Exact Solution of Ising Model in 2d Shortcut Network
NASA Astrophysics Data System (ADS)
Shanker, O.
We give the exact solution to the Ising model in the shortcut network in the 2D limit. The solution is found by mapping the model to the square lattice model with Brascamp and Kunz boundary conditions.
Duality Between Spin Networks and the 2D Ising Model
NASA Astrophysics Data System (ADS)
Bonzom, Valentin; Costantino, Francesco; Livine, Etera R.
2016-06-01
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.
Completeness of the classical 2D Ising model and universal quantum computation.
Van den Nest, M; Dür, W; Briegel, H J
2008-03-21
We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with complex inhomogeneous couplings and external fields. In the case where the original model is an Ising or Potts-type model, we find that the corresponding 2D square lattice requires only polynomially more spins with respect to the original one, and we give a constructive method to map such models to the 2D Ising model. For more general models the overhead in system size may be exponential. The results are established by connecting classical spin models with measurement-based quantum computation and invoking the universality of the 2D cluster states.
Approaches to numerical solution of 2D Ising model
NASA Astrophysics Data System (ADS)
Soldatov, K. S.; Nefedev, K. V.; Kapitan, V. Yu; Andriushchenko, P. D.
2016-08-01
Parallel algorithm of partition function calculation of two-dimensional Ising model for systems with a finite number of spins was developed. Within a method of complete enumeration by using MPI technology with subsequent optimization of a parallel code time of calculations was reduced considerably. Partition function was calculated for systems of 16, 25, 36 Ising spins. Based on the obtained results, main thermodynamic and magnetic values dependences (such as heat capacity, magnetic susceptibility, mean square magnetization) for ferromagnetic and antiferromagnetic interactions was investigated. The analysis of a different configurations contribution showed, that states with the minimum energy have essential influence on dependences of thermodynamic values. Comparison with the results obtained by the Wang Landau algorithm was performed.
Probabilistic Cellular Automata for Low-Temperature 2-d Ising Model
NASA Astrophysics Data System (ADS)
Procacci, Aldo; Scoppola, Benedetto; Scoppola, Elisabetta
2016-12-01
We construct a parallel stochastic dynamics with invariant measure converging to the Gibbs measure of the 2-d low-temperature Ising model. The proof of such convergence requires a polymer expansion based on suitably defined Peierls-type contours.
Multiple Ising models coupled to 2-d gravity: a CSD analysis
NASA Astrophysics Data System (ADS)
Bowick, Mark; Falcioni, Marco; Harris, Geoffrey; Marinari, Enzo
1994-04-01
We simulate single and multiple Ising models coupled to 2-d gravity and we measure critical slowing down (CSD) with the standard methods. We find that the Swendsen-Wang and Wolff cluster algorithms do not eliminate CSD. We interpret the result as an effect of the mesh dynamics.
Implementation of Minimal Representations in 2d Ising Model Calculations
1992-05-01
Re r’ u. 60:252-262.263-276. 1941. [Ons44] Lars Onsager . Crystal statistics I. A two-dimensional model with an order-disorder transition. Physical Re...ID lattices but the subject really came to life in 1944 when Onsager [Ons44] derived an exact closed form expression for the partition function (see
Critical slowing down of cluster algorithms for Ising models coupled to 2-d gravity
NASA Astrophysics Data System (ADS)
Bowick, Mark; Falcioni, Marco; Harris, Geoffrey; Marinari, Enzo
1994-02-01
We simulate single and multiple Ising models coupled to 2-d gravity using both the Swendsen-Wang and Wolff algorithms to update the spins. We study the integrated autocorrelation time and find that there is considerable critical slowing down, particularly in the magnetization. We argue that this is primarily due to the local nature of the dynamical triangulation algorithm and to the generation of a distribution of baby universes which inhibits cluster growth.
Spot size variation FCS in simulations of the 2D Ising model.
Burns, Margaret C; Nouri, Mariam; Veatch, Sarah L
2016-06-02
Spot variation fluorescence correlation spectroscopy (svFCS) was developed to study the movement and organization of single molecules in plasma membranes. This experimental technique varies the size of an illumination area while measuring correlations in time using standard fluorescence correlation methods. Frequently, this data is interpreted using the assumption that correlation measurements reflect the dynamics of single molecule motions, and not motions of the average composition. Here, we explore how svFCS measurements report on the dynamics of components diffusing within simulations of a 2D Ising model with a conserved order parameter. Simulated correlation functions report on both the fast dynamics of single component mobility and the slower dynamics of the average composition. Over a range of simulation conditions, a conventional svFCS analysis suggests the presence of anomalous diffusion even though single molecule motions are nearly Brownian in these simulations. This misinterpretation is most significant when the surface density of the fluorescent label is elevated, therefore we suggest future measurements be made over a range of tracer densities. Some simulation conditions reproduce qualitative features of published svFCS experimental data. Overall, this work emphasizes the need to probe membranes using multiple complimentary experimental methodologies in order to draw conclusions regarding the nature of spatial and dynamical heterogeneity in these systems.
Critical Casimir forces between defects in the 2D Ising model
NASA Astrophysics Data System (ADS)
Nowakowski, P.; Maciołek, A.; Dietrich, S.
2016-12-01
An exact statistical mechanical derivation is given of the critical Casimir interactions between two defects in a planar lattice-gas Ising model. Each defect is a finite group of nearest-neighbor spins with modified coupling constants. Such a system can be regarded as a model of a binary liquid mixture with the molecules confined to a membrane and the defects mimicking protein inclusions embedded into the membrane. As suggested by recent experiments, certain cellular membranes appear to be tuned to the proximity of a critical demixing point belonging to the two-dimensional Ising universality class. Therefore one can expect the emergence of critical Casimir forces between membrane inclusions. These forces are governed by universal scaling functions, which we derive for simple defects. We prove that the scaling law appearing at criticality is the same for all types of defects considered here.
Almost Gibbsianness and Parsimonious Description of the Decimated 2d-Ising Model
NASA Astrophysics Data System (ADS)
Le Ny, Arnaud
2013-07-01
In this paper, we complete and provide details for the existing characterizations of the decimation of the Ising model on {Z}2 in the generalized Gibbs context. We first recall a few features of the Dobrushin program of restoration of Gibbsianness and present the construction of global specifications consistent with the extremal decimated measures. We use them to prove that these renormalized measures are almost Gibbsian at any temperature and to analyse in detail its convex set of DLR measures. We also recall the weakly Gibbsian description and complete it using a potential that admits a quenched correlation decay, i.e. a well-defined configuration-dependent length beyond which this potential decays exponentially. We use these results to incorporate these decimated measures in the new framework of parsimonious random fields that has been recently developed to investigate probability aspects related to neurosciences.
Finite-size effects for anisotropic 2D Ising model with various boundary conditions
NASA Astrophysics Data System (ADS)
Izmailian, N. Sh
2012-12-01
We analyze the exact partition function of the anisotropic Ising model on finite M × N rectangular lattices under four different boundary conditions (periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa)) obtained by Kaufman (1949 Phys. Rev. 76 1232), Wu and Hu (2002 J. Phys. A: Math. Gen. 35 5189) and Kastening (2002 Phys. Rev. E 66 057103)). We express the partition functions in terms of the partition functions Zα, β(J, k) with (α, β) = (0, 0), (1/2, 0), (0, 1/2) and (1/2, 1/2), J is an interaction coupling and k is an anisotropy parameter. Based on such expressions, we then extend the algorithm of Ivashkevich et al (2002 J. Phys. A: Math. Gen. 35 5543) to derive the exact asymptotic expansion of the logarithm of the partition function for all boundary conditions mentioned above. Our result is f = fbulk + ∑∞p = 0fp(ρ, k)S-p - 1, where f is the free energy of the system, fbulk is the free energy of the bulk, S = MN is the area of the lattice and ρ = M/N is the aspect ratio. All coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio ρeff = ρ/sinh 2Jc and show that for pp and aa boundary conditions all finite size correction terms are invariant under the transformation ρeff → 1/ρeff. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.
Monte Carlo entropic sampling applied to Ising-like model for 2D and 3D systems
NASA Astrophysics Data System (ADS)
Jureschi, C. M.; Linares, J.; Dahoo, P. R.; Alayli, Y.
2016-08-01
In this paper we present the Monte Carlo entropic sampling (MCES) applied to an Ising-like model for 2D and 3D system in order to show the interaction influence of the edge molecules of the system with their local environment. We show that, as for the 1D and the 2D spin crossover (SCO) systems, the origin of multi steps transition in 3D SCO is the effect of the edge interaction molecules with its local environment together with short and long range interactions. Another important result worth noting is the co-existence of step transitions with hysteresis and without hysteresis. By increasing the value of the edge interaction, L, the transition is shifted to the lower temperatures: it means that the role of edge interaction is equivalent to an applied negative pressure because the edge interaction favours the HS state while the applied pressure favours the LS state. We also analyse, in this contribution, the role of the short- and long-range interaction, J respectively G, with respect to the environment interaction, L.
Analysis of Projections of the Transfer Matrix in 2d Ising Models
1992-01-01
Review, 60:252-262,263-276, 1941. [Ons44] Lars Onsager . Crystal statistics I. A two-dimensional model with an order-disorder transition. Physical Review...lattices but the subject really came to life in 1944 when Onsager [Ons44] derived an exact closed form expression for the partition ,unction (see below
NASA Astrophysics Data System (ADS)
Komura, Yukihiro; Okabe, Yutaka
2014-03-01
We present sample CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm. We deal with the classical spin models; the Ising model, the q-state Potts model, and the classical XY model. As for the lattice, both the 2D (square) lattice and the 3D (simple cubic) lattice are treated. We already reported the idea of the GPU implementation for 2D models (Komura and Okabe, 2012). We here explain the details of sample programs, and discuss the performance of the present GPU implementation for the 3D Ising and XY models. We also show the calculated results of the moment ratio for these models, and discuss phase transitions. Catalogue identifier: AERM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERM_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5632 No. of bytes in distributed program, including test data, etc.: 14688 Distribution format: tar.gz Programming language: C, CUDA. Computer: System with an NVIDIA CUDA enabled GPU. Operating system: System with an NVIDIA CUDA enabled GPU. Classification: 23. External routines: NVIDIA CUDA Toolkit 3.0 or newer Nature of problem: Monte Carlo simulation of classical spin systems. Ising, q-state Potts model, and the classical XY model are treated for both two-dimensional and three-dimensional lattices. Solution method: GPU-based Swendsen-Wang multi-cluster spin flip Monte Carlo method. The CUDA implementation for the cluster-labeling is based on the work by Hawick et al. [1] and that by Kalentev et al. [2]. Restrictions: The system size is limited depending on the memory of a GPU. Running time: For the parameters used in the sample programs, it takes about a minute for each program. Of course, it depends on the system size, the number of Monte Carlo steps, etc. References: [1] K
NASA Astrophysics Data System (ADS)
Abou Ghantous, M.; Moujaes, E. A.; Dunn, J. L.; Khater, A.
2012-06-01
Fullerene molecules adsorbed on surfaces often show macroscopic average distortions. As charged ions C60n- are known to be Jahn-Teller (JT) active, it is suggested that these distortions could be a manifestation of cooperative JT effects (CJTE) due to interactions between neighbouring fullerene ions. In order to understand the distortion properties it is necessary to take correlations between different distortions into account. However, this can't easily be done in the mean field approximation usually used to describe the CJTE. We therefore propose an alternative procedure to describe 2D mesoscopic islands of C60 ions in which a pseudo vector spin
Johnson, Jason K.; Oyen, Diane Adele; Chertkov, Michael; Netrapalli, Praneeth
2016-12-01
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the best planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geo-chemical depth trends from Mars rover data.
Johnson, Jason K.; Oyen, Diane Adele; Chertkov, Michael; ...
2016-12-01
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the bestmore » planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geo-chemical depth trends from Mars rover data.« less
Johnson, Jason K; Chertkov, Michael; Netrapalli, Praneeth
2010-11-12
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus our attention on the class of planar Ising models, for which inference is tractable using techniques of statistical physics [Kac and Ward; Kasteleyn]. Based on these techniques and recent methods for planarity testing and planar embedding [Chrobak and Payne], we propose a simple greedy algorithm for learning the best planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. We present the results of numerical experiments evaluating the performance of our algorithm.
ERIC Educational Resources Information Center
Singh, Satya Pal
2014-01-01
This paper presents a brief review of Ising's work done in 1925 for one dimensional spin chain with periodic boundary condition. Ising observed that no phase transition occurred at finite temperature in one dimension. He erroneously generalized his views in higher dimensions but that was not true. In 1941 Kramer and Wannier obtained…
Fermions as generalized Ising models
NASA Astrophysics Data System (ADS)
Wetterich, C.
2017-04-01
We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of products of observables. The map preserves locality properties and can be realized for arbitrary dimensions. We present a simple example where a quantum field theory for free massless Dirac fermions in two-dimensional Minkowski space is represented by an asymmetric Ising model on a euclidean square lattice.
The thermodynamic geometry of the Ising model
NASA Astrophysics Data System (ADS)
Rotskoff, Grant; Crooks, Gavin
2015-03-01
Biological machines have evolved to produce useful work in a finite time by operating out-of-equilibrium, but we do not know how evolution has guided the design of these machines: Are there generic design principles that direct motors towards higher efficiency? To answer this question, one must first calculate a finite-time efficiency, which poses a significant challenge--tools of equilibrium statistical mechanics fail to describe the relationship between a protocol and the efficiency of a machine subject to that protocol. Using a geometric framework, I will describe a procedure for predicting the protocol that minimizes the dissipated work during an irreversible process. My talk will focus on optimal control of the 2D Ising model; this example will provide strategies for employing geometric thermodynamics to models that cannot be solved analytically.
2D-Ising critical behavior in mixtures of water and 3-methylpyridine
Sadakane, Koichiro; Iguchi, Kazuya; Nagao, Michihiro; Seto, Hideki
2011-01-01
The effect of an antagonistic salt on the phase behavior and nanoscale structure of a mixture of D{sub 2}O and 3-methylpyridine was investigated by visual inspection and small-angle neutron scattering (SANS). The addition of the antagonistic salt, namely sodium tetraphenylborate (NaBPh{sub 4}), induces the shrinking of the two-phase region in contrast to the case in which a normal (hydrophilic) salt is added. Below the phase separation point, the SANS profiles cannot be described by the Ornstein-Zernike function owing to the existence of a long-range periodic structure. With increasing salt concentration, the critical exponents change from the values of 3D-Ising and approach those of 2D-Ising. These results suggest that the concentration fluctuation of the mixture of solvents is limited to a quasi two-dimensional space by the periodic structure induced by the adding the salt. The same behaviors were also observed in mixtures composed of water, 3-methylpyridine, and ionic surfactant.
Topological Characterization of Extended Quantum Ising Models.
Zhang, G; Song, Z
2015-10-23
We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.
SMJ's analysis of Ising model correlation functions
NASA Astrophysics Data System (ADS)
Kadanoff, Leo P.; Kohmoto, Mahito
1980-05-01
In a series of recent publications Sato, Miwa, and Jimbo (SMJ) have shown how to derive multispin correlation functions of the two-dimensional Ising model in the continuum, or scaling, limit by analyzing the behavior of the solutions to the two-dimensional version of the Dirac equation. The major purpose of the present work is to describe SMJ's analysis more discursively and in terms closer to that used in previous studies of the Ising model. In addition, new and more compact expressions for their basic equations are derived. A single new answer is obtained: the form of the three-spin correlation function at criticality.
Combinatorial approach to exactly solve the 1D Ising model
NASA Astrophysics Data System (ADS)
Seth, Swarnadeep
2017-01-01
The Ising model is a well known statistical model which can be solved exactly by various methods. The most familiar one is the transfer matrix method. Sometimes it can be difficult to approach the open boundary case rather than periodic boundary ones in higher dimensions. But physically it is more intuitive to study the open boundary case, as it gives a closer view of the real system. We have introduced a new method called the pairing method to determine the exact partition function for the simplest case, a 1D Ising lattice. This method simplifies the problem's complexities and reduces it to a pure combinatorial problem. The study also reveals that it is possible to apply this pairing method in the case of a 2D square lattice. The obtained results agree perfectly with the values in the literature and this new approach provides an algorithmic insight to deal with such problems.
Quantum Ising model coupled with conducting electrons
NASA Astrophysics Data System (ADS)
Yamashita, Yasufumi; Yonemitsu, Kenji
2005-01-01
The effect of photo-doping on the quantum paraelectric SrTiO3 is studied by using the one-dimensional quantum Ising model, where the Ising spin describes the effective lattice polarization of an optical phonon. Two types of electron-phonon couplings are introduced through the modulation of transfer integral via lattice deformations. After the exact diagonalization and the perturbation studies, we find that photo-induced low-density carriers can drastically alter quantum fluctuations when the system locates near the quantum critical point between the quantum para- and ferro-electric phases.
Ising model of a glass transition.
Langer, J S
2013-07-01
Numerical simulations by Tanaka and co-workers indicate that glass-forming systems of moderately polydisperse hard-core particles, in both two and three dimensions, exhibit diverging correlation lengths. These correlations are described by Ising-like critical exponents, and are associated with diverging, Vogel-Fulcher-Tamann, structural relaxation times. Related simulations of thermalized hard disks indicate that the curves of pressure versus packing fraction for different polydispersities exhibit a sequence of transition points, starting with a liquid-hexatic transition for the monodisperse case, and crossing over with increasing polydispersity to glassy, Ising-like critical points. I propose to explain these observations by assuming that glass-forming fluids contain twofold degenerate, locally ordered clusters of particles, similar to the two-state systems that have been invoked to explain other glassy phenomena. This paper starts with a brief statistical derivation of the thermodynamics of thermalized, hard-core particles. It then discusses how a two-state, Ising-like model can be described within that framework in terms of a small number of statistically relevant, internal state variables. The resulting theory agrees accurately with the simulation data. I also propose a rationale for the observed relation between the Ising-like correlation lengths and the Vogel-Fulcher-Tamann formula.
A sparse Ising model with covariates.
Cheng, Jie; Levina, Elizaveta; Wang, Pei; Zhu, Ji
2014-12-01
There has been a lot of work fitting Ising models to multivariate binary data in order to understand the conditional dependency relationships between the variables. However, additional covariates are frequently recorded together with the binary data, and may influence the dependence relationships. Motivated by such a dataset on genomic instability collected from tumor samples of several types, we propose a sparse covariate dependent Ising model to study both the conditional dependency within the binary data and its relationship with the additional covariates. This results in subject-specific Ising models, where the subject's covariates influence the strength of association between the genes. As in all exploratory data analysis, interpretability of results is important, and we use ℓ1 penalties to induce sparsity in the fitted graphs and in the number of selected covariates. Two algorithms to fit the model are proposed and compared on a set of simulated data, and asymptotic results are established. The results on the tumor dataset and their biological significance are discussed in detail.
Classical Ising model test for quantum circuits
NASA Astrophysics Data System (ADS)
Geraci, Joseph; Lidar, Daniel A.
2010-07-01
We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model partition function in terms of quadratically signed weight enumerators (QWGTs), which are polynomials that arise naturally in an expansion of quantum circuits in terms of rotations involving Pauli matrices. We combine this expression with a known efficient classical algorithm for the Ising partition function of any planar graph in the absence of an external magnetic field, and the Robertson-Seymour theorem from graph theory. We give as an example a set of quantum circuits with a small number of non-nearest-neighbor gates which admit an efficient classical simulation.
Engineering 2D Ising Interactions in a Large (N>100) Ensemble of Trapped Ions
NASA Astrophysics Data System (ADS)
Sawyer, Brian; Britton, Joseph; Keith, Adam; Wang, Joseph; Freericks, James; Uys, Hermann; Biercuk, Michael; Bollinger, John
2012-06-01
Experimental progress in atomic, molecular, and optical physics has enabled exquisite control over ensembles of cold trapped ions. We have recently engineered long-range Ising interactions in a two-dimensional, 1-mK Coulomb crystal of hundreds of ^9Be^+ ions confined within a Penning trap. Interactions between the ^9Be^+ valence spins are mediated via spin-dependent optical dipole forces (ODFs) coupling to transverse motional modes of the planar crystal. A continuous range of inverse power-law spin-spin interactions from infinite (1/r^0) to dipolar (1/r^3) are accessible by varying the ODF drive frequency relative to the transverse modes. The ions naturally form a triangular lattice structure within the planar array, allowing for simulation of spin frustration using our generated antiferromagnetic couplings. We report progress toward simulating the ferromagnetic/antiferromagnetic transverse quantum Ising Hamiltonians in this large ensemble. We also report spectroscopy, thermometry, and sensitive displacement detection (˜100 pm) via entanglement of valence spin and drumhead oscillations.
Three representations of the Ising model.
Kruis, Joost; Maris, Gunter
2016-10-04
Statistical models that analyse (pairwise) relations between variables encompass assumptions about the underlying mechanism that generated the associations in the observed data. In the present paper we demonstrate that three Ising model representations exist that, although each proposes a distinct theoretical explanation for the observed associations, are mathematically equivalent. This equivalence allows the researcher to interpret the results of one model in three different ways. We illustrate the ramifications of this by discussing concepts that are conceived as problematic in their traditional explanation, yet when interpreted in the context of another explanation make immediate sense.
Three representations of the Ising model
Kruis, Joost; Maris, Gunter
2016-01-01
Statistical models that analyse (pairwise) relations between variables encompass assumptions about the underlying mechanism that generated the associations in the observed data. In the present paper we demonstrate that three Ising model representations exist that, although each proposes a distinct theoretical explanation for the observed associations, are mathematically equivalent. This equivalence allows the researcher to interpret the results of one model in three different ways. We illustrate the ramifications of this by discussing concepts that are conceived as problematic in their traditional explanation, yet when interpreted in the context of another explanation make immediate sense. PMID:27698356
Three representations of the Ising model
NASA Astrophysics Data System (ADS)
Kruis, Joost; Maris, Gunter
2016-10-01
Statistical models that analyse (pairwise) relations between variables encompass assumptions about the underlying mechanism that generated the associations in the observed data. In the present paper we demonstrate that three Ising model representations exist that, although each proposes a distinct theoretical explanation for the observed associations, are mathematically equivalent. This equivalence allows the researcher to interpret the results of one model in three different ways. We illustrate the ramifications of this by discussing concepts that are conceived as problematic in their traditional explanation, yet when interpreted in the context of another explanation make immediate sense.
Brittle damage models in DYNA2D
Faux, D.R.
1997-09-01
DYNA2D is an explicit Lagrangian finite element code used to model dynamic events where stress wave interactions influence the overall response of the system. DYNA2D is often used to model penetration problems involving ductile-to-ductile impacts; however, with the advent of the use of ceramics in the armor-anti-armor community and the need to model damage to laser optics components, good brittle damage models are now needed in DYNA2D. This report will detail the implementation of four brittle damage models in DYNA2D, three scalar damage models and one tensor damage model. These new brittle damage models are then used to predict experimental results from three distinctly different glass damage problems.
Nonequilibrium antiferromagnetic mixed-spin Ising model.
Godoy, Mauricio; Figueiredo, Wagner
2002-09-01
We studied an antiferromagnetic mixed-spin Ising model on the square lattice subject to two competing stochastic processes. The model system consists of two interpenetrating sublattices of spins sigma=1/2 and S=1, and we take only nearest neighbor interactions between pairs of spins. The system is in contact with a heat bath at temperature T, and the exchange of energy with the heat bath occurs via one-spin flip (Glauber dynamics). Besides, the system interacts with an external agency of energy, which supplies energy to it whenever two nearest neighboring spins are simultaneously flipped. By employing Monte Carlo simulations and a dynamical pair approximation, we found the phase diagram for the stationary states of the model in the plane temperature T versus the competition parameter between one- and two-spin flips p. We observed the appearance of three distinct phases, that are separated by continuous transition lines. We also determined the static critical exponents along these lines and we showed that this nonequilibrium model belongs to the universality class of the two-dimensional equilibrium Ising model.
One-Dimensional Ising Model with "k"-Spin Interactions
ERIC Educational Resources Information Center
Fan, Yale
2011-01-01
We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…
Ginsparg, P.
1991-01-01
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Ginsparg, P.
1991-12-31
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Exact solutions to plaquette Ising models with free and periodic boundaries
NASA Astrophysics Data System (ADS)
Mueller, Marco; Johnston, Desmond A.; Janke, Wolfhard
2017-01-01
An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (1972) [1], who later dubbed it the fuki-nuke, or "no-ceiling", model. Defining new spin variables as the product of nearest-neighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fuki-nuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (2010) [2]. We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.
Bootstrapping the Three Dimensional Supersymmetric Ising Model.
Bobev, Nikolay; El-Showk, Sheer; Mazáč, Dalimil; Paulos, Miguel F
2015-07-31
We implement the conformal bootstrap program for three dimensional conformal field theories with N=2 supersymmetry and find universal constraints on the spectrum of operator dimensions in these theories. By studying the bounds on the dimension of the first scalar appearing in the operator product expansion of a chiral and an antichiral primary, we find a kink at the expected location of the critical three dimensional N=2 Wess-Zumino model, which can be thought of as a supersymmetric analog of the critical Ising model. Focusing on this kink, we determine, to high accuracy, the low-lying spectrum of operator dimensions of the theory, as well as the stress-tensor two-point function. We find that the latter is in an excellent agreement with an exact computation.
The Worm Process for the Ising Model is Rapidly Mixing
NASA Astrophysics Data System (ADS)
Collevecchio, Andrea; Garoni, Timothy M.; Hyndman, Timothy; Tokarev, Daniel
2016-09-01
We prove rapid mixing of the worm process for the zero-field ferromagnetic Ising model, on all finite connected graphs, and at all temperatures. As a corollary, we obtain a fully-polynomial randomized approximation scheme for the Ising susceptibility, and for a certain restriction of the two-point correlation function.
Universality of the Ising and the S=1 model on Archimedean lattices: a Monte Carlo determination.
Malakis, A; Gulpinar, G; Karaaslan, Y; Papakonstantinou, T; Aslan, G
2012-03-01
The Ising models S=1/2 and S=1 are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are briefly described and compared with the simple Metropolis algorithm. Accurate Monte Carlo data are produced at the exact critical temperatures of the Ising model for these lattices. Their finite-size analysis provide, with high accuracy, all critical exponents which, as expected, are the same with the well-known 2D Ising model exact values. A detailed finite-size scaling analysis of our Monte Carlo data for the S=1 model on the same lattices provides very clear evidence that this model obeys, also very well, the 2D Ising model critical exponents. As a result, we find that recent Monte Carlo simulations and attempts to define effective dimensionality for the S=1 model on these lattices are misleading. Accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two Archimedean lattices.
Universality of the Ising and the S=1 model on Archimedean lattices: A Monte Carlo determination
NASA Astrophysics Data System (ADS)
Malakis, A.; Gulpinar, G.; Karaaslan, Y.; Papakonstantinou, T.; Aslan, G.
2012-03-01
The Ising models S=1/2 and S=1 are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are briefly described and compared with the simple Metropolis algorithm. Accurate Monte Carlo data are produced at the exact critical temperatures of the Ising model for these lattices. Their finite-size analysis provide, with high accuracy, all critical exponents which, as expected, are the same with the well-known 2D Ising model exact values. A detailed finite-size scaling analysis of our Monte Carlo data for the S=1 model on the same lattices provides very clear evidence that this model obeys, also very well, the 2D Ising model critical exponents. As a result, we find that recent Monte Carlo simulations and attempts to define effective dimensionality for the S=1 model on these lattices are misleading. Accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two Archimedean lattices.
Eigenstate thermalization in the two-dimensional transverse field Ising model.
Mondaini, Rubem; Fratus, Keith R; Srednicki, Mark; Rigol, Marcos
2016-03-01
We study the onset of eigenstate thermalization in the two-dimensional transverse field Ising model (2D-TFIM) in the square lattice. We consider two nonequivalent Hamiltonians: the ferromagnetic 2D-TFIM and the antiferromagnetic 2D-TFIM in the presence of a uniform longitudinal field. We use full exact diagonalization to examine the behavior of quantum chaos indicators and of the diagonal matrix elements of operators of interest in the eigenstates of the Hamiltonian. An analysis of finite size effects reveals that quantum chaos and eigenstate thermalization occur in those systems whenever the fields are nonvanishing and not too large.
The Planar Ising Model and Total Positivity
NASA Astrophysics Data System (ADS)
Lis, Marcin
2017-01-01
A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no external field on a planar graph G. Let a_1,dots ,a_k,b_k,dots ,b_1 be vertices placed in a counterclockwise order on the outer face of G. We show that the k× k matrix of the two-point spin correlation functions M_{i,j} = < σ _{a_i} σ _{b_j} rangle is totally nonnegative. Moreover, det M > 0 if and only if there exist k pairwise vertex-disjoint paths that connect a_i with b_i. We also compute the scaling limit at criticality of the probability that there are k parallel and disjoint connections between a_i and b_i in the double random current model. Our results are based on a new distributional relation between double random currents and random alternating flows of Talaska [37].
Metastability in an open quantum Ising model.
Rose, Dominic C; Macieszczak, Katarzyna; Lesanovsky, Igor; Garrahan, Juan P
2016-11-01
We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a nonequilibrium phase transition or a smooth but sharp crossover, where the stationary state changes from paramagnetic to ferromagnetic, accompanied by strongly intermittent emission dynamics characteristic of first-order coexistence between dynamical phases. We show that for a range of parameters close to this transition or crossover point the dynamics of the finite system displays pronounced metastability, i.e., the system relaxes first to long-lived metastable states before eventual relaxation to the true stationary state. From the spectral properties of the quantum master operator we characterize the low-dimensional manifold of metastable states, which are shown to be probability mixtures of two, paramagnetic and ferromagnetic, metastable phases. We also show that for long times the dynamics can be approximated by a classical stochastic dynamics between the metastable phases that is directly related to the intermittent dynamics observed in quantum trajectories and thus the dynamical phases.
Metastability in an open quantum Ising model
NASA Astrophysics Data System (ADS)
Rose, Dominic C.; Macieszczak, Katarzyna; Lesanovsky, Igor; Garrahan, Juan P.
2016-11-01
We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a nonequilibrium phase transition or a smooth but sharp crossover, where the stationary state changes from paramagnetic to ferromagnetic, accompanied by strongly intermittent emission dynamics characteristic of first-order coexistence between dynamical phases. We show that for a range of parameters close to this transition or crossover point the dynamics of the finite system displays pronounced metastability, i.e., the system relaxes first to long-lived metastable states before eventual relaxation to the true stationary state. From the spectral properties of the quantum master operator we characterize the low-dimensional manifold of metastable states, which are shown to be probability mixtures of two, paramagnetic and ferromagnetic, metastable phases. We also show that for long times the dynamics can be approximated by a classical stochastic dynamics between the metastable phases that is directly related to the intermittent dynamics observed in quantum trajectories and thus the dynamical phases.
On Complexity of the Quantum Ising Model
NASA Astrophysics Data System (ADS)
Bravyi, Sergey; Hastings, Matthew
2017-01-01
We study complexity of several problems related to the Transverse field Ising Model (TIM). First, we consider the problem of estimating the ground state energy known as the Local Hamiltonian Problem (LHP). It is shown that the LHP for TIM on degree-3 graphs is equivalent modulo polynomial reductions to the LHP for general k-local `stoquastic' Hamiltonians with any constant {k ≥ 2}. This result implies that estimating the ground state energy of TIM on degree-3 graphs is a complete problem for the complexity class {StoqMA} —an extension of the classical class {MA}. As a corollary, we complete the complexity classification of 2-local Hamiltonians with a fixed set of interactions proposed recently by Cubitt and Montanaro. Secondly, we study quantum annealing algorithms for finding ground states of classical spin Hamiltonians associated with hard optimization problems. We prove that the quantum annealing with TIM Hamiltonians is equivalent modulo polynomial reductions to the quantum annealing with a certain subclass of k-local stoquastic Hamiltonians. This subclass includes all Hamiltonians representable as a sum of a k-local diagonal Hamiltonian and a 2-local stoquastic Hamiltonian.
Self-overlap as a method of analysis in Ising models.
Ferrera, A; Luque, B; Lacasa, L; Valero, E
2007-06-01
The damage spreading (DS) method provided a useful tool to obtain analytical results of the thermodynamics and stability of the two-dimensional (2D) Ising model--amongst many others--but it suffered both from ambiguities in its results and from large computational costs. In this paper we propose an alternative method, the so-called self-overlap method, based on the study of correlation functions measured at subsequent time steps as the system evolves towards its equilibrium. Applying Markovian and mean-field approximations to a 2D Ising system we obtain both analytical and numerical results on the thermodynamics that agree with the expected behavior. We also provide some analytical results on the stability of the system. Since only a single replica of the system needs to be studied, this method would seem to be free from the ambiguities that afflicted the DS method. It also seems to be numerically more efficient and analytically simpler.
Ising model for a Brownian donkey
NASA Astrophysics Data System (ADS)
Cleuren, B.; Van den Broeck, C.
2001-04-01
We introduce a thermal engine consisting of N interacting Brownian particles moving in a periodic potential, featuring an alternation of hot and cold symmetric peaks. A discretized Ising-like version is solved analytically. In response to an external force, absolute negative mobility is observed for N >= 4. For N → ∞ a nonequilibrium phase transition takes place with a spontaneous symmetry breaking entailing the appearance of a current in the absence of an external force.
Energy fluctuations and the singularity of specific heat in a 3D Ising model
NASA Astrophysics Data System (ADS)
Kaupuzs, Jevgenijs
2004-05-01
We study the energy fluctuations in 3D Ising model near the phase transition point. Specific heat is a relevant quantity which is directly related to the mean squared amplitude of the energy fluctuations in the system. We have made extensive Monte Carlo simulations in 3D Ising model to clarify the character of the singularity of the specific heat Cv based on the finite-size scaling of its maximal values Cvmax depending on the linear size of the lattice L. An original iterative method has been used which automatically finds the pseudocritical temperature corresponding to the maximum of Cv. The simulations made up to L <= 128 with application of the Wolff's cluster algorithm allowed us to verify the possible power-like as well as logarithmic singularity of the specific heat predicted by different theoretical treatments. The most challenging and interesting result we have obtained is that the finite-size scaling of Cvmax in 3D Ising model is well described by a logarithmic rather than power-like ansatz, just like in 2D case. Another modification of our iterative method has been considered to estimate the critical coupling of 3D Ising model from the Binder cumulant data within L ɛ [96; 384]. Furthermore, the critical exponent β has been evaluated from the simulated magnetization data within the range of reduced temperatures t >= 0.000086 and system sizes L <= 410.
Periodic Striped Ground States in Ising Models with Competing Interactions
NASA Astrophysics Data System (ADS)
Giuliani, Alessandro; Seiringer, Robert
2016-11-01
We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value J c ( p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2 d and J in a left neighborhood of J c ( p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes ( d = 2) or slabs ( d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.
Bootstrapping Critical Ising Model on Three Dimensional Real Projective Space.
Nakayama, Yu
2016-04-08
Given conformal data on a flat Euclidean space, we use crosscap conformal bootstrap equations to numerically solve the Lee-Yang model as well as the critical Ising model on a three dimensional real projective space. We check the rapid convergence of our bootstrap program in two dimensions from the exact solutions available. Based on the comparison, we estimate that our systematic error on the numerically solved one-point functions of the critical Ising model on a three dimensional real projective space is less than 1%. Our method opens up a novel way to solve conformal field theories on nontrivial geometries.
Interacting damage models mapped onto ising and percolation models
Toussaint, Renaud; Pride, Steven R.
2004-03-23
The authors introduce a class of damage models on regular lattices with isotropic interactions between the broken cells of the lattice. Quasistatic fiber bundles are an example. The interactions are assumed to be weak, in the sense that the stress perturbation from a broken cell is much smaller than the mean stress in the system. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in potential (elastic) energy in the system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, they obtain the probability distribution of each damage configuration at any level of the imposed external deformation. They demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, they show that damage models with global load sharing are isomorphic to standard percolation theory, that damage models with local load sharing rule are isomorphic to the standard ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. they also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, they also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based damage model
Large Scale Simulations of the Kinetic Ising Model
NASA Astrophysics Data System (ADS)
Münkel, Christian
We present Monte Carlo simulation results for the dynamical critical exponent z of the two- and three-dimensional kinetic Ising model. The z-values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at Tc for very large systems with up to (169984)2 and (3072)3 spins. To our knowledge, these are the largest Ising-systems simulated todate. We also report the successful simulation of very large lattices on a massively parallel MIMD computer with high speedups of approximately 1000 and an efficiency of about 0.93.
Phase transitions in Ising models on directed networks.
Lipowski, Adam; Ferreira, António Luis; Lipowska, Dorota; Gontarek, Krzysztof
2015-11-01
We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality class. On the directed square lattice the model remains paramagnetic at any positive temperature as already reported in some previous studies. We also examine random directed graphs and show that contrary to undirected ones, percolation of directed bonds does not guarantee ferromagnetic ordering. Only above a certain threshold can a random directed graph support finite-temperature ferromagnetic ordering. Such behavior is found also for out-homogeneous random graphs, but in this case the analysis of magnetic and percolative properties can be done exactly. Directed random graphs also differ from undirected ones with respect to zero-temperature freezing. Only at low connectivity do they remain trapped in a disordered configuration. Above a certain threshold, however, the zero-temperature dynamics quickly drives the model toward a broken symmetry (magnetized) state. Only above this threshold, which is almost twice as large as the percolation threshold, do we expect the Ising model to have a positive critical temperature. With a very good accuracy, the behavior on directed random graphs is reproduced within a certain approximate scheme.
Phase transitions in Ising models on directed networks
NASA Astrophysics Data System (ADS)
Lipowski, Adam; Ferreira, António Luis; Lipowska, Dorota; Gontarek, Krzysztof
2015-11-01
We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality class. On the directed square lattice the model remains paramagnetic at any positive temperature as already reported in some previous studies. We also examine random directed graphs and show that contrary to undirected ones, percolation of directed bonds does not guarantee ferromagnetic ordering. Only above a certain threshold can a random directed graph support finite-temperature ferromagnetic ordering. Such behavior is found also for out-homogeneous random graphs, but in this case the analysis of magnetic and percolative properties can be done exactly. Directed random graphs also differ from undirected ones with respect to zero-temperature freezing. Only at low connectivity do they remain trapped in a disordered configuration. Above a certain threshold, however, the zero-temperature dynamics quickly drives the model toward a broken symmetry (magnetized) state. Only above this threshold, which is almost twice as large as the percolation threshold, do we expect the Ising model to have a positive critical temperature. With a very good accuracy, the behavior on directed random graphs is reproduced within a certain approximate scheme.
Some Fruits of Genius: Lars Onsager and the Ising Model
NASA Astrophysics Data System (ADS)
Fisher, Michael E.
2006-03-01
The story of the exact solution of the two-dimensional Ising model by Lars Onsager in the 1940's will be sketched and some of the striking developments following from it, especially for the behavior of fluctuating interfaces, will be recounted.
