

    Vasseur, Romain, E-mail: rvasseur@berkeley.edu [Department of Physics, University of California, Berkeley, Berkeley, CA 94720 (United States); Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Jacobsen, Jesper Lykke [LPTENS, 24 rue Lhomond, 75231 Paris (France); Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris (France)

    2014-03-15

    Using the symmetric group S{sub Q} symmetry of the Q-state Potts model, we classify the (scalar) operator content of its underlying field theory in arbitrary dimension. In addition to the usual identity, energy and magnetization operators, we find fields that generalize the N-cluster operators well-known in two dimensions, together with their subleading counterparts. We give the explicit form of all these operators – up to non-universal constants – both on the lattice and in the continuum limit for the Landau theory. We compute exactly their two- and three-point correlation functions on an arbitrary graph in terms of simple probabilities, and give the general form of these correlation functions in the continuum limit at the critical point. Specializing to integer values of the parameter Q, we argue that the analytic continuation of the S{sub Q} symmetry yields logarithmic correlations at the critical point in arbitrary dimension, thus implying a mixing of some scaling fields by the scale transformation generator. All these logarithmic correlation functions are given a clear geometrical meaning, which can be checked in numerical simulations. Several physical examples are discussed, including bond percolation, spanning trees and forests, resistor networks and the Ising model. We also briefly address the generalization of our approach to the O(n) model.

  13. A two-dimensional algebraic quantum liquid produced by an atomic simulator of the quantum Lifshitz model.

    Science.gov (United States)

    Po, Hoi Chun; Zhou, Qi

    2015-08-13

    Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems.

  14. Reconstruction of a real world social network using the Potts model and Loopy Belief Propagation

    Directory of Open Access Journals (Sweden)

    Cristian eBisconti

    2015-11-01

    Full Text Available The scope of this paper is to test the adoption of a statistical model derived from Condensed Matter Physics, aiming at the reconstruction of a networked structure from observations of the states of the nodes in the network.The inverse Potts model, normally applied to observations of quantum states, is here addressed to observations of the node states in a network and their (anticorrelations, thus inferring interactions as links connecting the nodes. Adopting the Bethe approximation, such an inverse problem is known to be tractable.Within this operational framework, we discuss and apply this network-reconstruction method to a small real-world social network, where it is easy to track statuses of its members: the Italian parliament, adopted as a case study. The dataset is made of (cosponsorships of law proposals by parliament members. In previous studies of similar activity-based networks, the graph structure was inferred directly from activity co-occurrences: here we compare our statistical reconstruction with standard methods, outlining discrepancies and advantages.

  15. A cellular Potts model analyzing differentiated cell behavior during in vivo vascularization of a hypoxic tissue.

    Science.gov (United States)

    Scianna, Marco; Bassino, Eleonora; Munaron, Luca

    2015-08-01

    Angiogenesis, the formation of new blood vessel networks from existing capillary or post-capillary venules, is an intrinsically multiscale process occurring in several physio-pathological conditions. In particular, hypoxic tissue cells activate downstream cascades culminating in the secretion of a wide range of angiogenic factors, including VEGF isoforms. Such diffusive chemicals activate the endothelial cells (ECs) forming the external walls of the nearby vessels that chemotactically migrate toward the hypoxic areas of the tissue as multicellular sprouts. A functional network eventually emerges by further branching and anastomosis processes. We here propose a CPM-based approach reproducing selected features of the angiogenic progression necessary for the reoxygenation of a hypoxic tissue. Our model is able to span the different scale involved in the angiogenic progression as it incorporates reaction-diffusion equations for the description of the evolution of microenvironmental variables in a discrete mesoscopic cellular Potts model (CPM) that reproduces the dynamics of the vascular cells. A key feature of this work is the explicit phenotypic differentiation of the ECs themselves, distinguished in quiescent, stalk and tip. The simulation results allow identifying a set of key mechanisms underlying tissue vascularization. Further, we provide evidence that the nascent pattern is characterized by precise topological properties. Finally, we link abnormal sprouting angiogenesis with alteration in selected cell behavior. Copyright © 2015 Elsevier Ltd. All rights reserved.

  16. Reconstruction of a Real World Social Network using the Potts Model and Loopy Belief Propagation.

    Science.gov (United States)

    Bisconti, Cristian; Corallo, Angelo; Fortunato, Laura; Gentile, Antonio A; Massafra, Andrea; Pellè, Piergiuseppe

    2015-01-01

    The scope of this paper is to test the adoption of a statistical model derived from Condensed Matter Physics, for the reconstruction of the structure of a social network. The inverse Potts model, traditionally applied to recursive observations of quantum states in an ensemble of particles, is here addressed to observations of the members' states in an organization and their (anti)correlations, thus inferring interactions as links among the members. Adopting proper (Bethe) approximations, such an inverse problem is showed to be tractable. Within an operational framework, this network-reconstruction method is tested for a small real-world social network, the Italian parliament. In this study case, it is easy to track statuses of the parliament members, using (co)sponsorships of law proposals as the initial dataset. In previous studies of similar activity-based networks, the graph structure was inferred directly from activity co-occurrences: here we compare our statistical reconstruction with such standard methods, outlining discrepancies and advantages.

  17. Metastability of the Two-Dimensional Blume-Capel Model with Zero Chemical Potential and Small Magnetic Field

    Science.gov (United States)

    Landim, C.; Lemire, P.

    2016-07-01

    We consider the two-dimensional Blume-Capel model with zero chemical potential and small magnetic field evolving on a large but finite torus. We obtain sharp estimates for the transition time, we characterize the set of critical configurations, and we prove the metastable behavior of the dynamics as the temperature vanishes.