Metastability for the Ising Model on the Hypercube
NASA Astrophysics Data System (ADS)
Jovanovski, Oliver
2017-04-01
We consider Glauber dynamics for the low-temperature, ferromagnetic Ising Model on the n-dimensional hypercube. We derive precise asymptotic results for the crossover time (the time it takes for the dynamics to go from the configuration with a "-1" at every vertex, to the configuration with a "+1" at each vertex) in the limit as the inverse temperature β → ∞.
Ising Model Reprogramming of a Repeat Protein's Equilibrium Unfolding Pathway.
Millership, C; Phillips, J J; Main, E R G
2016-05-08
Repeat proteins are formed from units of 20-40 aa that stack together into quasi one-dimensional non-globular structures. This modular repetitive construction means that, unlike globular proteins, a repeat protein's equilibrium folding and thus thermodynamic stability can be analysed using linear Ising models. Typically, homozipper Ising models have been used. These treat the repeat protein as a series of identical interacting subunits (the repeated motifs) that couple together to form the folded protein. However, they cannot describe subunits of differing stabilities. Here we show that a more sophisticated heteropolymer Ising model can be constructed and fitted to two new helix deletion series of consensus tetratricopeptide repeat proteins (CTPRs). This analysis, showing an asymmetric spread of stability between helices within CTPR ensembles, coupled with the Ising model's predictive qualities was then used to guide reprogramming of the unfolding pathway of a variant CTPR protein. The designed behaviour was engineered by introducing destabilising mutations that increased the thermodynamic asymmetry within a CTPR ensemble. The asymmetry caused the terminal α-helix to thermodynamically uncouple from the rest of the protein and preferentially unfold. This produced a specific, highly populated stable intermediate with a putative dimerisation interface. As such it is the first step in designing repeat proteins with function regulated by a conformational switch.
Ising model on the generalized Bruhat-Tits tree
NASA Astrophysics Data System (ADS)
Zinoviev, Yu. M.
1990-06-01
The partition function and the correlation functions of the Ising model on the generalized Bruhat-Tits tree are calculated. We computed also the averages of these correlation functions when the corresponding vertices are attached to the boundary of the generalized Bruhat-Tits tree.
Ising model on the generalized Bruhat-Tits tree
NASA Astrophysics Data System (ADS)
Zinoviev, Yu. M.
1991-08-01
The partition function and the correlation functions of the Ising model on the generalized Bruhat-Tits tree are calculated. We computed also the averages of these correlation functions when the corresponding vertices are attached to the boundary of the generalized Bruhat-Tits tree.
On scaling properties of cluster distributions in Ising models
NASA Astrophysics Data System (ADS)
Ruge, C.; Wagner, F.
1992-01-01
Scaling relations of cluster distributions for the Wolff algorithm are derived. We found them to be well satisfied for the Ising model in d=3 dimensions. Using scaling and a parametrization of the cluster distribution, we determine the critical exponent β/ν=0.516(6) with moderate effort in computing time.
Critical region for an Ising model coupled to causal triangulations
NASA Astrophysics Data System (ADS)
Cerda-Hernández, J.
2017-02-01
This paper extends the results obtained by Hernández et al for the annealed Ising model coupled to two-dimensional causal dynamical triangulations. We employ the Fortuin‑Kasteleyn (FK) representation in order to determine a region in the quadrant of the parameters β,μ >0 where the critical curve for the annealed model is possibly located. This can be done by outlining a region where the model has a unique infinite-volume Gibbs measure, and a region where the finite-volume Gibbs measure does not have weak limit (in fact, does not exist if the volume is large enough). We also improve the region where the model has a one dimensional geometry with respect to the unique weak limit measure, which implies that the Ising model on causal triangulation does not have phase transition in this region. Furthermore, we provide a better approximation of the free energy for the coupled model.
Frustrated Ising model on the Cairo pentagonal lattice.
Rojas, M; Rojas, Onofre; de Souza, S M
2012-11-01
Through the direct decoration transformation approach, we obtain a general solution for the pentagonal Ising model, showing its equivalence to the isotropic free-fermion eight-vertex model. We study the ground-state phase diagram, in which one ferromagnetic (FM) state, one ferrimagnetic (FIM) state, and one frustrated state are found. Using the exact solution of the pentagonal Ising model, we discuss the finite-temperature phase diagrams and find a phase transition between the FIM state and the disordered state as well as a phase transition between the disordered state and the FM state. We also discuss some additional remarkable properties of the model, such as the magnetization, entropy, and specific heat, at finite temperature and at its low-temperature asymptotic limit. Because of the influence of the second-order phase transition between the frustrated and ferromagnetic phases, we obtain surprisingly low values of the entropy and the specific heat until the critical temperature is reached.
Two-dimensional XXZ-Ising model with quartic interactions.
Valverde, J S
2012-05-01
In this work we study a two-dimensional XXZ-Ising spin-1/2 model with quartic interactions. The model is composed of a two-dimensional lattice of edge-sharing unitary cells, where each cell consists of two triangular prisms, converging in a basal plane with four Ising spin-1/2 (open circles); the apical positions are also occupied by four Heisenberg spin-1/2 (solid circles). Interaction of the base plane containing the multispin Ising interaction has the parameter J_{4}, and the other pairwise interactions have parameter J. For the proposed model we construct the phase diagram at zero temperature and give all possible spin configurations. In addition, we investigate two regions where the model can be solved exactly, the free fermion condition (FFC) and the symmetrical eight-vertex condition (SEVC). For this purpose we perform a straightforward mapping for a zero-field eight-vertex model. The necessary conditions for the equivalence are analyzed for all ranges of the interaction parameters. Unfortunately, the present model does not satisfy the FFC unless the trivial case; however, it was possible to give a region where the model can be solved approximately. We study the SEVC and verify that this condition is always satisfied. We also explore and discuss the critical conditions giving the region where these critical points are relevant.
NASA Astrophysics Data System (ADS)
Coester, K.; Malitz, W.; Fey, S.; Schmidt, K. P.
2013-11-01
We investigate the transverse field Ising model on a diamond chain using series expansions about the high-field limit and exact diagonalizations. For the unfrustrated case we accurately determine the quantum critical point and its expected 2d Ising universality separating the polarized and the Z2 symmetry broken phase. In contrast, we find strong evidence for a disorder by disorder scenario for the fully-frustrated transverse field Ising model, i.e., except for the pure Ising model, having an extensive number of ground states, the system is always in a quantum disordered polarized phase. The low-energy excitations in this polarized phase are understood in terms of exact local modes of the model. Furthermore, an effective low-energy description for an infinitesimal transverse field allows us to pinpoint the quantum disordered nature of the ground state via mapping to an effective transverse field Ising chain and to determine the induced gap to the elementary effective domain wall excitation very accurately.
Critical dynamics of cluster algorithms in the dilute Ising model
NASA Astrophysics Data System (ADS)
Hennecke, M.; Heyken, U.
1993-08-01
Autocorrelation times for thermodynamic quantities at T C are calculated from Monte Carlo simulations of the site-diluted simple cubic Ising model, using the Swendsen-Wang and Wolff cluster algorithms. Our results show that for these algorithms the autocorrelation times decrease when reducing the concentration of magnetic sites from 100% down to 40%. This is of crucial importance when estimating static properties of the model, since the variances of these estimators increase with autocorrelation time. The dynamical critical exponents are calculated for both algorithms, observing pronounced finite-size effects in the energy autocorrelation data for the algorithm of Wolff. We conclude that, when applied to the dilute Ising model, cluster algorithms become even more effective than local algorithms, for which increasing autocorrelation times are expected.
Information cascade, Kirman's ant colony model, and kinetic Ising model
NASA Astrophysics Data System (ADS)
Hisakado, Masato; Mori, Shintaro
2015-01-01
In this paper, we discuss a voting model in which voters can obtain information from a finite number of previous voters. There exist three groups of voters: (i) digital herders and independent voters, (ii) analog herders and independent voters, and (iii) tanh-type herders. In our previous paper Hisakado and Mori (2011), we used the mean field approximation for case (i). In that study, if the reference number r is above three, phase transition occurs and the solution converges to one of the equilibria. However, the conclusion is different from mean field approximation. In this paper, we show that the solution oscillates between the two states. A good (bad) equilibrium is where a majority of r select the correct (wrong) candidate. In this paper, we show that there is no phase transition when r is finite. If the annealing schedule is adequately slow from finite r to infinite r, the voting rate converges only to the good equilibrium. In case (ii), the state of reference votes is equivalent to that of Kirman's ant colony model, and it follows beta binomial distribution. In case (iii), we show that the model is equivalent to the finite-size kinetic Ising model. If the voters are rational, a simple herding experiment of information cascade is conducted. Information cascade results from the quenching of the kinetic Ising model. As case (i) is the limit of case (iii) when tanh function becomes a step function, the phase transition can be observed in infinite size limit. We can confirm that there is no phase transition when the reference number r is finite.
Ising anyons in frustration-free Majorana-dimer models
NASA Astrophysics Data System (ADS)
Ware, Brayden; Son, Jun Ho; Cheng, Meng; Mishmash, Ryan V.; Alicea, Jason; Bauer, Bela
2016-09-01
Dimer models have long been a fruitful playground for understanding topological physics. Here, we introduce a class, termed Majorana-dimer models, wherein bosonic dimers are decorated with pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian quasiparticles, and a topological px-i py superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We describe two parent Hamiltonians: one generalizes the well-known dimer model on the triangular lattice, while the other is most naturally understood as a model of decorated fluctuating loops on a honeycomb lattice. Using modular transformations, we show that the ground-state manifold of the latter model unambiguously exhibits all properties of the Ising×(px-i py) theory. We also discuss generalizations with more than one Majorana mode per site, which realize phases related to Kitaev's 16-fold way in a similar fashion.
Phase transition of the Ising model on a fractal lattice.
Genzor, Jozef; Gendiar, Andrej; Nishino, Tomotoshi
2016-01-01
The phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a factor of 4. The free energy and the spontaneous magnetization of the system are obtained by means of the higher-order tensor renormalization group method. The system exhibits the order-disorder phase transition, where the critical indices are different from those of the square-lattice Ising model. An exponential decay is observed in the density-matrix spectrum even at the critical point. It is possible to interpret that the system is less entangled because of the fractal geometry.
Dynamical properties of random-field Ising model.
Sinha, Suman; Mandal, Pradipta Kumar
2013-02-01
Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter, and the spin-spin correlation functions are studied in the nonequilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two-dimensional random field Ising model possesses long-range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long-range order in the system.
A Binomial Approximation Method for the Ising Model
NASA Astrophysics Data System (ADS)
Streib, Noah; Streib, Amanda; Beichl, Isabel; Sullivan, Francis
2014-08-01
A large portion of the computation required for the partition function of the Ising model can be captured with a simple formula. In this work, we support this claim by defining an approximation to the partition function and other thermodynamic quantities of the Ising model that requires no algorithm at all. This approximation, which uses the high temperature expansion, is solely based on the binomial distribution, and performs very well at low temperatures. At high temperatures, we provide an alternative approximation, which also serves as a lower bound on the partition function and is trivial to compute. We provide theoretical evidence and the results of numerical experiments to support the strength of these approximations.
Repairing Stevenson's step in the 4d Ising model
NASA Astrophysics Data System (ADS)
Balog, Janos; Niedermayer, Ferenc; Weisz, Peter
2006-05-01
In a recent paper Stevenson claimed that analysis of the data on the wave function renormalization constant near the critical point of the 4d Ising model is not consistent with analytical expectations. Here we present data with improved statistics and show that the results are indeed consistent with conventional wisdom once one takes into account the uncertainty of lattice artifacts in the analytical computations.
Genus-two characters of the Ising model
NASA Astrophysics Data System (ADS)
Choi, J. H.; Koh, I. G.
1989-05-01
As a first step in studying conformal theories on a higher-genus Riemann surface, we construct genus-two characters of the Ising model from their behavior in zero- and nonzero-homology pinching limits, the Goddard-Kent-Olive coset-space construction, and the branching coefficients in the level-two A(1)1 Kac-Moody characters on the higher-genus Riemann surface.
Ising model observables and non-backtracking walks
Helmuth, Tyler
2014-08-15
This paper presents an alternative proof of the connection between the partition function of the Ising model on a finite graph G and the set of non-backtracking walks on G. The techniques used also give formulas for spin-spin correlation functions in terms of non-backtracking walks. The main tools used are Viennot's theory of heaps of pieces and turning numbers on surfaces.
Ground state nonuniversality in the random-field Ising model
Duxbury, P. M.; Meinke, J. H.
2001-09-01
Two attractive and often used ideas, namely, universality and the concept of a zero-temperature fixed point, are violated in the infinite-range random-field Ising model. In the ground state we show that the exponents can depend continuously on the disorder and so are nonuniversal. However, we also show that at finite temperature the thermal order-parameter exponent 1/2 is restored so that temperature is a relevant variable. Broader implications of these results are discussed.
A new molecular thermodynamic model for multicomponent Ising lattice
NASA Astrophysics Data System (ADS)
Yang, Jianyong; Xin, Qin; Sun, Lei; Liu, Honglai; Hu, Ying; Jiang, Jianwen
2006-10-01
A new molecular thermodynamic model is developed for multicomponent Ising lattice based on a generalized nonrandom factor from binary system. Predictions of the nonrandom factor and the internal energy of mixing for ternary and quaternary systems match accurately with simulation results. Predictions of liquid-liquid phase equilibrium for ternary systems are in nearly perfect agreement with simulation results, and substantially improved from Flory-Huggins theory and the lattice-cluster theory. The model also satisfactorily correlates the experimental data of real ternary systems. The concise expression and the accuracy of the new model make it well suited for practical engineering applications.
Simulating the Rayleigh-Taylor instability with the Ising model
Ball, Justin R.; Elliott, James B.
2011-08-26
The Ising model, implemented with the Metropolis algorithm and Kawasaki dynamics, makes a system with its own physics, distinct from the real world. These physics are sophisticated enough to model behavior similar to the Rayleigh-Taylor instability and by better understanding these physics, we can learn how to modify the system to better re ect reality. For example, we could add a v_{x} and a v_{y} to each spin and modify the exchange rules to incorporate them, possibly using two body scattering laws to construct a more realistic system.
Ising model of financial markets with many assets
NASA Astrophysics Data System (ADS)
Eckrot, A.; Jurczyk, J.; Morgenstern, I.
2016-11-01
Many models of financial markets exist, but most of them simulate single asset markets. We study a multi asset Ising model of a financial market. Each agent has two possible actions (buy/sell) for every asset. The agents dynamically adjust their coupling coefficients according to past market returns and external news. This leads to fat tails and volatility clustering independent of the number of assets. We find that a separation of news into different channels leads to sector structures in the cross correlations, similar to those found in real markets.
Some results on hyperscaling in the 3D Ising model
Baker, G.A. Jr.; Kawashima, Naoki
1995-09-01
The authors review exact studies on finite-sized 2 dimensional Ising models and show that the point for an infinite-sized model at the critical temperature is a point of nonuniform approach in the temperature-size plane. They also illuminate some strong effects of finite-size on quantities which do not diverge at the critical point. They then review Monte Carlo studies for 3 dimensional Ising models of various sizes (L = 2--100) at various temperatures. From these results they find that the data for the renormalized coupling constant collapses nicely when plotted against the correlation length, determined in a system of edge length L, divided by L. They also find that {zeta}{sub L}/L {ge} 0.26 is definitely too large for reliable studies of the critical value, g*, of the renormalized coupling constant. They have reasonable evidence that {zeta}{sub L}/L {approx} 0.1 is adequate for results that are within one percent of those for the infinite system size. On this basis, they have conducted a series of Monte Carlo calculations with this condition imposed. These calculations were made practical by the development of improved estimators for use in the Swendsen-Wang cluster method. The authors found from these results, coupled with a reversed limit computation (size increases with the temperature fixed at the critical temperature), that g* > 0, although there may well be a sharp downward drop in g as the critical temperature is approached in accord with the predictions of series analysis. The results support the validity of hyperscaling in the 3 dimensional Ising model.
Wenzel, Sandro; Coletta, Tommaso; Korshunov, Sergey E; Mila, Frédéric
2012-11-02
Using extensive classical and quantum Monte Carlo simulations, we investigate the ground-state phase diagram of the fully frustrated transverse field Ising model on the square lattice. We show that pure columnar order develops in the low-field phase above a surprisingly large length scale, below which an effective U(1) symmetry is present. The same conclusion applies to the quantum dimer model with purely kinetic energy, to which the model reduces in the zero-field limit, as well as to the stacked classical version of the model. By contrast, the 2D classical version of the model is shown to develop plaquette order. Semiclassical arguments show that the transition from plaquette to columnar order is a consequence of quantum fluctuations.
The hobbyhorse of magnetic systems: the Ising model
NASA Astrophysics Data System (ADS)
Ibarra-García-Padilla, Eduardo; Gerardo Malanche-Flores, Carlos; Poveda-Cuevas, Freddy Jackson
2016-11-01
In undergraduate statistical mechanics courses the Ising model always plays an important role because it is the simplest non-trivial model used to describe magnetic systems. The one-dimensional model is easily solved analytically, while the two-dimensional one can be solved exactly by the Onsager solution. For this reason, numerical simulations are usually used to solve the two-dimensional model. Keeping in mind that the two-dimensional model is the platform for studying phase transitions, it is usually an exercise in computational undergraduate courses because its numerical solution is relatively simple to implement and its critical exponents are perfectly known. The purpose of this article is to present a detailed numerical study of the second-order phase transition in the two-dimensional Ising model at an undergraduate level, allowing readers not only to compare the mean-field solution, the exact solution and the numerical one through a complete study of the order parameter, the correlation function and finite-size scaling, but to present the techniques, along with hints and tips, for solving it themselves. We present the elementary theory of phase transitions and explain how to implement Markov chain Monte Carlo simulations and perform them for different lattice sizes with periodic boundary conditions. Energy, magnetization, specific heat, magnetic susceptibility and the correlation function are calculated and the critical exponents determined by finite-size scaling techniques. The importance of the correlation length as the relevant parameter in phase transitions is emphasized.
Restricted Boltzmann machines for the long range Ising models
NASA Astrophysics Data System (ADS)
Aoki, Ken-Ichi; Kobayashi, Tamao
2016-12-01
We set up restricted Boltzmann machines (RBM) to reproduce the long range Ising (LRI) models of the Ohmic type in one dimension. The RBM parameters are tuned by using the standard machine learning procedure with an additional method of configuration with probability (CwP). The quality of resultant RBM is evaluated through the susceptibility with respect to the magnetic external field. We compare the results with those by block decimation renormalization group (BDRG) method, and our RBM clear the test with satisfactory precision.
Simulation of financial market via nonlinear Ising model
NASA Astrophysics Data System (ADS)
Ko, Bonggyun; Song, Jae Wook; Chang, Woojin
2016-09-01
In this research, we propose a practical method for simulating the financial return series whose distribution has a specific heaviness. We employ the Ising model for generating financial return series to be analogous to those of the real series. The similarity between real financial return series and simulated one is statistically verified based on their stylized facts including the power law behavior of tail distribution. We also suggest the scheme for setting the parameters in order to simulate the financial return series with specific tail behavior. The simulation method introduced in this paper is expected to be applied to the other financial products whose price return distribution is fat-tailed.
Ising model simulation in directed lattices and networks
NASA Astrophysics Data System (ADS)
Lima, F. W. S.; Stauffer, D.
2006-01-01
On directed lattices, with half as many neighbours as in the usual undirected lattices, the Ising model does not seem to show a spontaneous magnetisation, at least for lower dimensions. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law on the square and simple cubic lattice. On directed Barabási-Albert networks with two and seven neighbours selected by each added site, Metropolis and Glauber algorithms give similar results, while for Wolff cluster flipping the magnetisation decays exponentially with time.
Globally nilpotent differential operators and the square Ising model
NASA Astrophysics Data System (ADS)
Bostan, A.; Boukraa, S.; Hassani, S.; Maillard, J.-M.; Weil, J.-A.; Zenine, N.
2009-03-01
We recall various multiple integrals with one parameter, related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and to their λ-extensions. The univariate analytic functions defined by these integrals are holonomic and even G-functions: they satisfy Fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties. We recall the explicit forms, found in previous work, of these Fuchsian equations, as well as their Russian-doll and direct sum structures. These differential operators are selected Fuchsian linear differential operators, and their remarkable properties have a deep geometrical origin: they are all globally nilpotent, or, sometimes, even have zero p-curvature. We also display miscellaneous examples of globally nilpotent operators emerging from enumerative combinatorics problems for which no integral representation is yet known. Focusing on the factorized parts of all these operators, we find out that the global nilpotence of the factors (resp. p-curvature nullity) corresponds to a set of selected structures of algebraic geometry: elliptic curves, modular curves, curves of genus five, six,..., and even a remarkable weight-1 modular form emerging in the three-particle contribution χ(3) of the magnetic susceptibility of the square Ising model. Noticeably, this associated weight-1 modular form is also seen in the factors of the differential operator for another n-fold integral of the Ising class, Φ(3)H, for the staircase polygons counting, and in Apéry's study of ζ(3). G-functions naturally occur as solutions of globally nilpotent operators. In the case where we do not have G-functions, but Hamburger functions (one irregular singularity at 0 or ∞) that correspond to the confluence of singularities in the scaling limit, the p-curvature is also found to verify new
Oscillating hysteresis in the q-neighbor Ising model.
Jȩdrzejewski, Arkadiusz; Chmiel, Anna; Sznajd-Weron, Katarzyna
2015-11-01
We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with q spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with q≥3 exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature T*, which linearly increases with q. Moreover, we show that for q=3 the phase transition is continuous and that it is discontinuous for larger values of q. For q>3, the hysteresis exhibits oscillatory behavior-expanding for even values of q and shrinking for odd values of q. Due to the mean-field-like nature of the model, we are able to derive the analytical form of transition probabilities and, therefore, calculate not only the probability density function of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable, and metastable steady states. Our results show that a seemingly small modification of the kinetic Ising model leads not only to the switch from a continuous to a discontinuous phase transition, but also to an unexpected oscillating behavior of the hysteresis and a puzzling phenomenon for q=5, which might be taken as evidence for the so-called mixed-order phase transition.
Dynamical percolation transition in the Ising model studied using a pulsed magnetic field.
Biswas, Soumyajyoti; Kundu, Anasuya; Chandra, Anjan Kumar
2011-02-01
We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature and pulse width and are different from the (static) percolation transition associated with the thermal transition. For a different model that belongs to the Ising universality class, the exponents are found to be same, confirming that the behavior is a common feature of the Ising class. These observations, along with a universal critical Binder cumulant value, characterize the dynamical percolation of the Ising universality class.
Toward an Ising model of cancer and beyond.
Torquato, Salvatore
2011-02-01
The holy grail of tumor modeling is to formulate theoretical and computational tools that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth. In order to develop such a predictive model, one must account for the numerous complex mechanisms involved in tumor growth. Here we review the research work that we have done toward the development of an 'Ising model' of cancer. The Ising model is an idealized statistical-mechanical model of ferromagnetism that is based on simple local-interaction rules, but nonetheless leads to basic insights and features of real magnets, such as phase transitions with a critical point. The review begins with a description of a minimalist four-dimensional (three dimensions in space and one in time) cellular automaton (CA) model of cancer in which cells transition between states (proliferative, hypoxic and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to study the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment, including induced resistance, is then described. We then describe how to incorporate angiogenesis as well as the heterogeneous and confined environment in which a tumor grows in the CA model. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently discussed. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility
Toward an Ising model of cancer and beyond
NASA Astrophysics Data System (ADS)
Torquato, Salvatore
2011-02-01
The holy grail of tumor modeling is to formulate theoretical and computational tools that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth. In order to develop such a predictive model, one must account for the numerous complex mechanisms involved in tumor growth. Here we review the research work that we have done toward the development of an 'Ising model' of cancer. The Ising model is an idealized statistical-mechanical model of ferromagnetism that is based on simple local-interaction rules, but nonetheless leads to basic insights and features of real magnets, such as phase transitions with a critical point. The review begins with a description of a minimalist four-dimensional (three dimensions in space and one in time) cellular automaton (CA) model of cancer in which cells transition between states (proliferative, hypoxic and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to study the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment, including induced resistance, is then described. We then describe how to incorporate angiogenesis as well as the heterogeneous and confined environment in which a tumor grows in the CA model. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently discussed. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility
Studying Zeolite Catalysts with a 2D Model System
Boscoboinik, Anibal
2016-12-07
Anibal Boscoboinik, a materials scientist at Brookhaven’s Center for Functional Nanomaterials, discusses the surface-science tools and 2D model system he uses to study catalysis in nanoporous zeolites, which catalyze reactions in many industrial processes.
The Ising Model Applied on Chronification of Pain.
Granan, Lars-Petter
2016-01-01
This is a hypothesis-article suggesting an entirely new framework for understanding and treating longstanding pain. Most medical and psychological models are described with boxes and arrows. Such models are of little clinical and explanatory use when describing the phenomenon of chronification of pain due to unknown causes. To date no models that have been provided - and tested in a scientific satisfactory way - lays out a plan for specific assessment due to a specific causal explanation, and in the end serves the clinicians, patients and researcher with tools on how to address the specific pain condition to every individual pain patient's condition. By applying the Ising model (from physics) on the phenomenon of chronification of pain, one is able to detangle all these factors, and thus have a model that both suggests an explanation of the condition and outlines how one might target the treatment of chronic pain patients with the use of network science.
The Ising Model Applied on Chronification of Pain
2016-01-01
This is a hypothesis-article suggesting an entirely new framework for understanding and treating longstanding pain. Most medical and psychological models are described with boxes and arrows. Such models are of little clinical and explanatory use when describing the phenomenon of chronification of pain due to unknown causes. To date no models that have been provided - and tested in a scientific satisfactory way - lays out a plan for specific assessment due to a specific causal explanation, and in the end serves the clinicians, patients and researcher with tools on how to address the specific pain condition to every individual pain patient's condition. By applying the Ising model (from physics) on the phenomenon of chronification of pain, one is able to detangle all these factors, and thus have a model that both suggests an explanation of the condition and outlines how one might target the treatment of chronic pain patients with the use of network science. PMID:26398917
Nonequilibrium relaxation study of Ising spin glass models
NASA Astrophysics Data System (ADS)
Ozeki, Yukiyasu; Ito, Nobuyasu
2001-07-01
As an analysis of equilibrium phase transitions, the nonequilibrium relaxation method is extended to the spin glass (SG) transition. The +/-J Ising SG model is analyzed for three-dimensional (cubic) lattices up to the linear size of L=127 and for four-dimensional (hypercubic) lattice up to L=41. These sizes of systems are quite large as compared with those calculated, so far, by equilibrium simulations. As a dynamical order parameter, we calculate the clone correlation function (CCF) Q(t,tw)≡[F], which is a spin correlation of two replicas produced after the waiting time tw from a simple starting state. It is found that the CCF shows an exponential decay in the paramagnetic phase, and a power-law decay after aginglike development (t>>tw) in the SG phase. This provides a reliable upper bound of the transition temperature Tg. It is also found that a scaling relation, Q(t,tw)=t-λqwq¯(t/tw), holds just around the transition point providing the lower bound of Tg. Together with these two bounds, we propose a new dynamical way for the estimation of Tg from much larger systems. In the SG phase, the power-law behavior of the CCF for t>>tw suggests that the SG phase in short-range Ising models has a rugged phase space.
Block renormalization study on the nonequilibrium chiral Ising model.
Kim, Mina; Park, Su-Chan; Noh, Jae Dong
2015-01-01
We present a numerical study on the ordering dynamics of a one-dimensional nonequilibrium Ising spin system with chirality. This system is characterized by a direction-dependent spin update rule. Pairs of +- spins can flip to ++ or -- with probability (1-u) or to -+ with probability u while -+ pairs are frozen. The system was found to evolve into the ferromagnetic ordered state at any u<1 exhibiting the power-law scaling of the characteristic length scale ξ∼t(1/z) and the domain-wall density ρ∼t(-δ). The scaling exponents z and δ were found to vary continuously with the parameter u. To establish the anomalous power-law scaling firmly, we perform the block renormalization analysis proposed by Basu and Hinrichsen [U. Basu and H. Hinrichsen, J. Stat. Mech.: Theor. Exp. (2011)]. The block renormalization method predicts, under the assumption of dynamic scale invariance, a scaling relation that can be used to estimate the scaling exponent numerically. We find the condition under which the scaling relation is justified. We then apply the method to our model and obtain the critical exponent zδ at several values of u. The numerical result is in perfect agreement with that of the previous study. This study serves as additional evidence for the claim that the nonequilibrium chiral Ising model displays power-law scaling behavior with continuously varying exponents.
Quantum dimensions from local operator excitations in the Ising model
NASA Astrophysics Data System (ADS)
Caputa, Paweł; Rams, Marek M.
2017-02-01
We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Rényi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as the evolution of the relative entropy after local operator excitation and discuss universal features that emerge from numerics.
NASA Astrophysics Data System (ADS)
M, Y. Ali; J, Poulter
2013-06-01
In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.
Identifying differentially expressed genes in cancer patients using a non-parameter Ising model.
Li, Xumeng; Feltus, Frank A; Sun, Xiaoqian; Wang, James Z; Luo, Feng
2011-10-01
Identification of genes and pathways involved in diseases and physiological conditions is a major task in systems biology. In this study, we developed a novel non-parameter Ising model to integrate protein-protein interaction network and microarray data for identifying differentially expressed (DE) genes. We also proposed a simulated annealing algorithm to find the optimal configuration of the Ising model. The Ising model was applied to two breast cancer microarray data sets. The results showed that more cancer-related DE sub-networks and genes were identified by the Ising model than those by the Markov random field model. Furthermore, cross-validation experiments showed that DE genes identified by Ising model can improve classification performance compared with DE genes identified by Markov random field model.
Conformal symmetry of the critical 3D Ising model inside a sphere
NASA Astrophysics Data System (ADS)
Cosme, Catarina; Lopes, J. M. Viana Parente; Penedones, João
2015-08-01
We perform Monte-Carlo simulations of the three-dimensional Ising model at the critical temperature and zero magnetic field. We simulate the system in a ball with free boundary conditions on the two dimensional spherical boundary. Our results for one and two point functions in this geometry are consistent with the predictions from the conjectured conformal symmetry of the critical Ising model.
Ising models on the 2 x 2 x {infinity} lattices
Yurishchev, M. A.
2007-03-15
Exact analytic solutions are presented for two 2 x 2 x {infinity} Ising etageres. The first model has a simple cubic lattice with fully anisotropic interactions. The second model consists of two different types of linear chains and includes noncrossing diagonal bonds on the side faces of the 2 x 2 x {infinity} parallelepiped. In both cases, the solutions are expressed through square radicals and obtained by using the obvious symmetry of the Hamiltonians, Z{sub 2} x C{sub 2v}, and the hidden algebraic {lambda}{lambda} symmetry of the transfer matrix secular equations. The solution found for the second model is used to analyze the behavior of specific heat in a frustrated many-chain system.
Technical Review of the UNET2D Hydraulic Model
Perkins, William A.; Richmond, Marshall C.
2009-05-18
The Kansas City District of the US Army Corps of Engineers is engaged in a broad range of river management projects that require knowledge of spatially-varied hydraulic conditions such as velocities and water surface elevations. This information is needed to design new structures, improve existing operations, and assess aquatic habitat. Two-dimensional (2D) depth-averaged numerical hydraulic models are a common tool that can be used to provide velocity and depth information. Kansas City District is currently using a specific 2D model, UNET2D, that has been developed to meet the needs of their river engineering applications. This report documents a tech- nical review of UNET2D.
Maximum Likelihood Reconstruction for Ising Models with Asynchronous Updates
NASA Astrophysics Data System (ADS)
Zeng, Hong-Li; Alava, Mikko; Aurell, Erik; Hertz, John; Roudi, Yasser
2013-05-01
We describe how the couplings in an asynchronous kinetic Ising model can be inferred. We consider two cases: one in which we know both the spin history and the update times and one in which we know only the spin history. For the first case, we show that one can average over all possible choices of update times to obtain a learning rule that depends only on spin correlations and can also be derived from the equations of motion for the correlations. For the second case, the same rule can be derived within a further decoupling approximation. We study all methods numerically for fully asymmetric Sherrington-Kirkpatrick models, varying the data length, system size, temperature, and external field. Good convergence is observed in accordance with the theoretical expectations.
Propagation of fluctuations in the quantum Ising model
NASA Astrophysics Data System (ADS)
Navez, P.; Tsironis, G. P.; Zagoskin, A. M.
2017-02-01
We investigate entanglement dynamics and correlations in the quantum Ising model in arbitrary dimensions using a large-coordination-number expansion. We start from the pure paramagnetic regime obtained through zero spin-spin coupling and subsequently turn on the interspin interaction in a time-dependent fashion. We investigate analytically and compare results for both the slow adiabatic onset of the interactions and the fast instantaneous switching. We find that in the latter case of an initial excitation mode a quantum correlation wave spreads through the system, propagating with twice the group velocity of the linearized equilibrium modes. This wave establishes the spatiotemporal regime of entangled quantum properties of the system for time scales shorter than the decoherence time and thus provides an indicator for the "quantumness" of the physical system that the specific system models.
2D microscopic model of graphene fracture properties
NASA Astrophysics Data System (ADS)
Hess, Peter
2015-05-01
An analytical two-dimensional (2D) microscopic fracture model based on Morse-type interaction is derived containing no adjustable parameter. From the 2D Young’s moduli and 2D intrinsic strengths of graphene measured by nanoindentation based on biaxial tension and calculated by density functional theory for uniaxial tension the widely unknown breaking force, line or edge energy, surface energy, fracture toughness, and strain energy release rate were determined. The simulated line energy agrees well with ab initio calculations and the fracture toughness of perfect graphene sheets is in good agreement with molecular dynamics simulations and the fracture toughness evaluated for defective graphene using the Griffith relation. Similarly, the estimated critical strain energy release rate agrees well with result of various theoretical approaches based on the J-integral and surface energy. The 2D microscopic model, connecting 2D and three-dimensional mechanical properties in a consistent way, provides a versatile relationship to easily access all relevant fracture properties of pristine 2D solids.
Information flow in a kinetic Ising model peaks in the disordered phase.
Barnett, Lionel; Lizier, Joseph T; Harré, Michael; Seth, Anil K; Bossomaier, Terry
2013-10-25
There is growing evidence that for a range of dynamical systems featuring complex interactions between large ensembles of interacting elements, mutual information peaks at order-disorder phase transitions. We conjecture that, by contrast, information flow in such systems will generally peak strictly on the disordered side of a phase transition. This conjecture is verified for a ferromagnetic 2D lattice Ising model with Glauber dynamics and a transfer entropy-based measure of systemwide information flow. Implications of the conjecture are considered, in particular, that for a complex dynamical system in the process of transitioning from disordered to ordered dynamics (a mechanism implicated, for example, in financial market crashes and the onset of some types of epileptic seizures); information dynamics may be able to predict an imminent transition.
Scale invariance implies conformal invariance for the three-dimensional Ising model.
Delamotte, Bertrand; Tissier, Matthieu; Wschebor, Nicolás
2016-01-01
Using the Wilson renormalization group, we show that if no integrated vector operator of scaling dimension -1 exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that scale invariance implies conformal invariance for the three-dimensional Ising model.
The linear Ising model and its analytic continuation, random walk
NASA Astrophysics Data System (ADS)
Lavenda, B. H.
2004-02-01
A generalization of Gauss's principle is used to derive the error laws corresponding to Types II and VII distributions in Pearson's classification scheme. Student's r-p.d.f. (Type II) governs the distribution of the internal energy of a uniform, linear chain, Ising model, while the analytic continuation of the uniform exchange energy converts it into a Student t-density (Type VII) for the position of a random walk in a single spatial dimension. Higher-dimensional spaces, corresponding to larger degrees of freedom and generalizations to multidimensional Student r- and t-densities, are obtained by considering independent and identically random variables, having rotationally invariant densities, whose entropies are additive and generating functions are multiplicative.
Robust criticality of an Ising model on rewired directed networks
NASA Astrophysics Data System (ADS)
Lipowski, Adam; Gontarek, Krzysztof; Lipowska, Dorota
2015-06-01
We show that preferential rewiring, which is supposed to mimic the behavior of financial agents, changes a directed-network Ising ferromagnet with a single critical point into a model with robust critical behavior. For the nonrewired random graph version, due to a constant number of out-links for each site, we write a simple mean-field-like equation describing the behavior of magnetization; we argue that it is exact and support the claim with extensive Monte Carlo simulations. For the rewired version, this equation is obeyed only at low temperatures. At higher temperatures, rewiring leads to strong heterogeneities, which apparently invalidates mean-field arguments and induces large fluctuations and divergent susceptibility. Such behavior is traced back to the formation of a relatively small core of agents that influence the entire system.
Maximum caliber inference and the stochastic Ising model.
Cafaro, Carlo; Ali, Sean Alan
2016-11-01
We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we maximize the path entropy over discrete time step trajectories subject to normalization, stationarity, and detailed balance constraints together with a path-dependent dynamical information constraint reflecting a given average global behavior of the complex system. A general expression for the transition probability values associated with the stationary random Markov processes describing the nonequilibrium stationary system is computed. By virtue of our analysis, we uncover that a convenient choice of the dynamical information constraint together with a perturbative asymptotic expansion with respect to its corresponding Lagrange multiplier of the general expression for the transition probability leads to a formal overlap with the well-known Glauber hyperbolic tangent rule for the transition probability for the stochastic Ising model in the limit of very high temperatures of the heat reservoir.
Droplet model for autocorrelation functions in an Ising ferromagnet
NASA Technical Reports Server (NTRS)
Tang, Chao; Nakanishi, Hiizu; Langer, J. S.
1989-01-01
The autocorrelation function of Ising spins in an ordered phase is studied via a droplet model. Only noninteracting spherical droplets are considered. The Langevin equation which describes fluctuations in the radius of a single droplet is studied in detail. A general description of the transformation to a Fokker-Planck equations and the ways in which a spectral analysis of that equation can be used to compute the autocorrelation function is given. It is shown that the eigenvalues of the Fokker-Planck operator form (1) a continuous spectrum of relaxation rates starting from zero for d = 2, (2) a continuous spectrum with a finite gap for d = 3, and (3) a discrete spectrum for d greater than 4, where d is the spatial dimensionality. Detailed solutions for various cases are presented.
Robust criticality of an Ising model on rewired directed networks.
Lipowski, Adam; Gontarek, Krzysztof; Lipowska, Dorota
2015-06-01
We show that preferential rewiring, which is supposed to mimic the behavior of financial agents, changes a directed-network Ising ferromagnet with a single critical point into a model with robust critical behavior. For the nonrewired random graph version, due to a constant number of out-links for each site, we write a simple mean-field-like equation describing the behavior of magnetization; we argue that it is exact and support the claim with extensive Monte Carlo simulations. For the rewired version, this equation is obeyed only at low temperatures. At higher temperatures, rewiring leads to strong heterogeneities, which apparently invalidates mean-field arguments and induces large fluctuations and divergent susceptibility. Such behavior is traced back to the formation of a relatively small core of agents that influence the entire system.
Maximum caliber inference and the stochastic Ising model
NASA Astrophysics Data System (ADS)
Cafaro, Carlo; Ali, Sean Alan
2016-11-01
We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we maximize the path entropy over discrete time step trajectories subject to normalization, stationarity, and detailed balance constraints together with a path-dependent dynamical information constraint reflecting a given average global behavior of the complex system. A general expression for the transition probability values associated with the stationary random Markov processes describing the nonequilibrium stationary system is computed. By virtue of our analysis, we uncover that a convenient choice of the dynamical information constraint together with a perturbative asymptotic expansion with respect to its corresponding Lagrange multiplier of the general expression for the transition probability leads to a formal overlap with the well-known Glauber hyperbolic tangent rule for the transition probability for the stochastic Ising model in the limit of very high temperatures of the heat reservoir.
Double resonance in the infinite-range quantum Ising model.
Han, Sung-Guk; Um, Jaegon; Kim, Beom Jun
2012-08-01
We study quantum resonance behavior of the infinite-range kinetic Ising model at zero temperature. Numerical integration of the time-dependent Schrödinger equation in the presence of an external magnetic field in the z direction is performed at various transverse field strengths g. It is revealed that two resonance peaks occur when the energy gap matches the external driving frequency at two distinct values of g, one below and the other above the quantum phase transition. From the similar observations already made in classical systems with phase transitions, we propose that the double resonance peaks should be a generic feature of continuous transitions, for both quantum and classical many-body systems.
Hysteresis in an Ising model with mobile bonds
NASA Astrophysics Data System (ADS)
Čapeta, D.; Sunko, D. K.
2005-04-01
Hysteresis is studied in a disordered Ising model in which diffusion of antiferromagnetic bonds is allowed in addition to spin flips. Saturation behavior changes to a figure-eight loop when diffusion is introduced. The upper and lower fields delimiting the figure-eight are determined by the Hamiltonian, while its surface and the crossing point depend on the temperature and details of the dynamics. The main avalanche is associated with the disappearance of hidden order. Some experimental observations of figure-eight anomalies are discussed. It is argued they are a signal of a transient rearrangement of domain couplings, characteristic of amorphous and/or magnetically soft samples, and similar to evolution of kinetic glasses.
An Intercomparison of 2-D Models Within a Common Framework
NASA Technical Reports Server (NTRS)
Weisenstein, Debra K.; Ko, Malcolm K. W.; Scott, Courtney J.; Jackman, Charles H.; Fleming, Eric L.; Considine, David B.; Kinnison, Douglas E.; Connell, Peter S.; Rotman, Douglas A.; Bhartia, P. K. (Technical Monitor)
2002-01-01
A model intercomparison among the Atmospheric and Environmental Research (AER) 2-D model, the Goddard Space Flight Center (GSFC) 2-D model, and the Lawrence Livermore National Laboratory 2-D model allows us to separate differences due to model transport from those due to the model's chemical formulation. This is accomplished by constructing two hybrid models incorporating the transport parameters of the GSFC and LLNL models within the AER model framework. By comparing the results from the native models (AER and e.g. GSFC) with those from the hybrid model (e.g. AER chemistry with GSFC transport), differences due to chemistry and transport can be identified. For the analysis, we examined an inert tracer whose emission pattern is based on emission from a High Speed Civil Transport (HSCT) fleet; distributions of trace species in the 2015 atmosphere; and the response of stratospheric ozone to an HSCT fleet. Differences in NO(y) in the upper stratosphere are found between models with identical transport, implying different model representations of atmospheric chemical processes. The response of O3 concentration to HSCT aircraft emissions differs in the models from both transport-dominated differences in the HSCT-induced perturbations of H2O and NO(y) as well as from differences in the model represent at ions of O3 chemical processes. The model formulations of cold polar processes are found to be the most significant factor in creating large differences in the calculated ozone perturbations
Leblanc, M D; Whitehead, J P; Plumer, M L
2013-05-15
A combination of Metropolis and modified Wolff cluster algorithms is used to examine the impact of uniaxial single-ion anisotropy on the phase transition to ferromagnetic order of Heisenberg macrospins on a 2D square lattice. This forms the basis of a model for granular perpendicular recording media where macrospins represent the magnetic moment of grains. The focus of this work is on the interplay between anisotropy D, intragrain exchange J' and intergrain exchange J on the ordering temperature T(C) and extends our previous reported analysis of the granular Ising model. The role of intragrain degrees of freedom in heat assisted magnetic recording is discussed.
NASA Astrophysics Data System (ADS)
Leblanc, M. D.; Whitehead, J. P.; Plumer, M. L.
2013-05-01
A combination of Metropolis and modified Wolff cluster algorithms is used to examine the impact of uniaxial single-ion anisotropy on the phase transition to ferromagnetic order of Heisenberg macrospins on a 2D square lattice. This forms the basis of a model for granular perpendicular recording media where macrospins represent the magnetic moment of grains. The focus of this work is on the interplay between anisotropy D, intragrain exchange J‧ and intergrain exchange J on the ordering temperature TC and extends our previous reported analysis of the granular Ising model. The role of intragrain degrees of freedom in heat assisted magnetic recording is discussed.
Studying Zeolite Catalysts with a 2D Model System
Boscoboinik, Anibal
2016-12-14
Anibal Boscoboinik, a materials scientist at Brookhavenâs Center for Functional Nanomaterials, discusses the surface-science tools and 2D model system he uses to study catalysis in nanoporous zeolites, which catalyze reactions in many industrial processes.
Probing strong correlations with light scattering: Example of the quantum Ising model
Babujian, H. M.; Karowski, M.; Tsvelik, A. M.
2016-10-01
In this article we calculate the nonlinear susceptibility and the resonant Raman cross section for the paramagnetic phase of the ferromagnetic quantum Ising model in one dimension. In this region the spectrum of the Ising model has a gap m. The Raman cross section has a strong singularity when the energy of the outgoing photon is at the spectral gap ωf ≈ m and a square root threshold when the frequency difference between the incident and outgoing photons ωi₋ωf≈2m. Finally, the latter feature reflects the fermionic nature of the Ising model excitations.
Probing strong correlations with light scattering: Example of the quantum Ising model
Babujian, H. M.; Karowski, M.; Tsvelik, A. M.
2016-10-01
In this article we calculate the nonlinear susceptibility and the resonant Raman cross section for the paramagnetic phase of the ferromagnetic quantum Ising model in one dimension. In this region the spectrum of the Ising model has a gap m. The Raman cross section has a strong singularity when the energy of the outgoing photon is at the spectral gap ω_{f} ≈ m and a square root threshold when the frequency difference between the incident and outgoing photons ω_{i}₋ω_{f}≈2m. Finally, the latter feature reflects the fermionic nature of the Ising model excitations.
Gold-standard performance for 2D hydrodynamic modeling
NASA Astrophysics Data System (ADS)
Pasternack, G. B.; MacVicar, B. J.
2013-12-01
Two-dimensional, depth-averaged hydrodynamic (2D) models are emerging as an increasingly useful tool for environmental water resources engineering. One of the remaining technical hurdles to the wider adoption and acceptance of 2D modeling is the lack of standards for 2D model performance evaluation when the riverbed undulates, causing lateral flow divergence and convergence. The goal of this study was to establish a gold-standard that quantifies the upper limit of model performance for 2D models of undulating riverbeds when topography is perfectly known and surface roughness is well constrained. A review was conducted of published model performance metrics and the value ranges exhibited by models thus far for each one. Typically predicted velocity differs from observed by 20 to 30 % and the coefficient of determination between the two ranges from 0.5 to 0.8, though there tends to be a bias toward overpredicting low velocity and underpredicting high velocity. To establish a gold standard as to the best performance possible for a 2D model of an undulating bed, two straight, rectangular-walled flume experiments were done with no bed slope and only different bed undulations and water surface slopes. One flume tested model performance in the presence of a porous, homogenous gravel bed with a long flat section, then a linear slope down to a flat pool bottom, and then the same linear slope back up to the flat bed. The other flume had a PVC plastic solid bed with a long flat section followed by a sequence of five identical riffle-pool pairs in close proximity, so it tested model performance given frequent undulations. Detailed water surface elevation and velocity measurements were made for both flumes. Comparing predicted versus observed velocity magnitude for 3 discharges with the gravel-bed flume and 1 discharge for the PVC-bed flume, the coefficient of determination ranged from 0.952 to 0.987 and the slope for the regression line was 0.957 to 1.02. Unsigned velocity
Linear relaxation in large two-dimensional Ising models
NASA Astrophysics Data System (ADS)
Lin, Y.; Wang, F.
2016-02-01
Critical dynamics in two-dimension Ising lattices up to 2048 ×2048 is simulated on field-programmable-gate-array- based computing devices. Linear relaxation times are measured from extremely long Monte Carlo simulations. The longest simulation has 7.1 ×1016 spin updates, which would take over 37 years to simulate on a general purpose computer. The linear relaxation time of the Ising lattices is found to follow the dynamic scaling law for correlation lengths as long as 2048. The dynamic exponent z of the system is found to be 2.179(12), which is consistent with previous studies of Ising lattices with shorter correlation lengths. It is also found that Monte Carlo simulations of critical dynamics in Ising lattices larger than 512 ×512 are very sensitive to the statistical correlations between pseudorandom numbers, making it even more difficult to study such large systems.
Stochastic bifurcations in the nonlinear parallel Ising model.
Bagnoli, Franco; Rechtman, Raúl
2016-11-01
We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.
Stochastic bifurcations in the nonlinear parallel Ising model
NASA Astrophysics Data System (ADS)
Bagnoli, Franco; Rechtman, Raúl
2016-11-01
We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.
Instantons in 2D U(1) Higgs model and 2D CP(N-1) sigma models
NASA Astrophysics Data System (ADS)
Lian, Yaogang
2007-12-01
In this thesis I present the results of a study of the topological structures of 2D U(1) Higgs model and 2D CP N-1 sigma models. Both models have been studied using the overlap Dirac operator construction of topological charge density. The overlap operator provides a more incisive probe into the local topological structure of gauge field configurations than the traditional plaquette-based operator. In the 2D U(1) Higgs model, we show that classical instantons with finite sizes violate the negativity of topological charge correlator by giving a positive contribution to the correlator at non-zero separation. We argue that instantons in 2D U(1) Higgs model must be accompanied by large quantum fluctuations in order to solve this contradiction. In 2D CPN-1 sigma models, we observe the anomalous scaling behavior of the topological susceptibility chi t for N ≤ 3. The divergence of chi t in these models is traced to the presence of small instantons with a radius of order a (= lattice spacing), which are directly observed on the lattice. The observation of these small instantons provides detailed confirmation of Luscher's argument that such short-distance excitations, with quantized topological charge, should be the dominant topological fluctuations in CP1 and CP 2, leading to a divergent topological susceptibility in the continuum limit. For the CPN-1 models with N > 3 the topological susceptibility is observed to scale properly with the mass gap. Another topic presented in this thesis is an implementation of the Zolotarev optimal rational approximation for the overlap Dirac operator. This new implementation has reduced the time complexity of the overlap routine from O(N3 ) to O(N), where N is the total number of sites on the lattice. This opens up a door to more accurate lattice measurements in the future.
2-D Magnetohydrodynamic Modeling of A Pulsed Plasma Thruster
NASA Technical Reports Server (NTRS)
Thio, Y. C. Francis; Cassibry, J. T.; Wu, S. T.; Rodgers, Stephen L. (Technical Monitor)
2002-01-01
Experiments are being performed on the NASA Marshall Space Flight Center (MSFC) MK-1 pulsed plasma thruster. Data produced from the experiments provide an opportunity to further understand the plasma dynamics in these thrusters via detailed computational modeling. The detailed and accurate understanding of the plasma dynamics in these devices holds the key towards extending their capabilities in a number of applications, including their applications as high power (greater than 1 MW) thrusters, and their use for producing high-velocity, uniform plasma jets for experimental purposes. For this study, the 2-D MHD modeling code, MACH2, is used to provide detailed interpretation of the experimental data. At the same time, a 0-D physics model of the plasma initial phase is developed to guide our 2-D modeling studies.
Ising percolation in a three-state majority vote model
NASA Astrophysics Data System (ADS)
Balankin, Alexander S.; Martínez-Cruz, M. A.; Gayosso Martínez, Felipe; Mena, Baltasar; Tobon, Atalo; Patiño-Ortiz, Julián; Patiño-Ortiz, Miguel; Samayoa, Didier
2017-02-01
In this Letter, we introduce a three-state majority vote model in which each voter adopts a state of a majority of its active neighbors, if exist, but the voter becomes uncommitted if its active neighbors are in a tie, or all neighbors are the uncommitted. Numerical simulations were performed on square lattices of different linear size with periodic boundary conditions. Starting from a random distribution of active voters, the model leads to a stable non-consensus state in which three opinions coexist. We found that the "magnetization" of the non-consensus state and the concentration of uncommitted voters in it are governed by an initial composition of system and are independent of the lattice size. Furthermore, we found that a configuration of the stable non-consensus state undergoes a second order percolation transition at a critical concentration of voters holding the same opinion. Numerical simulations suggest that this transition belongs to the same universality class as the Ising percolation. These findings highlight the effect of an updating rule for a tie between voter neighbors on the critical behavior of models obeying the majority vote rule whenever a strict majority exists.
Flow transitions in a 2D directional solidification model
NASA Technical Reports Server (NTRS)
Larroude, Philippe; Ouazzani, Jalil; Alexander, J. Iwan D.
1992-01-01
Flow transitions in a Two Dimensional (2D) model of crystal growth were examined using the Bridgman-Stockbarger me thod. Using a pseudo-spectral Chebyshev collocation method, the governing equations yield solutions which exhibit a symmetry breaking flow tansition and oscillatory behavior indicative of a Hopf bifurcation at higher values of Ra. The results are discussed from fluid dynamic viewpoint, and broader implications for process models are also addressed.
Numerical modelling of spallation in 2D hydrodynamics codes
NASA Astrophysics Data System (ADS)
Maw, J. R.; Giles, A. R.
1996-05-01
A model for spallation based on the void growth model of Johnson has been implemented in 2D Lagrangian and Eulerian hydrocodes. The model has been extended to treat complete separation of material when voids coalesce and to describe the effects of elevated temperatures and melting. The capabilities of the model are illustrated by comparison with data from explosively generated spall experiments. Particular emphasis is placed on the prediction of multiple spall effects in weak, low melting point, materials such as lead. The correlation between the model predictions and observations on the strain rate dependence of spall strength is discussed.
Domain walls in the quantum transverse Ising model
NASA Astrophysics Data System (ADS)
Henkel, Malte; Harris, A. Brooks; Cieplak, Marek
1995-08-01
We discuss several problems concerning domain walls in the spin-S Ising model at zero temeprature in a magnetic field, H/(2S), applied in the x direction. Some results are also given for the planar (y-z) model in a transverse field. We treat the quantum problem in one dimension by perturbation theory at small H and numerically over a large range of H. We obtain the spin-density profile by fixing the spins at opposite ends of the chain to have opposite signs of Sz. One dimensional is special in that there the quantum width of the wall is proportional to the size L of the system. We also study the quantitative features of the ``particle'' band which extends up to energies of order H above the ground state. Except for the planar limit, this particle band is well separated from excitations having energy J/S involving creation of more walls. At large S this particle band develops energy gaps and the lowest subband has tunnel splittings of order H21-2S. This scale of of energy gives rise to anomalous scaling with respect to (a) finite size, (b) temperature, or (c) random potentials. The intrinsic width of the domain wall and the pinning energy are also defined and calculated in certain limiting cases. The general conclusion is that quantum effects prevent the wall from being sharp and in higher dimension would prevent sudden excursions in the configuration of the wall.
Large-scale Monte Carlo simulations for the depinning transition in Ising-type lattice models
NASA Astrophysics Data System (ADS)
Si, Lisha; Liao, Xiaoyun; Zhou, Nengji
2016-12-01
With the developed "extended Monte Carlo" (EMC) algorithm, we have studied the depinning transition in Ising-type lattice models by extensive numerical simulations, taking the random-field Ising model with a driving field and the driven bond-diluted Ising model as examples. In comparison with the usual Monte Carlo method, the EMC algorithm exhibits greater efficiency of the simulations. Based on the short-time dynamic scaling form, both the transition field and critical exponents of the depinning transition are determined accurately via the large-scale simulations with the lattice size up to L = 8912, significantly refining the results in earlier literature. In the strong-disorder regime, a new universality class of the Ising-type lattice model is unveiled with the exponents β = 0.304(5) , ν = 1.32(3) , z = 1.12(1) , and ζ = 0.90(1) , quite different from that of the quenched Edwards-Wilkinson equation.
NGMIX: Gaussian mixture models for 2D images
NASA Astrophysics Data System (ADS)
Sheldon, Erin
2015-08-01
NGMIX implements Gaussian mixture models for 2D images. Both the PSF profile and the galaxy are modeled using mixtures of Gaussians. Convolutions are thus performed analytically, resulting in fast model generation as compared to methods that perform the convolution in Fourier space. For the galaxy model, NGMIX supports exponential disks and de Vaucouleurs and Sérsic profiles; these are implemented approximately as a sum of Gaussians using the fits from Hogg & Lang (2013). Additionally, any number of Gaussians can be fit, either completely free or constrained to be cocentric and co-elliptical.
Critical behavior of the Ising model on random fractals.
Monceau, Pascal
2011-11-01
We study the critical behavior of the Ising model in the case of quenched disorder constrained by fractality on random Sierpinski fractals with a Hausdorff dimension d(f) is approximately equal to 1.8928. This is a first attempt to study a situation between the borderline cases of deterministic self-similarity and quenched randomness. Intensive Monte Carlo simulations were carried out. Scaling corrections are much weaker than in the deterministic cases, so that our results enable us to ensure that finite-size scaling holds, and that the critical behavior is described by a new universality class. The hyperscaling relation is compatible with an effective dimension equal to the Hausdorff one; moreover the two eigenvalues exponents of the renormalization flows are shown to be different from the ones calculated from ε expansions, and from the ones obtained for fourfold symmetric deterministic fractals. Although the space dimensionality is not integer, lack of self-averaging properties exhibits some features very close to the ones of a random fixed point associated with a relevant disorder.
Phase transitions and relaxation dynamics of Ising models exchanging particles
NASA Astrophysics Data System (ADS)
Goh, Segun; Fortin, Jean-Yves; Choi, M. Y.
2017-01-01
A variety of systems in nature and in society are open and subject to exchanging their constituents with other systems (e.g., environments). For instance, in biological systems, cells collect necessary energy and material by exchange of molecules or ions. Similarly, countries, cities or research institutes evolve as their constituents move in or out. To probe the corresponding particle exchange dynamics in such systems, we consider two Ising models exchanging particles and establish a master equation describing the equilibrium phases as well as the non-equilibrium dynamics of the system. It is found that an additional stable phase emerges as a consequence of the particle exchange process. Furthermore, we formulate the Ginzburg-Landau theory which allows to probe correlation effects. Accordingly, critical slowing down is manifested and the associated dynamic exponent is computed in the linear relaxation regime. In particular, this approach is relevant for investigating the grand canonical description of the system plus environment, with particle exchange and state transitions taken into account explicitly.
The appropriateness of ignorance in the inverse kinetic Ising model
NASA Astrophysics Data System (ADS)
Dunn, Benjamin; Battistin, Claudia
2017-03-01
We develop efficient ways to consider and correct for the effects of hidden units for the paradigmatic case of the inverse kinetic Ising model with fully asymmetric couplings. We identify two sources of error in reconstructing the connectivity among the observed units while ignoring part of the network. One leads to a systematic bias in the inferred parameters, whereas the other involves correlations between the visible and hidden populations and has a magnitude that depends on the coupling strength. We estimate these two terms using a mean field approach and derive self-consistent equations for the couplings accounting for the systematic bias. Through application of these methods on simple networks of varying relative population size and connectivity strength, we assess how and under what conditions the hidden portion can influence inference and to what degree it can be crudely estimated. We find that for weak to moderately coupled systems, the effects of the hidden units is a simple rotation that can be easily corrected for. For strongly coupled systems, the non-systematic term becomes large and can no longer be safely ignored, further highlighting the importance of understanding the average strength of couplings for a given system of interest.
Numerical 2D-modeling of multiroll leveling
NASA Astrophysics Data System (ADS)
Mathieu, N.; Potier-Ferry, M.; Zahrouni, H.
2016-10-01
Multiroll leveling is a forming process used in the metals industries (aluminum, steel, …) in order to correct flatness defects and minimize residual stresses in strips thanks to alternating bending. This work proposes a Finite Element 2D model to simulate the metal sheet conveying through the machine. Obtained results (plastic strain and residual stress distributions through thickness) are analysed. Strip deformation, after elastic springback and potential buckling, is also predicted (residual curvatures).
Spasojević, Djordje; Janićević, Sanja; Knežević, Milan
2014-01-01
We present a numerical analysis of spanning avalanches in a two-dimensional (2D) nonequilibrium zero-temperature random field Ising model. Finite-size scaling analysis, performed for distribution of the average number of spanning avalanches per single run, spanning avalanche size distribution, average size of spanning avalanche, and contribution of spanning avalanches to magnetization jump, is augmented by analysis of spanning field (i.e., field triggering spanning avalanche), which enabled us to collapse averaged magnetization curves below critical disorder. Our study, based on extensive simulations of sufficiently large systems, reveals the dominant role of subcritical 2D-spanning avalanches in model behavior below and at the critical disorder. Other types of avalanches influence finite systems, but their contribution for large systems remains small or vanish.
Monte Carlo Studies of the Fcc Ising Model.
NASA Astrophysics Data System (ADS)
Polgreen, Thomas Lee
Monte Carlo simulations are performed on the antiferromagnetic fcc Ising model which is relevant to the binary alloy CuAu. The model exhibits a first-order ordering transition as a function of temperature. The lattice free energy of the model is determined for all temperatures. By matching free energies of the ordered and disordered phases, the transition temperature is determined to be T(,t) = 1.736 J where J is the coupling constant of the model. The free energy as determined by series expansion and the Kikuchi cluster variation method is compared with the Monte Carlo results. These methods work well for the ordered phase, but not for the disordered phase. A determination of the pair correlation in the disordered phase along the {100} direction indicates a correlation length of (DBLTURN) 2.5a at the phase transition. The correlation length exhibits mean-field-like temperature dependence. The Cowley-Warren short range order parameters are determined as a function of temperature for the first twelve nearest-neighbor shells of this model. The Monte Carlo results are used to determine the free parameter in a mean-field-like class of theories described by Clapp and Moss. The ability of these theories to predict ratios between pair potentials is tested with these results. In addition, evidence of a region of heterophase fluctuations is presented in agreement with x-ray diffuse scattering measurements on Cu(,3)Au. The growth of order following a rapid quench from disorder is studied by means of a dynamic Monte Carlo simulation. The results compare favorably with the Landau theory proposed by Chan for temperatures near the first-order phase transition. For lower temperatures, the results are in agreement with the theories of Lifshitz and Allen and Chan. In the intermediate temperature range, our extension of Chan's theory is able to explain our simulation results and recent experimental results.
Influence of Elevation Data Source on 2D Hydraulic Modelling
NASA Astrophysics Data System (ADS)
Bakuła, Krzysztof; StĘpnik, Mateusz; Kurczyński, Zdzisław
2016-08-01
The aim of this paper is to analyse the influence of the source of various elevation data on hydraulic modelling in open channels. In the research, digital terrain models from different datasets were evaluated and used in two-dimensional hydraulic models. The following aerial and satellite elevation data were used to create the representation of terrain-digital terrain model: airborne laser scanning, image matching, elevation data collected in the LPIS, EuroDEM, and ASTER GDEM. From the results of five 2D hydrodynamic models with different input elevation data, the maximum depth and flow velocity of water were derived and compared with the results of the most accurate ALS data. For such an analysis a statistical evaluation and differences between hydraulic modelling results were prepared. The presented research proved the importance of the quality of elevation data in hydraulic modelling and showed that only ALS and photogrammetric data can be the most reliable elevation data source in accurate 2D hydraulic modelling.
Fracture surfaces of heterogeneous materials: A 2D solvable model
NASA Astrophysics Data System (ADS)
Katzav, E.; Adda-Bedia, M.; Derrida, B.
2007-05-01
Using an elastostatic description of crack growth based on the Griffith criterion and the principle of local symmetry, we present a stochastic model describing the propagation of a crack tip in a 2D heterogeneous brittle material. The model ensures the stability of straight cracks and allows for the study of the roughening of fracture surfaces. When neglecting the effect of the nonsingular stress, the problem becomes exactly solvable and yields analytic predictions for the power spectrum of the paths. This result suggests an alternative to the conventional power law analysis often used in the analysis of experimental data.
±J Ising model on homogeneous Archimedean lattices
NASA Astrophysics Data System (ADS)
Valdés, J. F.; Lebrecht, W.; Vogel, E. E.
2012-04-01
We tackle the problem of finding analytical expressions describing the ground state properties of homogeneous Archimedean lattices over which a generalized Edwards-Anderson model (±J Ising model) is defined. A local frustration analysis is performed based on representative cells for square lattices, triangular lattices and honeycomb lattices. The concentration of ferromagnetic (F) bonds x is used as the independent variable in the analysis (1-x is the concentration for antiferromagnetic (A) bonds), where x spans the range [0.0,1.0]. The presence of A bonds brings frustration, whose clear manifestation is when bonds around the minimum possible circuit of bonds (plaquette) cannot be simultaneously satisfied. The distribution of curved (frustrated) plaquettes within the representative cell is determinant for the evaluation of the parameters of interest such as average frustration segment, energy per bond, and fractional content of unfrustrated bonds. Two methods are developed to cope with this analysis: one based on the direct probability of a plaquette being curved; the other one is based on the consideration of the different ways bonds contribute to the particular plaquette configuration. Exact numerical simulations on a large number of randomly generated samples allow to validate previously described theoretical analysis. It is found that the second method presents slight advantages over the first one. However, both methods give an excellent description for most of the range for x. The small deviations at specific intervals of x for each lattice have to do with the self-imposed limitations of both methods due to practical reasons. A particular discussion for the point x=0.5 for each one of the lattices also shines light on the general trends of the properties described here.
Ising model in clustered scale-free networks.
Herrero, Carlos P
2015-05-01
The Ising model in clustered scale-free networks has been studied by Monte Carlo simulations. These networks are characterized by a degree distribution of the form P(k)∼k(-γ) for large k. Clustering is introduced in the networks by inserting triangles, i.e., triads of connected nodes. The transition from a ferromagnetic (FM) to a paramagnetic (PM) phase has been studied as a function of the exponent γ and the triangle density. For γ>3 our results are in line with earlier simulations, and a phase transition appears at a temperature T(c)(γ) in the thermodynamic limit (system size N→∞). For γ≤3, a FM-PM crossover appears at a size-dependent temperature T(co), so the system remains in a FM state at any finite temperature in the limit N→∞. Thus, for γ=3, T(co) scales as lnN, whereas for γ<3, we find T(co)∼JN(z), where the exponent z decreases for increasing γ. Adding motifs (triangles in our case) to the networks causes an increase in the transition (or crossover) temperature for exponent γ>3 (or ≤3). For γ>3, this increase is due to changes in the mean values 〈k〉 and 〈k(2)〉, i.e., the transition is controlled by the degree distribution (nearest-neighbor connectivities). For γ≤3, however, we find that clustered and unclustered networks with the same size and distribution P(k) have different crossover temperature, i.e., clustering favors FM correlations, thus increasing the temperature T(co). The effect of a degree cutoff k(cut) on the asymptotic behavior of T(co) is discussed.
2D Quantum Transport Modeling in Nanoscale MOSFETs
NASA Technical Reports Server (NTRS)
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, B.
2001-01-01
We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions, oxide tunneling and phase-breaking scattering are treated on an equal footing. Electron bandstructure is treated within the anisotropic effective mass approximation. We present the results of our simulations of MIT 25 and 90 nm "well-tempered" MOSFETs and compare them to those of classical and quantum corrected models. The important feature of quantum model is smaller slope of Id-Vg curve and consequently higher threshold voltage. These results are consistent with 1D Schroedinger-Poisson calculations. The effect of gate length on gate-oxide leakage and subthreshold current has been studied. The shorter gate length device has an order of magnitude smaller leakage current than the longer gate length device without a significant trade-off in on-current.
Model dielectric function for 2D semiconductors including substrate screening
Trolle, Mads L.; Pedersen, Thomas G.; Véniard, Valerie
2017-01-01
Dielectric screening of excitons in 2D semiconductors is known to be a highly non-local effect, which in reciprocal space translates to a strong dependence on momentum transfer q. We present an analytical model dielectric function, including the full non-linear q-dependency, which may be used as an alternative to more numerically taxing ab initio screening functions. By verifying the good agreement between excitonic optical properties calculated using our model dielectric function, and those derived from ab initio methods, we demonstrate the versatility of this approach. Our test systems include: Monolayer hBN, monolayer MoS2, and the surface exciton of a 2 × 1 reconstructed Si(111) surface. Additionally, using our model, we easily take substrate screening effects into account. Hence, we include also a systematic study of the effects of substrate media on the excitonic optical properties of MoS2 and hBN. PMID:28117326
2D Numerical MHD Models of Solar Explosive Events
NASA Astrophysics Data System (ADS)
Roussev, I.
2001-10-01
Observations of the Sun reveal a great variety of dynamic phenomena interpretable as a manifestation of magnetic reconnection. These range from small-scale 'Explosive events' seen in the 'quiet' Sun, through violent flares observed in active regions. The high degree of complexity of the magnetic field inferred from observations may locally produce a fruitful environment for the process of magnetic reconnection to take place. Explosive events are associated with regions undergoing magnetic flux cancellation. This thesis presents a 2-dimensional (2D) numerical study devoted to explore the idea that the salient spectral signatures seen in explosive events are most probably caused by bi-directional outflow jets as a results of an ongoing magnetic reconnection. In order to provide qualitative results needed for the better physical interpretation of solar explosive events, several models intended to represent a 'quiet' Sun transition of solar explosive events, several models intended to represent a 'quiet' Sun transition region undergoing magnetic reconnection are examined, in both unstratified and gravitationally stratified atmospheres. The magnetic reconnection is initiated in an ad hoc manner, and the dynamic evolution is followed by numerically solving the equations of 2D dissipative magnetohydrodynamics (MHD), including the effects of field-aligned thermal conduction, radiative losses, volumetric heating, and anomalous resistivity.
The quantum Ising model: finite sums and hyperbolic functions
NASA Astrophysics Data System (ADS)
Damski, Bogdan
2015-10-01
We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and Products.
The quantum Ising model: finite sums and hyperbolic functions.
Damski, Bogdan
2015-10-30
We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and Products.
2D Quantum Transport Modeling in Nanoscale MOSFETs
NASA Technical Reports Server (NTRS)
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan
2001-01-01
With the onset of quantum confinement in the inversion layer in nanoscale MOSFETs, behavior of the resonant level inevitably determines all device characteristics. While most classical device simulators take quantization into account in some simplified manner, the important details of electrostatics are missing. Our work addresses this shortcoming and provides: (a) a framework to quantitatively explore device physics issues such as the source-drain and gate leakage currents, DIBL, and threshold voltage shift due to quantization, and b) a means of benchmarking quantum corrections to semiclassical models (such as density- gradient and quantum-corrected MEDICI). We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions, oxide tunneling and phase-breaking scattering are treated on equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Quantum simulations are focused on MIT 25, 50 and 90 nm "well- tempered" MOSFETs and compared to classical and quantum corrected models. The important feature of quantum model is smaller slope of Id-Vg curve and consequently higher threshold voltage. These results are quantitatively consistent with I D Schroedinger-Poisson calculations. The effect of gate length on gate-oxide leakage and sub-threshold current has been studied. The shorter gate length device has an order of magnitude smaller current at zero gate bias than the longer gate length device without a significant trade-off in on-current. This should be a device design consideration.
Mass loss in 2D rotating stellar models
Lovekin, Caterine; Deupree, Bob
2010-10-05
Radiatively driven mass loss is an important factor in the evolution of massive stars . The mass loss rates depend on a number of stellar parameters, including the effective temperature and luminosity. Massive stars are also often rapidly rotating, which affects their structure and evolution. In sufficiently rapidly rotating stars, both the effective temperature and radius vary significantly as a function of latitude, and hence mass loss rates can vary appreciably between the poles and the equator. In this work, we discuss the addition of mass loss to a 2D stellar evolution code (ROTORC) and compare evolution sequences with and without mass loss. Preliminary results indicate that a full 2D calculation of mass loss using the local effective temperature and luminosity can significantly affect the distribution of mass loss in rotating main sequence stars. More mass is lost from the pole than predicted by 1D models, while less mass is lost at the equator. This change in the distribution of mass loss will affect the angular momentum loss, the surface temperature and luminosity, and even the interior structure of the star. After a single mass loss event, these effects are small, but can be expected to accumulate over the course of the main sequence evolution.
Cyclic period-3 window in antiferromagnetic potts and Ising models on recursive lattices
NASA Astrophysics Data System (ADS)
Ananikian, N. S.; Ananikyan, L. N.; Chakhmakhchyan, L. A.
2011-09-01
The magnetic properties of the antiferromagnetic Potts model with two-site interaction and the antiferromagnetic Ising model with three-site interaction on recursive lattices have been studied. A cyclic period-3 window has been revealed by the recurrence relation method in the antiferromagnetic Q-state Potts model on the Bethe lattice (at Q < 2) and in the antiferromagnetic Ising model with three-site interaction on the Husimi cactus. The Lyapunov exponents have been calculated, modulated phases and a chaotic regime in the cyclic period-3 window have been found for one-dimensional rational mappings determined the properties of these systems.
The Method of Minimal Representations in 2d Ising Model Calculations
1992-05-01
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The specific edge effects of 2D core/shell model for spin-crossover nanoparticles
NASA Astrophysics Data System (ADS)
Muraoka, Azusa; Boukheddaden, Kamel; Linarès, Jorge; Varret, Francois
2012-02-01
We analyzed the size effect of spin-crossover nanoparticles at the edges of the 2D square lattices core/shell model, where the edge atoms are constrained to the high spin (HS) state. We performed MC simulations using the Ising-like Hamiltonian, [ H=-J∑(i,j)∑l i'=±1; j'=±1 S( i,j )S( i+i',j+j' ) +( δ2-kBT2g )∑(i,j)S( i,j ) ] The molar entropy change is δS 50J/K/mol, lng=δS/R 6 (R is the perfect gas constant), energy gap is δ=1300K. The HS fixed edges were based on the observation of an increasing residual HS fraction at low temperature upon particle size reduction. This specific boundary condition acts as a negative pressure which shifts downwards the equilibrium temperature. The interplay between the equilibrium temperature (=δ/kBlng) variation and the expected variation of the effective interactions in the system leads to a non-monotonous dependence of the hysteresis loop width upon the particle size. We described how the occurrence condition of the first-order transition has to be adapted to the nanoscale.
Ising-model description of long-range correlations in DNA sequences.
Colliva, A; Pellegrini, R; Testori, A; Caselle, M
2015-05-01
We model long-range correlations of nucleotides in the human DNA sequence using the long-range one-dimensional (1D) Ising model. We show that, for distances between 10(3) and 10(6) bp, the correlations show a universal behavior and may be described by the non-mean-field limit of the long-range 1D Ising model. This allows us to make some testable hypothesis on the nature of the interaction between distant portions of the DNA chain which led to the DNA structure that we observe today in higher eukaryotes.
Universality class of the two-dimensional site-diluted Ising model.
Martins, P H L; Plascak, J A
2007-07-01
In this work, we evaluate the probability distribution function of the order parameter for the two-dimensional site-diluted Ising model. Extensive Monte Carlo simulations have been performed for different spin concentrations p (0.70
Ising-model description of long-range correlations in DNA sequences
NASA Astrophysics Data System (ADS)
Colliva, A.; Pellegrini, R.; Testori, A.; Caselle, M.
2015-05-01
We model long-range correlations of nucleotides in the human DNA sequence using the long-range one-dimensional (1D) Ising model. We show that, for distances between 103 and 106 bp, the correlations show a universal behavior and may be described by the non-mean-field limit of the long-range 1D Ising model. This allows us to make some testable hypothesis on the nature of the interaction between distant portions of the DNA chain which led to the DNA structure that we observe today in higher eukaryotes.
Minority-spin dynamics in the nonhomogeneous Ising model: Diverging time scales and exponents.
Mullick, Pratik; Sen, Parongama
2016-05-01
We investigate the dynamical behavior of the Ising model under a zero-temperature quench with the initial fraction of up spins 0≤x≤1. In one dimension, the known results for persistence probability are verified; it shows algebraic decay for both up and down spins asymptotically with different exponents. It is found that the conventional finite-size scaling is valid here. In two dimensions, however, the persistence probabilities are no longer algebraic; in particular for x≤0.5, persistence for the up (minority) spins shows the behavior P_{min}(t)∼t^{-γ}exp[-(t/τ)^{δ}] with time t, while for the down (majority) spins, P_{maj}(t) approaches a finite value. We find that the timescale τ diverges as (x_{c}-x)^{-λ}, where x_{c}=0.5 and λ≃2.31. The exponent γ varies as θ_{2d}+c_{0}(x_{c}-x)^{β} where θ_{2d}≃0.215 is very close to the persistence exponent in two dimensions; β≃1. The results in two dimensions can be understood qualitatively by studying the exit probability, which for different system size is found to have the form E(x)=f[(x-x_{c}/x_{c})L^{1/ν}], with ν≈1.47. This result suggests that τ∼L^{z[over ̃]}, where z[over ̃]=λ/ν=1.57±0.11 is an exponent not explored earlier.
NASA Astrophysics Data System (ADS)
O'Hare, A.; Kusmartsev, F. V.; Kugel, K. I.
2009-01-01
The two-dimensional Ising model with competing nearest-neighbor and diagonal interactions on the square lattice is studied by the transfer-matrix technique and by the Monte Carlo simulations. The phase diagram of this model is constructed with a special emphasis to the analysis of a glassy state arising as an order to disorder transition at low temperatures. Evidence of the glassy state (based, in particular, on the calculation of the average length of domain walls and on the Edwards-Anderson order parameter) and its characteristics are presented. It was shown that, in the frustrated Ising model, the domain-wall length correlates to the onset of the glassy state, that is, it may play the role of the order parameter for the Ising glass or for glasslike states in other frustrated magnetic systems.
GPU-based single-cluster algorithm for the simulation of the Ising model
NASA Astrophysics Data System (ADS)
Komura, Yukihiro; Okabe, Yutaka
2012-02-01
We present the GPU calculation with the common unified device architecture (CUDA) for the Wolff single-cluster algorithm of the Ising model. Proposing an algorithm for a quasi-block synchronization, we realize the Wolff single-cluster Monte Carlo simulation with CUDA. We perform parallel computations for the newly added spins in the growing cluster. As a result, the GPU calculation speed for the two-dimensional Ising model at the critical temperature with the linear size L = 4096 is 5.60 times as fast as the calculation speed on a current CPU core. For the three-dimensional Ising model with the linear size L = 256, the GPU calculation speed is 7.90 times as fast as the CPU calculation speed. The idea of quasi-block synchronization can be used not only in the cluster algorithm but also in many fields where the synchronization of all threads is required.