  18. Improved energy extrapolation with infinite projected entangled-pair states applied to the two-dimensional Hubbard model

    NARCIS (Netherlands)

    Corboz, P.

    2016-01-01

    An infinite projected entangled-pair state (iPEPS) is a variational tensor network ansatz for two-dimensional wave functions in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension D. We show that for the doped Hubbard model in the strongly correlated reg

  19. Application of two-dimensional infrared spectroscopy to benchmark models for the amide I band of proteins

    NARCIS (Netherlands)

    Bondarenko, Anna S.; Jansen, Thomas L. C.

    2015-01-01

    In this paper, we present a novel benchmarking method for validating the modelling of vibrational spectra for the amide I region of proteins. We use the linear absorption spectra and two-dimensional infrared spectra of four experimentally well-studied proteins as a reference and test nine combinatio

  20. Two-dimensional vertical moisture-pressure dynamics above groundwater waves: Sand flume experiments and modelling

    Science.gov (United States)

    Shoushtari, Seyed Mohammad Hossein Jazayeri; Cartwright, Nick; Perrochet, Pierre; Nielsen, Peter

    2017-01-01

    This paper presents a new laboratory dataset on the moisture-pressure relationship above a dispersive groundwater wave in a two-dimensional vertical unconfined sand flume aquifer driven by simple harmonic forcing. A total of five experiments were conducted in which all experimental parameters were kept constant except for the oscillation period, which ranged from 268 s to 2449 s between tests. Moisture content and suction head sensor pairings were co-located at two locations in the unsaturated zone both approximately 0.2 m above the mean watertable elevation and respectively 0.3 m and 0.75 m from the driving head boundary. For all oscillation periods except for the shortest (T = 268s), the formation of a hysteretic moisture-pressure scanning loop was observed. Consistent with the decay of the saturated zone groundwater wave, the size of the observed moisture-pressure scanning loops decayed with increasing distance landward and the decay rate is larger for the shorter oscillation periods. At the shortest period (T = 268s), the observed moisture-pressure relationship was observed to be non-hysteretic but with a capillary capacity that differs from that of the static equilibrium wetting and drying curves. This finding is consistent with observations from existing one-dimensional vertical sand column experiments. The relative damping of the moisture content with distance landward is higher than that for the suction head consistent with the fact that transmission of pressure through a porous medium occurs more readily than mass transfer. This is further supported by the fact that observed phase lags for the unsaturated zone variables (i.e. suction head and moisture content) relative to the driving head are greater than the saturated zone variables (i.e. piezometric head). Harmonic analysis of the data reveals no observable generation of higher harmonics in either moisture or pressure despite the strongly non-linear relationship between the two. In addition, a phase lag

  1. Cellular Potts modeling of tumor growth, tumor invasion and tumor evolution

    Directory of Open Access Journals (Sweden)

    András eSzabó

    2013-04-01

    Full Text Available Despite a growing wealth of available molecular data, the growth of tumors, invasion of tumors into healthy tissue, and response of tumors to therapies are still poorly understood. Although genetic mutations are in general the first step in the development of a cancer, for the mutated cell to persist in a tissue, it must compete against the other, healthy or diseased cells, for example by becoming more motile, adhesive, or multiplying faster. Thus, the cellular phenotype determines the success of a cancer cell in competition with its neighbors, irrespective of the genetic mutations or physiological alterations that gave rise to the altered phenotype.What phenotypes can make a cell successful in an environment of healthy and cancerous cells, and how? A widely-used tool for getting more insight into that question is cell-based modeling. Cell based models constitute a class of computational, agent-based models that mimic biophysical and molecular interactions between cells. One of the most widely used cell-based modeling formalisms is the cellular Potts model (CPM, a lattice-based, multi particle cell-based modeling approach. The CPM has become a popular and accessible method for modeling mechanisms of multicellular processes including cell sorting, gastrulation,or angiogenesis. The CPM accounts for biophysical cellular properties, including cell proliferation, cell motility, and cell adhesion, which play a key role in cancer. Multiscale models are constructed by extending the agents with intracellular processes including metabolism, growth, and signaling. Here we review the use of the CPM for modeling tumor growth, tumor invasion, and tumor progression. We argue that the accessibility and flexibility of the CPM, and its accurate, yet coarse-grained and computationally efficient representation of cell- and tissue biophysics, make the CPM the method of choice for modeling cellular processesin tumor development.

  2. Cellular potts modeling of tumor growth, tumor invasion, and tumor evolution.

    Science.gov (United States)

    Szabó, András; Merks, Roeland M H

    2013-01-01

    Despite a growing wealth of available molecular data, the growth of tumors, invasion of tumors into healthy tissue, and response of tumors to therapies are still poorly understood. Although genetic mutations are in general the first step in the development of a cancer, for the mutated cell to persist in a tissue, it must compete against the other, healthy or diseased cells, for example by becoming more motile, adhesive, or multiplying faster. Thus, the cellular phenotype determines the success of a cancer cell in competition with its neighbors, irrespective of the genetic mutations or physiological alterations that gave rise to the altered phenotype. What phenotypes can make a cell "successful" in an environment of healthy and cancerous cells, and how? A widely used tool for getting more insight into that question is cell-based modeling. Cell-based models constitute a class of computational, agent-based models that mimic biophysical and molecular interactions between cells. One of the most widely used cell-based modeling formalisms is the cellular Potts model (CPM), a lattice-based, multi particle cell-based modeling approach. The CPM has become a popular and accessible method for modeling mechanisms of multicellular processes including cell sorting, gastrulation, or angiogenesis. The CPM accounts for biophysical cellular properties, including cell proliferation, cell motility, and cell adhesion, which play a key role in cancer. Multiscale models are constructed by extending the agents with intracellular processes including metabolism, growth, and signaling. Here we review the use of the CPM for modeling tumor growth, tumor invasion, and tumor progression. We argue that the accessibility and flexibility of the CPM, and its accurate, yet coarse-grained and computationally efficient representation of cell and tissue biophysics, make the CPM the method of choice for modeling cellular processes in tumor development.