Generalization Technique for 2D+SCALE Dhe Data Model
NASA Astrophysics Data System (ADS)
Karim, Hairi; Rahman, Alias Abdul; Boguslawski, Pawel
2016-10-01
Different users or applications need different scale model especially in computer application such as game visualization and GIS modelling. Some issues has been raised on fulfilling GIS requirement of retaining the details while minimizing the redundancy of the scale datasets. Previous researchers suggested and attempted to add another dimension such as scale or/and time into a 3D model, but the implementation of scale dimension faces some problems due to the limitations and availability of data structures and data models. Nowadays, various data structures and data models have been proposed to support variety of applications and dimensionality but lack research works has been conducted in terms of supporting scale dimension. Generally, the Dual Half Edge (DHE) data structure was designed to work with any perfect 3D spatial object such as buildings. In this paper, we attempt to expand the capability of the DHE data structure toward integration with scale dimension. The description of the concept and implementation of generating 3D-scale (2D spatial + scale dimension) for the DHE data structure forms the major discussion of this paper. We strongly believed some advantages such as local modification and topological element (navigation, query and semantic information) in scale dimension could be used for the future 3D-scale applications.
Physics and financial economics (1776-2014): puzzles, Ising and agent-based models
NASA Astrophysics Data System (ADS)
Sornette, Didier
2014-06-01
This short review presents a selected history of the mutual fertilization between physics and economics—from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistical physics. Recent extensions in terms of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it did not cover the dynamical field of agent-based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the ‘Emerging Intelligence Market Hypothesis’ to reconcile the pervasive presence of ‘noise traders’ with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets.
Physics and financial economics (1776-2014): puzzles, Ising and agent-based models.
Sornette, Didier
2014-06-01
This short review presents a selected history of the mutual fertilization between physics and economics--from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistical physics. Recent extensions in terms of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it did not cover the dynamical field of agent-based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the 'Emerging Intelligence Market Hypothesis' to reconcile the pervasive presence of 'noise traders' with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets.
Long-range transverse Ising model built with dipolar condensates in two-well arrays
NASA Astrophysics Data System (ADS)
Li, Yongyao; Pang, Wei; Xu, Jun; Lee, Chaohong; Malomed, Boris A.; Santos, Luis
2017-01-01
Dipolar Bose–Einstein condensates in an array of double-well potentials realize an effective transverse Ising model with peculiar inter-layer interactions, that may result under proper conditions in an anomalous first-order ferromagnetic–antiferromagnetic phase transition, and non-trivial phases due to frustration. The considered setup allows as well for the study of Kibble–Zurek defect formation, whose kink statistics follows that expected from the universality class of the mean-field one-dimensional transverse Ising model. Furthermore, random occupation of each layer of the stack leads to random effective Ising interactions and local transverse fields, that may lead to the Anderson-like localization of imbalance perturbations.
Monte Carlo Simulations of Compressible Ising Models: Do We Understand Them?
NASA Astrophysics Data System (ADS)
Landau, D. P.; Dünweg, B.; Laradji, M.; Tavazza, F.; Adler, J.; Cannavaccioulo, L.; Zhu, X.
Extensive Monte Carlo simulations have begun to shed light on our understanding of phase transitions and universality classes for compressible Ising models. A comprehensive analysis of a Landau-Ginsburg-Wilson hamiltonian for systems with elastic degrees of freedom resulted in the prediction that there should be four distinct cases that would have different behavior, depending upon symmetries and thermodynamic constraints. We shall provide an account of the results of careful Monte Carlo simulations for a simple compressible Ising model that can be suitably modified so as to replicate all four cases.
Gauge model with Ising vacancies: Multicritical behavior of self-avoiding surfaces
NASA Astrophysics Data System (ADS)
Maritan, A.; Seno, F.; Stella, A. L.
1991-08-01
A openZ2 gauge model with n-component-vector degrees of freedom on a dodecahedral lattice is coupled to an Ising system on the dual lattice. The statistics of interacting self-avoiding surfaces (SAS) is obtained in the n-->0 limit. At the percolative critical point an exact identification of the SAS critical behavior with that of Ising cluster hulls holds. This condition corresponds to a multicritical point for SAS, in universality class different from that of branched polymers. The model allows application of standard statistical methods to SAS. A mean-field calculation gives a phase diagram remarkably consistent with the above results.
Empirical relations between static and dynamic exponents for Ising model cluster algorithms
NASA Astrophysics Data System (ADS)
Coddington, Paul D.; Baillie, Clive F.
1992-02-01
We have measured the autocorrelations for the Swendsen-Wang and the Wolff cluster update algorithms for the Ising model in two, three, and four dimensions. The data for the Wolff algorithm suggest that the autocorrelations are linearly related to the specific heat, in which case the dynamic critical exponent is zint,EW=α/ν. For the Swendsen-Wang algorithm, scaling the autocorrelations by the average maximum cluster size gives either a constant or a logarithm, which implies that zint,ESW=β/ν for the Ising model.
Effects of Agent's Repulsion in 2d Flocking Models
NASA Astrophysics Data System (ADS)
Moussa, Najem; Tarras, Iliass; Mazroui, M'hammed; Boughaleb, Yahya
In nature many animal groups, such as fish schools or bird flocks, clearly display structural order and appear to move as a single coherent entity. In order to understand the complex behavior of these systems, many models have been proposed and tested so far. This paper deals with an extension of the Vicsek model, by including a second zone of repulsion, where each agent attempts to maintain a minimum distance from the others. The consideration of this zone in our study seems to play an important role during the travel of agents in the two-dimensional (2D) flocking models. Our numerical investigations show that depending on the basic ingredients such as repulsion radius (R1), effect of density of agents (ρ) and noise (η), our nonequilibrium system can undergo a kinetic phase transition from no transport to finite net transport. For different values of ρ, kinetic phase diagrams in the plane (η ,R1) are found. Implications of these findings are discussed.
2-D Model for Normal and Sickle Cell Blood Microcirculation
NASA Astrophysics Data System (ADS)
Tekleab, Yonatan; Harris, Wesley
2011-11-01
Sickle cell disease (SCD) is a genetic disorder that alters the red blood cell (RBC) structure and function such that hemoglobin (Hb) cannot effectively bind and release oxygen. Previous computational models have been designed to study the microcirculation for insight into blood disorders such as SCD. Our novel 2-D computational model represents a fast, time efficient method developed to analyze flow dynamics, O2 diffusion, and cell deformation in the microcirculation. The model uses a finite difference, Crank-Nicholson scheme to compute the flow and O2 concentration, and the level set computational method to advect the RBC membrane on a staggered grid. Several sets of initial and boundary conditions were tested. Simulation data indicate a few parameters to be significant in the perturbation of the blood flow and O2 concentration profiles. Specifically, the Hill coefficient, arterial O2 partial pressure, O2 partial pressure at 50% Hb saturation, and cell membrane stiffness are significant factors. Results were found to be consistent with those of Le Floch [2010] and Secomb [2006].
Monte Carlo Study of One-Dimensional Ising Models with Long-Range Interactions
NASA Astrophysics Data System (ADS)
Tomita, Yusuke
2009-01-01
Recently, Fukui and Todo have proposed a new effective Monte Carlo algorithm for long-range interacting systems. Using the algorithm with the nonequilibrium relaxation method, we investigated long-range interacting one-dimensional Ising models both ferromagnetic and antiferromagnetic with the nearest-neighbor ferromagnetic interaction. For the antiferromagnetic model, we found the systems are paramagnetic at finite temperatures.
Ab initio modeling of 2D layered organohalide lead perovskites
NASA Astrophysics Data System (ADS)
Fraccarollo, Alberto; Cantatore, Valentina; Boschetto, Gabriele; Marchese, Leonardo; Cossi, Maurizio
2016-04-01
A number of 2D layered perovskites A2PbI4 and BPbI4, with A and B mono- and divalent ammonium and imidazolium cations, have been modeled with different theoretical methods. The periodic structures have been optimized (both in monoclinic and in triclinic systems, corresponding to eclipsed and staggered arrangements of the inorganic layers) at the DFT level, with hybrid functionals, Gaussian-type orbitals and dispersion energy corrections. With the same methods, the various contributions to the solid stabilization energy have been discussed, separating electrostatic and dispersion energies, organic-organic intralayer interactions and H-bonding effects, when applicable. Then the electronic band gaps have been computed with plane waves, at the DFT level with scalar and full relativistic potentials, and including the correlation energy through the GW approximation. Spin orbit coupling and GW effects have been combined in an additive scheme, validated by comparing the computed gap with well known experimental and theoretical results for a model system. Finally, various contributions to the computed band gaps have been discussed on some of the studied systems, by varying some geometrical parameters and by substituting one cation in another's place.
Mathematical model for silicon electrode - Part I. 2-d model
NASA Astrophysics Data System (ADS)
Sikha, Godfrey; De, Sumitava; Gordon, Joseph
2014-09-01
This paper presents a 2-dimensional transient numerical model to simulate the electrochemical lithium insertion in a silicon nanowire (Si NW) electrode. The model geometry is a cylindrical Si NW electrode anchored to a copper current collector (Cu CC) substrate. The model solves for diffusion of lithium in Si NW, stress generation in the Si NW due to chemical and elastic strains, stress generation in the Cu CC due to elastic strain, and volume expansion in the Si NW and Cu CC geometries. The evolution of stress components, i.e., radial, axial and tangential stresses in different regions in the Si NW are presented and discussed. The effect of radius of Si NW and lithiation rate, on the maximum stresses developed in the Si NW are also discussed.
Degenerate Ising model for atomistic simulation of crystal-melt interfaces
Schebarchov, D.; Schulze, T. P.; Hendy, S. C.
2014-02-21
One of the simplest microscopic models for a thermally driven first-order phase transition is an Ising-type lattice system with nearest-neighbour interactions, an external field, and a degeneracy parameter. The underlying lattice and the interaction coupling constant control the anisotropic energy of the phase boundary, the field strength represents the bulk latent heat, and the degeneracy quantifies the difference in communal entropy between the two phases. We simulate the (stochastic) evolution of this minimal model by applying rejection-free canonical and microcanonical Monte Carlo algorithms, and we obtain caloric curves and heat capacity plots for square (2D) and face-centred cubic (3D) lattices with periodic boundary conditions. Since the model admits precise adjustment of bulk latent heat and communal entropy, neither of which affect the interface properties, we are able to tune the crystal nucleation barriers at a fixed degree of undercooling and verify a dimension-dependent scaling expected from classical nucleation theory. We also analyse the equilibrium crystal-melt coexistence in the microcanonical ensemble, where we detect negative heat capacities and find that this phenomenon is more pronounced when the interface is the dominant contributor to the total entropy. The negative branch of the heat capacity appears smooth only when the equilibrium interface-area-to-volume ratio is not constant but varies smoothly with the excitation energy. Finally, we simulate microcanonical crystal nucleation and subsequent relaxation to an equilibrium Wulff shape, demonstrating the model's utility in tracking crystal-melt interfaces at the atomistic level.
Palma, G; Zambrano, D
2008-12-01
In this paper we propose a method to study critical systems numerically, which combines collective-mode algorithms and renormalization group on the lattice. This method is an improved version of the Monte Carlo renormalization group in the sense that it has all the advantages of cluster algorithms. As an application we considered the 2D Ising model and studied whether scale invariance or universality are possible underlying mechanisms responsible for the approximate "universal fluctuations" close to a so-called bulk temperature T(L) . "Universal fluctuations" were first proposed in the work of Bramwell, Holdsworth, and Pinton [Nature (London) 396, 552 (1998)] and stated that the probability density function of a global quantity for very dissimilar systems, such as a confined turbulent flow and a two-dimensional (2D) magnetic system, properly normalized to the first two moments, becomes similar to the "universal distribution," originally obtained for magnetization in the 2D XY model in the low-temperature region. The results for the critical exponents and the renormalization-group flow of the probability density function are very accurate and show no evidence to support that the approximate common shape of the PDF should be related to both scale invariance or universal behavior.
2D modeling of electromagnetic waves in cold plasmas
Crombé, K.; Van Eester, D.; Koch, R.; Kyrytsya, V.
2014-02-12
The consequences of sheath (rectified) electric fields, resulting from the different mobility of electrons and ions as a response to radio frequency (RF) fields, are a concern for RF antenna design as it can cause damage to antenna parts, limiters and other in-vessel components. As a first step to a more complete description, the usual cold plasma dielectric description has been adopted, and the density profile was assumed to be known as input. Ultimately, the relevant equations describing the wave-particle interaction both on the fast and slow timescale will need to be tackled but prior to doing so was felt as a necessity to get a feeling of the wave dynamics involved. Maxwell's equations are solved for a cold plasma in a 2D antenna box with strongly varying density profiles crossing also lower hybrid and ion-ion hybrid resonance layers. Numerical modelling quickly becomes demanding on computer power, since a fine grid spacing is required to capture the small wavelengths effects of strongly evanescent modes.
Accelerated rare event sampling: Refinement and Ising model analysis
NASA Astrophysics Data System (ADS)
Yevick, David; Lee, Yong Hwan
In this paper, a recently introduced accelerated sampling technique [D. Yevick, Int. J. Mod. Phys. C 27, 1650041 (2016)] for constructing transition matrices is further developed and applied to a two-dimensional 32×32 Ising spin system. By permitting backward displacements up to a certain limit for each forward step while evolving the system to first higher and then lower energies within a restricted interval that is steadily displaced toward zero temperature as the computation proceeds, accuracy can be greatly enhanced. Simultaneously, the elements obtained from numerous independent calculations are collected in a single transition matrix. The relative accuracy of this novel method is established through a comparison to a transition matrix procedure based on the Metropolis algorithm in which the temperature is appropriately varied during the calculation and the results interpreted in terms of the distribution of realizations over both energy and magnetization.
Cluster Monte Carlo: Scaling of systematic errors in the two-dimensional Ising model
Shchur, L.N.; Bloete, H.W.
1997-05-01
We present an extensive analysis of systematic deviations in Wolff cluster simulations of the critical Ising model, using random numbers generated by binary shift registers. We investigate how these deviations depend on the lattice size, the shift-register length, and the number of bits correlated by the production rule. They appear to satisfy scaling relations. {copyright} {ital 1997} {ital The American Physical Society}
Fluctuation-dissipation relation in an Ising model without detailed balance.
Andrenacci, Natascia; Corberi, Federico; Lippiello, Eugenio
2006-04-01
We consider the modified Ising model introduced by de Oliveira, Mendes, and Santos [J. Phys. A 26, 2317 (1993)], where the temperature depends locally on the spin configuration and detailed balance and local equilibrium are not obeyed. We derive a relation between the linear response function and correlation functions that generalizes the fluctuation-dissipation theorem. In the stationary states of the model, which are the counterparts of the Ising equilibrium states, the fluctuation-dissipation theorem breaks down due to the lack of time reversal invariance. In the nonstationary phase-ordering kinetics, the parametric plot of the integrated response function chi(t,t(w)) vs the autocorrelation function is different from that of the kinetic Ising model. However, splitting chi(t,t(w)) into a stationary and an aging term chi(t,t(w)) = chi(st)(t-t(w)) + chi(ag)(t,t(w)), we find chi(ag)(t,t(w)) approximately t(w)(-a(chi)) f(t/t(w)), and a numerical value of a(chi) consistent with a(chi)= 1/4, as in the kinetic Ising model.
Red-bond exponents of the critical and the tricritical Ising model in three dimensions
NASA Astrophysics Data System (ADS)
Deng, Youjin; Blöte, Henk W. J.
2004-11-01
Using the Wolff and geometric cluster algorithms and finite-size scaling analysis, we investigate the critical Ising and the tricritical Blume-Capel models with nearest-neighbor interactions on the simple-cubic lattice. The sampling procedure involves the decomposition of the Ising configuration into geometric clusters, each of which consists of a set of nearest-neighboring spins of the same sign connected with bond probability p . These clusters include the well-known Kasteleyn-Fortuin clusters as a special case for p=1-exp(-2K) , where K is the Ising spin-spin coupling. Along the critical line K=Kc , the size distribution of geometric clusters is investigated as a function of p . We observe that, unlike in the case of two-dimensional tricriticality, the percolation threshold in both models lies at pc=1-exp(-2Kc) . Further, we determine the corresponding red-bond exponents as yr=0.757(2) and 0.501(5) for the critical Ising and the tricritical Blume-Capel models, respectively. On this basis, we conjecture yr=1/2 for the latter model.
Red-bond exponents of the critical and the tricritical Ising model in three dimensions.
Deng, Youjin; Blöte, Henk W J
2004-11-01
Using the Wolff and geometric cluster algorithms and finite-size scaling analysis, we investigate the critical Ising and the tricritical Blume-Capel models with nearest-neighbor interactions on the simple-cubic lattice. The sampling procedure involves the decomposition of the Ising configuration into geometric clusters, each of which consists of a set of nearest-neighboring spins of the same sign connected with bond probability p. These clusters include the well-known Kasteleyn-Fortuin clusters as a special case for p=1-exp(-2K) , where K is the Ising spin-spin coupling. Along the critical line K=Kc , the size distribution of geometric clusters is investigated as a function of p . We observe that, unlike in the case of two-dimensional tricriticality, the percolation threshold in both models lies at pc =1-exp(-2Kc) . Further, we determine the corresponding red-bond exponents as yr =0.757(2) and 0.501(5) for the critical Ising and the tricritical Blume-Capel models, respectively. On this basis, we conjecture yr =1/2 for the latter model.
Critical Dynamics Behavior of the Wolff Algorithm in the Site-Bond-Correlated Ising Model
NASA Astrophysics Data System (ADS)
Campos, P. R. A.; Onody, R. N.
Here we apply the Wolff single-cluster algorithm to the site-bond-correlated Ising model and study its critical dynamical behavior. We have verified that the autocorrelation time diminishes in the presence of dilution and correlation, showing that the Wolff algorithm performs even better in such situations. The critical dynamical exponents are also estimated.
2D DEM model of sand transport with wind interaction
NASA Astrophysics Data System (ADS)
Oger, L.; Valance, A.
2013-06-01
The advance of the dunes in the desert is a threat to the life of the local people. The dunes invade houses, agricultural land and perturb the circulation on the roads. It is therefore very important to understand the mechanism of sand transport in order to fight against desertification. Saltation in which sand grains are propelled by the wind along the surface in short hops, is the primary mode of blown sand movement [1]. The saltating grains are very energetic and when impact a sand surface, they rebound and consequently eject other particles from the sand bed. The ejected grains, called reptating grains, contribute to the augmentation of the sand flux. Some of them can be promoted to the saltation motion. We use a mechanical model based on the Discrete Element Method to study successive collisions of incident energetic beads with granular packing in the context of Aeolian saltation transport. We investigate the collision process for the case where the incident bead and those from the packing have identical mechanical properties. We analyze the features of the consecutive collision processes made by the transport of the saltating disks by a wind in which its profile is obtained from the counter-interaction between air flow and grain flows. We used a molecular dynamics method known as DEM (soft Discrete Element Method) with a initial static packing of 20000 2D particles. The dilation of the upper surface due to the consecutive collisions is responsible for maintaining the flow at a given energy input due to the wind.
Solution of the antiferromagnetic Ising model on a tetrahedron recursive lattice.
Jurčišinová, E; Jurčišin, M
2014-03-01
We consider the antiferromagnetic spin-1/2 Ising model on the recursive tetrahedron lattice on which two elementary tetrahedrons are connected at each site. The model represents the simplest approximation of the antiferromagnetic Ising model on the real three-dimensional tetrahedron lattice which takes into account effects of frustration. An exact analytical solution of the model is found and discussed. It is shown that the model exhibits neither the first-order nor the second-order phase transitions. A detailed analysis of the magnetization of the model in the presence of the external magnetic field is performed and the existence of the magnetization plateaus for low temperatures is shown. All possible ground states of the model are found and discussed. The existence of nontrivial singular ground states is proven and exact explicit expressions for them are found.
Spin-one Ising model for ice VII-plastic ice phase transitions.
Matsumoto, Masakazu; Himoto, Kazuhiro; Tanaka, Hideki
2014-11-26
We propose a spin model compatible with ice VII-plastic ice phase transitions and critical phenomena discovered recently by computer simulations. The Blume-Capel spin-1 Ising model is extended in order to describe the entropic stabilization effect in the plastic ice phase. The model shares the same set of tricritical exponents with simulation, indicating that they are of the same universality class.
NASA Astrophysics Data System (ADS)
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.
An analysis of intergroup rivalry using Ising model and reinforcement learning
NASA Astrophysics Data System (ADS)
Zhao, Feng-Fei; Qin, Zheng; Shao, Zhuo
2014-01-01
Modeling of intergroup rivalry can help us better understand economic competitions, political elections and other similar activities. The result of intergroup rivalry depends on the co-evolution of individual behavior within one group and the impact from the rival group. In this paper, we model the rivalry behavior using Ising model. Different from other simulation studies using Ising model, the evolution rules of each individual in our model are not static, but have the ability to learn from historical experience using reinforcement learning technique, which makes the simulation more close to real human behavior. We studied the phase transition in intergroup rivalry and focused on the impact of the degree of social freedom, the personality of group members and the social experience of individuals. The results of computer simulation show that a society with a low degree of social freedom and highly educated, experienced individuals is more likely to be one-sided in intergroup rivalry.
A 2D simulation model for urban flood management
NASA Astrophysics Data System (ADS)
Price, Roland; van der Wielen, Jonathan; Velickov, Slavco; Galvao, Diogo
2014-05-01
The European Floods Directive, which came into force on 26 November 2007, requires member states to assess all their water courses and coast lines for risk of flooding, to map flood extents and assets and humans at risk, and to take adequate and coordinated measures to reduce the flood risk in consultation with the public. Flood Risk Management Plans are to be in place by 2015. There are a number of reasons for the promotion of this Directive, not least because there has been much urban and other infrastructural development in flood plains, which puts many at risk of flooding along with vital societal assets. In addition there is growing awareness that the changing climate appears to be inducing more frequent extremes of rainfall with a consequent increases in the frequency of flooding. Thirdly, the growing urban populations in Europe, and especially in the developing countries, means that more people are being put at risk from a greater frequency of urban flooding in particular. There are urgent needs therefore to assess flood risk accurately and consistently, to reduce this risk where it is important to do so or where the benefit is greater than the damage cost, to improve flood forecasting and warning, to provide where necessary (and possible) flood insurance cover, and to involve all stakeholders in decision making affecting flood protection and flood risk management plans. Key data for assessing risk are water levels achieved or forecasted during a flood. Such levels should of course be monitored, but they also need to be predicted, whether for design or simulation. A 2D simulation model (PriceXD) solving the shallow water wave equations is presented specifically for determining flood risk, assessing flood defense schemes and generating flood forecasts and warnings. The simulation model is required to have a number of important properties: -Solve the full shallow water wave equations using a range of possible solutions; -Automatically adjust the time step and
NASA Astrophysics Data System (ADS)
Miwa, Tetsuji
2013-03-01
Studies on integrable models in statistical mechanics and quantum field theory originated in the works of Bethe on the one-dimensional quantum spin chain and the work of Onsager on the two-dimensional Ising model. I will talk on the discovery in 1977 of the link between quantum field theory in the scaling limit of the two-dimensional Ising model and the theory of monodromy preserving linear ordinary differential equations. This work was the staring point of our journey with Michio Jimbo in integrable models, the journey which finally led us to the exact results on the correlation functions of quantum spin chains in 1992.
Nonequilibrium random-field Ising model on a diluted triangular lattice.
Kurbah, Lobisor; Thongjaomayum, Diana; Shukla, Prabodh
2015-01-01
We study critical hysteresis in the random-field Ising model on a two-dimensional periodic lattice with a variable coordination number z(eff) in the range 3≤z(eff)≤6. We find that the model supports critical behavior in the range 4
Strecka, Jozef; Canová, Lucia; Minami, Kazuhiko
2009-05-01
The spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions is exactly solved by establishing a precise mapping relationship with the corresponding zero-field (symmetric) eight-vertex model. It is shown that the Ising-Heisenberg model with the ferromagnetic Heisenberg interaction exhibits a striking critical behavior, which manifests itself through re-entrant phase transitions as well as continuously varying critical exponents. The changes in critical exponents are in accordance with the weak universality hypothesis in spite of a peculiar singular behavior that emerges at a quantum critical point of the infinite order, which occurs at the isotropic limit of the Heisenberg interaction. On the other hand, the Ising-Heisenberg model with the antiferromagnetic Heisenberg interaction surprisingly exhibits less significant changes in both critical temperatures and critical exponents upon varying the strength of the exchange anisotropy in the Heisenberg interaction.
Nonequilibrium phase transition in an exactly solvable driven Ising model with friction.
Hucht, Alfred
2009-12-01
A driven Ising model with friction due to magnetic correlations was proposed by Kadau [Phys. Rev. Lett. 101, 137205 (2008)]. The nonequilibrium phase transition present in this system is investigated in detail using analytical methods as well as Monte Carlo simulations. In the limit of high driving velocities v the model shows mean-field behavior due to dimensional reduction and can be solved exactly for various geometries. The simulations are performed with three different single spin-flip rates: the common Metropolis and Glauber rates as well as a multiplicative rate. Due to the nonequilibrium nature of the model all rates lead to different critical temperatures at v>0, while the exact solution matches the multiplicative rate. Finally, the crossover from Ising to mean-field behavior as function of velocity and system size is analyzed in one and two dimensions.
Emerging Modified Transverse-Field Ising Model On A Hydrogenated Silicon Surface
NASA Astrophysics Data System (ADS)
Ritter, Burkhard; Beach, Kevin
2014-03-01
Advances in the precise placement of dangling bonds on a hydrogenated silicon surface open the prospect of manufacturing large scale quantum dot arrays. Small clusters of specifically arranged quantum dots comprise a system of bistable, interacting cells. Starting from an extended Hubbard model and using a set of controlled Hilbert space truncations, we show that such a system of quantum dot cells can be mapped to a modified transverse-field Ising model with long-ranged interactions. Each cell is described by a pseudo-spin. Because we control cell orientation and placement, we can construct a wide range of structures, with ferromagnetic and antiferromagnetic chains as simple examples. The Ising-like model is amenable to stochastic series expansion Monte Carlo, allowing the simulation and characterization of large systems. Work supported by Alberta Innovates Technology Futures.
Ising Model Spin S = 1 ON Directed BARABÁSI-ALBERT Networks
NASA Astrophysics Data System (ADS)
Lima, F. W. S.
On directed Barabási-Albert networks with two and seven neighbours selected by each added site, the Ising model with spin S = 1/2 was seen not to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation followed an Arrhenius law for Metropolis and Glauber algorithms, but for Wolff cluster flipping the magnetisation decayed exponentially with time. On these networks the Ising model spin S = 1 is now studied through Monte Carlo simulations. However, in this model, the order-disorder phase transition is well defined in this system. We have obtained a first-order phase transition for values of connectivity m = 2 and m = 7 of the directed Barabási-Albert network.
Spin-1 Ising model: exact damage-spreading relations and numerical simulations.
Anjos, A S; Mariz, A M; Nobre, F D; Araujo, I G
2008-09-01
The nearest-neighbor-interaction spin-1 Ising model is investigated within the damage-spreading approach. Exact relations involving quantities computable through damage-spreading simulations and thermodynamic properties are derived for such a model, defined in terms of a very general Hamiltonian that covers several spin-1 models of interest in the literature. Such relations presuppose translational invariance and hold for any ergodic dynamical procedure, leading to an efficient tool for obtaining thermodynamic properties. The implementation of the method is illustrated through damage-spreading simulations for the ferromagnetic spin-1 Ising model on a square lattice. The two-spin correlation function and the magnetization are obtained, with precise estimates of their associated critical exponents and of the critical temperature of the model, in spite of the small lattice sizes considered. These results are in good agreement with the universality hypothesis, with critical exponents in the same universality class of the spin- 12 Ising model. The advantage of the present method is shown through a significant reduction of finite-size effects by comparing its results with those obtained from standard Monte Carlo simulations.
Salmon, Octavio R; Crokidakis, Nuno; Nobre, Fernando D
2009-02-04
A random-field Ising model that is capable of exhibiting a rich variety of multicritical phenomena, as well as a smearing of such behavior, is investigated. The model consists of an infinite-range-interaction Ising ferromagnet in the presence of a triple Gaussian random magnetic field, which is defined as a superposition of three Gaussian distributions with the same width σ, centered at H = 0 and H = ± H(0), with probabilities p and (1-p)/2, respectively. Such a distribution is very general and recovers, as limiting cases, the trimodal, bimodal and Gaussian probability distributions. In particular, the special case of the random-field Ising model in the presence of a trimodal probability distribution (limit [Formula: see text]) is able to present a rather nontrivial multicritical behavior. It is argued that the triple Gaussian probability distribution is appropriate for a physical description of some diluted antiferromagnets in the presence of a uniform external field, for which the corresponding physical realization consists of an Ising ferromagnet under random fields whose distribution appears to be well represented in terms of a superposition of two parts, namely a trimodal and a continuous contribution. The model is investigated by means of the replica method, and phase diagrams are obtained within the replica-symmetric solution, which is known to be stable for the present system. A rich variety of phase diagrams is presented, with one or two distinct ferromagnetic phases, continuous and first-order transition lines, tricritical, fourth-order, critical end points and many other interesting multicritical phenomena. Additionally, the present model carries the possibility of destroying such multicritical phenomena due to an increase in the randomness, i.e. increasing σ, which represents a very common feature in real systems.
Rényi information flow in the Ising model with single-spin dynamics.
Deng, Zehui; Wu, Jinshan; Guo, Wenan
2014-12-01
The n-index Rényi mutual information and transfer entropies for the two-dimensional kinetic Ising model with arbitrary single-spin dynamics in the thermodynamic limit are derived as functions of ensemble averages of observables and spin-flip probabilities. Cluster Monte Carlo algorithms with different dynamics from the single-spin dynamics are thus applicable to estimate the transfer entropies. By means of Monte Carlo simulations with the Wolff algorithm, we calculate the information flows in the Ising model with the Metropolis dynamics and the Glauber dynamics, respectively. We find that not only the global Rényi transfer entropy, but also the pairwise Rényi transfer entropy, peaks in the disorder phase.
Monte Carlo method for critical systems in infinite volume: The planar Ising model.
Herdeiro, Victor; Doyon, Benjamin
2016-10-01
In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume. The algorithm corrects the problem of the long-range effects of boundaries associated to generating critical distributions on finite lattices. It uses the advantage of scale invariance combined with ideas of the renormalization group in order to construct a type of "holographic" boundary condition that encodes the presence of an infinite volume beyond it. We check the quality of the distribution obtained in the case of the planar Ising model by comparing various observables with their infinite-plane prediction. We accurately reproduce planar two-, three-, and four-point of spin and energy operators. We also define a lattice stress-energy tensor, and numerically obtain the associated conformal Ward identities and the Ising central charge.
Finite-size corrections in the Ising model with special boundary conditions
NASA Astrophysics Data System (ADS)
Izmailian, N. Sh.
2010-11-01
The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz (BK) is analyzed. We derive exact finite-size corrections for the free energy F of the critical ferromagnetic Ising model on the M×N square lattice with Brascamp-Kunz boundary conditions [H.J. Brascamp, H. Kunz, J. Math. Phys. 15 (1974) 66]. We show that finite-size corrections strongly depend not only on the boundary conditions but also on the shape and pattern of the lattice. In the limit N→∞ we obtain the expansion of the free energy and the inverse correlation lengths for infinitely long strip with BK boundary conditions. Our results are consistent with the conformal field theory prediction for the mixed boundary conditions.
Static and dynamic structure factors in three-dimensional randomly diluted Ising models.
Calabrese, Pasquale; Pelissetto, Andrea; Vicari, Ettore
2008-02-01
We consider the three-dimensional randomly diluted Ising model and study the critical behavior of the static and dynamic spin-spin correlation functions (static and dynamic structure factors) at the paramagnetic-ferromagnetic transition in the high-temperature phase. We consider a purely relaxational dynamics without conservation laws, the so-called model A. We present Monte Carlo simulations and perturbative field-theoretical calculations. While the critical behavior of the static structure factor is quite similar to that occurring in pure Ising systems, the dynamic structure factor shows a substantially different critical behavior. In particular, the dynamic correlation function shows a large-time decay rate which is momentum independent. This effect is not related to the presence of the Griffiths tail, which is expected to be irrelevant in the critical limit, but rather to the breaking of translational invariance, which occurs for any sample and which, at the critical point, is not recovered even after the disorder average.
Rényi information flow in the Ising model with single-spin dynamics
NASA Astrophysics Data System (ADS)
Deng, Zehui; Wu, Jinshan; Guo, Wenan
2014-12-01
The n -index Rényi mutual information and transfer entropies for the two-dimensional kinetic Ising model with arbitrary single-spin dynamics in the thermodynamic limit are derived as functions of ensemble averages of observables and spin-flip probabilities. Cluster Monte Carlo algorithms with different dynamics from the single-spin dynamics are thus applicable to estimate the transfer entropies. By means of Monte Carlo simulations with the Wolff algorithm, we calculate the information flows in the Ising model with the Metropolis dynamics and the Glauber dynamics, respectively. We find that not only the global Rényi transfer entropy, but also the pairwise Rényi transfer entropy, peaks in the disorder phase.
Smeared quantum phase transition in the dissipative random quantum Ising model
NASA Astrophysics Data System (ADS)
Vojta, Thomas; Hoyos, José A.
2010-01-01
We investigate the quantum phase transition in the random transverse-field Ising model under the influence of Ohmic dissipation. To this end, we numerically implement a strong-disorder renormalization-group scheme. We find that Ohmic dissipation destroys the quantum critical point and the associated quantum Griffiths phase by smearing. Our results quantitatively confirm a recent theory [J.A. Hoyos, T. Vojta, Phys. Rev. Lett. 100 (2008) 240601] of smeared quantum phase transitions.
Finite-size scaling and corrections in the Ising model with Brascamp-Kunz boundary conditions
NASA Astrophysics Data System (ADS)
Janke, W.; Kenna, R.
2002-02-01
The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz is analyzed. Leading and subdominant scaling behavior of the Fisher zeros are determined exactly. The exact finite-size scaling, with corrections, of the specific heat is determined both at critical and effective critical (pseudocritical) points. The shift exponents associated with the scaling of these effective critical points are not the same as the inverse correlation length critical exponent. All corrections to scaling are analytic.
NASA Astrophysics Data System (ADS)
Kastening, Boris
2002-11-01
A recent simplified transfer matrix solution of the two-dimensional Ising model on a square lattice with periodic boundary conditions is generalized to periodic-antiperiodic, antiperiodic-periodic, and antiperiodic-antiperiodic boundary conditions. It is suggested to employ linear combinations of the resulting partition functions to investigate finite-size scaling. An exact relation of such a combination to the partition function corresponding to Brascamp-Kunz boundary conditions is found.
Condensation of Helium in Aerogel and Athermal Dynamics of the Random-Field Ising Model
NASA Astrophysics Data System (ADS)
Aubry, Geoffroy J.; Bonnet, Fabien; Melich, Mathieu; Guyon, Laurent; Spathis, Panayotis; Despetis, Florence; Wolf, Pierre-Etienne
2014-08-01
High resolution measurements reveal that condensation isotherms of He4 in high porosity silica aerogel become discontinuous below a critical temperature. We show that this behavior does not correspond to an equilibrium phase transition modified by the disorder induced by the aerogel structure, but to the disorder-driven critical point predicted for the athermal out-of-equilibrium dynamics of the random-field Ising model. Our results evidence the key role of nonequilibrium effects in the phase transitions of disordered systems.
Thermodynamic quantities and phase diagrams of spin-1 Blume-Capel bilayer Ising model
NASA Astrophysics Data System (ADS)
Kantar, Ersin; Ertaş, Mehmet
2015-06-01
An effective field theory with correlations has been used to study the critical behavior of the spin-1 Blume-Capel bilayer Ising model on a square lattice. The effects of the Hamiltonian parameters on thermodynamic quantities and phase diagrams are investigated in detail. We found that the system exhibits the first and the second order transitions as well as tricritical point. Furthermore, we have observed that the change of tricritical point values depends on interaction parameters.
Cluster Monte Carlo dynamics for the antiferromagnetic Ising model on a triangular lattice
NASA Astrophysics Data System (ADS)
Zhang, G. M.; Yang, C. Z.
1994-11-01
Within the general cluster framework of Kandel, Ben-Av, and Domany, we develop a cluster algorithm for Monte Carlo simulations of the antiferromagnetic Ising model on a triangular lattice. The algorithm does not suffer from problems of metastability and is extremely efficient even at T=0, which allows us to extract the static exponent η=0.5 as well as the effective dynamical critical exponent of the algorithm z=0.64+/-0.02.
NASA Astrophysics Data System (ADS)
Neto, Minos A.; de Sousa, J. Ricardo; Padilha, Igor T.; Rodriguez Salmon, Octavio D.; Roberto Viana, J.; Dinóla Neto, F.
2016-06-01
We study the three-dimensional antiferromagnetic Ising model in both uniform longitudinal (H) and transverse (Ω) magnetic fields by using the effective-field theory (EFT) with finite cluster N = 1 spin (EFT-1). We analyzed the behavior of the magnetic susceptibility to investigate the reentrant phenomena that we have seen in the same phase diagram previously obtained in other papers. Our results shows the presence of two divergences in the susceptibility that indicates the existence of a reentrant behavior.
Single-cluster algorithm for the site-bond-correlated Ising model
NASA Astrophysics Data System (ADS)
Campos, P. R. A.; Onody, R. N.
1997-12-01
We extend the Wolff algorithm to include correlated spin interactions in diluted magnetic systems. This algorithm is applied to study the site-bond-correlated Ising model on a two-dimensional square lattice. We use a finite-size scaling procedure to obtain the phase diagram in the temperature-concentration space. We also have verified that the autocorrelation time diminishes in the presence of dilution and correlation, showing that the Wolff algorithm performs even better in such situations.
NASA Astrophysics Data System (ADS)
Merdan, Ziya; Karakuş, Özlem
2016-11-01
The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.
Schlittmeier, Sabine J; Weissgerber, Tobias; Kerber, Stefan; Fastl, Hugo; Hellbrück, Jürgen
2012-01-01
Background sounds, such as narration, music with prominent staccato passages, and office noise impair verbal short-term memory even when these sounds are irrelevant. This irrelevant sound effect (ISE) is evoked by so-called changing-state sounds that are characterized by a distinct temporal structure with varying successive auditory-perceptive tokens. However, because of the absence of an appropriate psychoacoustically based instrumental measure, the disturbing impact of a given speech or nonspeech sound could not be predicted until now, but necessitated behavioral testing. Our database for parametric modeling of the ISE included approximately 40 background sounds (e.g., speech, music, tone sequences, office noise, traffic noise) and corresponding performance data that was collected from 70 behavioral measurements of verbal short-term memory. The hearing sensation fluctuation strength was chosen to model the ISE and describes the percept of fluctuations when listening to slowly modulated sounds (f(mod) < 20 Hz). On the basis of the fluctuation strength of background sounds, the algorithm estimated behavioral performance data in 63 of 70 cases within the interquartile ranges. In particular, all real-world sounds were modeled adequately, whereas the algorithm overestimated the (non-)disturbance impact of synthetic steady-state sounds that were constituted by a repeated vowel or tone. Implications of the algorithm's strengths and prediction errors are discussed.