  3. Computer model of two-dimensional solute transport and dispersion in ground water

    Science.gov (United States)

    Konikow, Leonard F.; Bredehoeft, J.D.

    1978-01-01

    This report presents a model that simulates solute transport in flowing ground water. The model is both general and flexible in that it can be applied to a wide range of problem types. It is applicable to one- or two-dimensional problems involving steady-state or transient flow. The model computes changes in concentration over time caused by the processes of convective transport, hydrodynamic dispersion, and mixing (or dilution) from fluid sources. The model assumes that the solute is non-reactive and that gradients of fluid density, viscosity, and temperature do not affect the velocity distribution. However, the aquifer may be heterogeneous and (or) anisotropic. The model couples the ground-water flow equation with the solute-transport equation. The digital computer program uses an alternating-direction implicit procedure to solve a finite-difference approximation to the ground-water flow equation, and it uses the method of characteristics to solve the solute-transport equation. The latter uses a particle- tracking procedure to represent convective transport and a two-step explicit procedure to solve a finite-difference equation that describes the effects of hydrodynamic dispersion, fluid sources and sinks, and divergence of velocity. This explicit procedure has several stability criteria, but the consequent time-step limitations are automatically determined by the program. The report includes a listing of the computer program, which is written in FORTRAN IV and contains about 2,000 lines. The model is based on a rectangular, block-centered, finite difference grid. It allows the specification of any number of injection or withdrawal wells and of spatially varying diffuse recharge or discharge, saturated thickness, transmissivity, boundary conditions, and initial heads and concentrations. The program also permits the designation of up to five nodes as observation points, for which a summary table of head and concentration versus time is printed at the end of the

  4. Construction of two-dimensional quantum field models through Longo-Witten endomorphisms

    CERN Document Server

    Tanimoto, Yoh

    2013-01-01

    We present a procedure to construct families of local, massive and interacting Haag-Kastler nets on the two-dimensional spacetime through an operator-algebraic method. An existence proof of local observable is given without relying on modular nuclearity. By a similar technique, another family of wedge-local nets is constructed using certain endomorphisms of conformal nets recently studied by Longo and Witten.

  5. Graphene as a Prototypical Model for Two-Dimensional Continuous Mechanics

    Directory of Open Access Journals (Sweden)

    Philippe Lambin

    2017-08-01

    Full Text Available This paper reviews a few problems where continuous-medium theory specialized to two-dimensional media provides a qualitatively correct picture of the mechanical behavior of graphene. A critical analysis of the parameters involved is given. Among other results, a simple mathematical description of a folded graphene sheet is proposed. It is also shown how the graphene–graphene adhesion interaction is related to the cleavage energy of graphite and its C 33 bulk elastic constant.

  6. An immersed interface method for two-dimensional modelling of stratified flow in pipes

    OpenAIRE

    Berthelsen, Petter Andreas

    2004-01-01

    This thesis deals with the construction of a numerical method for solving two-dimensional elliptic interface problems, such as fully developed stratified flow in pipes. Interface problems are characterized by its non-smooth and often discontinuous behaviour along a sharp boundary separating the fluids or other materials. Classical numerical schemes are not suitable for these problems due to the irregular geometry of the interface. Standard finite difference discretization across the interface...

  7. Dynamics of kinks in one- and two-dimensional hyperbolic models with quasidiscrete nonlinearities.

    Science.gov (United States)

    Rotstein, H G; Mitkov, I; Zhabotinsky, A M; Epstein, I R

    2001-06-01

    We study the evolution of fronts in the Klein-Gordon equation when the nonlinear term is inhomogeneous. Extending previous works on homogeneous nonlinear terms, we describe the derivation of an equation governing the front motion, which is strongly nonlinear, and, for the two-dimensional case, generalizes the damped Born-Infeld equation. We study the motion of one- and two-dimensional fronts finding a much richer dynamics than in the homogeneous system case, leading, in most cases, to the stabilization of one phase inside the other. For a one-dimensional front, the function describing the inhomogeneity of the nonlinear term acts as a "potential function" for the motion of the front, i.e., a front initially placed between two of its local maxima asymptotically approaches the intervening minimum. Two-dimensional fronts, with radial symmetry and without dissipation can either shrink to a point in finite time, grow unboundedly, or their radius can oscillate, depending on the initial conditions. When dissipation effects are present, the oscillations either decay spirally or not depending on the value of the damping dissipation parameter. For fronts with a more general shape, we present numerical simulations showing the same behavior.