The Implementation of C-ID, R2D2 Model on Learning Reading Comprehension
ERIC Educational Resources Information Center
Rayanto, Yudi Hari; Rusmawan, Putu Ngurah
2016-01-01
The purposes of this research are to find out, (1) whether C-ID, R2D2 model is effective to be implemented on learning Reading comprehension, (2) college students' activity during the implementation of C-ID, R2D2 model on learning Reading comprehension, and 3) college students' learning achievement during the implementation of C-ID, R2D2 model on…
Critical behavior of the quantum Ising model on a fractal structure.
Yi, Hangmo
2013-07-01
We study the critical behavior of the transverse-field quantum Ising model on a fractal structure, namely the Sierpinski carpet. When a magnetic field Δ is applied perpendicular to the Ising spin direction, quantum fluctuations affect the transition between the ferromagnetic and the paramagnetic phases. Employing the continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, we investigate the interplay between the quantum fluctuations and the exotic dimensionality of the fractal structure and its effect on the critical behavior. As the transverse magnetic field increases, the critical temperature monotonically decreases until it apparently vanishes at a critical field Δ(c), beyond which the system becomes paramagnetic at all temperatures. However, the critical exponents are independent of Δ and remain the same as in the purely classical(Δ=0) case.
Effective field study of ising model on a double perovskite structure
NASA Astrophysics Data System (ADS)
Ngantso, G. Dimitri; El Amraoui, Y.; Benyoussef, A.; El Kenz, A.
2017-02-01
By using the effective field theory (EFT), the mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model adapted to a double perovskite structure has been studied. The EFT calculations have been carried out from Ising Hamiltonian by taking into account first and second nearest-neighbors interactions and the crystal and external magnetic fields. Both first- and second-order phase transitions have been found in phase diagrams of interest. Depending on crystal-field values, the thermodynamic behavior of total magnetization indicated the compensation phenomenon existence. The hysteresis behaviors are studied by investigating the reduced magnetic field dependence of total magnetization and a series of hysteresis loops are shown for different reduced temperatures around the critical one.
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.
Inference of the sparse kinetic Ising model using the decimation method.
Decelle, Aurélien; Zhang, Pan
2015-05-01
In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in Decelle and Ricci-Tersenghi [Phys. Rev. Lett. 112, 070603 (2014)] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the ℓ(1)-optimization-based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done auto-matically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudolikelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that, on various topologies and with different distribution of couplings, the decimation method outperforms the widely used ℓ(1)-optimization-based methods.
Ising t-J model close to half filling: a Monte Carlo study.
Maśka, M M; Mierzejewski, M; Ferraz, A; Kochetov, E A
2009-01-28
Within the recently proposed doped-carrier representation of the projected lattice electron operators we derive a full Ising version of the t-J model. This model possesses the global discrete Z(2) symmetry as a maximal spin symmetry of the Hamiltonian at any values of the coupling constants, t and J. In contrast, in the spin anisotropic limit of the t-J model, usually referred to as the t-J(z) model, the global SU(2) invariance is fully restored at J(z) = 0, so that only the spin-spin interaction has in this model the true Ising form. We discuss a relationship between these two models and the standard isotropic t-J model. We show that the low-energy quasiparticles in all three models share qualitatively similar properties at low doping and small values of J/t. The main advantage of the proposed Ising t-J model over the t-J(z) one is that the former allows for the unbiased Monte Carlo calculations on large clusters of up to 10(3) sites. Within this model we discuss in detail the destruction of the antiferromagnetic (AF) order by doping as well as the interplay between the AF order and hole mobility. We also discuss the effect of the exchange interaction and that of the next-nearest-neighbour hoppings on the destruction of the AF order at finite doping. We show that the short-range AF order is observed in a wide range of temperatures and dopings, much beyond the boundaries of the AF phase. We explicitly demonstrate that the local no-double-occupancy constraint plays the dominant role in destroying the magnetic order at finite doping. Finally, a role of inhomogeneities is discussed.
Navas-Portella, Víctor; Vives, Eduard
2016-02-01
This work studies universal finite size scaling functions for the number of one-dimensional spanning avalanches in a two-dimensional (2D) disordered system with boundary conditions of different nature and different aspect ratios. To this end, we will consider the 2D random field Ising model at T=0 driven by the external field H with athermal dynamics implemented with periodic and forced boundary conditions. We have chosen a convenient scaling variable z that accounts for the deformation of the distance to the critical point caused by the aspect ratio. In addition, assuming that the dependence of the finite size scaling functions on the aspect ratio can be accounted for by an additional multiplicative factor, we have been able to collapse data for different system sizes, different aspect ratios, and different types of the boundary conditions into a single scaling function Q̂.
Phase transition of p-adic Ising λ-model
Dogan, Mutlay; Akın, Hasan; Mukhamedov, Farrukh
2015-09-18
We consider an interaction of the nearest-neighbors and next nearest-neighbors for the mixed type p-adic λ-model with spin values (−1, +1) on a Cayley tree of order two. In the previous work we have proved the existence of the p-adic Gibbs measure for the model. In this work we have proved the existence of the phase transition occurs for the model.
An Implicit 2-D Shallow Water Flow Model on Unstructured Quadtree Rectangular Mesh
2011-01-01
Hanson, H.; Wamsley, T., and Zundel, A. K., 2006. Two-dimensional depth-averaged circulation model CMS- M2D : Version 3.0, Report 2: Sediment...Militello, A.; Reed, C.W.; Zundel, A.K. and Kraus, N.C., 2004. Two-dimensional depth-averaged circulation model M2D : Version 2.0, Report 1, Technical
Improvement of a 2D numerical model of lava flows
NASA Astrophysics Data System (ADS)
Ishimine, Y.
2013-12-01
I propose an improved procedure that reduces an improper dependence of lava flow directions on the orientation of Digital Elevation Model (DEM) in two-dimensional simulations based on Ishihara et al. (in Lava Flows and Domes, Fink, JH eds., 1990). The numerical model for lava flow simulations proposed by Ishihara et al. (1990) is based on two-dimensional shallow water model combined with a constitutive equation for a Bingham fluid. It is simple but useful because it properly reproduces distributions of actual lava flows. Thus, it has been regarded as one of pioneer work of numerical simulations of lava flows and it is still now widely used in practical hazard prediction map for civil defense officials in Japan. However, the model include an improper dependence of lava flow directions on the orientation of DEM because the model separately assigns the condition for the lava flow to stop due to yield stress for each of two orthogonal axes of rectangular calculating grid based on DEM. This procedure brings a diamond-shaped distribution as shown in Fig. 1 when calculating a lava flow supplied from a point source on a virtual flat plane although the distribution should be circle-shaped. To improve the drawback, I proposed a modified procedure that uses the absolute value of yield stress derived from both components of two orthogonal directions of the slope steepness to assign the condition for lava flows to stop. This brings a better result as shown in Fig. 2. Fig. 1. (a) Contour plots calculated with the original model of Ishihara et al. (1990). (b) Contour plots calculated with a proposed model.
Anomalous invasion in a 2d model of chemotactic predation
NASA Astrophysics Data System (ADS)
Willemsen, Jorge F.
2010-09-01
It has been hypothesized that plankton predators sense the presence of their prey through detection of chemical signals exuded by the prey. This process is formulated using elements of existing models, tailored to correspond to the specific process under investigation. The motivation for the resulting model is discussed in detail. Numerical results are then presented. It is found that the front representing the advance of the predator into the prey is irregular in a novel way, and the reasons for this anomalous invasion are discussed. It is recognized that reaction-diffusion models, starting perhaps with Turing, can lead to what might have been thought of as anomalous patterns - yet the “flicker” front advance discovered here is indeed novel.
Two-Dimensional Wang-Landau Sampling of AN Asymmetric Ising Model
NASA Astrophysics Data System (ADS)
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.
Goncalves; Lopez De Haro M; Taguena-Martinez; Stinchcombe
2000-02-14
The dynamic critical exponent and the frequency and wave-vector dependent susceptibility of the kinetic Ising model on an alternating isotopic chain with Glauber dynamics are examined. The analysis provides a connection between a microscopic model and the Nagel scaling curve originally proposed to describe dielectric susceptibility measurements of several glass-forming liquids. While support is given to the hypothesis relating the Nagel scaling to multiple relaxation processes, it is also found that the scaling function may exhibit plateau regions and does not hold for all temperatures.
Development of CCHE2D embankment break model
Technology Transfer Automated Retrieval System (TEKTRAN)
Earthen embankment breach often results in detrimental impact on downstream residents and infrastructure, especially those located in the flooding zone. Embankment failures are most commonly caused by overtopping or internal erosion. This study is to develop a practical numerical model for simulat...
A mathematical model for foreign body reactions in 2D
Su, Jianzhong; Gonzales, Humberto Perez; Todorov, Michail; Kojouharov, Hristo; Tang, Liping
2010-01-01
The foreign body reactions are commonly referred to the network of immune and inflammatory reactions of human or animals to foreign objects placed in tissues. They are basic biological processes, and are also highly relevant to bioengineering applications in implants, as fibrotic tissue formations surrounding medical implants have been found to substantially reduce the effectiveness of devices. Despite of intensive research on determining the mechanisms governing such complex responses, few mechanistic mathematical models have been developed to study such foreign body reactions. This study focuses on a kinetics-based predictive tool in order to analyze outcomes of multiple interactive complex reactions of various cells/proteins and biochemical processes and to understand transient behavior during the entire period (up to several months). A computational model in two spatial dimensions is constructed to investigate the time dynamics as well as spatial variation of foreign body reaction kinetics. The simulation results have been consistent with experimental data and the model can facilitate quantitative insights for study of foreign body reaction process in general. PMID:21532988
Monte Carlo Studies of Phase Separation in Compressible 2-dim Ising Models
NASA Astrophysics Data System (ADS)
Mitchell, S. J.; Landau, D. P.
2006-03-01
Using high resolution Monte Carlo simulations, we study time-dependent domain growth in compressible 2-dim ferromagnetic (s=1/2) Ising models with continuous spin positions and spin-exchange moves [1]. Spins interact with slightly modified Lennard-Jones potentials, and we consider a model with no lattice mismatch and one with 4% mismatch. For comparison, we repeat calculations for the rigid Ising model [2]. For all models, large systems (512^2) and long times (10^ 6 MCS) are examined over multiple runs, and the growth exponent is measured in the asymptotic scaling regime. For the rigid model and the compressible model with no lattice mismatch, the growth exponent is consistent with the theoretically expected value of 1/3 [1] for Model B type growth. However, we find that non-zero lattice mismatch has a significant and unexpected effect on the growth behavior.Supported by the NSF.[1] D.P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, second ed. (Cambridge University Press, New York, 2005).[2] J. Amar, F. Sullivan, and R.D. Mountain, Phys. Rev. B 37, 196 (1988).
Conservation laws and LETKF with 2D Shallow Water Model
NASA Astrophysics Data System (ADS)
Zeng, Yuefei; Janjic, Tijana
2016-04-01
Numerous approaches have been proposed to maintain physical conservation laws in the numerical weather prediction models. However, to achieve a reliable prediction, adequate initial conditions are also necessary, which are produced by a data assimilation algorithm. If an ensemble Kalman filters (EnKF) is used for this purpose, it has been shown that it could yield unphysical analysis ensemble that for example violates principles of mass conservation and positivity preservation (e.g. Janjic et al 2014) . In this presentation, we discuss the selection of conservation criteria for the analysis step, and start with testing the conservation of mass, energy and enstrophy. The simple experiments deal with nonlinear shallow water equations and simulated observations that are assimilated with LETKF (Localized Ensemble Transform Kalman Filter, Hunt et al. 2007). The model is discretized in a specific way to conserve mass, angular momentum, energy and enstrophy. The effects of the data assimilation on the conserved quantities (of mass, energy and enstrophy) depend on observation covarage, localization radius, observed variable and observation operator. Having in mind that Arakawa (1966) and Arakawa and Lamb (1977) showed that the conservation of both kinetic energy and enstrophy by momentum advection schemes in the case of nondivergent flow prevents systematic and unrealistic energy cascade towards high wave numbers, a cause of excessive numerical noise and possible eventual nonlinear instability, we test the effects on prediction depending on the type of errors in the initial condition. The performance with respect to nonlinear energy cascade is assessed as well.
Simulation of multi-steps thermal transition in 2D spin-crossover nanoparticles
NASA Astrophysics Data System (ADS)
Jureschi, Catalin-Maricel; Pottier, Benjamin-Louis; Linares, Jorge; Richard Dahoo, Pierre; Alayli, Yasser; Rotaru, Aurelian
2016-04-01
We have used an Ising like model to study the thermal behavior of a 2D spin crossover (SCO) system embedded in a matrix. The interaction parameter between edge SCO molecules and its local environment was included in the standard Ising like model as an additional term. The influence of the system's size and the ratio between the number of edge molecules and the other molecules were also discussed.
NASA Astrophysics Data System (ADS)
Shirakura, T.; Matsubara, F.; Suzuki, N.
2014-10-01
The spin structure of an axial next-nearest-neighbor Ising (ANNNI) model in two dimensions (2D) is a renewed problem because different Monte Carlo (MC) simulation methods predicted different spin orderings. The usual equilibrium simulation predicts the occurrence of a floating incommensurate (IC) Kosterlitz-Thouless (KT) type phase, which never emerges in non-equilibrium relaxation (NER) simulations. In this paper, we first examine previously published results of both methods, and then investigate a higher transition temperature Tc1 between the IC and paramagnetic phases. In the usual equilibrium simulation, we calculate the chain magnetization on larger lattices (up to 512×512 sites) and estimate Tc1≈1.16J with frustration ratio κ (≡-J2/J1)=0.6. We examine the nature of the phase transition in terms of the Binder ratio gL of spin overlap functions and the correlation-length ratio ξ /L. In the NER simulation, we observe the spin dynamics in equilibrium states by means of an autocorrelation function and also observe the chain magnetization relaxations from the ground and disordered states. These quantities exhibit an algebraic decay at T ≲1.17J. We conclude that the two-dimensional ANNNI model actually admits an IC phase transition of the KT type.
Simulation of subgrid orographic precipitation with an embedded 2-D cloud-resolving model
NASA Astrophysics Data System (ADS)
Jung, Joon-Hee; Arakawa, Akio
2016-03-01
By explicitly resolving cloud-scale processes with embedded two-dimensional (2-D) cloud-resolving models (CRMs), superparameterized global atmospheric models have successfully simulated various atmospheric events over a wide range of time scales. Up to now, however, such models have not included the effects of topography on the CRM grid scale. We have used both 3-D and 2-D CRMs to simulate the effects of topography with prescribed "large-scale" winds. The 3-D CRM is used as a benchmark. The results show that the mean precipitation can be simulated reasonably well by using a 2-D representation of topography as long as the statistics of the topography such as the mean and standard deviation are closely represented. It is also shown that the use of a set of two perpendicular 2-D grids can significantly reduce the error due to a 2-D representation of topography.
From Cycle Rooted Spanning Forests to the Critical Ising Model: an Explicit Construction
NASA Astrophysics Data System (ADS)
de Tilière, Béatrice
2013-04-01
Fisher established an explicit correspondence between the 2-dimensional Ising model defined on a graph G and the dimer model defined on a decorated version {{G}} of this graph (Fisher in J Math Phys 7:1776-1781, 1966). In this paper we explicitly relate the dimer model associated to the critical Ising model and critical cycle rooted spanning forests (CRSFs). This relation is established through characteristic polynomials, whose definition only depends on the respective fundamental domains, and which encode the combinatorics of the model. We first show a matrix-tree type theorem establishing that the dimer characteristic polynomial counts CRSFs of the decorated fundamental domain {{G}_1}. Our main result consists in explicitly constructing CRSFs of {{G}_1} counted by the dimer characteristic polynomial, from CRSFs of G 1, where edges are assigned Kenyon's critical weight function (Kenyon in Invent Math 150(2):409-439, 2002); thus proving a relation on the level of configurations between two well known 2-dimensional critical models.
Critical behavior of the mixed-spin Ising model with two competing dynamics.
Godoy, Mauricio; Figueiredo, Wagner
2002-02-01
In this work we investigate the stationary states of a nonequilibrium mixed-spin Ising model on a square lattice. The model system consists of two interpenetrating sublattices of spins sigma=1/2 and S=1, and we take only nearest neighbor interactions between pairs of spins. The system is in contact with a heat bath at temperature T and subject to an external flux of energy. The contact with the heat bath is simulated by single spin flips according to the Metropolis rule, while the input of energy is mimicked by the simultaneous flipping of pairs of neighboring spins. We performed Monte Carlo simulations on this model in order to find its phase diagram in the plane of temperature T versus the competition parameter between one- and two-spin flips, p. The phase diagram of the model exhibits two ordered phases with sublattice magnetizations m(1), m(2)>0 and m(1)>0, m(2)<0. These phases are separated from the paramagnetic phase (m(1)=m(2)=0) by continuous transition lines. We found the static critical exponents along these lines and showed that this nonequilibrium model belongs to the universality class of the two-dimensional equilibrium Ising model.
Bond Order Correlations in the 2D Hubbard Model
NASA Astrophysics Data System (ADS)
Moore, Conrad; Abu Asal, Sameer; Yang, Shuxiang; Moreno, Juana; Jarrell, Mark
We use the dynamical cluster approximation to study the bond correlations in the Hubbard model with next nearest neighbor (nnn) hopping to explore the region of the phase diagram where the Fermi liquid phase is separated from the pseudogap phase by the Lifshitz line at zero temperature. We implement the Hirsch-Fye cluster solver that has the advantage of providing direct access to the computation of the bond operators via the decoupling field. In the pseudogap phase, the parallel bond order susceptibility is shown to persist at zero temperature while it vanishes for the Fermi liquid phase which allows the shape of the Lifshitz line to be mapped as a function of filling and nnn hopping. Our cluster solver implements NVIDIA's CUDA language to accelerate the linear algebra of the Quantum Monte Carlo to help alleviate the sign problem by allowing for more Monte Carlo updates to be performed in a reasonable amount of computation time. Work supported by the NSF EPSCoR Cooperative Agreement No. EPS-1003897 with additional support from the Louisiana Board of Regents.
A 2D model to design MHD induction pumps
NASA Astrophysics Data System (ADS)
Stieglitz, R.; Zeininger, J.
2006-09-01
Technical liquid metal systems accompanied by a thermal transfer of energy such as reactor systems, metallurgical processes, metal refinement, casting, etc., require a forced convection of the fluid. The increased temperatures and more often the environmental conditions as, e.g., in a nuclear environment, pumping principles are required, in which rotating parts are absent. Additionally, in many applications a controlled atmosphere is indispensable, in order to ensure the structural integrity of the duct walls. An interesting option to overcome the sealing problem of a mechanical pump towards the surrounding is offered by induction systems. Although their efficiency compared to that of turbo machines is quite low, they have several advantages, which are attractive to the specific requirements in liquid metal applications such as: - low maintenance costs due to the absence of sealings, bearings and moving parts; - low degradation rate of the structural material; - simple replacement of the inductor without cut of the piping system; - fine regulation of flow rate by different inductor connections; - change of pump characteristics without change of the mechanical set-up. Within the article, general design requirements of electromagnetic pumps (EMP) are elaborated. The design of two annular linear induction pumps operating with sodium and lead-bismuth are presented and the calculated pump characteristics and experimentally obtained data are compared. In this context, physical effects leading to deviations between the model and the real data are addressed. Finally, the main results are summarized. Tables 4, Figs 4, Refs 12.
Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model
NASA Astrophysics Data System (ADS)
Jalabert, Rodolfo A.; Sachdev, Subir
1991-07-01
The Ising model on a three-dimensional cubic lattice with all plaquettes in the x-y frustrated plane is studied by use of a Monte Carlo technique; the exchange constants are of equal magnitude, but have varying signs. At zero temperature, the model has a finite entropy and no long-range order. The low-temperature phase is characterized by an order parameter measuring the openZ4 symmetry of lattice rotations which is invariant under Mattis gauge transformation; fluctuations lead to the alignment of frustrated bonds into columns and a fourfold degeneracy. An additional factor-of-2 degeneracy is obtained from a global spin flip. The order vanishes at a critical temperature by a transition that appears to be in the universality class of the D=3, XY model. These results are consistent with the theoretical predictions of Blankschtein et al. This Ising model is related by duality to phenomenological models of two-dimensional frustrated quantum antiferromagnets.
Onsager and Kaufman's Calculation of the Spontaneous Magnetization of the Ising Model
NASA Astrophysics Data System (ADS)
Baxter, R. J.
2011-11-01
Lars Onsager announced in 1949 that he and Bruria Kaufman had proved a simple formula for the spontaneous magnetization of the square-lattice Ising model, but did not publish their derivation. It was three years later when C.N. Yang published a derivation in Physical Review. In 1971 Onsager gave some clues to his and Kaufman's method, and there are copies of their correspondence in 1950 now available on the Web and elsewhere. Here we review how the calculation appears to have developed, and add a copy of a draft paper, almost certainly by Onsager and Kaufman, that obtains the result.
Butera, P; Pernici, M
2012-07-01
The high-temperature expansion coefficients of the ordinary and the higher susceptibilities of the spin-1/2 nearest-neighbor Ising model are calculated exactly up to the 20th order for the general d-dimensional (hyper)simple-cubical lattices. These series are analyzed to study the dependence of critical parameters on the lattice dimensionality. Using the general d expression of the ordinary susceptibility, we have more than doubled the length of the existing series expansion of the critical temperature in powers of 1/d.
Density of zeros of the ferromagnetic Ising model on a family of fractals.
Knežević, Milan; Knežević, Dragica
2012-06-01
We studied distribution of zeros of the partition function of the ferromagnetic Ising model near the Yang-Lee edge on a family of Sierpinski gasket lattices whose members are labeled by an integer b (2 ≤ b<∞). The obtained exact results on the first seven members of this family show that, for b ≥ 4, associated correlation length diverges more slowly than any power law when distance δh from the edge tends to zero, ξ_{YL}∼exp[ln(b)sqrt[|ln(δh)|/ln(λ{0})
Constraining quantum critical dynamics: (2+1)D Ising model and beyond.
Witczak-Krempa, William
2015-05-01
Quantum critical (QC) phase transitions generally lead to the absence of quasiparticles. The resulting correlated quantum fluid, when thermally excited, displays rich universal dynamics. We establish nonperturbative constraints on the linear-response dynamics of conformal QC systems at finite temperature, in spatial dimensions above 1. Specifically, we analyze the large frequency or momentum asymptotics of observables, which we use to derive powerful sum rules and inequalities. The general results are applied to the O(N) Wilson-Fisher fixed point, describing the QC Ising model when N=1. We focus on the order parameter and scalar susceptibilities, and the dynamical shear viscosity. Connections to simulations, experiments, and gauge theories are made.
The Ising model for changes in word ordering rules in natural languages
NASA Astrophysics Data System (ADS)
Itoh, Yoshiaki; Ueda, Sumie
2004-11-01
The order of ‘noun and adposition’ is an important parameter of word ordering rules in the world’s languages. The seven parameters, ‘adverb and verb’ and others, depend strongly on the ‘noun and adposition’. Japanese as well as Korean, Tamil and several other languages seem to have a stable structure of word ordering rules, while Thai and other languages, which have the opposite word ordering rules to Japanese, are also stable in structure. It seems therefore that each language in the world fluctuates between these two structures like the Ising model for finite lattice.
Scaling and universality in the two-dimensional Ising model with a magnetic field.
Mangazeev, Vladimir V; Dudalev, Michael Yu; Bazhanov, Vladimir V; Batchelor, Murray T
2010-06-01
The scaling function of the two-dimensional Ising model on the square and triangular lattices is obtained numerically via Baxter's variational corner transfer-matrix approach. The use of Aharony-Fisher nonlinear scaling variables allowed us to perform calculations sufficiently away from the critical point and to confirm all predictions of the scaling and universality hypotheses. Our results are in excellent agreement with quantum field theory calculations of Fonseca and Zamolodchikov as well as with many previously known exact and numerical calculations, including susceptibility results by Barouch, McCoy, Tracy, and Wu.
Critical behavior of the Ising model on a hierarchical lattice with aperiodic interactions
NASA Astrophysics Data System (ADS)
Pinho, S. T. R.; Haddad, T. A. S.; Salinas, S. R.
We write the exact renormalization-group recursion relations for nearest-neighbor ferromagnetic Ising models on Migdal-Kadanoff hierarchical lattices with a distribution of aperiodic exchange interactions according to a class of substitutional sequences. For small geometric fluctuations, the critical behavior is unchanged with respect to the uniform case. For large fluctuations, as in the case of the Rudin-Shapiro sequence, the uniform fixed point in the parameter space cannot be reached from any physical initial conditions. We derive a criterion to check the relevance of the geometric fluctuations.
Monte Carlos studies of critical and dynamic phenomena in mixed bond Ising model
NASA Astrophysics Data System (ADS)
Santos-Filho, J. B.; Moreno, N. O.; de Albuquerque, Douglas F.
2010-11-01
The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied both numerically and analytically. In this work, we use the Metropolis and Wolff algorithm with histogram technique and finite size scaling theory to simulate the dynamics of the system. We obtained the thermodynamic quantities such as magnetization, susceptibility, and specific heat. Our results were compared with those obtained using a new technique in effective field theory that employs similar probability distribution within the framework of two-site clusters.
NASA Astrophysics Data System (ADS)
Guo, Y. G.; Zhu, J. G.; Zhong, J. J.
2006-07-01
This paper reports the measurement and modelling of magnetic properties of SOMALOY TM 500, a soft magnetic composite (SMC) material, under different 2D vector magnetisations, such as alternating along one direction, circularly and elliptically rotating in a 2D plane. By using a 2D magnetic property tester, the B- H curves and core losses of the SMC material have been measured with different flux density patterns on a single sheet square sample. The measurements can provide useful information for modelling of the magnetic properties, such as core losses. The core loss models have been successfully applied in the design of rotating electrical machines with SMC core.
Flocking with discrete symmetry: The two-dimensional active Ising model.
Solon, A P; Tailleur, J
2015-10-01
We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a two-dimensional lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density-velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density-temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular, we predict analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.
Thermodynamics and Phase Transitions of Ising Model on Inhomogeneous Stochastic Recursive Lattice
NASA Astrophysics Data System (ADS)
Huang, Ran
As one of the few exactly solvable thermodynamic models, the Ising model on recursive lattice is featured by its impressive advantages and successful applications in various thermodynamic and statistical researches. However this model was considered that, since the recursive calculation demands homogeneous structure, it can only describe the bulk and even systems with narrow utilization. In this work we figured out a practical methodology to extend the conventional homogeneous structure of single-unit Husimi lattice to be random inhomogeneous lattices with variable units and structures, while keeping the feature of exact calculation. Three designs of inhomogeneous recursive lattices: the random-angled rhombus lattice, the Husimi lattice of variable units, and the randomly multi-branched Husimi square lattice; and the corresponding exact recursive calculations based on the partial partition function algorithm, which is derived from the Bethe Cavity method, have been investigated and developed. With the ``total-symmetry assumption'' and the ``iterative-replica trick'' we were able to exactly solve the classical ferromagnetic spin-1 Ising models on these lattices, to describe the complex systems that can only be solved by approximations or simulations on regular lattices. Our work may enhance the application of the exact calculation on recursive lattices in various fields of materials science and applied physics, especially it may serve as a powerful tool to explore the cross-dimensional thermodynamics and phase transitions. National Natural Science Foundation of China (Grant No. 11505110).
Algebraic and group structure for bipartite anisotropic Ising model on a non-local basis
NASA Astrophysics Data System (ADS)
Delgado, Francisco
2015-01-01
Entanglement is considered a basic physical resource for modern quantum applications as Quantum Information and Quantum Computation. Interactions based on specific physical systems able to generate and sustain entanglement are subject to deep research to get understanding and control on it. Atoms, ions or quantum dots are considered key pieces in quantum applications because they are elements in the development toward a scalable spin-based quantum computer through universal and basic quantum operations. Ising model is a type of interaction generating entanglement in quantum systems based on matter. In this work, a general bipartite anisotropic Ising model including an inhomogeneous magnetic field is analyzed in a non-local basis. This model summarizes several particular models presented in literature. When evolution is expressed in the Bell basis, it shows a regular block structure suggesting a SU(2) decomposition. Then, their algebraic properties are analyzed in terms of a set of physical parameters which define their group structure. In particular, finite products of pulses in this interaction are analyzed in terms of SU(4) covering. Thus, evolution denotes remarkable properties, in particular those related potentially with entanglement and control, which give a fruitful arena for further quantum developments and generalization.
The random-bond Ising model in 2.01 and 3 dimensions
NASA Astrophysics Data System (ADS)
Komargodski, Zohar; Simmons-Duffin, David
2017-04-01
We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2 < d < 4 this disorder is a relevant perturbation that drives the system to a new fixed point of the renormalization group. At d = 2 such disorder is marginally irrelevant and can be studied using conformal perturbation theory. Combining conformal perturbation theory with recent results from the conformal bootstrap we compute some scaling exponents in an expansion around d = 2. If one trusts these computations also in d = 3, one finds results consistent with experimental data and Monte Carlo simulations. In addition, we perform a direct uncontrolled computation in d = 3 using new results for low-lying operator dimensions and OPE coefficients in the 3d Ising model. We compare these new methods with previous studies. Finally, we comment about the O(2) model in d = 3, where we predict a large logarithmic correction to the infrared scaling of disorder.
Mixed Algorithms in the Ising Model on Directed BARABÁSI-ALBERT Networks
NASA Astrophysics Data System (ADS)
Lima, F. W. S.
On directed Barabási-Albert networks with two and seven neighbours selected by each added site, the Ising model does not seem to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law for Metropolis and Glauber algorithms, but for Wolff cluster flipping the magnetisation decays exponentially with time. On these networks the magnetisation behaviour of the Ising model, with Glauber, HeatBath, Metropolis, Wolf or Swendsen-Wang algorithm competing against Kawasaki dynamics, is studied by Monte Carlo simulations. We show that the model exhibits the phenomenon of self-organisation (= stationary equilibrium) defined in Ref. 8 when Kawasaki dynamics is not dominant in its competition with Glauber, HeatBath and Swendsen-Wang algorithms. Only for Wolff cluster flipping the magnetisation, this phenomenon occurs after an exponentially decay of magnetisation with time. The Metropolis results are independent of competition. We also study the same process of competition described above but with Kawasaki dynamics at the same temperature as the other algorithms. The obtained results are similar for Wolff cluster flipping, Metropolis and Swendsen-Wang algorithms but different for HeatBath.
Creutz, M.
1986-03-01
A deterministic cellular automation rule is presented which simulates the Ising model. On each cell in addition to an Ising spin is a space-time parity bit and a variable playing the role of a momentum conjugate to the spin. The procedure permits study of nonequilibrium phenomena, heat flow, mixing, and time correlations. The algorithm can make full use of multispin coding, thus permitting fast programs involving parallel processing on serial machines.
Hintermann, Edith; Holdener, Martin; Bayer, Monika; Loges, Stephanie; Pfeilschifter, Josef M; Granier, Claude; Manns, Michael P; Christen, Urs
2011-11-01
Autoimmune hepatitis (AIH) is a serious chronic inflammatory disease of the liver with yet unknown etiology and largely uncertain immunopathology. The hallmark of type 2 AIH is the generation of liver kidney microsomal-1 (LKM-1) autoantibodies, which predominantly react to cytochrome P450 2D6 (CYP2D6). The identification of disease initiating factors has been hampered in the past, since antibody epitope mapping was mostly performed using serum samples collected late during disease resulting in the identification of immunodominant epitopes not necessarily representing those involved in disease initiation. In order to identify possible environmental triggers for AIH, we analyzed for the first time the spreading of the anti-CYP2D6 antibody response over a prolonged period of time in AIH patients and in the CYP2D6 mouse model, in which mice infected with Adenovirus-human CYP2D6 (Ad-h2D6) develop antibodies with a similar specificity than AIH patients. Epitope spreading was analyzed in six AIH-2-patients and in the CYP2D6 mouse model using SPOTs membranes containing peptides covering the entire CYP2D6 protein. Despite of a considerable variation, both mice and AIH patients largely focus their humoral immune response on an immunodominant epitope early after infection (mice) or diagnosis (patients). The CYP2D6 mouse model revealed that epitope spreading is initiated at the immunodominant epitope and later expands to neighboring and remote regions. Sequence homologies to human pathogens have been detected for all identified epitopes. Our study demonstrates that epitope spreading does indeed occur during the pathogenesis of AIH and supports the concept of molecular mimicry as a possible initiating mechanism for AIH.
Quantum Supremacy for Simulating a Translation-Invariant Ising Spin Model.
Gao, Xun; Wang, Sheng-Tao; Duan, L-M
2017-01-27
We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being nonuniversal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses. Equipped with the intrinsic single-instance-hardness property, a single fixed unitary evolution in our model is sufficient to produce classically intractable results, compared to several other models that rely on implementation of an ensemble of different unitaries (instances). We propose a feasible experimental scheme to implement our Hamiltonian model using cold atoms trapped in a square optical lattice. We formulate a procedure to certify the correct functioning of this quantum machine. The certification requires only a polynomial number of local measurements assuming measurement imperfections are sufficiently small.
Solution of the antiferromagnetic Ising model with multisite interaction on a zigzag ladder.
Jurčišinová, E; Jurčišin, M
2014-09-01
We consider the antiferromagnetic spin-1/2 Ising model with multisite interaction in an external magnetic field on an infinite zigzag ladder. The model is solved exactly by using the transfer matrix method. Using the exact expression for the total magnetization per site, the magnetic properties of the model are investigated in detail. The model exhibits the formation of magnetization plateaus for low temperatures, and it is shown that their properties depend strongly on the strength of the multisite interaction. All possible ground states of the model are found and discussed. The existence of nontrivial singular ground states is proven and exact explicit expressions for them are found. The macroscopic degeneracy of the ground states is investigated and discussed.
Quantum Supremacy for Simulating a Translation-Invariant Ising Spin Model
NASA Astrophysics Data System (ADS)
Gao, Xun; Wang, Sheng-Tao; Duan, L.-M.
2017-01-01
We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being nonuniversal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses. Equipped with the intrinsic single-instance-hardness property, a single fixed unitary evolution in our model is sufficient to produce classically intractable results, compared to several other models that rely on implementation of an ensemble of different unitaries (instances). We propose a feasible experimental scheme to implement our Hamiltonian model using cold atoms trapped in a square optical lattice. We formulate a procedure to certify the correct functioning of this quantum machine. The certification requires only a polynomial number of local measurements assuming measurement imperfections are sufficiently small.
The immunoreceptor NKG2D promotes tumour growth in a model of hepatocellular carcinoma
Sheppard, Sam; Guedes, Joana; Mroz, Anna; Zavitsanou, Anastasia-Maria; Kudo, Hiromi; Rothery, Stephen M.; Angelopoulos, Panagiotis; Goldin, Robert; Guerra, Nadia
2017-01-01
Inflammation is recognized as one of the drivers of cancer. Yet, the individual immune components that possess pro- and anti-tumorigenic functions in individual cancers remain largely unknown. NKG2D is a potent activating immunoreceptor that has emerged as an important player in inflammatory disorders besides its well-established function as tumour suppressor. Here, we provide genetic evidence of an unexpected tumour-promoting effect of NKG2D in a model of inflammation-driven liver cancer. Compared to NKG2D-deficient mice, NKG2D-sufficient mice display accelerated tumour growth associated with, an increased recruitment of memory CD8+T cells to the liver and exacerbated pro-inflammatory milieu. In addition, we show that NKG2D contributes to liver damage and consequent hepatocyte proliferation known to favour tumorigenesis. Thus, the NKG2D/NKG2D-ligand pathway provides an additional mechanism linking chronic inflammation to tumour development in hepatocellular carcinoma. Our findings expose the need to selectively target the types of cancer that could benefit from NKG2D-based immunotherapy. PMID:28128200
Anomalous mean-field behavior of the fully connected Ising model.
Colonna-Romano, Louis; Gould, Harvey; Klein, W
2014-10-01
Although the fully connected Ising model does not have a length scale, we show that the critical exponents for thermodynamic quantities such as the mean magnetization and the susceptibility can be obtained using finite size scaling with the scaling variable equal to N, the number of spins. Surprisingly, the mean value and the most probable value of the magnetization are found to scale differently with N at the critical temperature of the infinite system, and the magnetization probability distribution is not a Gaussian, even for large N. Similar results inconsistent with the usual understanding of mean-field theory are found at the spinodal. We relate these results to the breakdown of hyperscaling and show that hyperscaling can be restored by increasing N while holding the Ginzburg parameter rather than the temperature fixed, or by doing finite size scaling at the pseudocritical temperature where the susceptibility is a maximum for a given value of N. We conclude that finite size scaling for the fully connected Ising model yields different results depending on how the mean-field limit is approached.
The square lattice Ising model on the rectangle I: finite systems
NASA Astrophysics Data System (ADS)
Hucht, Alfred
2017-02-01
The partition function of the square lattice Ising model on the rectangle with open boundary conditions in both directions is calculated exactly for arbitrary system size L× M and temperature. We start with the dimer method of Kasteleyn, McCoy and Wu, construct a highly symmetric block transfer matrix and derive a factorization of the involved determinant, effectively decomposing the free energy of the system into two parts, F(L,M)={{F}\\text{strip}}(L,M)+F\\text{strip}\\text{res}(L,M) , where the residual part F\\text{strip}\\text{res}(L,M) contains the nontrivial finite-L contributions for fixed M. It is given by the determinant of a M/2× M/2 matrix and can be mapped onto an effective spin model with M Ising spins and long-range interactions. While F\\text{strip}\\text{res}(L,M) becomes exponentially small for large L/M or off-critical temperatures, it leads to important finite-size effects such as the critical Casimir force near criticality. The relations to the Casimir potential and the Casimir force are discussed.
Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system
NASA Astrophysics Data System (ADS)
Gong, Ming; Wen, Xueda; Sun, Guozhu; Zhang, Dan-Wei; Lan, Dong; Zhou, Yu; Fan, Yunyi; Liu, Yuhao; Tan, Xinsheng; Yu, Haifeng; Yu, Yang; Zhu, Shi-Liang; Han, Siyuan; Wu, Peiheng
2016-03-01
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena.
Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system
Gong, Ming; Wen, Xueda; Sun, Guozhu; Zhang, Dan-Wei; Lan, Dong; Zhou, Yu; Fan, Yunyi; Liu, Yuhao; Tan, Xinsheng; Yu, Haifeng; Yu, Yang; Zhu, Shi-Liang; Han, Siyuan; Wu, Peiheng
2016-01-01
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena. PMID:26951775
Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system.