  8. Phase diagram and two-particle structure of the $Z_3$-chiral Potts model

    CERN Document Server

    Von Gehlen, G

    1992-01-01

    We calculate the low-lying part of the spectrum of the $Z_3$-symmetrical chiral Potts quantum chain in its self-dual and integrable versions, using numerical diagonalisation of the hamiltonian for $N \\leq 12$ sites and extrapolation $N \\ra \\infty$. From the sequences of levels crossing we show that the massive phases have oscillatory correlation functions. We calculate the wave vector scaling exponent. In the high-temperature massive phase the pattern of the low-lying levels can be explained assuming the existence of two particles, with $Z_3$-charge $Q\\!=\\!1$ and $Q\\!=\\!2$, and their scattering states. In the superintegrable case the $Q\\!=\\!2$-particle has twice the mass of the $Q\\!=\\!1$-particle. Exponential convergence in $N$ is observed for the single particle gaps, while power convergence is seen for the scattering levels. In the high temperature limit of the self-dual model the parity violation in the particle dispersion relation is equivalent to the presence of a macroscopic momentum $P_m = \\pm \\vph/3$,...

  9. Competitive heterogeneous nucleation onto a microscopic impurity in a Potts model

    Science.gov (United States)

    Asuquo, Cletus C.; McArthur, Danielle; Bowles, Richard K.

    2016-08-01

    Many metastable systems can nucleate to multiple competing stable or intermediate metastable states. In this work, a Potts model, subject to external fields, is used to study the competitive nucleation of two phases attempting to grow on a microscopic impurity. Monte Carlo simulations are used to calculate the free energy surfaces for the system under different conditions, where the relative stability of the phases is adjusted by changing the interaction parameters, and the nucleation rates obtained using multicomponent transition state theory (TST) are compared with the rates measured using the survival probability method. We find that the two methods predict similar nucleation rates when the free energy barrier used in the transition state theory is defined as the work required to form a critical embryo from the metastable phase. An analysis of the free energy surfaces also reveals that the competition between the nucleating phases leads to an effective drying of the impurity which slows down the nucleation rate compared to the single phase case.

  10. Numerical model for two-dimensional hydrodynamics and energy transport. [VECTRA code

    Energy Technology Data Exchange (ETDEWEB)

    Trent, D.S.

    1973-06-01

    The theoretical basis and computational procedure of the VECTRA computer program are presented. VECTRA (Vorticity-Energy Code for TRansport Analysis) is designed for applying numerical simulation to a broad range of intake/discharge flows in conjunction with power plant hydrological evaluation. The code computational procedure is based on finite-difference approximation of the vorticity-stream function partial differential equations which govern steady flow momentum transport of two-dimensional, incompressible, viscous fluids in conjunction with the transport of heat and other constituents.

  11. Modeling A.C. Electronic Transport through a Two-Dimensional Quantum Point Contact

    Energy Technology Data Exchange (ETDEWEB)

    Aronov, I.E.; Beletskii, N.N.; Berman, G.P.; Campbell, D.K.; Doolen, G.D.; Dudiy, S.V.

    1998-12-07

    We present the results on the a.c. transport of electrons moving through a two-dimensional (2D) semiconductor quantum point contact (QPC). We concentrate our attention on the characteristic properties of the high frequency admittance ({omega}{approximately}0 - 50 GHz), and on the oscillations of the admittance in the vicinity of the separatrix (when a channel opens or closes), in presence of the relaxation effects. The experimental verification of such oscillations in the admittance would be a strong confirmation of the semi-classical approach to the a.c. transport in a QPC, in the separatrix region.

  12. Modelling and design of complete photonic band gaps in two-dimensional photonic crystals

    Indian Academy of Sciences (India)

    Yogita Kalra; R K Sinha

    2008-01-01

    In this paper, we investigate the existence and variation of complete photonic band gap size with the introduction of asymmetry in the constituent dielectric rods with honeycomb lattices in two-dimensional photonic crystals (PhC) using the plane-wave expansion (PWE) method. Two examples, one consisting of elliptical rods and the other comprising of rectangular rods in honeycomb lattices are considered with a view to estimate the design parameters for maximizing the complete photonic band gap. Further, it has been shown that complete photonic band gap size changes with the variation in the orientation angle of the constituent dielectric rods.

  13. A discontinuous Galerkin method for two-dimensional PDE models of Asian options

    Science.gov (United States)

    Hozman, J.; Tichý, T.; Cvejnová, D.

    2016-06-01

    In our previous research we have focused on the problem of plain vanilla option valuation using discontinuous Galerkin method for numerical PDE solution. Here we extend a simple one-dimensional problem into two-dimensional one and design a scheme for valuation of Asian options, i.e. options with payoff depending on the average of prices collected over prespecified horizon. The algorithm is based on the approach combining the advantages of the finite element methods together with the piecewise polynomial generally discontinuous approximations. Finally, an illustrative example using DAX option market data is provided.

  14. An efficient two-dimensional ALE modelling and experimental validation for pulsed laser-matter interaction

    Science.gov (United States)

    Zhao, Qiang; Dong, Zhiwei

    2016-11-01

    We have developed two-dimensional Arbitrary Lagrangian Eulerian (ALE) code which is used to study the physical processes, the plasma absorption, the crater profile, and the temperature distribution on metallic target and below the surface. The ALE method overcomes problems with Lagrangian moving mesh distortion by mesh smoothing and conservative quantities remapping from Lagrangian mesh to smoothed one. The results of numerical simulation of pulsed laser ablation are presented. The study presents particular interest for the analysis of experimental results obtained during pulsed laser ablation.

  15. Modeling strong motions produced by earthquakes with two-dimensional numerical codes

    OpenAIRE

    Helmberger, Donald V.; Vidale, John E.

    1988-01-01

    We present a scheme for generating synthetic point-source seismograms for shear dislocation sources using line source (two-dimensional) theory. It is based on expanding the complete three-dimensional solution of the wave equation expressed in cylindrical coordinates in an asymptotic form which provides for the separation of the motions into SH and P-SV systems. We evaluate the equations of motion with the aid of the Cagniard-de Hoop technique and derive close-formed expressions appropriate fo...

  16. Spin-Orbit Splitting in Semiconductor Quantum Dots with a Two-Dimensional Ring Model

    Institute of Scientific and Technical Information of China (English)

    FENG Jun-Sheng; LIU Zheng

    2009-01-01

    We present a theoretical study of the energy levels with two-dimensional ring confining potential in the presence of the Rashba spin-orbit interaction.The features of some low-lying states in various strengths of the Rashba spin-orbit interaction are investigated.The Rashba spin-orbit splitting can also be influenced by the width of the potential barrier.The computed results show that the spin-polarized electronic states can be more easily achieved in a weakly confined dot when the confinement strength for the Rashba spin-orbit interaction is larger than a critical value.

  17. Modeling of pressure sensors based on two-dimensional photonic crystals

    Institute of Scientific and Technical Information of China (English)

    Xuehui XIONG; Ping LU; Deming LIU

    2009-01-01

    A pressure sensor based on the two-dimensional photonic crystal (2D PC) has been proposed. Under the condition of different pressure, the photonic band gap of the sensor has been studied by means of the plane wave expansion method (PWM). The results show that there is a good linear relation between the cutoff wavelength and the pressure. Apart from being easily implemented, the presented 2D PC pressure sensor holds many characteristics such as high-pressure sensitivity and convenience in achieving demanded pressure range.

  18. Validation and application of a two-dimensional model to simulate soil salt transport under mulched drip irrigation

    Science.gov (United States)

    Jiao, Huiqing; Zhao, Chengyi; Sheng, Yu; Chen, Yan; Shi, Jianchu; Li, Baoguo

    2017-04-01

    Water shortage and soil salinization increasingly become the main constraints for sustainable development of agriculture in Southern Xinjiang, China. Mulched drip irrigation, as a high-efficient water-saving irrigation method, has been widely applied in Southern Xinjiang for cotton production. In order to analyze the reasonability of describing the three-dimensional soil water and salt transport processes under mulched drip irrigation with a relatively simple two-dimensional model, a field experiment was conducted from 2007 to 2015 at Aksu of Southern Xinjiang, and soil water and salt transport processes were simulated through the three-dimensional and two-dimensional models based on COMSOL. Obvious differences were found between three-dimensional and two-dimensional simulations for soil water flow within the early 12 h of irrigation event and for soil salt transport in the area within 15 cm away from drip tubes during the whole irrigation event. The soil water and salt contents simulated by the two-dimensional model, however, agreed well with the mean values between two adjacent emitters simulated by the three-dimensional model, and also coincided with the measurements as corresponding RMSE less than 0.037 cm3 cm-3 and 1.80 g kg-1, indicating that the two-dimensional model was reliable for field irrigation management. Subsequently, the two-dimensional model was applied to simulate the dynamics of soil salinity for five numerical situations and for a widely adopted irrigation pattern in Southern Xinjiang (about 350 mm through mulched drip irrigation during growing season of cotton and total 400 mm through flooding irrigations before sowing and after harvesting). The simulation results indicated that the contribution of transpiration to salt accumulation in root layer was about 75% under mulched drip irrigation. Moreover, flooding irrigations before sowing and after harvesting were of great importance for salt leaching of arable layer, especially in bare strip where

  19. Validating two-dimensional leadership models on three-dimensionally structured fish schools

    Science.gov (United States)

    Nagy, Máté; Holbrook, Robert I.; Biro, Dora; Burt de Perera, Theresa

    2017-01-01

    Identifying leader–follower interactions is crucial for understanding how a group decides where or when to move, and how this information is transferred between members. Although many animal groups have a three-dimensional structure, previous studies investigating leader–follower interactions have often ignored vertical information. This raises the question of whether commonly used two-dimensional leader–follower analyses can be used justifiably on groups that interact in three dimensions. To address this, we quantified the individual movements of banded tetra fish (Astyanax mexicanus) within shoals by computing the three-dimensional trajectories of all individuals using a stereo-camera technique. We used these data firstly to identify and compare leader–follower interactions in two and three dimensions, and secondly to analyse leadership with respect to an individual's spatial position in three dimensions. We show that for 95% of all pairwise interactions leadership identified through two-dimensional analysis matches that identified through three-dimensional analysis, and we reveal that fish attend to the same shoalmates for vertical information as they do for horizontal information. Our results therefore highlight that three-dimensional analyses are not always required to identify leader–follower relationships in species that move freely in three dimensions. We discuss our results in terms of the importance of taking species' sensory capacities into account when studying interaction networks within groups.

  20. Second-order phase transition in two-dimensional cellular automaton model of traffic flow containing road sections

    Science.gov (United States)

    Shi, Xiao-Qiu; Wu, Yi-Qi; Li, Hong; Zhong, Rui

    2007-11-01

    Two-dimensional cellular automaton model has been broadly researched for traffic flow, as it reveals the main characteristics of the traffic networks in cities. Based on the BML models, a first-order phase transition occurs between the low-density moving phase in which all cars move at maximal speed and the high-density jammed phase in which all cars are stopped. However, it is not a physical result of a realistic system. We propose a new traffic rule in a two-dimensional traffic flow model containing road sections, which reflects that a car cannot enter into a road crossing if the road section in front of the crossing is occupied by another car. The simulation results reveal a second-order phase transition that separates the free flow phase from the jammed phase. In this way the system will not be entirely jammed (“don’t block the box” as in New York City).