Gong, Ming; Wen, Xueda; Sun, Guozhu; Zhang, Dan-Wei; Lan, Dong; Zhou, Yu; Fan, Yunyi; Liu, Yuhao; Tan, Xinsheng; Yu, Haifeng; Yu, Yang; Zhu, Shi-Liang; Han, Siyuan; Wu, Peiheng
2016-03-08
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena.
Emergent 1d Ising Behavior in AN Elementary Cellular Automaton Model
NASA Astrophysics Data System (ADS)
Kassebaum, Paul G.; Iannacchione, Germano S.
The fundamental nature of an evolving one-dimensional (1D) Ising model is investigated with an elementary cellular automaton (CA) simulation. The emergent CA simulation employs an ensemble of cells in one spatial dimension, each cell capable of two microstates interacting with simple nearest-neighbor rules and incorporating an external field. The behavior of the CA model provides insight into the dynamics of coupled two-state systems not expressible by exact analytical solutions. For instance, state progression graphs show the causal dynamics of a system through time in relation to the system's entropy. Unique graphical analysis techniques are introduced through difference patterns, diffusion patterns, and state progression graphs of the 1D ensemble visualizing the evolution. All analyses are consistent with the known behavior of the 1D Ising system. The CA simulation and new pattern recognition techniques are scalable (in both dimension, complexity, and size) and have many potential applications such as complex design of materials, control of agent systems, and evolutionary mechanism design.
GEO2D - Two-Dimensional Computer Model of a Ground Source Heat Pump System
James Menart
2013-06-07
This file contains a zipped file that contains many files required to run GEO2D. GEO2D is a computer code for simulating ground source heat pump (GSHP) systems in two-dimensions. GEO2D performs a detailed finite difference simulation of the heat transfer occurring within the working fluid, the tube wall, the grout, and the ground. Both horizontal and vertical wells can be simulated with this program, but it should be noted that the vertical wall is modeled as a single tube. This program also models the heat pump in conjunction with the heat transfer occurring. GEO2D simulates the heat pump and ground loop as a system. Many results are produced by GEO2D as a function of time and position, such as heat transfer rates, temperatures and heat pump performance. On top of this information from an economic comparison between the geothermal system simulated and a comparable air heat pump systems or a comparable gas, oil or propane heating systems with a vapor compression air conditioner. The version of GEO2D in the attached file has been coupled to the DOE heating and cooling load software called ENERGYPLUS. This is a great convenience for the user because heating and cooling loads are an input to GEO2D. GEO2D is a user friendly program that uses a graphical user interface for inputs and outputs. These make entering data simple and they produce many plotted results that are easy to understand. In order to run GEO2D access to MATLAB is required. If this program is not available on your computer you can download the program MCRInstaller.exe, the 64 bit version, from the MATLAB website or from this geothermal depository. This is a free download which will enable you to run GEO2D..
CAST2D: A finite element computer code for casting process modeling
Shapiro, A.B.; Hallquist, J.O.
1991-10-01
CAST2D is a coupled thermal-stress finite element computer code for casting process modeling. This code can be used to predict the final shape and stress state of cast parts. CAST2D couples the heat transfer code TOPAZ2D and solid mechanics code NIKE2D. CAST2D has the following features in addition to all the features contained in the TOPAZ2D and NIKE2D codes: (1) a general purpose thermal-mechanical interface algorithm (i.e., slide line) that calculates the thermal contact resistance across the part-mold interface as a function of interface pressure and gap opening; (2) a new phase change algorithm, the delta function method, that is a robust method for materials undergoing isothermal phase change; (3) a constitutive model that transitions between fluid behavior and solid behavior, and accounts for material volume change on phase change; and (4) a modified plot file data base that allows plotting of thermal variables (e.g., temperature, heat flux) on the deformed geometry. Although the code is specialized for casting modeling, it can be used for other thermal stress problems (e.g., metal forming).
Light cone in the two-dimensional transverse-field Ising model in time-dependent mean-field theory
NASA Astrophysics Data System (ADS)
Hafner, J.; Blass, B.; Rieger, H.
2016-12-01
We investigate the propagation of a local perturbation in the two-dimensional transverse-field Ising model with a time-dependent application of the mean-field theory based on the BBGKY hierarchy. We show that the perturbation propagates through the system with a finite velocity and that there is a transition from Manhattan to Euclidian metric, resulting in a light cone with an almost circular shape at sufficiently large distances. The propagation velocity of the perturbation defining the front of the light cone is discussed with respect to the parameters of the Hamiltonian and compared to exact results for the transverse-field Ising model in one dimension.
Representativeness of 2D models to simulate 3D unstable variable density flow in porous media
NASA Astrophysics Data System (ADS)
Knorr, Bastian; Xie, Yueqing; Stumpp, Christine; Maloszewski, Piotr; Simmons, Craig T.
2016-11-01
Variable density flow in porous media has been studied primarily using numerical models because it is a semi-chaotic and transient process. Most of these studies have been 2D, owing to the computational restrictions on 3D simulations, and the ability to observe variable density flow in 2D experimentation. However, it is recognised that variable density flow is a three-dimensional process. A 3D system may cause weaker variable density flow than a 2D system due to stronger dispersion, but may also result in bigger fingers and hence stronger variable density flow because of more space for fingers to coalesce. This study aimed to determine the representativeness of 2D modelling to simulate 3D variable density flow. 3D homogeneous sand column experiments were conducted at three different water flow velocities with three different bromide tracer solutions mixed with methanol resulting in different density ratios. Both 2D axisymmetric and 3D numerical simulations were performed to reproduce experimental data. Experimental results showed that the magnitude of variable density flow increases with decreasing flow rates and decreasing density ratios. The shapes of the observed breakthrough curves differed significantly from those produced by 2D axisymmetric and 3D simulations. Compared to 2D simulations, the onset of instabilities was delayed but the growth was more pronounced in 3D simulations. Despite this difference, both 2D axisymmetric and 3D models successfully simulated mass recovery with high efficiency (between 77% and 99%). This study indicates that 2D simulations are sufficient to understand integrated features of variable density flow in homogeneous sand column experiments.
New 2D diffraction model and its applications to terahertz parallel-plate waveguide power splitters
NASA Astrophysics Data System (ADS)
Zhang, Fan; Song, Kaijun; Fan, Yong
2017-02-01
A two-dimensional (2D) diffraction model for the calculation of the diffraction field in 2D space and its applications to terahertz parallel-plate waveguide power splitters are proposed in this paper. Compared with the Huygens-Fresnel principle in three-dimensional (3D) space, the proposed model provides an approximate analytical expression to calculate the diffraction field in 2D space. The diffraction filed is regarded as the superposition integral in 2D space. The calculated results obtained from the proposed diffraction model agree well with the ones by software HFSS based on the element method (FEM). Based on the proposed 2D diffraction model, two parallel-plate waveguide power splitters are presented. The splitters consist of a transmitting horn antenna, reflectors, and a receiving antenna array. The reflector is cylindrical parabolic with superimposed surface relief to efficiently couple the transmitted wave into the receiving antenna array. The reflector is applied as computer-generated holograms to match the transformed field to the receiving antenna aperture field. The power splitters were optimized by a modified real-coded genetic algorithm. The computed results of the splitters agreed well with the ones obtained by software HFSS verify the novel design method for power splitter, which shows good applied prospects of the proposed 2D diffraction model.
New 2D diffraction model and its applications to terahertz parallel-plate waveguide power splitters
Zhang, Fan; Song, Kaijun; Fan, Yong
2017-01-01
A two-dimensional (2D) diffraction model for the calculation of the diffraction field in 2D space and its applications to terahertz parallel-plate waveguide power splitters are proposed in this paper. Compared with the Huygens-Fresnel principle in three-dimensional (3D) space, the proposed model provides an approximate analytical expression to calculate the diffraction field in 2D space. The diffraction filed is regarded as the superposition integral in 2D space. The calculated results obtained from the proposed diffraction model agree well with the ones by software HFSS based on the element method (FEM). Based on the proposed 2D diffraction model, two parallel-plate waveguide power splitters are presented. The splitters consist of a transmitting horn antenna, reflectors, and a receiving antenna array. The reflector is cylindrical parabolic with superimposed surface relief to efficiently couple the transmitted wave into the receiving antenna array. The reflector is applied as computer-generated holograms to match the transformed field to the receiving antenna aperture field. The power splitters were optimized by a modified real-coded genetic algorithm. The computed results of the splitters agreed well with the ones obtained by software HFSS verify the novel design method for power splitter, which shows good applied prospects of the proposed 2D diffraction model. PMID:28181514
New 2D diffraction model and its applications to terahertz parallel-plate waveguide power splitters.
Zhang, Fan; Song, Kaijun; Fan, Yong
2017-02-09
A two-dimensional (2D) diffraction model for the calculation of the diffraction field in 2D space and its applications to terahertz parallel-plate waveguide power splitters are proposed in this paper. Compared with the Huygens-Fresnel principle in three-dimensional (3D) space, the proposed model provides an approximate analytical expression to calculate the diffraction field in 2D space. The diffraction filed is regarded as the superposition integral in 2D space. The calculated results obtained from the proposed diffraction model agree well with the ones by software HFSS based on the element method (FEM). Based on the proposed 2D diffraction model, two parallel-plate waveguide power splitters are presented. The splitters consist of a transmitting horn antenna, reflectors, and a receiving antenna array. The reflector is cylindrical parabolic with superimposed surface relief to efficiently couple the transmitted wave into the receiving antenna array. The reflector is applied as computer-generated holograms to match the transformed field to the receiving antenna aperture field. The power splitters were optimized by a modified real-coded genetic algorithm. The computed results of the splitters agreed well with the ones obtained by software HFSS verify the novel design method for power splitter, which shows good applied prospects of the proposed 2D diffraction model.
Hearing the shape of the Ising model with a programmable superconducting-flux annealer.
Vinci, Walter; Markström, Klas; Boixo, Sergio; Roy, Aidan; Spedalieri, Federico M; Warburton, Paul A; Severini, Simone
2014-07-16
Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful spectral invariants. In this context, we introduce a family of refinements of the classical spectrum and consider the quantum partition function. We demonstrate that the energy spectrum of the quantum Ising Hamiltonian is a stronger invariant than the classical one without refinements. For the purpose of implementing the related physical systems, we perform experiments on a programmable annealer with superconducting flux technology. Departing from the paradigm of adiabatic computation, we take advantage of a noisy evolution of the device to generate statistics of low energy states. The graphs considered in the experiments have the same classical partition functions, but different quantum spectra. The data obtained from the annealer distinguish non-isomorphic graphs via information contained in the classical refinements of the functions but not via the differences in the quantum spectra.
Phase transitions and multicritical behavior in the Ising model with dipolar interactions.
Bab, M A; Horowitz, C M; Rubio Puzzo, M L; Saracco, G P
2016-10-01
In this work, the phase diagram of the ferromagnetic Ising model with dipole interactions is revisited with the aim of determining the nature of the phase transition between stripe-ordered phases with width n (h_{n}) and tetragonal liquid (TL) phases. Extensive Monte Carlo simulations are performed in order to study the short-time dynamic behavior of the observables for selected values of the ratio between the ferromagnetic exchange and dipolar constants δ. The obtained results indicate that the h_{1}-TL phase transition line is continuous up to δ=1.2585, while for the h_{2}-TL line a weak first-order character is found in the interval 1.2585≤δ≤1.36 and becomes continuous for 1.37≤δ≤1.9. This result suggests the existence of a tricritical point close to δ=1.37. When it is appropriate, the complete set of critical exponents is obtained, and in all the studied cases they depend on δ but do not belong to the Ising universality class. Furthermore, short-time dynamic studies reveal that at the point where the mentioned lines meet the h_{1}-h_{2} line, i.e., at δ=1.2585, the critical phase corresponding to the h_{1}-TL transition coexists with the h_{2} phase.
Hearing the Shape of the Ising Model with a Programmable Superconducting-Flux Annealer
Vinci, Walter; Markström, Klas; Boixo, Sergio; Roy, Aidan; Spedalieri, Federico M.; Warburton, Paul A.; Severini, Simone
2014-01-01
Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful spectral invariants. In this context, we introduce a family of refinements of the classical spectrum and consider the quantum partition function. We demonstrate that the energy spectrum of the quantum Ising Hamiltonian is a stronger invariant than the classical one without refinements. For the purpose of implementing the related physical systems, we perform experiments on a programmable annealer with superconducting flux technology. Departing from the paradigm of adiabatic computation, we take advantage of a noisy evolution of the device to generate statistics of low energy states. The graphs considered in the experiments have the same classical partition functions, but different quantum spectra. The data obtained from the annealer distinguish non-isomorphic graphs via information contained in the classical refinements of the functions but not via the differences in the quantum spectra. PMID:25029660
Hearing the Shape of the Ising Model with a Programmable Superconducting-Flux Annealer
NASA Astrophysics Data System (ADS)
Vinci, Walter; Markström, Klas; Boixo, Sergio; Roy, Aidan; Spedalieri, Federico M.; Warburton, Paul A.; Severini, Simone
2014-07-01
Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful spectral invariants. In this context, we introduce a family of refinements of the classical spectrum and consider the quantum partition function. We demonstrate that the energy spectrum of the quantum Ising Hamiltonian is a stronger invariant than the classical one without refinements. For the purpose of implementing the related physical systems, we perform experiments on a programmable annealer with superconducting flux technology. Departing from the paradigm of adiabatic computation, we take advantage of a noisy evolution of the device to generate statistics of low energy states. The graphs considered in the experiments have the same classical partition functions, but different quantum spectra. The data obtained from the annealer distinguish non-isomorphic graphs via information contained in the classical refinements of the functions but not via the differences in the quantum spectra.
Kriz, Igor; Loebl, Martin; Somberg, Petr
2013-05-15
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding conjectured limits realized by fermions in rational conformal field theories.
Annealed Ising model with site dilution on self-similar structures.
Silva, V S T; Andrade, R F S; Salinas, S R
2014-11-01
We consider an Ising model on the triangular Apollonian network (AN), with a thermalized distribution of vacant sites. The statistical problem is formulated in a grand canonical ensemble, in terms of the temperature T and a chemical potential μ associated with the concentration of active magnetic sites. We use a well-known transfer-matrix method, with a number of adaptations, to write recursion relations between successive generations of this hierarchical structure. We also investigate the analogous model on the diamond hierarchical lattice (DHL). From the numerical analysis of the recursion relations, we obtain various thermodynamic quantities. In the μ→∞ limit, we reproduce the results for the uniform models: in the AN, the system is magnetically ordered at all temperatures, while in the DHL there is a ferromagnetic-paramagnetic transition at a finite value of T. Magnetic ordering, however, is shown to disappear for sufficiently large negative values of the chemical potential.
Type-dependent stochastic Ising model describing the dynamics of a non-symmetric feedback module.
Gonzalez-Navarrete, Manuel
2016-10-01
We study an alternative approach to model the dynamical behaviors of biological feedback loop, that is, a type-dependent spin system, this class of stochastic models was introduced by Fernández et. al [13], and are useful since take account to inherent variability of gene expression. We analyze a non-symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, invented by Elowitz and Leibler [7]. We consider a mean-field dynamics for a type-dependent Ising model, and then study the empirical-magnetization vector representing concentration of molecules. We apply a convergence result from stochastic jump processes to deterministic trajectories and present a bifurcation analysis for the associated dynamical system. We show that non-symmetric module under study can exhibit very rich behaviours, including the empirical oscillations described by repressilator.
Slow relaxation in a constrained Ising spin chain: toy model for granular compaction.
Majumdar, Satya N; Dean, David S
2002-11-01
We present detailed analytical studies on the zero-temperature coarsening dynamics in an Ising spin chain in the presence of a dynamically induced field that favors locally the "-" phase compared to the "+" phase. We show that the presence of such a local kinetic bias drives the system into a late time state with average magnetization m equal to -1. However the magnetization relaxes into this final value extremely slowly in an inverse logarithmic fashion. We further map this spin model exactly onto a simple lattice model of granular compaction that includes the minimal microscopic moves needed for compaction. This toy model then predicts analytically an inverse logarithmic law for the growth of density of granular particles, as seen in recent experiments and thereby provides a mechanism for the inverse logarithmic relaxation. Our analysis utilizes an independent interval approximation for the particle and the hole clusters and is argued to be exact at late times (supported also by numerical simulations).
Relaxational processes in the one-dimensional Ising model with long-range interactions
NASA Astrophysics Data System (ADS)
Tomita, Yusuke
2016-12-01
Relaxational processes in ordered phases of one-dimensional Ising models with long-range interactions are investigated by Monte Carlo simulations. Three types of spin model, the pure ferromagnetic, the diluted ferromagnetic, and the spin glass models, are examined. The effective dimension of the one-dimensional systems are controlled by a parameter σ , which tunes the rate of interaction decay. Systematical investigations of droplet dynamics, from the lower to the upper critical dimension, are conducted by changing the value of σ . Comparing numerical data with the droplet theory, it is found that the surface dimension of droplets is distributed around the effective dimension. The distribution in the surface dimension makes the droplet dynamics complex and extremely enhances dynamical crossover.
Relaxational processes in the one-dimensional Ising model with long-range interactions.
Tomita, Yusuke
2016-12-01
Relaxational processes in ordered phases of one-dimensional Ising models with long-range interactions are investigated by Monte Carlo simulations. Three types of spin model, the pure ferromagnetic, the diluted ferromagnetic, and the spin glass models, are examined. The effective dimension of the one-dimensional systems are controlled by a parameter σ, which tunes the rate of interaction decay. Systematical investigations of droplet dynamics, from the lower to the upper critical dimension, are conducted by changing the value of σ. Comparing numerical data with the droplet theory, it is found that the surface dimension of droplets is distributed around the effective dimension. The distribution in the surface dimension makes the droplet dynamics complex and extremely enhances dynamical crossover.
A 2D spring model for the simulation of ultrasonic wave propagation in nonlinear hysteretic media.
Delsanto, P P; Gliozzi, A S; Hirsekorn, M; Nobili, M
2006-07-01
A two-dimensional (2D) approach to the simulation of ultrasonic wave propagation in nonclassical nonlinear (NCNL) media is presented. The approach represents the extension to 2D of a previously proposed one dimensional (1D) Spring Model, with the inclusion of a PM space treatment of the intersticial regions between grains. The extension to 2D is of great practical relevance for its potential applications in the field of quantitative nondestructive evaluation and material characterization, but it is also useful, from a theoretical point of view, to gain a better insight of the interaction mechanisms involved. The model is tested by means of virtual 2D experiments. The expected NCNL behaviors are qualitatively well reproduced.
NASA Astrophysics Data System (ADS)
Roudi, Yasser; Tyrcha, Joanna; Hertz, John
2009-05-01
We study pairwise Ising models for describing the statistics of multineuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their statistical properties. To do this, we extract the optimal couplings for subsets of size up to 200 neurons, essentially exactly, using Boltzmann learning. We then study the quality of several approximate methods for finding the couplings by comparing their results with those found from Boltzmann learning. Two of these methods—inversion of the Thouless-Anderson-Palmer equations and an approximation proposed by Sessak and Monasson—are remarkably accurate. Using these approximations for larger subsets of neurons, we find that extracting couplings using data from a subset smaller than the full network tends systematically to overestimate their magnitude. This effect is described qualitatively by infinite-range spin-glass theory for the normal phase. We also show that a globally correlated input to the neurons in the network leads to a small increase in the average coupling. However, the pair-to-pair variation in the couplings is much larger than this and reflects intrinsic properties of the network. Finally, we study the quality of these models by comparing their entropies with that of the data. We find that they perform well for small subsets of the neurons in the network, but the fit quality starts to deteriorate as the subset size grows, signaling the need to include higher-order correlations to describe the statistics of large networks.
Multi-Scale Modeling, Design Strategies and Physical Properties of 2D Composite Sheets
2015-01-15
of Pennsylvania. The breakthrough results obtained are 1) prediction and subsequent experimental observation of strain induced changes in electronic...structure of TMD materials 2) Prediction and experimental observation of using defects in 2D materials to enhance charge storage capacity and 3...221 Philadelphia , PA 19104 -6205 4-Mar-2014 ABSTRACT Final Report: 9.4: Multi-scale modeling, design strategies and physical properties of 2D
Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model
NASA Astrophysics Data System (ADS)
Fytas, N. G.; Martín-Mayor, V.; Picco, M.; Sourlas, N.
2017-03-01
We report a high-precision numerical estimation of the critical exponent α of the specific heat of the random-field Ising model in four dimensions. Our result α =0.12(1) indicates a diverging specific-heat behavior and is consistent with the estimation coming from the modified hyperscaling relation using our estimate of θ via the anomalous dimensions η and \\barη . Our analysis benefited from a high-statistics zero-temperature numerical simulation of the model for two distributions of the random fields, namely a Gaussian and Poissonian distribution, as well as recent advances in finite-size scaling and reweighting methods for disordered systems. An original estimate of the critical slowing down exponent z of the maximum-flow algorithm used is also provided.
Phase transitions in the three-state Ising spin-glass model with finite connectivity.
Erichsen, R; Theumann, W K
2011-06-01
The statistical mechanics of a two-state Ising spin-glass model with finite random connectivity, in which each site is connected to a finite number of other sites, is extended in this work within the replica technique to study the phase transitions in the three-state Ghatak-Sherrington (or random Blume-Capel) model of a spin glass with a crystal-field term. The replica symmetry ansatz for the order function is expressed in terms of a two-dimensional effective-field distribution, which is determined numerically by means of a population dynamics procedure. Phase diagrams are obtained exhibiting phase boundaries that have a reentrance with both a continuous and a genuine first-order transition with a discontinuity in the entropy. This may be seen as "inverse freezing," which has been studied extensively lately, as a process either with or without exchange of latent heat.
Slicing the three-dimensional Ising model: Critical equilibrium and coarsening dynamics.
Arenzon, Jeferson J; Cugliandolo, Leticia F; Picco, Marco
2015-03-01
We study the evolution of spin clusters on two-dimensional slices of the three-dimensional Ising model in contact with a heat bath after a sudden quench to a subcritical temperature. We analyze the evolution of some simple initial configurations, such as a sphere and a torus, of one phase embedded into the other, to confirm that their area disappears linearly with time and to establish the temperature dependence of the prefactor in each case. Two generic kinds of initial states are later used: equilibrium configurations either at infinite temperature or at the paramagnetic-ferromagnetic phase transition. We investigate the morphological domain structure of the coarsening configurations on two-dimensional slices of the three-dimensional system, compared with the behavior of the bidimensional model.
The bulk, surface and corner free energies of the square lattice Ising model
NASA Astrophysics Data System (ADS)
Baxter, R. J.
2017-01-01
We use Kaufman’s spinor method to calculate the bulk, surface and corner free energies {f}{{b}},{f}{{s}},{f}{{s}}\\prime ,{f}{{c}} of the anisotropic square lattice zero-field Ising model for the ordered ferromagnetic case. For {f}{{b}},{f}{{s}},{f}{{s}}\\prime our results of course agree with the early work of Onsager, McCoy and Wu. We also find agreement with the conjectures made by Vernier and Jacobsen (VJ) for the isotropic case. We note that the corner free energy f c depends only on the elliptic modulus k that enters the working, and not on the argument v, which means that VJ’s conjecture applies for the full anisotropic model. The only aspect of this paper that is new is the actual derivation of f c, but by reporting all four free energies together we can see interesting structures linking them.
Effective time reversal and echo dynamics in the transverse field Ising model
NASA Astrophysics Data System (ADS)
Schmitt, Markus; Kehrein, Stefan
2016-09-01
The question of thermalisation in closed quantum many-body systems has received a lot of attention in the past few years. An intimately related question is whether a closed quantum system shows irreversible dynamics. However, irreversibility and what we actually mean by this in a quantum many-body system with unitary dynamics has been explored very little. In this work we investigate the dynamics of the Ising model in a transverse magnetic field involving an imperfect effective time reversal. We propose a definition of irreversibility based on the echo peak decay of observables. Inducing the effective time reversal by different protocols we find an algebraic decay of the echo peak heights or an ever persisting echo peak indicating that the dynamics in this model is well reversible.
Clusel, Maxime; Fortin, Jean-Yves; Holdsworth, Peter C W
2004-10-01
Order parameter fluctuations for the two-dimensional Ising model in the region of the critical temperature are presented. A locus of temperatures T(*) (L) and a locus of magnetic fields B(*) (L) are identified, for which the probability density function is similar to that for the two-dimensional XY model in the spin wave approximation. The characteristics of the fluctuations along these points are largely independent of universality class. We show that the largest range of fluctuations relative to the variance of the distribution occurs along these loci of points, rather than at the critical temperature itself and we discuss this observation in terms of intermittency. Our motivation is the identification of a generic form for fluctuations in correlated systems in accordance with recent experimental and numerical observations. We conclude that a universality-class-dependent form for the fluctuations is a particularity of critical phenomena related to the change in symmetry at a phase transition.
Quantum Phase Transition in the Two-Dimensional Random Transverse-Field Ising Model
NASA Astrophysics Data System (ADS)
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.
Analysis of vegetation effect on waves using a vertical 2-D RANS model
Technology Transfer Automated Retrieval System (TEKTRAN)
A vertical two-dimensional (2-D) model has been applied in the simulation of wave propagation through vegetated water bodies. The model is based on an existing model SOLA-VOF which solves the Reynolds-Averaged Navier-Stokes (RANS) equations with the finite difference method on a staggered rectangula...
Simulation of Cardiac Arrhythmias Using a 2D Heterogeneous Whole Heart Model
Balakrishnan, Minimol; Chakravarthy, V. Srinivasa; Guhathakurta, Soma
2015-01-01
Simulation studies of cardiac arrhythmias at the whole heart level with electrocardiogram (ECG) gives an understanding of how the underlying cell and tissue level changes manifest as rhythm disturbances in the ECG. We present a 2D whole heart model (WHM2D) which can accommodate variations at the cellular level and can generate the ECG waveform. It is shown that, by varying cellular-level parameters like the gap junction conductance (GJC), excitability, action potential duration (APD) and frequency of oscillations of the auto-rhythmic cell in WHM2D a large variety of cardiac arrhythmias can be generated including sinus tachycardia, sinus bradycardia, sinus arrhythmia, sinus pause, junctional rhythm, Wolf Parkinson White syndrome and all types of AV conduction blocks. WHM2D includes key components of the electrical conduction system of the heart like the SA (Sino atrial) node cells, fast conducting intranodal pathways, slow conducting atriovenctricular (AV) node, bundle of His cells, Purkinje network, atrial, and ventricular myocardial cells. SA nodal cells, AV nodal cells, bundle of His cells, and Purkinje cells are represented by the Fitzhugh-Nagumo (FN) model which is a reduced model of the Hodgkin-Huxley neuron model. The atrial and ventricular myocardial cells are modeled by the Aliev-Panfilov (AP) two-variable model proposed for cardiac excitation. WHM2D can prove to be a valuable clinical tool for understanding cardiac arrhythmias. PMID:26733873
Simulation of Cardiac Arrhythmias Using a 2D Heterogeneous Whole Heart Model.
Balakrishnan, Minimol; Chakravarthy, V Srinivasa; Guhathakurta, Soma
2015-01-01
Simulation studies of cardiac arrhythmias at the whole heart level with electrocardiogram (ECG) gives an understanding of how the underlying cell and tissue level changes manifest as rhythm disturbances in the ECG. We present a 2D whole heart model (WHM2D) which can accommodate variations at the cellular level and can generate the ECG waveform. It is shown that, by varying cellular-level parameters like the gap junction conductance (GJC), excitability, action potential duration (APD) and frequency of oscillations of the auto-rhythmic cell in WHM2D a large variety of cardiac arrhythmias can be generated including sinus tachycardia, sinus bradycardia, sinus arrhythmia, sinus pause, junctional rhythm, Wolf Parkinson White syndrome and all types of AV conduction blocks. WHM2D includes key components of the electrical conduction system of the heart like the SA (Sino atrial) node cells, fast conducting intranodal pathways, slow conducting atriovenctricular (AV) node, bundle of His cells, Purkinje network, atrial, and ventricular myocardial cells. SA nodal cells, AV nodal cells, bundle of His cells, and Purkinje cells are represented by the Fitzhugh-Nagumo (FN) model which is a reduced model of the Hodgkin-Huxley neuron model. The atrial and ventricular myocardial cells are modeled by the Aliev-Panfilov (AP) two-variable model proposed for cardiac excitation. WHM2D can prove to be a valuable clinical tool for understanding cardiac arrhythmias.
MODELING THE TRANSVERSE THERMAL CONDUCTIVITY OF 2D-SICF/SIC COMPOSITES
Youngblood, Gerald E.; Senor, David J.; Jones, Russell H.
2002-09-01
A hierarchical model was developed to describe the effective transverse thermal conductivity, K effective, of a 2D-SiC/SiC composite made from stacked and infiltrated woven fabric layers in terms of constituent properties and microstructural and architectural variables. The model includes the expected effects of fiber-matrix interfacial conductance as well as the effects of high fiber packing fractions within individual tows and the non-uniform nature of 2D-fabric layers that include a significant amount of interlayer porosity. Model predictions were obtained for two versions of DuPont 2D-Hi Nicalon(Trademark)/PyC/ICVI-SiC composite, one with a thin (0.110 micron) and the other with a thick (1.040 micron) PyC fiber coating. The model predicts that the matrix porosity content and porosity shape factor have a major influence on K effective(T) for such a composite.
Missing mass approximations for the partition function of stimulus driven Ising models.
Haslinger, Robert; Ba, Demba; Galuske, Ralf; Williams, Ziv; Pipa, Gordon
2013-01-01
Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few) occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many) by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data). We use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNNpat) where is L the data length, N the number of neurons and N pat the number of unique patterns in the data, contrasting with the O(L2 (N) ) complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding.
Seepage and Piping through Levees and Dikes using 2D and 3D Modeling Codes
2016-06-01
Modeling Codes Co as ta l a nd H yd ra ul ic s La bo ra to ry Hwai-Ping Cheng, Stephen M. England, and Clarissa M. Murray June 2016...Flood & Coastal Storm Damage Reduction Program ERDC/CHL TR-16-6 June 2016 Seepage and Piping through Levees and Dikes Using 2D and 3D Modeling Codes ...TYPE Final Report 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE Seepage and Piping through Levees and Dikes using 2D and 3D Modeling Codes
A simple 2-D inundation model for incorporating flood damage in urban drainage planning
NASA Astrophysics Data System (ADS)
Pathirana, A.; Tsegaye, S.; Gersonius, B.; Vairavamoorthy, K.
2011-08-01
An urban inundation model was developed and coupled with 1-D drainage network model (EPA-SWMM5). The objective was to achieve a 1-D/2-D coupled model that is simple and fast enough to be consistently used in planning stages of urban drainage projects. The 2-D inundation model is based on a non-standard simplification of the shallow water equation, lays between diffusion-wave and full dynamic models. Simplifications were made in the process representation and numerical solving mechanisms and a depth scaled Manning coefficient was introduced to achieve stability in the cell wetting-drying process. The 2-D model is coupled with SWMM for simulation of both network flow and surcharge induced inundation. The coupling is archived by mass transfer from the network system to the 2-D system. A damage calculation block is integrated within the model code for assessing flood damage costs in optimal planning of urban drainage networks. The model is stable in dealing with complex flow conditions, and cell wetting/drying processes, as demonstrated by a number of idealised experiments. The model application is demonstrated by applying to a case study in Brazil.
Stable spins in the zero temperature spinodal decomposition of 2D Potts models
NASA Astrophysics Data System (ADS)
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.
Renormalization-group study of the ferromagnetic Ising model on the triangular lattice
NASA Astrophysics Data System (ADS)
Unger, Chris
1984-08-01
The dynamic real-space renormalization group of Mazenko and Valls is applied to the zero-field ferromagnetic Ising model on the triangular lattice. Renormalization equations valid for all temperatures above the critical temperature Tc are derived for the susceptibility, specific heat, structure factor, and correlation length. The magnetization is found for T
Wu, Xintian; Izmailyan, Nickolay
2015-01-01
The critical two-dimensional Ising model is studied with four types boundary conditions: free, fixed ferromagnetic, fixed antiferromagnetic, and fixed double antiferromagnetic. Using bond propagation algorithms with surface fields, we obtain the free energy, internal energy, and specific heat numerically on square lattices with a square shape and various combinations of the four types of boundary conditions. The calculations are carried out on the square lattices with size N×N and 30
Optimal control in nonequilibrium systems: Dynamic Riemannian geometry of the Ising model.
Rotskoff, Grant M; Crooks, Gavin E
2015-12-01
A general understanding of optimal control in nonequilibrium systems would illuminate the operational principles of biological and artificial nanoscale machines. Recent work has shown that a system driven out of equilibrium by a linear response protocol is endowed with a Riemannian metric related to generalized susceptibilities, and that geodesics on this manifold are the nonequilibrium control protocols with the lowest achievable dissipation. While this elegant mathematical framework has inspired numerous studies of exactly solvable systems, no description of the thermodynamic geometry yet exists when the metric cannot be derived analytically. Herein, we numerically construct the dynamic metric of the two-dimensional Ising model in order to study optimal protocols for reversing the net magnetization.
The cellular Ising model: a framework for phase transitions in multicellular environments.
Weber, Marc; Buceta, Javier
2016-06-01
Inspired by the Ising model, we introduce a gene regulatory network that induces a phase transition that coordinates robustly the behaviour of cell ensembles. The building blocks of the design are the so-called toggle switch interfaced with two quorum sensing modules, Las and Lux. We show that as a function of the transport rate of signalling molecules across the cell membrane the population undergoes a spontaneous symmetry breaking from cells individually switching their phenotypes to a global collective phenotypic organization. By characterizing the critical behaviour, we reveal some properties, such as phenotypic memory and hypersensitivity, with relevance in the field of synthetic biology. We argue that our results can be extrapolated to other multicellular systems and be a generic framework for collective decision-making processes.
Dynamics of the transverse Ising model with next-nearest-neighbor interactions.
Guimarães, P R C; Plascak, J A; de Alcantara Bonfim, O F; Florencio, J
2015-10-01
We study the effects of next-nearest-neighbor (NNN) interactions on the dynamics of the one-dimensional spin-1/2 transverse Ising model in the high-temperature limit. We use exact diagonalization to obtain the time-dependent transverse correlation function and the corresponding spectral density for a tagged spin. Our results for chains of 13 spins with periodic boundary conditions produce results which are valid in the infinite-size limit. In general we find that the NNN coupling produces slower dynamics accompanied by an enhancement of the central mode behavior. Even in the case of a strong transverse field, if the NNN coupling is sufficiently large, then there is a crossover from collective mode to central mode behavior. We also obtain several recurrants for the continued fraction representation of the relaxation function.
Rhythmic behavior in a two-population mean-field Ising model.
Collet, Francesca; Formentin, Marco; Tovazzi, Daniele
2016-10-01
Many real systems composed of a large number of interacting components, as, for instance, neural networks, may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean-field Ising model with the scope of investigating simple mechanisms capable to generate rhythms in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intrapopulation interactions of different strengths suffices for the emergence of a robust periodic behavior.
Behavior of Early Warnings near the Critical Temperature in the Two-Dimensional Ising Model.
Morales, Irving O; Landa, Emmanuel; Angeles, Carlos Calderon; Toledo, Juan C; Rivera, Ana Leonor; Temis, Joel Mendoza; Frank, Alejandro
2015-01-01
Among the properties that are common to complex systems, the presence of critical thresholds in the dynamics of the system is one of the most important. Recently, there has been interest in the universalities that occur in the behavior of systems near critical points. These universal properties make it possible to estimate how far a system is from a critical threshold. Several early-warning signals have been reported in time series representing systems near catastrophic shifts. The proper understanding of these early-warnings may allow the prediction and perhaps control of these dramatic shifts in a wide variety of systems. In this paper we analyze this universal behavior for a system that is a paradigm of phase transitions, the Ising model. We study the behavior of the early-warning signals and the way the temporal correlations of the system increase when the system is near the critical point.
Apparent First-Order Wetting and Anomalous Scaling in the Two-Dimensional Ising Model.
Wu, X-T; Abraham, D B; Indekeu, J O
2016-01-29
The global phase diagram of wetting in the two-dimensional Ising model is obtained through the exact calculation of the surface excess free energy. In addition to a surface field for inducing wetting, a surface-coupling enhancement is also included. The wetting transition (of second order) is critical for any finite ratio of surface coupling J_{s} to bulk coupling J, and becomes of first order in the limit J_{s}/J→∞. However, for J_{s}/J≫1, the critical region is exponentially small and is practically invisible to numerical studies. A distinct preasymptotic regime exists in which the transition displays first-order character. In this regime, surprisingly, the surface susceptibility and surface specific heat develop a divergence and show anomalous scaling with an exponent equal to 3/2.
Nonequilibrium variational cluster perturbation theory: Quench dynamics of the quantum Ising model
NASA Astrophysics Data System (ADS)
Asadzadeh, Mohammad Zhian; Fabrizio, Michele; Arrigoni, Enrico
2016-11-01
We introduce a variational implementation of cluster perturbation theory (CPT) to address the dynamics of spin systems driven out of equilibrium. We benchmark the method with the quantum Ising model subject to a sudden quench of the transverse magnetic field across the transition or within a phase. We treat both the one-dimensional case, for which an exact solution is available, as well the two-dimensional case, for which we have to resort to numerical results. Comparison with exact results shows that the approach provides a quite accurate description of the real-time dynamics up to a characteristic timescale τ that increases with the size of the cluster used for CPT. In addition, and not surprisingly, τ is small for quenches across the equilibrium phase transition point, but can be quite larger for quenches within the ordered or disordered phases.
Magnetic behavior of a mixed Ising 3/2 and 5/2 spin model.
De la Espriella, N; Buendía, G M
2011-05-04
We perform Monte Carlo simulations in order to study the magnetic properties of the mixed spin-S = ± 3/2, ± 1/2 and spin-σ = ± 5/2, ± 3/2, ± 1/2 Ising model. The spins are alternated on a square lattice such that S and σ are nearest neighbors. We found that when the Hamiltonian includes antiferromagnetic interactions between the S and σ spins, ferromagnetic interactions between the spins S, and a crystal field, the system presents compensation temperatures in a certain range of the parameters. The compensation temperatures are temperatures below the critical point where the total magnetization is zero, and they have important technological applications. We calculate the finite-temperature phase diagrams of the system. We found that the existence of compensation temperatures depends on the strength of the ferromagnetic interaction between the S spins.
Magnetic behavior of a mixed Ising 3/2 and 5/2 spin model
NASA Astrophysics Data System (ADS)
De La Espriella, N.; Buendía, G. M.
2011-05-01
We perform Monte Carlo simulations in order to study the magnetic properties of the mixed spin-S = ± 3/2, ± 1/2 and spin-σ = ± 5/2, ± 3/2, ± 1/2 Ising model. The spins are alternated on a square lattice such that S and σ are nearest neighbors. We found that when the Hamiltonian includes antiferromagnetic interactions between the S and σ spins, ferromagnetic interactions between the spins S, and a crystal field, the system presents compensation temperatures in a certain range of the parameters. The compensation temperatures are temperatures below the critical point where the total magnetization is zero, and they have important technological applications. We calculate the finite-temperature phase diagrams of the system. We found that the existence of compensation temperatures depends on the strength of the ferromagnetic interaction between the S spins.