  1. Dynamic Critical Behavior of Multi-Grid Monte Carlo for Two-Dimensional Nonlinear $\\sigma$-Models

    OpenAIRE

    Mana, Gustavo; Mendes, Tereza; Pelissetto, Andrea; Sokal, Alan D.

    1995-01-01

    We introduce a new and very convenient approach to multi-grid Monte Carlo (MGMC) algorithms for general nonlinear $\\sigma$-models: it is based on embedding an $XY$ model into the given $\\sigma$-model, and then updating the induced $XY$ model using a standard $XY$-model MGMC code. We study the dynamic critical behavior of this algorithm for the two-dimensional $O(N)$ $\\sigma$-models with $N = 3,4,8$ and for the $SU(3)$ principal chiral model. We find that the dynamic critical exponent $z$ vari...

  2. A two-dimensional threshold voltage analytical model for metal-gate/high-k/SiO2/Si stacked MOSFETs

    Institute of Scientific and Technical Information of China (English)

    Ma Fei; Liu Hong-Xia; Fan Ji-Bin; Wang Shu-Long

    2012-01-01

    In this paper the influences of the metal-gate and high-k/SiO2/Si stacked structure on the metal-oxidesemiconductor field-effect transistor (MOSFET) axe investigated.The flat-band voltage is revised by considering the influences of stacked structure and metal-semiconductor work function fluctuation. The two-dimensional Poisson's equation of potential distribution is presented.A threshold voltage analytical model for metal-gate/high-k/SiO2/Si stacked MOSFETs is developed by solving these Poisson's equations using the boundary conditions.The model is verified by a two-dimensional device simulator,which provides the basic design guidance for metal-gate/high-k/SiO2/Si stacked MOSFETs.

  3. Two-grain nanoindentation using the quasicontinuum method: Two-dimensional model approach

    Energy Technology Data Exchange (ETDEWEB)

    Iglesias, Rodrigo A. [Instituto de Investigaciones en Fisicoquimica de Cordoba (INFIQC), Consejo Nacional de Investigaciones, Cientificas y Tecnicas (CONICET), Facultad de Ciencias Quimicas, Universidad Nacional de Cordoba, Edificio Integrador, Ciudad Universitaria, Cordoba, CP 5000 (Argentina)]. E-mail: riglesias@mail.fcq.unc.edu.ar; Leiva, Ezequiel P.M. [Instituto de Investigaciones en Fisicoquimica de Cordoba (INFIQC), Consejo Nacional de Investigaciones, Cientificas y Tecnicas (CONICET), Facultad de Ciencias Quimicas, Universidad Nacional de Cordoba, Edificio Integrador, Ciudad Universitaria, Cordoba, CP 5000 (Argentina)

    2006-06-15

    The quasicontinuum method (two-dimensional) developed by Tadmor et al. [Tadmor EB, Ortiz M, Phillips R. Philos Mag 1996;73:1529] is applied to an indentation process taking account of the atomic structure of the indenter and the substrate subject to indentation. Slip vectors, dislocation nucleation and nanostructure formation are analyzed for different indenter materials (Ag, Cu and Pd) and indenter crystal orientations. Slip vectors near to the contact region show that, depending on the material and orientation of the indenter, plastic deformations occur either inside the indenter or the substrate. Long-range material deformations appear during the indentation or retraction of the indenter. All of these aspects mainly dictate the formation of nanoclusters or nanoholes on the substrate surface.

  4. Two-dimensional-lattice spin models with long-range antiferromagnetic interactions

    Science.gov (United States)

    Romano, S.

    1991-10-01

    We consider a classical system, consisting of m-component unit vectors (m=2,3), associated with a two-dimensional lattice \\{uk||k∈openZ2\\} and interacting via translationally and rotationally invariant antiferromagnetic pair potentials of the long-range form W=Wjk=ɛ||xj-xk||-puj.uk, p>2, where ɛ is a positive quantity, setting energy and temperature scales (i.e., T*=kBT/ɛ), and xk are the coordinates of the lattice sites. A spin-wave approach predicts orientational disorder (in the thermodynamic limit) at all finite temperatures and for all p>2 this agrees with available rigorous results for p>=4, whereas no such theorems are known in the literature when 22.

  5. Hydrodynamic limit for an evolutional model of two-dimensional Young diagrams

    CERN Document Server

    Funaki, Tadahisa

    2009-01-01

    We construct dynamics of two-dimensional Young diagrams, which are naturally associated with their grandcanonical ensembles, by allowing the creation and annihilation of unit squares located at the boundary of the diagrams. The grandcanonical ensembles, which were introduced by Vershik, are uniform measures under conditioning on their size (or equivalently, area). We then show that, as the averaged size of the diagrams diverges, the corresponding height variable converges to a solution of a certain non-linear partial differential equation under a proper hydrodynamic scaling. Furthermore, the stationary solution of the limit equation is identified with the so-called Vershik curve. We discuss both uniform and restricted uniform statistics for the Young diagrams.

  6. Two-dimensional structure in a generic model of triangular proteins and protein trimers.

    Science.gov (United States)

    Camp, Philip J; Duncan, Peter D

    2006-04-01

    Motivated by the diversity and complexity of two-dimensional (2D) crystals formed by triangular proteins and protein trimers, we have investigated the structures and phase behavior of hard-disk trimers. In order to mimic specific binding interactions, each trimer possesses an "attractive" disk which can interact with similar disks on other trimers via an attractive square-well potential. At low density and low temperature, the fluid phase mainly consists of tetramers, pentamers, or hexamers. Hexamers provide the structural motif for a high-density, low-temperature periodic solid phase, but we also identify a metastable periodic structure based on a tetramer motif. At high density there is a transition between orientationally ordered and disordered solid phases. The connections between simulated structures and those of 2D protein crystals--as seen in electron microscopy--are briefly discussed.