Quantum phase transition of the transverse-field quantum Ising model on scale-free networks.
Yi, Hangmo
2015-01-01
I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent λ=6, I obtain results that are consistent with the mean-field theory. For λ=4.5 and 4, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. Further simulations indicate that the quantum critical point remains mean-field-like if λ>5, but it continuously deviates from the mean-field theory as λ becomes smaller.
First-order transition and tricritical behavior of the transverse crystal field spin-1 Ising model
NASA Astrophysics Data System (ADS)
Costabile, Emanuel; Viana, J. Roberto; de Sousa, J. Ricardo; de Arruda, Alberto S.
2015-06-01
The phase diagram of the spin-1 Ising model in the presence of a transverse crystal-field anisotropy (Dx) is studied within the framework of an effective-field theory with correlation. The effect of the coordination number (z) on the phase diagram in the T -Dx plane is investigated. We observe only second-order transitions for coordination number z < 7, while that for z ≥ 7 we have first- and second-order transitions, with the presence of two tricritical points. The lower tricritical temperature (Tt) decreases monotonically with the increasing value of z, and in the limit of z → ∞ we found Tt = 0, corresponding to the mean-field solution [Ricardo de Sousa and Branco, Phys. Rev. E 77 (2008) 012104] with a single tricritical point in the phase diagram.
Applicability of n-vicinity method for calculation of free energy of Ising model
NASA Astrophysics Data System (ADS)
Kryzhanovsky, Boris; Litinskii, Leonid
2017-02-01
Here we apply the n-vicinity method of approximate calculation of the partition function to an Ising Model with the nearest neighbor interaction on D-dimensional hypercube lattice. We solve the equation of state for an arbitrary dimension D and analyze the behavior of the free energy. As expected, for large dimensions (D ≥ 3) the system demonstrates a phase transition of the second kind. In this case, we obtain a simple analytical expression for the critical value of the inverse temperature. When 3 ≤ D ≤ 7 this expression is in a very good agreement with the results of computer simulations. In the case of small dimensions (D = 1 , 2), there is a noticeable discrepancy with the known exact results.
Apparent First-Order Wetting and Anomalous Scaling in the Two-Dimensional Ising Model
NASA Astrophysics Data System (ADS)
Wu, X.-T.; Abraham, D. B.; Indekeu, J. O.
2016-01-01
The global phase diagram of wetting in the two-dimensional Ising model is obtained through the exact calculation of the surface excess free energy. In addition to a surface field for inducing wetting, a surface-coupling enhancement is also included. The wetting transition (of second order) is critical for any finite ratio of surface coupling Js to bulk coupling J , and becomes of first order in the limit Js/J →∞ . However, for Js/J ≫1 , the critical region is exponentially small and is practically invisible to numerical studies. A distinct preasymptotic regime exists in which the transition displays first-order character. In this regime, surprisingly, the surface susceptibility and surface specific heat develop a divergence and show anomalous scaling with an exponent equal to 3 /2 .
Rhythmic behavior in a two-population mean-field Ising model
NASA Astrophysics Data System (ADS)
Collet, Francesca; Formentin, Marco; Tovazzi, Daniele
2016-10-01
Many real systems composed of a large number of interacting components, as, for instance, neural networks, may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean-field Ising model with the scope of investigating simple mechanisms capable to generate rhythms in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intrapopulation interactions of different strengths suffices for the emergence of a robust periodic behavior.
Exact enumeration of an Ising model for Ni2MnGa
NASA Astrophysics Data System (ADS)
Eisenbach, Markus; Brown, Gregory; Nicholson, Don M.
2014-03-01
Exact evaluations of partition functions are generally prohibitively expensive due to exponential growth of phase space with the degrees of freedom. An Ising model with N sites has 2N possible states, requiring the use of better scaling methods, such as importance sampling Monte-Carlo for all but the smallest systems. Yet the ability to obtain exact solutions for large systems can provide important benchmark results and opportunities for unobscured insight into the underlying physics of the system. Here we present an Ising model for the magnetic sublattices of the important magneto-caloric material Ni2MnGa and use an exact enumeration algorithm to calculate the number of states g(E ,M1 ,M2) for each energy E and sublattice magnetization M1 and M2. This allows the efficient calculation of the partition function and derived thermodynamic quantities such as specific heat and susceptibility. Utilizing resources at the Oak Ridge Leadership Facility we are able to calculate g(E ,M1 ,M2) for systems of up to 48 sites, which provides important insight into the mechanism for the large magnet-caloric effect in Mn2NiGa as well as an important benchmark for Monte-Carlo based calculations (esp. Wang-Landau) of g(E ,M1 ,M2) . Work sponsored by the Division of Materials Science and Engineering, Office of Basic Energy Science, U.S. DOE. The research used resources of the Oak Ridge Leadership Computing Facility, supported by the Office of Science of DOE (DE-AC05-00OR22725).
NASA Astrophysics Data System (ADS)
Sarakorn, Weerachai
2017-04-01
In this research, the finite element (FE) method incorporating quadrilateral elements for solving 2-D MT modeling was presented. The finite element software was developed, employing a paving algorithm to generate the unstructured quadrilateral mesh. The accuracy, efficiency, reliability, and flexibility of our FE forward modeling are presented, compared and discussed. The numerical results indicate that our FE codes using an unstructured quadrilateral mesh provide good accuracy when the local mesh refinement is applied around sites and in the area of interest, with superior results when compared to other FE methods. The reliability of the developed codes was also confirmed when comparing both analytical solutions and COMMEMI2D model. Furthermore, our developed FE codes incorporating an unstructured quadrilateral mesh showed useful and powerful features such as handling irregular and complex subregions and providing local refinement of the mesh for a 2-D domain as closely as unstructured triangular mesh but it requires less number of elements in a mesh.
On Limits of Embedding in 3D Images Based on 2D Watson's Model
NASA Astrophysics Data System (ADS)
Kavehvash, Zahra; Ghaemmaghami, Shahrokh
We extend the Watson image quality metric to 3D images through the concept of integral imaging. In the Watson's model, perceptual thresholds for changes to the DCT coefficients of a 2D image are given for information hiding. These thresholds are estimated in a way that the resulting distortion in the 2D image remains undetectable by the human eyes. In this paper, the same perceptual thresholds are estimated for a 3D scene in the integral imaging method. These thresholds are obtained based on the Watson's model using the relation between 2D elemental images and resulting 3D image. The proposed model is evaluated through subjective tests in a typical image steganography scheme.
Modeling Tear Film Dynamics on a 2-D Eye-shaped Domain
NASA Astrophysics Data System (ADS)
Li, Longfei; Braun, Richard; Maki, Kara; Henshaw, William
2012-11-01
We study tear film dynamics on a 2-D eye-shaped domain using a lubrication model. Time dependent flux boundary conditions that model the lacrimal gland tear supply and punctal drainage are imposed. We solved the model equations with Overture computational framework. Results reveals our model captures the hydraulic connectivity and other key physics of human tear film observed in vivo. Comparisons are made with existing models and experiments. Should time permit, osmolarity dynamics (salt ion concentration) will be included.
Integrated Navigation, Guidance, and Control of Missile Systems: 2-D Dynamic Models
2012-05-01
Plane Simulation Model Block Diagram .......................................................... 21 Figure A.1. Aerodynamic variables for a missile ...Figure A.1. Aerodynamic variables for a missile Page classification: UNCLASSIFIED DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION DOCUMENT...UNCLASSIFIED Integrated Navigation, Guidance, and Control of Missile Systems: 2-D Dynamic Models Farhan A. Faruqi Weapons
Evaluation of 2D shallow-water model for spillway flow with a complex geometry
Technology Transfer Automated Retrieval System (TEKTRAN)
Although the two-dimensional (2D) shallow water model is formulated based on several assumptions such as hydrostatic pressure distribution and vertical velocity is negligible, as a simple alternative to the complex 3D model, it has been used to compute water flows in which these assumptions may be ...
Disorder and interaction in 2D: exact diagonalization study of the Anderson-Hubbard-Mott model.
Kotlyar, R; Das Sarma, S
2001-03-12
We investigate, by numerically calculating the charge stiffness, the effects of random diagonal disorder and electron-electron interaction on the nature of the ground state in the 2D Hubbard model through the finite-size exact diagonalization technique. By comparing with the corresponding 1D Hubbard model results and by using heuristic arguments we conclude that it is unlikely that there is a 2D metal-insulator quantum phase transition, although the effect of interaction in some range of parameters is to substantially enhance the noninteracting charge stiffness.
Non-trivial θ-vacuum effects in the 2-d O(3) model
NASA Astrophysics Data System (ADS)
Bögli, M.; Niedermayer, F.; Pepe, M.; Wiese, U.-J.
2012-04-01
We study θ-vacua in the 2-d lattice O(3) model using the standard action and an optimized constraint action with very small cut-off effects, combined with the geometric topological charge. Remarkably, dislocation lattice artifacts do not spoil the non-trivial continuum limit at θ ne 0 , and there are different continuum theories for each value 0 ≤ θ ≤ π. A very precise Monte Carlo study of the step scaling function indirectly confirms the exact S-matrix of the 2-d O(3) model at θ = π.
Thermal entanglement of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain.
Ananikian, N S; Ananikyan, L N; Chakhmakhchyan, L A; Rojas, Onofre
2012-06-27
The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.
Towards more realistic 2D & 3D numerical models of Earth's mantle
NASA Astrophysics Data System (ADS)
Ghias, Sanaz
2011-12-01
There are a number of simplifying assumptions in modeling Earth's deep interior. These are mostly simplifying assumptions that make the mathematics simpler either for less complicated modeling or for numerical efficiency purposes. The aim of this study is to investigate the effects of some of these simplifying assumptions on 2D and 3D mantle convection models. In particular, the cases with variable coefficients of thermal expansion, alpha, and the inclusion of mineral phase transitions and viscosity stratification have been studied. The coefficient of thermal expansion is temperature- and depth-dependent in Earth. But for simplicity, it has been considered as constant in most mantle convection models and only depth-dependent in others. 2D mantle convection models (2D Cartesian and 2D cylindrical) have been created based on an existing model from Jarvis [1992] to investigate the effects of temperature- and depth-dependent alpha on mantle convection compared with the simplified cases. Also an existing version of a 3D parallel mantle convection model, MC3D, from Lowman et al. [2001] have been modified to include the temperature- and depth-dependent alpha. In the 3D study it has also been investigated that how the effects of temperature- and depth-dependent alpha vary with or without lithospheric plates. There are at least two mineral phase transitions in Earth. There is an exothermic phase boundary at 410km below the surface and an endothermic phase boundary at 660km below the surface. For simplicity, most mantle convection models do not consider any of the phase boundaries. Some consider only the endothermic phase boundary. A 2D cylindrical model from Shahnas and Jarvas [2005] has been employed to investigate the effects of considering both phase boundaries compared to models with either no, or one, phase boundary. Different viscosity stratifications have been used in addition to the phase boundaries.
Long-range Ising model for credit portfolios with heterogeneous credit exposures
NASA Astrophysics Data System (ADS)
Kato, Kensuke
2016-11-01
We propose the finite-size long-range Ising model as a model for heterogeneous credit portfolios held by a financial institution in the view of econophysics. The model expresses the heterogeneity of the default probability and the default correlation by dividing a credit portfolio into multiple sectors characterized by credit rating and industry. The model also expresses the heterogeneity of the credit exposure, which is difficult to evaluate analytically, by applying the replica exchange Monte Carlo method to numerically calculate the loss distribution. To analyze the characteristics of the loss distribution for credit portfolios with heterogeneous credit exposures, we apply this model to various credit portfolios and evaluate credit risk. As a result, we show that the tail of the loss distribution calculated by this model has characteristics that are different from the tail of the loss distribution of the standard models used in credit risk modeling. We also show that there is a possibility of different evaluations of credit risk according to the pattern of heterogeneity.
Is the full susceptibility of the square-lattice Ising model a differentially algebraic function?
NASA Astrophysics Data System (ADS)
Guttmann, A. J.; Jensen, I.; Maillard, J.-M.; Pantone, J.
2016-12-01
We study the class of non-holonomic power series with integer coefficients that reduce, modulo primes, or powers of primes, to algebraic functions. In particular we try to determine whether the susceptibility of the square-lattice Ising model belongs to this class, and more broadly whether the susceptibility is a solution of a differentially algebraic equation. Initial results on Tutte's nonlinear ordinary differential equation (ODE) and other simple quadratic nonlinear ODEs suggest that a large set of differentially algebraic power series solutions with integer coefficients might reduce to algebraic functions modulo primes, or powers of primes. Since diagonals of rational functions are well-known to reduce, modulo primes, or powers of primes, to algebraic functions, a large subset of differentially algebraic power series with integer coefficients may be viewed as a natural ‘nonlinear’ generalisation of diagonals of rational functions. Here we give several examples of series with integer coefficients and non-zero radius of convergence that reduce to algebraic functions modulo (almost) every prime (or power of a prime). These examples satisfy differentially algebraic equations with the encoding polynomial occasionally possessing quite high degree (and thus difficult to identify even with long series). These examples shed important light on the very nature of such differentially algebraic series. Additionally, we have extended both the high- and low-temperature Ising square-lattice susceptibility series to 5043 coefficients. We find that even this long series is insufficient to determine whether it reduces to algebraic functions modulo 3, 5, etc. This negative result is in contrast to the comparatively easy confirmation that the corresponding series reduce to algebraic functions modulo powers of 2. Finally we show that even with 5043 terms we are unable to identify an underlying differentially algebraic equation for the susceptibility, ruling out a number of
NASA Astrophysics Data System (ADS)
Hamerly, Ryan; Inaba, Kensuke; Inagaki, Takahiro; Takesue, Hiroki; Yamamoto, Yoshihisa; Mabuchi, Hideo
2016-09-01
A network of optical parametric oscillators (OPOs) is used to simulate classical Ising and XY spin chains. The collective nonlinear dynamics of this network, driven by quantum noise rather than thermal fluctuations, seeks out the Ising/XY ground state as the system transitions from below to above the lasing threshold. We study the behavior of this “Ising machine” for three canonical problems: a 1D ferromagnetic spin chain, a 2D square lattice and problems where next-nearest-neighbor couplings give rise to frustration. If the pump turn-on time is finite, topological defects form (domain walls for the Ising model, winding number and vortices for XY) and their density can be predicted from a numerical model involving a linear “growth stage” and a nonlinear “saturation stage”. These predictions are compared against recent data for a 10,000-spin 1D Ising machine.
The simulation of 3D mass models in 2D digital mammography and breast tomosynthesis
Shaheen, Eman De Keyzer, Frederik; Bosmans, Hilde; Ongeval, Chantal Van; Dance, David R.; Young, Kenneth C.
2014-08-15
Purpose: This work proposes a new method of building 3D breast mass models with different morphological shapes and describes the validation of the realism of their appearance after simulation into 2D digital mammograms and breast tomosynthesis images. Methods: Twenty-five contrast enhanced MRI breast lesions were collected and each mass was manually segmented in the three orthogonal views: sagittal, coronal, and transversal. The segmented models were combined, resampled to have isotropic voxel sizes, triangularly meshed, and scaled to different sizes. These masses were referred to as nonspiculated masses and were then used as nuclei onto which spicules were grown with an iterative branching algorithm forming a total of 30 spiculated masses. These 55 mass models were projected into 2D projection images to obtain mammograms after image processing and into tomographic sequences of projection images, which were then reconstructed to form 3D tomosynthesis datasets. The realism of the appearance of these mass models was assessed by five radiologists via receiver operating characteristic (ROC) analysis when compared to 54 real masses. All lesions were also given a breast imaging reporting and data system (BIRADS) score. The data sets of 2D mammography and tomosynthesis were read separately. The Kendall's coefficient of concordance was used for the interrater observer agreement assessment for the BIRADS scores per modality. Further paired analysis, using the Wilcoxon signed rank test, of the BIRADS assessment between 2D and tomosynthesis was separately performed for the real masses and for the simulated masses. Results: The area under the ROC curves, averaged over all observers, was 0.54 (95% confidence interval [0.50, 0.66]) for the 2D study, and 0.67 (95% confidence interval [0.55, 0.79]) for the tomosynthesis study. According to the BIRADS scores, the nonspiculated and the spiculated masses varied in their degrees of malignancy from normal (BIRADS 1) to highly
Ising model of cardiac thin filament activation with nearest-neighbor cooperative interactions
NASA Technical Reports Server (NTRS)
Rice, John Jeremy; Stolovitzky, Gustavo; Tu, Yuhai; de Tombe, Pieter P.; Bers, D. M. (Principal Investigator)
2003-01-01
We have developed a model of cardiac thin filament activation using an Ising model approach from equilibrium statistical physics. This model explicitly represents nearest-neighbor interactions between 26 troponin/tropomyosin units along a one-dimensional array that represents the cardiac thin filament. With transition rates chosen to match experimental data, the results show that the resulting force-pCa (F-pCa) relations are similar to Hill functions with asymmetries, as seen in experimental data. Specifically, Hill plots showing (log(F/(1-F)) vs. log [Ca]) reveal a steeper slope below the half activation point (Ca(50)) compared with above. Parameter variation studies show interplay of parameters that affect the apparent cooperativity and asymmetry in the F-pCa relations. The model also predicts that Ca binding is uncooperative for low [Ca], becomes steeper near Ca(50), and becomes uncooperative again at higher [Ca]. The steepness near Ca(50) mirrors the steep F-pCa as a result of thermodynamic considerations. The model also predicts that the correlation between troponin/tropomyosin units along the one-dimensional array quickly decays at high and low [Ca], but near Ca(50), high correlation occurs across the whole array. This work provides a simple model that can account for the steepness and shape of F-pCa relations that other models fail to reproduce.
Linking market interaction intensity of 3D Ising type financial model with market volatility
NASA Astrophysics Data System (ADS)
Fang, Wen; Ke, Jinchuan; Wang, Jun; Feng, Ling
2016-11-01
Microscopic interaction models in physics have been used to investigate the complex phenomena of economic systems. The simple interactions involved can lead to complex behaviors and help the understanding of mechanisms in the financial market at a systemic level. This article aims to develop a financial time series model through 3D (three-dimensional) Ising dynamic system which is widely used as an interacting spins model to explain the ferromagnetism in physics. Through Monte Carlo simulations of the financial model and numerical analysis for both the simulation return time series and historical return data of Hushen 300 (HS300) index in Chinese stock market, we show that despite its simplicity, this model displays stylized facts similar to that seen in real financial market. We demonstrate a possible underlying link between volatility fluctuations of real stock market and the change in interaction strengths of market participants in the financial model. In particular, our stochastic interaction strength in our model demonstrates that the real market may be consistently operating near the critical point of the system.
Highlighting the structure-function relationship of the brain with the Ising model and graph theory.
Das, T K; Abeyasinghe, P M; Crone, J S; Sosnowski, A; Laureys, S; Owen, A M; Soddu, A
2014-01-01
With the advent of neuroimaging techniques, it becomes feasible to explore the structure-function relationships in the brain. When the brain is not involved in any cognitive task or stimulated by any external output, it preserves important activities which follow well-defined spatial distribution patterns. Understanding the self-organization of the brain from its anatomical structure, it has been recently suggested to model the observed functional pattern from the structure of white matter fiber bundles. Different models which study synchronization (e.g., the Kuramoto model) or global dynamics (e.g., the Ising model) have shown success in capturing fundamental properties of the brain. In particular, these models can explain the competition between modularity and specialization and the need for integration in the brain. Graphing the functional and structural brain organization supports the model and can also highlight the strategy used to process and organize large amount of information traveling between the different modules. How the flow of information can be prevented or partially destroyed in pathological states, like in severe brain injured patients with disorders of consciousness or by pharmacological induction like in anaesthesia, will also help us to better understand how global or integrated behavior can emerge from local and modular interactions.
Ising Critical Behavior of Inhomogeneous Curie-Weiss Models and Annealed Random Graphs
NASA Astrophysics Data System (ADS)
Dommers, Sander; Giardinà, Cristian; Giberti, Claudio; van der Hofstad, Remco; Prioriello, Maria Luisa
2016-11-01
We study the critical behavior for inhomogeneous versions of the Curie-Weiss model, where the coupling constant {J_{ij}(β)} for the edge {ij} on the complete graph is given by {J_{ij}(β)=β w_iw_j/( {sum_{kin[N]}w_k})}. We call the product form of these couplings the rank-1 inhomogeneous Curie-Weiss model. This model also arises [with inverse temperature {β} replaced by {sinh(β)} ] from the annealed Ising model on the generalized random graph. We assume that the vertex weights {(w_i)_{iin[N]}} are regular, in the sense that their empirical distribution converges and the second moment converges as well. We identify the critical temperatures and exponents for these models, as well as a non-classical limit theorem for the total spin at the critical point. These depend sensitively on the number of finite moments of the weight distribution. When the fourth moment of the weight distribution converges, then the critical behavior is the same as on the (homogeneous) Curie-Weiss model, so that the inhomogeneity is weak. When the fourth moment of the weights converges to infinity, and the weights satisfy an asymptotic power law with exponent {τ} with {τin(3,5)}, then the critical exponents depend sensitively on {τ}. In addition, at criticality, the total spin {S_N} satisfies that {S_N/N^{(τ-2)/(τ-1)}} converges in law to some limiting random variable whose distribution we explicitly characterize.
NASA Astrophysics Data System (ADS)
Thomaz, M. T.; Corrêa Silva, E. V.
2016-03-01
We derive the exact Helmholtz free energy (HFE) of the standard and staggered one-dimensional Blume-Emery-Griffiths (BEG) model in the presence of an external longitudinal magnetic field. We discuss in detail the thermodynamic behavior of the ferromagnetic version of the model, which exhibits magnetic field-dependent plateaux in the z-component of its magnetization at low temperatures. We also study the behavior of its specific heat and entropy, both per site, at finite temperature. The degeneracy of the ground state, at T=0, along the lines that separate distinct phases in the phase diagram of the ferromagnetic BEG model is calculated, extending the study of the phase diagram of the spin-1 antiferromagnetic (AF) Ising model in S.M. de Souza and M.T. Thomaz, J. Magn. and Magn. Mater. 354 (2014) 205 [5]. We explore the implications of the equality of phase diagrams, at T=0, of the ferromagnetic BEG model with K/|J| = - 2 and of the spin-1 AF Ising model for D/|J| > 1/2.
2D-Raman-THz spectroscopy: A sensitive test of polarizable water models
NASA Astrophysics Data System (ADS)
Hamm, Peter
2014-11-01
In a recent paper, the experimental 2D-Raman-THz response of liquid water at ambient conditions has been presented [J. Savolainen, S. Ahmed, and P. Hamm, Proc. Natl. Acad. Sci. U. S. A. 110, 20402 (2013)]. Here, all-atom molecular dynamics simulations are performed with the goal to reproduce the experimental results. To that end, the molecular response functions are calculated in a first step, and are then convoluted with the laser pulses in order to enable a direct comparison with the experimental results. The molecular dynamics simulation are performed with several different water models: TIP4P/2005, SWM4-NDP, and TL4P. As polarizability is essential to describe the 2D-Raman-THz response, the TIP4P/2005 water molecules are amended with either an isotropic or a anisotropic polarizability a posteriori after the molecular dynamics simulation. In contrast, SWM4-NDP and TL4P are intrinsically polarizable, and hence the 2D-Raman-THz response can be calculated in a self-consistent way, using the same force field as during the molecular dynamics simulation. It is found that the 2D-Raman-THz response depends extremely sensitively on details of the water model, and in particular on details of the description of polarizability. Despite the limited time resolution of the experiment, it could easily distinguish between various water models. Albeit not perfect, the overall best agreement with the experimental data is obtained for the TL4P water model.
ERIC Educational Resources Information Center
Park, Elisa L.
2009-01-01
The purpose of this study is to understand the dynamics of Korean students' international mobility to study abroad by using the 2-D Model. The first D, "the driving force factor," explains how and what components of the dissatisfaction with domestic higher education perceived by Korean students drives students' outward mobility to seek…
2D-Raman-THz spectroscopy: A sensitive test of polarizable water models
Hamm, Peter
2014-11-14
In a recent paper, the experimental 2D-Raman-THz response of liquid water at ambient conditions has been presented [J. Savolainen, S. Ahmed, and P. Hamm, Proc. Natl. Acad. Sci. U. S. A. 110, 20402 (2013)]. Here, all-atom molecular dynamics simulations are performed with the goal to reproduce the experimental results. To that end, the molecular response functions are calculated in a first step, and are then convoluted with the laser pulses in order to enable a direct comparison with the experimental results. The molecular dynamics simulation are performed with several different water models: TIP4P/2005, SWM4-NDP, and TL4P. As polarizability is essential to describe the 2D-Raman-THz response, the TIP4P/2005 water molecules are amended with either an isotropic or a anisotropic polarizability a posteriori after the molecular dynamics simulation. In contrast, SWM4-NDP and TL4P are intrinsically polarizable, and hence the 2D-Raman-THz response can be calculated in a self-consistent way, using the same force field as during the molecular dynamics simulation. It is found that the 2D-Raman-THz response depends extremely sensitively on details of the water model, and in particular on details of the description of polarizability. Despite the limited time resolution of the experiment, it could easily distinguish between various water models. Albeit not perfect, the overall best agreement with the experimental data is obtained for the TL4P water model.
New technologies of 2-D and 3-D modeling for analysis and management of natural resources
NASA Astrophysics Data System (ADS)
Cheremisina, E. N.; Lyubimova, A. V.; Kirpicheva, E. Yu.
2016-09-01
For ensuring technological support of research and administrative activity in the sphere of environmental management a specialized modular program complex was developed. The special attention in developing a program complex is focused to creation of convenient and effective tools for creation and visualization 2d and 3D models providing the solution of tasks of the analysis and management of natural resources.
Breach modelling by overflow with TELEMAC 2D: Comparison with large-scale experiments
Technology Transfer Automated Retrieval System (TEKTRAN)
An erosion law has been implemented in TELEMAC 2D to represent the surface erosion process to model the breach formation of a levee. We focus on homogeneous and earth fill levee to simplify this first implementation. The first part of this study reveals the ability of this method to represent simu...
Parallelized CCHE2D flow model with CUDA Fortran on Graphics Process Units
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper presents the CCHE2D implicit flow model parallelized using CUDA Fortran programming technique on Graphics Processing Units (GPUs). A parallelized implicit Alternating Direction Implicit (ADI) solver using Parallel Cyclic Reduction (PCR) algorithm on GPU is developed and tested. This solve...
Ground states of the Ising model on an anisotropic triangular lattice: stripes and zigzags.
Dublenych, Yu I
2013-10-09
A complete solution of the ground-state problem for the Ising model on an anisotropic triangular lattice with the nearest-neighbor interactions in a magnetic field is presented. It is shown that this problem can be reduced to the ground-state problem for an infinite chain with the interactions up to the second neighbors. In addition to the known ground-state structures (which correspond to full-dimensional regions in the parameter space of the model), new structures are found (at the boundaries of these regions), in particular, zigzagging stripes similar to those observed experimentally in colloidal monolayers. Though the number of parameters is relatively large (four), all the ground-state structures of the model are constructed and analyzed and therefore the paper can be considered as an example of a complete solution of a ground-state problem for classical spin or lattice-gas models. The paper can also help to verify the correctness of some results obtained previously by other authors and concerning the ground states of the model under consideration.
A novel explicit 2D+t cyclic shape model applied to echocardiography.
Casero, Ramón; Noble, J Alison
2008-01-01
In this paper, we propose a novel explicit 2D+t cyclic shape model that extends the Point Distribution Model (PDM) to shapes like myocardial contours with cyclic dynamics. We also propose an extension to Procrustes alignment that removes pose and subject size variability while maintaining dynamic effects. Our model draws on ideas from Principal Component Analysis (PCA), Multidimensional Scaling (MDS) and Kernel PCA (KPCA) and solves 3 shortcomings of previous implicit models: (1) cardiac cycles in the data set do not each need to have the same number of frames, (2) the required number of subjects for statistically significant results is substantially reduced and (3) the displacement of contour points incorporates time as an explicit variable. We illustrate our method by computing models of the myocardium in the 4 principal planes of 2D+t echocardiography data.
Molecular Dynamics implementation of BN2D or 'Mercedes Benz' water model
NASA Astrophysics Data System (ADS)
Scukins, Arturs; Bardik, Vitaliy; Pavlov, Evgen; Nerukh, Dmitry
2015-05-01
Two-dimensional 'Mercedes Benz' (MB) or BN2D water model (Naim, 1971) is implemented in Molecular Dynamics. It is known that the MB model can capture abnormal properties of real water (high heat capacity, minima of pressure and isothermal compressibility, negative thermal expansion coefficient) (Silverstein et al., 1998). In this work formulas for calculating the thermodynamic, structural and dynamic properties in microcanonical (NVE) and isothermal-isobaric (NPT) ensembles for the model from Molecular Dynamics simulation are derived and verified against known Monte Carlo results. The convergence of the thermodynamic properties and the system's numerical stability are investigated. The results qualitatively reproduce the peculiarities of real water making the model a visually convenient tool that also requires less computational resources, thus allowing simulations of large (hydrodynamic scale) molecular systems. We provide the open source code written in C/C++ for the BN2D water model implementation using Molecular Dynamics.
NASA Astrophysics Data System (ADS)
Huang, Ran; Zhang, Ling; Chen, Chong; Wu, Chengjie; Yan, Linyin
2015-07-01
The ferromagnetic Ising spins are modeled on a recursive lattice constructed from random-angled rhombus units with stochastic configurations, to study the magnetic properties of the bulk Fe-based metallic glass. The integration of spins on the structural glass model well represents the magnetic moments in the glassy metal. The model is exactly solved by the recursive calculation technique. The magnetization of the amorphous Ising spins, i.e. the glassy metallic magnet is investigated by our modeling and calculation on a theoretical base. The results show that the glassy metallic magnets have a lower Curie temperature, weaker magnetization, and higher entropy compared to the regular ferromagnet in crystal form. These findings can be understood with the randomness of the amorphous system, and agree well with other experimental observations.
MODELING THE TRANSVERSE THERMAL CONDUCTIVITY OF 2-D SICF/SIC COMPOSITES MADE WITH WOVEN FABRIC
Youngblood, Gerald E; Senor, David J; Jones, Russell H
2004-06-01
The hierarchical two-layer (H2L) model describes the effective transverse thermal conductivity (Keff) of a 2D-SiCf/SiC composite plate made from stacked and infiltrated woven fabric layers in terms of constituent properties and microstructural and architectural variables. The H2L model includes the effects of fiber-matrix interfacial conductance, high fiber packing fractions within individual tows and the non-uniform nature of 2D fabric/matrix layers that usually include a significant amount of interlayer porosity. Previously, H2L model Keff-predictions were compared to measured values for two versions of 2D Hi-Nicalon/PyC/ICVI-SiC composite, one with a “thin” (0.11m) and the other with a “thick” (1.04m) pyrocarbon (PyC) fiber coating, and for a 2D Tyranno SA/”thin” PyC/FCVI-SIC composite. In this study, H2L model Keff-predictions were compared to measured values for a 2D-SiCf/SiC composite made using the ICVI-process with Hi-Nicalon type S fabric and a “thin” PyC fiber coating. The values of Keff determined for the latter composite were significantly greater than the Keff-values determined for the composites made with either the Hi-Nicalon or the Tyranno SA fabrics. Differences in Keff-values were expected for the different fiber types, but major differences also were due to observed microstructural and architectural variations between the composite systems, and as predicted by the H2L model.
A Deformed Shape Monitoring Model for Building Structures Based on a 2D Laser Scanner
Choi, Se Woon; Kim, Bub Ryur; Lee, Hong Min; Kim, Yousok; Park, Hyo Seon
2013-01-01
High-rise buildings subjected to lateral loads such as wind and earthquake loads must be checked not to exceed the limits on the maximum lateral displacement or the maximum inter-story drift ratios. In this paper, a sensing model for deformed shapes of a building structure in motion is presented. The deformed shape sensing model based on a 2D scanner consists of five modules: (1) module for acquiring coordinate information of a point in a building; (2) module for coordinate transformation and data arrangement for generation of time history of the point; (3) module for smoothing by adjacent averaging technique; (4) module for generation of the displacement history for each story and deformed shape of a building, and (5) module for evaluation of the serviceability of a building. The feasibility of the sensing model based on a 2D laser scanner is tested through free vibration tests of a three-story steel frame structure with a relatively high slenderness ratio of 5.0. Free vibration responses measured from both laser displacement sensors and a 2D laser scanner are compared. In the experimentation, the deformed shapes were obtained from three different methods: the model based on the 2D laser scanner, the direct measurement based on laser displacement sensors, and the numerical method using acceleration data and the displacements from GPS. As a result, it is confirmed that the deformed shape measurement model based on a 2D laser scanner can be a promising alternative for high-rise buildings where installation of laser displacement sensors is impossible. PMID:23698269
A new force-extension formula for stretched macromolecules and polymers based on the Ising model
NASA Astrophysics Data System (ADS)
Chan, Yue; Haverkamp, Richard G.
2016-12-01
In this paper, we derive a new force-extension formula for stretched macromolecules and homogeneous polymer matrices. The Ising model arising from paramagnetism is employed, where the magnetic force is replaced by the external force, and the resistance energy is addressed in this model instead of the usual persistent length arising from the freely jointed chain and worm-like chain models. While the force-extension formula reveals the distinctive stretching features for stretched polymers, the resistance energy is found to increase almost linearly with the external force for our two polysaccharides stretching examples with and without ring conformational changes. In particular, a jump in the resistance energy which is caused by a conformational transition is investigated, and the gap between the jump determines the energy barrier between two conformational configurations. Our theoretical model matches well with experimental results undergoing no and single conformational transitions, and a Monte Carlo simulation has also been performed to ensure the correctness of the resistance energy. This technique might also be employed to determine the binding energy from other causes during molecular stretching and provide vital information for further theoretical investigations.
Critical behavior of entropy production and learning rate: Ising model with an oscillating field
NASA Astrophysics Data System (ADS)
Zhang, Yirui; Barato, Andre C.
2016-11-01
We study the critical behavior of the entropy production of the Ising model subject to a magnetic field that oscillates in time. The mean-field model displays a phase transition that can be either first or second-order, depending on the amplitude of the field and on the frequency of oscillation. Within this approximation the entropy production rate is shown to have a discontinuity when the transition is first-order and to be continuous, with a jump in its first derivative, if the transition is second-order. In two dimensions, we find with numerical simulations that the critical behavior of the entropy production rate is the same, independent of the frequency and amplitude of the field. Its first derivative has a logarithmic divergence at the critical point. This result is in agreement with the lack of a first-order phase transition in two dimensions. We analyze a model with a field that changes at stochastic time-intervals between two values. This model allows for an informational theoretic interpretation, with the system as a sensor that follows the external field. We calculate numerically a lower bound on the learning rate, which quantifies how much information the system obtains about the field. Its first derivative with respect to temperature is found to have a jump at the critical point.
Relations between short-range and long-range Ising models.
Angelini, Maria Chiara; Parisi, Giorgio; Ricci-Tersenghi, Federico
2014-06-01
We perform a numerical study of the long-range (LR) ferromagnetic Ising model with power law decaying interactions (J∝r{-d-σ}) on both a one-dimensional chain (d=1) and a square lattice (d=2). We use advanced cluster algorithms to avoid the critical slowing down. We first check the validity of the relation connecting the critical behavior of the LR model with parameters (d,σ) to that of a short-range (SR) model in an equivalent dimension D. We then study the critical behavior of the d=2 LR model close to the lower critical σ, uncovering that the spatial correlation function decays with two different power laws: The effect of the subdominant power law is much stronger than finite-size effects and actually makes the estimate of critical exponents very subtle. By including this subdominant power law, the numerical data are consistent with the standard renormalization group (RG) prediction by Sak [Phys. Rev. B 8, 281 (1973)], thus making not necessary (and unlikely, according to Occam's razor) the recent proposal by Picco [arXiv:1207.1018] of having a new set of RG fixed points in addition to the mean-field one and the SR one.
Ising Models, Universality and the Non Renormalization of the Quantum Anomalies
NASA Astrophysics Data System (ADS)
Mastropietro, Vieri
2010-03-01
A number of universal relations (proposed by Kadanoff, Luther, Peschel and Haldane) are believed to be true in a wide class of systems with continuously varying indices, among which are interacting planar Ising models, vertex or Ashkin-Teller models, quantum spin chains and 1D Fermi systems; by such relations one can predict several quantities in terms of a few measurable parameters without relying on the specific microscopic details. The validity of such relations can be checked in special solvable models but, despite several attempts, the proof of their general validity was up to now an open problem. A rigorous derivation of several of such relations (for solvable and not solvable models and without any use of exact solutions) has been recently obtained in [8] and [11] through Renormalization Group methods. The proof is based on the representation in terms of Grassmann integrals and the validity of the Adler-Bardeen property of the non renormalization of the quantum anomalies in the asymptotic Ward identities. Gauge invariance is exact only in the scaling limit but the lattice corrections can be rigorously taken into account.
Numerical Simulation of Slinger Combustor Using 2-D Axisymmetric Computational Model
NASA Astrophysics Data System (ADS)
Lee, Semin; Park, Soo Hyung; Lee, Donghun
2010-06-01
Small-size turbojet engines have difficulties in maintaining the chemical reaction due to the limitation of chamber size. The combustion chamber is generally designed to improve the reaction efficiency by the generation of vortices in the chamber and to enhance air-fuel mixing characteristics. In the initial stage of designing the combustor, analysis of the 3-D full configuration is not practical due to the huge time consuming computation and grid generation followed by modifications of the geometry. In the present paper, an axisymmetric model maintaining geometric similarity and flow characteristic of 3-D configuration is developed. Based on numerical results from the full 3-D configuration, model reduction is achieved toward 2-D axisymmetric configuration. In the modeling process, the area and location of each hole in 3-D full configuration are considered reasonably and replaced to the 2-D axisymmetric model. By using the 2-D axisymmetric model, the factor that can affect the performance is investigated with the assumption that the flow is non-reacting and turbulent. Numerical results from the present model show a good agreement with numerical results from 3-D full configuration model such as existence of vortex pair in forward region and total pressure loss. By simplifying the complex 3-D model, computing time can be remarkably reduced and it makes easy to find effects of geometry modification.