  7. An Investigation of Two-Dimensional CAD Generated Models with Body Decoupled Cartesian Grids for DSMC

    Energy Technology Data Exchange (ETDEWEB)

    OTAHAL,THOMAS J.; GALLIS,MICHAIL A.; BARTEL,TIMOTHY J.

    2000-06-27

    This paper presents an investigation of a technique for using two-dimensional bodies composed of simple polygons with a body decoupled uniform Cmtesian grid in the Direct Simulation Monte Carlo method (DSMC). The method employs an automated grid pre-processing scheme beginning form a CAD geometry definition file, and is based on polygon triangulation using a trapezoid algorithm. A particle-body intersection time comparison is presented between the Icarus DSMC code using a body-fitted structured grid and using a structured body-decoupled Cartesian grid with both linear and logarithmic search techniques. A comparison of neutral flow over a cylinder is presented using the structured body fitted grid and the Cartesian body de-coupled grid.

  8. Immobilization of single argon atoms in nano-cages of two-dimensional zeolite model systems

    Science.gov (United States)

    Zhong, Jian-Qiang; Wang, Mengen; Akter, Nusnin; Kestell, John D.; Boscoboinik, Alejandro M.; Kim, Taejin; Stacchiola, Dario J.; Lu, Deyu; Boscoboinik, J. Anibal

    2017-07-01

    The confinement of noble gases on nanostructured surfaces, in contrast to bulk materials, at non-cryogenic temperatures represents a formidable challenge. In this work, individual Ar atoms are trapped at 300 K in nano-cages consisting of (alumino)silicate hexagonal prisms forming a two-dimensional array on a planar surface. The trapping of Ar atoms is detected in situ using synchrotron-based ambient pressure X-ray photoelectron spectroscopy. The atoms remain in the cages upon heating to 400 K. The trapping and release of Ar is studied combining surface science methods and density functional theory calculations. While the frameworks stay intact with the inclusion of Ar atoms, the permeability of gasses (for example, CO) through them is significantly affected, making these structures also interesting candidates for tunable atomic and molecular sieves. These findings enable the study of individually confined noble gas atoms using surface science methods, opening up new opportunities for fundamental research.

  9. Immobilization of single argon atoms in nano-cages of two-dimensional zeolite model systems.

    Science.gov (United States)

    Zhong, Jian-Qiang; Wang, Mengen; Akter, Nusnin; Kestell, John D; Boscoboinik, Alejandro M; Kim, Taejin; Stacchiola, Dario J; Lu, Deyu; Boscoboinik, J Anibal

    2017-07-17

    The confinement of noble gases on nanostructured surfaces, in contrast to bulk materials, at non-cryogenic temperatures represents a formidable challenge. In this work, individual Ar atoms are trapped at 300 K in nano-cages consisting of (alumino)silicate hexagonal prisms forming a two-dimensional array on a planar surface. The trapping of Ar atoms is detected in situ using synchrotron-based ambient pressure X-ray photoelectron spectroscopy. The atoms remain in the cages upon heating to 400 K. The trapping and release of Ar is studied combining surface science methods and density functional theory calculations. While the frameworks stay intact with the inclusion of Ar atoms, the permeability of gasses (for example, CO) through them is significantly affected, making these structures also interesting candidates for tunable atomic and molecular sieves. These findings enable the study of individually confined noble gas atoms using surface science methods, opening up new opportunities for fundamental research.

  10. Superfluid-insulator transition in a disordered two-dimensional quantum rotor model with random on-site interactions

    Science.gov (United States)

    An, Taeyang; Cha, Min-Chul

    2013-03-01

    We study the superfluid-insulator quantum phase transition in a disordered two-dimensional quantum rotor model with random on-site interactions in the presence of particle-hole symmetry. Via worm-algorithm Monte Carlo calculations of superfluid density and compressibility, we find the dynamical critical exponent z ~ 1 . 13 (2) and the correlation length critical exponent 1 / ν ~ 1 . 1 (1) . These exponents suggest that the insulating phase is a incompressible Mott glass rather than a Bose glass.

  11. A Hybrid Support Vector Machines and Two-dimensional Risk Matrix Model for Supply Chain Risk Assessment

    OpenAIRE

    Fan Jiang; Junfei Chen

    2014-01-01

    In recent years, the supply chain managements have been paid more and more attention. The supply chain risk management is an important content for enterprises implementing supply chain management. Therefore, how to measure the risk of supply chain is quite important. In this study, a supply chain risk evaluation model based on support vector machines and two-dimensional risk matrix is proposed. The index system of supply chain risk assessment which includes 14 indices is established. The case...

  12. Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

    OpenAIRE

    de Mendonça, J. Ricardo G.

    2012-01-01

    We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang universality class of critical behavior. We re...

  13. Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the potts model.

    Science.gov (United States)

    Jacobsen, J L; Saleur, H

    2008-02-29

    We determine exactly the probability distribution of the number N_(c) of valence bonds connecting a subsystem of length L>1 to the rest of the system in the ground state of the XXX antiferromagnetic spin chain. This provides, in particular, the asymptotic behavior of the valence-bond entanglement entropy S_(VB)=N_(c)ln2=4ln2/pi(2)lnL disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/3lnL. Our results generalize to the Q-state Potts model.

  14. Hierarchy of the low-lying excitations for the (2 + 1)-dimensional q = 3 Potts model in the ordered phase

    Science.gov (United States)

    Nishiyama, Yoshihiro

    2017-03-01

    The (2 + 1)-dimensional q = 3 Potts model was simulated with the exact diagonalization method. In the ordered phase, the elementary excitations (magnons) are attractive, forming a series of bound states in the low-energy spectrum. We investigate the low-lying spectrum through a dynamical susceptibility, which is readily tractable with the exact diagonalization method via the continued-fraction expansion. As a result, we estimate the series of (scaled) mass gaps, m 2 , 3 , 4 /m1 (m1: single-magnon mass), in proximity to the transition point.

  15. Evidence of a one-step replica symmetry breaking in a three-dimensional Potts glass model.

    Science.gov (United States)

    Takahashi, Takashi; Hukushima, Koji

    2015-02-01

    We study a seven-state Potts glass model in three dimensions with first-, second-, and third-nearest-neighbor interactions with a bimodal distribution of couplings by Monte Carlo simulations. Our results show the existence of a spin-glass transition at a finite temperature T(c), a discontinuous jump of an order parameter at T(c) without latent heat, and a nontrivial structure in the order parameter distribution below T(c). They are compatible with one-step replica symmetry breaking.

  16. The Research of Mobile phone Entrance Guard System Model based on the Encryption Two-dimensional Code

    Directory of Open Access Journals (Sweden)

    Chu Jianli

    2013-09-01

    Full Text Available This article designs a new mobile-phone entrance guard system, uses the encryption two-dimensional code for identity authentication. Different from other similar products in the market, this system does not rely on specialized mobile phone card or NFC (near field communication module. It can be directly realized through mobile-phone software, and it can be operated simple and safer. This article designs the whole system model, includes structure, function and workflow. It also analyzes and researches the main algorithms used in the system, which include security policy algorithm, encryption two-dimensional code algorithm and image recognition algorithm. Finally, it provides the solution method for the problem in the experimental simulation. It also evaluated and summarized the experimental results.

  17. Analysis of bandgap characteristics of two-dimensional periodic structures by using the source-model technique.

    Science.gov (United States)

    Ludwig, Alon; Leviatan, Yehuda

    2003-08-01

    We introduce a solution based on the source-model technique for periodic structures for the problem of electromagnetic scattering by a two-dimensional photonic bandgap crystal slab illuminated by a transverse-magnetic plane wave. The proposed technique takes advantage of the periodicity of the slab by solving the problem within the unit cell of the periodic structure. The results imply the existence of a frequency bandgap and provide a valuable insight into the relationship between the dimensions of a finite periodic structure and its frequency bandgap characteristics. A comparison shows a discrepancy between the frequency bandgap obtained for a very thick slab and the bandgap obtained by solving the corresponding two-dimensionally infinite periodic structure. The final part of the paper is devoted to explaining in detail this apparent discrepancy.

  18. Properties of the two-dimensional spin-1/2 Heisenberg model on a honeycomb lattice with interlayer coupling

    Directory of Open Access Journals (Sweden)

    U. Löw

    2009-01-01

    Full Text Available The magnetic properties of the two-dimensional S=1/2 (quantum antiferromagnetic Heisenberg model on a honeycomb lattice with and without interlayer coupling are studied by means of a continuous Euclidean time Quantum Monte-Carlo algorithm. The internal energy, the magnetic susceptibility and the staggered magnetization are determined in the full temperature range. For the two-dimensional system the ground-state energy/bond is found to be E0hc=-0.36303(13, and the zero temperature staggered magnetization mst=0.2681(8. For coupled planes of honeycomb systems a phase transition from an ordered phase to a disordered phase is found at T/J=0.695(10.

  19. Modelling of Oscillations in Two-Dimensional Echo-Spectra of the Fenna-Matthews-Olson Complex

    CERN Document Server

    Hein, Birgit; Kramer, Tobias; Rodríguez, Mirta

    2011-01-01

    Recent experimental observations of time-dependent beatings in the two-dimensional echo-spectra of light-harvesting complexes at ambient temperatures have opened up the question whether coherence and wave-like behaviour plays a significant role in photosynthesis. We perform a numerical study of the absorption and echo-spectra of the Fenna-Matthews-Olson (FMO) complex in chlorobium tepidum and analyse the requirements in the theoretical model needed to reproduce beatings in the calculated spectra. The energy transfer in the FMO pigment-protein complex is theoretically described by an exciton Hamiltonian coupled to a phonon bath which account for the pigments electronic and vibrational excitations respectively. We use the hierarchical equations of motions method to treat the strong couplings in a non-perturbative way. We show that the oscillations in the two-dimensional echo-spectra persist in the presence of thermal noise and static disorder.

  20. Accurate two-dimensional model of an arrayed-waveguide grating demultiplexer and optimal design based on the reciprocity theory.

    Science.gov (United States)

    Dai, Daoxin; He, Sailing

    2004-12-01

    An accurate two-dimensional (2D) model is introduced for the simulation of an arrayed-waveguide grating (AWG) demultiplexer by integrating the field distribution along the vertical direction. The equivalent 2D model has almost the same accuracy as the original three-dimensional model and is more accurate for the AWG considered here than the conventional 2D model based on the effective-index method. To further improve the computational efficiency, the reciprocity theory is applied to the optimal design of a flat-top AWG demultiplexer with a special input structure.