Simplified 2D Bidomain Model of Whole Heart Electrical Activity and ECG Generation
NASA Astrophysics Data System (ADS)
Sovilj, Siniša; Magjarević, Ratko; Abed, Amr Al; Lovell, Nigel H.; Dokos, Socrates
2014-06-01
The aim of this study was the development of a geometrically simple and highly computationally-efficient two dimensional (2D) biophysical model of whole heart electrical activity, incorporating spontaneous activation of the sinoatrial node (SAN), the specialized conduction system, and realistic surface ECG morphology computed on the torso. The FitzHugh-Nagumo (FHN) equations were incorporated into a bidomain finite element model of cardiac electrical activity, which was comprised of a simplified geometry of the whole heart with the blood cavities, the lungs and the torso as an extracellular volume conductor. To model the ECG, we placed four electrodes on the surface of the torso to simulate three Einthoven leads VI, VII and VIII from the standard 12-lead system. The 2D model was able to reconstruct ECG morphology on the torso from action potentials generated at various regions of the heart, including the sinoatrial node, atria, atrioventricular node, His bundle, bundle branches, Purkinje fibers, and ventricles. Our 2D cardiac model offers a good compromise between computational load and model complexity, and can be used as a first step towards three dimensional (3D) ECG models with more complex, precise and accurate geometry of anatomical structures, to investigate the effect of various cardiac electrophysiological parameters on ECG morphology.
Pair correlations and structure factor of the J1-J2 square lattice Ising model in an external field
NASA Astrophysics Data System (ADS)
Guerrero, Alejandra I.; Stariolo, Daniel A.
2017-01-01
We compute the structure factor of the J1-J2 Ising model in an external field on the square lattice within the Cluster Variation Method. We use a four point plaquette approximation, which is the minimal one able to capture phases with broken orientational order in real space, like the recently reported Ising-nematic phase in the model. The analysis of different local maxima in the structure factor allows us to track the different phases and phase transitions against temperature and external field. Although the nematic susceptibility is not directly related to the structure factor, we show that because of the close relationship between the nematic order parameter and the structure factor, the latter shows unambiguous signatures of the presence of a nematic phase, in agreement with results from direct minimization of a variational free energy. The disorder variety of the model is identified and the possibility that the CVM four point approximation be exact on the disorder variety is discussed.
NASA Astrophysics Data System (ADS)
Pinto, Oscar A.; Romá, Federico; Bustingorry, Sebastian
2014-12-01
We study the critical behavior and the out-of-equilibrium dynamics of a two-dimensional Ising model with non-static interactions. In our model, bonds are dynamically changing according to a majority rule depending on the set of closest neighbors of each spin pair, which prevents the system from ordering in a full ferromagnetic or antiferromagnetic state. Using a parallel-tempering Monte Carlo algorithm, we find that the model undergoes a continuous phase transition at finite temperature, which belongs to the Ising universality class. The properties of the bond structure and the ground-state entropy are also studied. Finally, we analyze the out-of-equilibrium dynamics which displays typical glassy characteristics at a temperature well below the critical one.
Ising-like agent-based technology diffusion model: Adoption patterns vs. seeding strategies
NASA Astrophysics Data System (ADS)
Laciana, Carlos E.; Rovere, Santiago L.
2011-03-01
The well-known Ising model used in statistical physics was adapted to a social dynamics context to simulate the adoption of a technological innovation. The model explicitly combines (a) an individual's perception of the advantages of an innovation and (b) social influence from members of the decision-maker's social network. The micro-level adoption dynamics are embedded into an agent-based model that allows exploration of macro-level patterns of technology diffusion throughout systems with different configurations (number and distributions of early adopters, social network topologies). In the present work we carry out many numerical simulations. We find that when the gap between the individual's perception of the options is high, the adoption speed increases if the dispersion of early adopters grows. Another test was based on changing the network topology by means of stochastic connections to a common opinion reference (hub), which resulted in an increment in the adoption speed. Finally, we performed a simulation of competition between options for both regular and small world networks.
Information transfer and criticality in the Ising model on the human connectome.
Marinazzo, Daniele; Pellicoro, Mario; Wu, Guorong; Angelini, Leonardo; Cortés, Jesús M; Stramaglia, Sebastiano
2014-01-01
We implement the Ising model on a structural connectivity matrix describing the brain at two different resolutions. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information transfer between the spin variables. At this point the amount of information that can be redistributed by some nodes reaches a limit and the net dynamics exhibits signature of the law of diminishing marginal returns, a fundamental principle connected to saturated levels of production. Our results extend the recent analysis of dynamical oscillators models on the connectome structure, taking into account lagged and directional influences, focusing only on the nodes that are more prone to became bottlenecks of information. The ratio between the outgoing and the incoming information at each node is related to the the sum of the weights to that node and to the average time between consecutive time flips of spins. The results for the connectome of 66 nodes and for that of 998 nodes are similar, thus suggesting that these properties are scale-independent. Finally, we also find that the brain dynamics at criticality is organized maximally to a rich-club w.r.t. the network of information flows.
Nonbacktracking operator for the Ising model and its applications in systems with multiple states.
Zhang, Pan
2015-04-01
The nonbacktracking operator for a graph is the adjacency matrix defined on directed edges of the graph. The operator was recently shown to perform optimally in spectral clustering in sparse synthetic graphs and have a deep connection to belief propagation algorithm. In this paper we consider nonbacktracking operator for Ising model on a general graph with a general coupling distribution and study the spectrum of this operator analytically. We show that spectral algorithms based on this operator is equivalent to belief propagation algorithm linearized at the paramagnetic fixed point and recovers replica-symmetry results on phase boundaries obtained by replica methods. This operator can be applied directly to systems with multiple states like Hopfield model. We show that spectrum of the operator can be used to determine number of patterns that stored successfully in the network, and the associated eigenvectors can be used to retrieve all the patterns simultaneously. We also give an example on how to control the Hopfield model, i.e., making network more sparse while keeping patterns stable, using the nonbacktracking operator and matrix perturbation theory.
Break of universality for an Ising model with aperiodic Rudin-Shapiro interactions
NASA Astrophysics Data System (ADS)
Andrade, R. F. S.; Pinho, S. T. R.
2003-08-01
We analyze the ferromagnetic Ising model on non-Euclidean scale invariant lattices with aperiodic interactions ( J A , J B , J C , J D ) defined by Rudin-Shapiro substitution rules with Migdal-Kadanoff renormalization (MKR) and transfer matrix (TM) techniques. The analysis of the invariant sets of the zero-field MKR transformation indicates that the critical behavior, completely distinct from the one of the uniform model, is described by a new off-diagonal fixed point. This contrasts with other aperiodic models where the new critical behavior is described by a period-two cycle. With the new fixed point, values for the thermal critical exponents, α and ν, as well as the period of log-periodic oscillations, are obtained. Exact recursive maps for all thermodynamical functions are derived within the TM approach. The explicit dependence of the thermodynamical functions with respect to temperature is evaluated by the numerical iteration of the set of maps until a previously chosen convergence is achieved. They also indicate that, depending on the actual choice for the aperiodic coupling constants, the magnetic exponents (β and γ) assume different values. However the Rushbrook relation is always satisfied.
Coupled BOUSS-2D and CMS-Wave Modeling Approach for Harbor Projects
2012-08-01
channels, erosion problems at coastal inlets, and aid in design and Report Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for...Harbor Projects by Lihwa Lin and Zeki Demirbilek PURPOSE: This Coastal and Hydraulics Engineering Technical Note (CHETN) describes the coupled...application of two advanced coastal wave models, BOUSS-2D and CMS-Wave, for harbor applications. The two models have different computational features and
In vitro systems to study nephropharmacology: 2D versus 3D models.
Sánchez-Romero, Natalia; Schophuizen, Carolien M S; Giménez, Ignacio; Masereeuw, Rosalinde
2016-11-05
The conventional 2-dimensional (2D) cell culture is an invaluable tool in, amongst others, cell biology and experimental pharmacology. However, cells cultured in 2D, on the top of stiff plastic plates lose their phenotypical characteristics and fail in recreating the physiological environment found in vivo. This is a fundamental requirement when the goal of the study is to get a rigorous predictive response of human drug action and safety. Recent approaches in the field of renal cell biology are focused on the generation of 3D cell culture models due to the more bona fide features that they exhibit and the fact that they are more closely related to the observed physiological conditions, and better predict in vivo drug handling. In this review, we describe the currently available 3D in vitro models of the kidney, and some future directions for studying renal drug handling, disease modeling and kidney regeneration.
Inverse freezing in a cluster Ising spin-glass model with antiferromagnetic interactions.
Silva, C F; Zimmer, F M; Magalhaes, S G; Lacroix, C
2012-11-01
Inverse freezing is analyzed in a cluster spin-glass (SG) model that considers infinite-range disordered interactions between magnetic moments of different clusters (intercluster interaction) and short-range antiferromagnetic coupling J(1) between Ising spins of the same cluster (intracluster interaction). The intercluster disorder J is treated within a mean-field theory by using a framework of one-step replica symmetry breaking. The effective model obtained by this treatment is computed by means of an exact diagonalization method. With the results we build phase diagrams of temperature T/J versus J(1)/J for several sizes of clusters n(s) (number of spins in the cluster). The phase diagrams show a second-order transition from the paramagnetic phase to the SG order at the freezing temperature T(f) when J(1)/J is small. The increase in J(1)/J can then destroy the SG phase. It decreases T(f)/J and introduces a first-order transition. In addition, inverse freezing can arise at a certain range of J(1)/J and large enough n(s). Therefore, the nontrivial frustration generated by disorder and short-range antiferromagnetic coupling can introduce inverse freezing spontaneously.
Bayesian Feature Selection with Strongly Regularizing Priors Maps to the Ising Model.
Fisher, Charles K; Mehta, Pankaj
2015-11-01
Identifying small subsets of features that are relevant for prediction and classification tasks is a central problem in machine learning and statistics. The feature selection task is especially important, and computationally difficult, for modern data sets where the number of features can be comparable to or even exceed the number of samples. Here, we show that feature selection with Bayesian inference takes a universal form and reduces to calculating the magnetizations of an Ising model under some mild conditions. Our results exploit the observation that the evidence takes a universal form for strongly regularizing priors--priors that have a large effect on the posterior probability even in the infinite data limit. We derive explicit expressions for feature selection for generalized linear models, a large class of statistical techniques that includes linear and logistic regression. We illustrate the power of our approach by analyzing feature selection in a logistic regression-based classifier trained to distinguish between the letters B and D in the notMNIST data set.
Two-dimensional Ising transition through a technique from two-state opinion-dynamics models
NASA Astrophysics Data System (ADS)
Galam, Serge; Martins, André C. R.
2015-01-01
The Ising ferromagnetic model on a square lattice is revisited using the Galam unifying frame (GUF), set to investigate two-state opinion-dynamics models. When combined with Metropolis dynamics, an unexpected intermediate "dis/order" regime is found with the coexistence of two attractors associated, respectively, to an ordered and a disordered phases. The basin of attraction of initial conditions for the disordered phase attractor starts from zero size at a first critical temperature Tc 1 to embody the total landscape of initial conditions at a second critical temperature Tc 2, with Tc 1≈1.59 and Tc 2≈2.11 in J /kB units. It appears that Tc 2 is close to the Onsager result Tc≈2.27 . The transition, which is first-order-like, exhibits a vertical jump to the disorder phase at Tc 2, reminiscent of the rather abrupt vanishing of the corresponding Onsager second-order transition. However, using Glauber dynamics combined with GUF does not yield the intermediate phase and instead the expected classical mean-field transition is recovered at Tc≈3.09 . Accordingly, although the "dis/order" regime produced by the GUF-Metropolis combination is not physical, it is an intriguing result to be understood. In particular the fact that Glauber and Metropolis dynamics yield so different results using GUF needs an explanation. The possibility of extending GUF to larger clusters is discussed.
Quantum Quench Dynamics in the Transverse Field Ising Model at Non-zero Temperatures
NASA Astrophysics Data System (ADS)
Abeling, Nils; Kehrein, Stefan
The recently discovered Dynamical Phase Transition denotes non-analytic behavior in the real time evolution of quantum systems in the thermodynamic limit and has been shown to occur in different systems at zero temperature [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. In this talk we present the extension of the analysis to non-zero temperature by studying a generalized form of the Loschmidt echo, the work distribution function, of a quantum quench in the transverse field Ising model. Although the quantitative behavior at non-zero temperatures still displays features derived from the zero temperature non-analyticities, it is shown that in this model dynamical phase transitions do not exist if T > 0 . This is a consequence of the system being initialized in a thermal state. Moreover, we elucidate how the Tasaki-Crooks-Jarzynski relation can be exploited as a symmetry relation for a global quench or to obtain the change of the equilibrium free energy density. This work was supported through CRC SFB 1073 (Project B03) of the Deutsche Forschungsgemeinschaft (DFG).
A depth-averaged 2-D model of flow and sediment transport in coastal waters
NASA Astrophysics Data System (ADS)
Sanchez, Alejandro; Wu, Weiming; Beck, Tanya M.
2016-11-01
A depth-averaged 2-D model has been developed to simulate unsteady flow and nonuniform sediment transport in coastal waters. The current motion is computed by solving the phase-averaged 2-D shallow water flow equations reformulated in terms of total-flux velocity, accounting for the effects of wave radiation stresses and general diffusion or mixing induced by current, waves, and wave breaking. The cross-shore boundary conditions are specified by assuming fully developed longshore current and wave setup that are determined using the reduced 1-D momentum equations. A 2-D wave spectral transformation model is used to calculate the wave height, period, direction, and radiation stresses, and a surface wave roller model is adopted to consider the effects of surface roller on the nearshore currents. The nonequilibrium transport of nonuniform total-load sediment is simulated, considering sediment entrainment by current and waves, the lag of sediment transport relative to the flow, and the hiding and exposure effect of nonuniform bed material. The flow and sediment transport equations are solved using an implicit finite volume method on a variety of meshes including nonuniform rectangular, telescoping (quadtree) rectangular, and hybrid triangular/quadrilateral meshes. The flow and wave models are integrated through a carefully designed steering process. The model has been tested in three field cases, showing generally good performance.
NASA Astrophysics Data System (ADS)
Monceau, P.; Hsiao, P.-Y.
2003-02-01
We study the cluster size distributions generated by the Wolff algorithm in the framework of the Ising model on Sierpinski fractals with Hausdorff dimension Df between 1 and 2. We show that these distributions exhibit a scaling property involving the magnetic exponent yh associated with one of the eigen-direction of the renormalization flows. We suggest that a single cluster tends to invade the whole lattice as Df tends towards the lower critical dimension of the Ising model, namely 1. The autocorrelation times associated with the Wolff and Swendsen-Wang algorithms enable us to calculate dynamical exponents; the cluster algorithms are shown to be more efficient in reducing the critical slowing down when Df is lowered.
TRENT2D WG: a smart web infrastructure for debris-flow modelling and hazard assessment
NASA Astrophysics Data System (ADS)
Zorzi, Nadia; Rosatti, Giorgio; Zugliani, Daniel; Rizzi, Alessandro; Piffer, Stefano
2016-04-01
Mountain regions are naturally exposed to geomorphic flows, which involve large amounts of sediments and induce significant morphological modifications. The physical complexity of this class of phenomena represents a challenging issue for modelling, leading to elaborate theoretical frameworks and sophisticated numerical techniques. In general, geomorphic-flows models proved to be valid tools in hazard assessment and management. However, model complexity seems to represent one of the main obstacles to the diffusion of advanced modelling tools between practitioners and stakeholders, although the UE Flood Directive (2007/60/EC) requires risk management and assessment to be based on "best practices and best available technologies". Furthermore, several cutting-edge models are not particularly user-friendly and multiple stand-alone software are needed to pre- and post-process modelling data. For all these reasons, users often resort to quicker and rougher approaches, leading possibly to unreliable results. Therefore, some effort seems to be necessary to overcome these drawbacks, with the purpose of supporting and encouraging a widespread diffusion of the most reliable, although sophisticated, modelling tools. With this aim, this work presents TRENT2D WG, a new smart modelling solution for the state-of-the-art model TRENT2D (Armanini et al., 2009, Rosatti and Begnudelli, 2013), which simulates debris flows and hyperconcentrated flows adopting a two-phase description over a mobile bed. TRENT2D WG is a web infrastructure joining advantages offered by the software-delivering model SaaS (Software as a Service) and by WebGIS technology and hosting a complete and user-friendly working environment for modelling. In order to develop TRENT2D WG, the model TRENT2D was converted into a service and exposed on a cloud server, transferring computational burdens from the user hardware to a high-performing server and reducing computational time. Then, the system was equipped with an
NASA Technical Reports Server (NTRS)
Gao, Shou-Ting; Ping, Fan; Li, Xiao-Fan; Tao, Wei-Kuo
2004-01-01
Although dry/moist potential vorticity is a useful physical quantity for meteorological analysis, it cannot be applied to the analysis of 2D simulations. A convective vorticity vector (CVV) is introduced in this study to analyze 2D cloud-resolving simulation data associated with 2D tropical convection. The cloud model is forced by the vertical velocity, zonal wind, horizontal advection, and sea surface temperature obtained from the TOGA COARE, and is integrated for a selected 10-day period. The CVV has zonal and vertical components in the 2D x-z frame. Analysis of zonally-averaged and mass-integrated quantities shows that the correlation coefficient between the vertical component of the CVV and the sum of the cloud hydrometeor mixing ratios is 0.81, whereas the correlation coefficient between the zonal component and the sum of the mixing ratios is only 0.18. This indicates that the vertical component of the CVV is closely associated with tropical convection. The tendency equation for the vertical component of the CVV is derived and the zonally-averaged and mass-integrated tendency budgets are analyzed. The tendency of the vertical component of the CVV is determined by the interaction between the vorticity and the zonal gradient of cloud heating. The results demonstrate that the vertical component of the CVV is a cloud-linked parameter and can be used to study tropical convection.
NASA Astrophysics Data System (ADS)
Mukhamedov, Farrukh; Barhoumi, Abdessatar; Souissi, Abdessatar
2016-12-01
It is known that the disordered phase of the classical Ising model on the Caley tree is extreme in some region of the temperature. If one considers the Ising model with competing interactions on the same tree, then about the extremity of the disordered phase there is no any information. In the present paper, we first aiming to analyze the correspondence between Gibbs measures and QMC's on trees. Namely, we establish that states associated with translation invariant Gibbs measures of the model can be seen as diagonal quantum Markov chains on some quasi local algebra. Then as an application of the established correspondence, we study some algebraic property of the disordered phase of the Ising model with competing interactions on the Cayley tree of order two. More exactly, we prove that a state corresponding to the disordered phase is not quasi-equivalent to other states associated with translation invariant Gibbs measures. This result shows how the translation invariant states relate to each other, which is even a new phenomena in the classical setting. To establish the main result we basically employ methods of quantum Markov chains.
Fekkes, Stein; Swillens, Abigail E S; Hansen, Hendrik H G; Saris, Anne E C M; Nillesen, Maartje M; Iannaccone, Francesco; Segers, Patrick; de Korte, Chris L
2016-08-25
Three-dimensional strain estimation might improve the detection and localization of high strain regions in the carotid artery for identification of vulnerable plaques. This study compares 2D vs. 3D displacement estimation in terms of radial and circumferential strain using simulated ultrasound images of a patient specific 3D atherosclerotic carotid artery model at the bifurcation embedded in surrounding tissue generated with ABAQUS software. Global longitudinal motion was superimposed to the model based on literature data. A Philips L11-3 linear array transducer was simulated which transmitted plane waves at 3 alternating angles at a pulse repetition rate of 10 kHz. Inter-frame radiofrequency ultrasound data were simulated in Field II for 191 equally spaced longitudinal positions of the internal carotid artery. Accumulated radial and circumferential displacements were estimated using tracking of the inter-frame displacements estimated by a two-step normalized cross-correlation method and displacement compounding. Least squares strain estimation was performed to determine accumulated radial and circumferential strain. The performance of the 2D and 3D method was compared by calculating the root-mean-squared error of the estimated strains with respect to the reference strains obtained from the model. More accurate strain images were obtained using the 3D displacement estimation for the entire cardiac cycle. The 3D technique clearly outperformed the 2D technique in phases with high inter-frame longitudinal motion. In fact the large inter-frame longitudinal motion rendered it impossible to accurately track the tissue and cumulate strains over the entire cardiac cycle with the 2D technique.
Fekkes, Stein; Swillens, Abigail E S; Hansen, Hendrik H G; Saris, Anne E C M; Nillesen, Maartje M; Iannaccone, Francesco; Segers, Patrick; de Korte, Chris L
2016-10-01
Three-dimensional (3-D) strain estimation might improve the detection and localization of high strain regions in the carotid artery (CA) for identification of vulnerable plaques. This paper compares 2-D versus 3-D displacement estimation in terms of radial and circumferential strain using simulated ultrasound (US) images of a patient-specific 3-D atherosclerotic CA model at the bifurcation embedded in surrounding tissue generated with ABAQUS software. Global longitudinal motion was superimposed to the model based on the literature data. A Philips L11-3 linear array transducer was simulated, which transmitted plane waves at three alternating angles at a pulse repetition rate of 10 kHz. Interframe (IF) radio-frequency US data were simulated in Field II for 191 equally spaced longitudinal positions of the internal CA. Accumulated radial and circumferential displacements were estimated using tracking of the IF displacements estimated by a two-step normalized cross-correlation method and displacement compounding. Least-squares strain estimation was performed to determine accumulated radial and circumferential strain. The performance of the 2-D and 3-D methods was compared by calculating the root-mean-squared error of the estimated strains with respect to the reference strains obtained from the model. More accurate strain images were obtained using the 3-D displacement estimation for the entire cardiac cycle. The 3-D technique clearly outperformed the 2-D technique in phases with high IF longitudinal motion. In fact, the large IF longitudinal motion rendered it impossible to accurately track the tissue and cumulate strains over the entire cardiac cycle with the 2-D technique.
A preliminary 3D model for cytochrome P450 2D6 constructed by homology model building.
Koymans, L M; Vermeulen, N P; Baarslag, A; Donné-Op den Kelder, G M
1993-06-01
A homology model building study of cytochrome P450 2D6 has been carried out based on the crystal structure of cytochrome P450 101. The primary sequences of P450 101 and P450 2D6 were aligned by making use of an automated alignment procedure. This alignment was adjusted manually by matching alpha-helices (C, D, G, I, J, K and L) and beta-sheets (beta 3/beta 4) of P450 101 that are proposed to be conserved in membrane-bound P450s (Ouzounis and Melvin [Eur. J. Biochem., 198 (1991) 307]) to the corresponding regions in the primary amino acid sequence of P450 2D6. Furthermore, alpha-helices B, B' and F were found to be conserved in P450 2D6. No significant homology between the remaining regions of P450 101 and P450 2D6 could be found and these regions were therefore deleted. A 3D model of P450 2D6 was constructed by copying the coordinates of the residues from the crystal structure of P450 101 to the corresponding residues in P450 2D6. The regions without a significant homology with P450 101 were not incorporated into the model. After energy-minimization of the resulting 3D model of P450 2D6, possible active site residues were identified by fitting the substrates debrisoquine and dextrometorphan into the proposed active site. Both substrates could be positioned into a planar pocket near the heme region formed by residues Val370, Pro371, Leu372, Trp316, and part of the oxygen binding site of P450 2D6. Furthermore, the carboxylate group of either Asp100 or Asp301 was identified as a possible candidate for the proposed interaction with basic nitrogen atom(s) of the substrates.(ABSTRACT TRUNCATED AT 250 WORDS)
NASA Astrophysics Data System (ADS)
Ma, Jian; Xu, Lei; Wang, Xiao-Guang
2010-01-01
We study critical behaviors of the reduced fidelity susceptibility for two neighboring sites in the one-dimensional transverse field Ising model. It is found that the divergent behaviors of the susceptibility take the form of square of logarithm, in contrast with the global ground-state fidelity susceptibility which is power divergence. In order to perform a scaling analysis, we take the square root of the susceptibility and determine the scaling exponent analytically and the result is further confirmed by numerical calculations.
A Neural-FEM tool for the 2-D magnetic hysteresis modeling
NASA Astrophysics Data System (ADS)
Cardelli, E.; Faba, A.; Laudani, A.; Lozito, G. M.; Riganti Fulginei, F.; Salvini, A.
2016-04-01
The aim of this work is to present a new tool for the analysis of magnetic field problems considering 2-D magnetic hysteresis. In particular, this tool makes use of the Finite Element Method to solve the magnetic field problem in real device, and fruitfully exploits a neural network (NN) for the modeling of 2-D magnetic hysteresis of materials. The NS has as input the magnetic inductions components B at the k-th simulation step and returns as output the corresponding values of the magnetic field H corresponding to the input pattern. It is trained by vector measurements performed on the magnetic material to be modeled. This input/output scheme is directly implemented in a FEM code employing the magnetic potential vector A formulation. Validations through measurements on a real device have been performed.
Laser irradiated fluorescent perfluorocarbon microparticles in 2-D and 3-D breast cancer cell models
NASA Astrophysics Data System (ADS)
Niu, Chengcheng; Wang, Long; Wang, Zhigang; Xu, Yan; Hu, Yihe; Peng, Qinghai
2017-03-01
Perfluorocarbon (PFC) droplets were studied as new generation ultrasound contrast agents via acoustic or optical droplet vaporization (ADV or ODV). Little is known about the ODV irradiated vaporization mechanisms of PFC-microparticle complexs and the stability of the new bubbles produced. In this study, fluorescent perfluorohexane (PFH) poly(lactic-co-glycolic acid) (PLGA) particles were used as a model to study the process of particle vaporization and bubble stability following excitation in two-dimensional (2-D) and three-dimensional (3-D) cell models. We observed localization of the fluorescent agent on the microparticle coating material initially and after vaporization under fluorescence microscopy. Furthermore, the stability and growth dynamics of the newly created bubbles were observed for 11 min following vaporization. The particles were co-cultured with 2-D cells to form 3-D spheroids and could be vaporized even when encapsulated within the spheroids via laser irradiation, which provides an effective basis for further work.
Nematic phase in the J(1)-J(2) square-lattice Ising model in an external field.
Guerrero, Alejandra I; Stariolo, Daniel A; Almarza, Noé G
2015-05-01
The J(1)-J(2) Ising model in the square lattice in the presence of an external field is studied by two approaches: the cluster variation method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined, and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter κ=J(2)/|J(1)| which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.
Papakonstantinou, T; Malakis, A
2013-01-01
We study the ±J three-dimensional (3D) Ising model with a spatially uniaxial anisotropic bond randomness on the simple cubic lattice. The ±J random exchange is applied on the xy planes, whereas, in the z direction, only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied at the ferromagnetic-paramagnetic transition line using parallel tempering and a convenient concentration of antiferromagnetic bonds (p(z)=0;p(xy)=0.176). The numerical data clearly point out a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3D random Ising model. The smooth finite-size behavior of the effective exponents, describing the peaks of the logarithmic derivatives of the order parameter, provides an accurate estimate of the critical exponent 1/ν=1.463(3), and a collapse analysis of magnetization data gives an estimate of β/ν=0.516(7). These results are in agreement with previous papers and, in particular, with those of the isotropic ±J three-dimensional Ising model at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.
NASA Astrophysics Data System (ADS)
Papakonstantinou, T.; Malakis, A.
2013-01-01
We study the ±J three-dimensional (3D) Ising model with a spatially uniaxial anisotropic bond randomness on the simple cubic lattice. The ±J random exchange is applied on the xy planes, whereas, in the z direction, only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied at the ferromagnetic-paramagnetic transition line using parallel tempering and a convenient concentration of antiferromagnetic bonds (pz=0;pxy=0.176). The numerical data clearly point out a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3D random Ising model. The smooth finite-size behavior of the effective exponents, describing the peaks of the logarithmic derivatives of the order parameter, provides an accurate estimate of the critical exponent 1/ν=1.463(3), and a collapse analysis of magnetization data gives an estimate of β/ν=0.516(7). These results are in agreement with previous papers and, in particular, with those of the isotropic ±J three-dimensional Ising model at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.
Test of quantum thermalization in the two-dimensional transverse-field Ising model
Blaß, Benjamin; Rieger, Heiko
2016-01-01
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. PMID:27905523
Hysteresis in DNA compaction by Dps is described by an Ising model.
Vtyurina, Natalia N; Dulin, David; Docter, Margreet W; Meyer, Anne S; Dekker, Nynke H; Abbondanzieri, Elio A
2016-05-03
In all organisms, DNA molecules are tightly compacted into a dynamic 3D nucleoprotein complex. In bacteria, this compaction is governed by the family of nucleoid-associated proteins (NAPs). Under conditions of stress and starvation, an NAP called Dps (DNA-binding protein from starved cells) becomes highly up-regulated and can massively reorganize the bacterial chromosome. Although static structures of Dps-DNA complexes have been documented, little is known about the dynamics of their assembly. Here, we use fluorescence microscopy and magnetic-tweezers measurements to resolve the process of DNA compaction by Dps. Real-time in vitro studies demonstrated a highly cooperative process of Dps binding characterized by an abrupt collapse of the DNA extension, even under applied tension. Surprisingly, we also discovered a reproducible hysteresis in the process of compaction and decompaction of the Dps-DNA complex. This hysteresis is extremely stable over hour-long timescales despite the rapid binding and dissociation rates of Dps. A modified Ising model is successfully applied to fit these kinetic features. We find that long-lived hysteresis arises naturally as a consequence of protein cooperativity in large complexes and provides a useful mechanism for cells to adopt unique epigenetic states.
Quantum critical behavior of the quantum Ising model on fractal lattices.
Yi, Hangmo
2015-01-01
I study the properties of the quantum critical point of the transverse-field quantum Ising model on various fractal lattices such as the Sierpiński carpet, Sierpiński gasket, and Sierpiński tetrahedron. Using a continuous-time quantum Monte Carlo simulation method and finite-size scaling analysis, I identify the quantum critical point and investigate its scaling properties. Among others, I calculate the dynamic critical exponent and find that it is greater than one for all three structures. The fact that it deviates from one is a direct consequence of the fractal structures not being integer-dimensional regular lattices. Other critical exponents are also calculated. The exponents are different from those of the classical critical point and satisfy the quantum scaling relation, thus confirming that I have indeed found the quantum critical point. I find that the Sierpiński tetrahedron, of which the dimension is exactly 2, belongs to a different universality class than that of the two-dimensional square lattice. I conclude that the critical exponents depend on more details of the structure than just the dimension and the symmetry.
Random-field Ising model on isometric lattices: Ground states and non-Porod scattering.
Bupathy, Arunkumar; Banerjee, Varsha; Puri, Sanjay
2016-01-01
We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δ_{c} at zero temperature with high accuracy. For the SC lattice, our estimate (Δ_{c}=2.278±0.002) is consistent with earlier reports. For the BCC and FCC lattices, Δ_{c}=3.316±0.002 and 5.160±0.002, respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α=0.5±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy E_{i}(L) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.
Hysteresis in DNA compaction by Dps is described by an Ising model
Vtyurina, Natalia N.; Dulin, David; Docter, Margreet W.; Meyer, Anne S.; Dekker, Nynke H.; Abbondanzieri, Elio A.
2016-01-01
In all organisms, DNA molecules are tightly compacted into a dynamic 3D nucleoprotein complex. In bacteria, this compaction is governed by the family of nucleoid-associated proteins (NAPs). Under conditions of stress and starvation, an NAP called Dps (DNA-binding protein from starved cells) becomes highly up-regulated and can massively reorganize the bacterial chromosome. Although static structures of Dps–DNA complexes have been documented, little is known about the dynamics of their assembly. Here, we use fluorescence microscopy and magnetic-tweezers measurements to resolve the process of DNA compaction by Dps. Real-time in vitro studies demonstrated a highly cooperative process of Dps binding characterized by an abrupt collapse of the DNA extension, even under applied tension. Surprisingly, we also discovered a reproducible hysteresis in the process of compaction and decompaction of the Dps–DNA complex. This hysteresis is extremely stable over hour-long timescales despite the rapid binding and dissociation rates of Dps. A modified Ising model is successfully applied to fit these kinetic features. We find that long-lived hysteresis arises naturally as a consequence of protein cooperativity in large complexes and provides a useful mechanism for cells to adopt unique epigenetic states. PMID:27091987
Exact Enumeration of the Phase Space of an Ising Model of Ni2MnGa
Eisenbach, Markus; Brown, Greg; Rusanu, Aurelian; Odbadrakh, Khorgolkhuu; Nicholson, Don M; McCarthy, Carrie V.
2013-01-01
Exact evaluations of partition functions are generally prohibitively expensive due to exponential growth of phase space with the number of degrees of freedom. For an Ising model with sites the number of possible states is requiring the use of better scaling methods such as importance sampling Monte-Carlo calculations for all but the smallest systems. Yet the ability to obtain exact solutions for as large as possible systems can provide important benchmark results and opportunities for unobscured insight into the underlying physicsofthesystem.HerewepresentanIsingmodelforthemagneticsublatticesoftheimportantmagneto-caloricmaterialNi MnGa and use an exact enumeration algorithm to calculate the number of states for each energy and sublattice magne- tizations and . This allows the efficient calculation of the partition function and derived thermodynamic quantities such as specific heat and susceptibility. Utilizing the jaguarpf system at Oak Ridge we are able to calculate for systems of up to48sites,whichprovidesimportantinsightintothemechanismforthelargemagnet-caloriceffectinNi MnGaaswellasanimportant benchmark for Monte-Carlo (esp. Wang-Landau method).
Quantum correlated cluster mean-field theory applied to the transverse Ising model.
Zimmer, F M; Schmidt, M; Maziero, Jonas
2016-06-01
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.
Random-field Ising model on isometric lattices: Ground states and non-Porod scattering
NASA Astrophysics Data System (ADS)
Bupathy, Arunkumar; Banerjee, Varsha; Puri, Sanjay
2016-01-01
We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δc at zero temperature with high accuracy. For the SC lattice, our estimate (Δc=2.278 ±0.002 ) is consistent with earlier reports. For the BCC and FCC lattices, Δc=3.316 ±0.002 and 5.160 ±0.002 , respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α =0.5 ±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy Ei(L ) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.
Operator product expansion coefficients of the 3D Ising model with a trapping potential
NASA Astrophysics Data System (ADS)
Costagliola, Gianluca
2016-03-01
Recently the operator product expansion coefficients of the 3D Ising model universality class have been calculated by studying via Monte Carlo simulation the two-point functions perturbed from the critical point with a relevant field. We show that this method can be applied also when the perturbation is performed with a relevant field coupled to a nonuniform potential acting as a trap. This setting is described by the trap size scaling ansatz, which can be combined with the general framework of the conformal perturbation in order to write down the correlators ⟨σ (r )σ (0 )⟩, ⟨σ (r )ɛ (0 )⟩ and ⟨ɛ (r )ɛ (0 )⟩, from which the operator product expansion coefficients can be estimated. We find Cσɛ σ=1.051 (3 ), in agreement with the results already known in the literature, and Cɛɛ ɛ=1.32 (15 ), confirming and improving the previous estimate obtained in the uniform perturbation case.
Critical Casimir force scaling functions of the two-dimensional Ising model at finite aspect ratios
NASA Astrophysics Data System (ADS)
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.
Magnetization-driven random-field Ising model at T=0
NASA Astrophysics Data System (ADS)
Illa, Xavier; Rosinberg, Martin-Luc; Shukla, Prabodh; Vives, Eduard
2006-12-01
We study the hysteretic evolution of the random field Ising model at T=0 when the magnetization M is controlled externally and the magnetic field H becomes the output variable. The dynamics is a simple modification of the single-spin-flip dynamics used in the H -driven situation and consists in flipping successively the spins with the largest local field. This allows one to perform a detailed comparison between the microscopic trajectories followed by the system with the two protocols. Simulations are performed on random graphs with connectivity z=4 (Bethe lattice) and on the three-dimensional cubic lattice. The same internal energy U(M) is found with the two protocols when there is no macroscopic avalanche and it does not depend on whether the microscopic states are stable or not. On the Bethe lattice, the energy inside the macroscopic avalanche also coincides with the one that is computed analytically with the H -driven algorithm along the unstable branch of the hysteresis loop. The output field, defined here as ΔU/ΔM , exhibits very large fluctuations with the magnetization and is not self-averaging. The relation to the experimental situation is discussed.
Study of spin crossover nanoparticles thermal hysteresis using FORC diagrams on an Ising-like model
NASA Astrophysics Data System (ADS)
Atitoaie, Alexandru; Tanasa, Radu; Stancu, Alexandru; Enachescu, Cristian
2014-11-01
Recent developments in the synthesis and characterization of spin crossover (SCO) nanoparticles and their prospects of switching at molecular level turned these bistable compounds into possible candidates for replacing the materials used in recording media industry for development of solid state pressure and temperature sensors or for bringing contributions in engineering. Compared to bulk samples with the same chemical structure, SCO nanoparticles display different characteristics of the hysteretic and relaxation properties like the shift of the transition temperature towards lower values along with decrease of the hysteresis width with nanoparticles size. Using an Ising-like model with specific boundary conditions within a Monte Carlo procedure, we here reproduce most of the hysteretic properties of SCO nanoparticles by considering the interaction between spin crossover edge molecules and embedding surfactant molecules and we propose a complex analysis concerning the effect of the interactions and sizes during the thermal transition in systems of SCO nanoparticles by using the First Order Reversal Curves diagram method and by comparison with similar effects in mixed crystal systems.
Influence of thermal fluctuations on the geometry of interfaces of the quenched Ising model.
Corberi, Federico; Lippiello, Eugenio; Zannetti, Marco
2008-07-01
We study the role of the quench temperature Tf in the phase-ordering kinetics of the Ising model with single spin flip in d=2,3 . Equilibrium interfaces are flat at Tf=0 , whereas at Tf>0 they are curved and rough (above the roughening temperature in d=3 ). We show, by means of scaling arguments and numerical simulations, that this geometrical difference is important for the phase-ordering kinetics as well. In particular, while the growth exponent z=2 of the size of domains L(t) approximately t 1/z is unaffected by Tf, other exponents related to the interface geometry take different values at Tf=0 or Tf>0 . For Tf>0 a crossover phenomenon is observed from an early stage where interfaces are still flat and the system behaves as at Tf=0 , to the asymptotic regime with curved interfaces characteristic of Tf>0 . Furthermore, it is shown that the roughening length, although subdominant with respect to L(t) , produces appreciable correction to scaling up to very long times in d=2 .
Test of quantum thermalization in the two-dimensional transverse-field Ising model
NASA Astrophysics Data System (ADS)
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.
Test of quantum thermalization in the two-dimensional transverse-field Ising model.
Blaß, Benjamin; Rieger, Heiko
2016-12-01
We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems.
Local and cluster critical dynamics of the 3d random-site Ising model
NASA Astrophysics Data System (ADS)
Ivaneyko, D.; Ilnytskyi, J.; Berche, B.; Holovatch, Yu.
2006-10-01
We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well as to the Swendsen-Wang and Wolff cluster algorithms. The lattice sizes of L=10-96 are analysed by a finite-size-scaling technique. The site dilution concentration p=0.85 was chosen to minimize the correction-to-scaling effects. We calculate numerical values of the dynamical critical exponents for the integrated and exponential autocorrelation times for energy and magnetization. As expected, cluster algorithms are characterized by lower values of dynamical critical exponent than the local one: also in the case of dilution critical slowing down is more pronounced for the Metropolis algorithm. However, the striking feature of our estimates is that they suggest that dilution leads to decrease of the dynamical critical exponent for the cluster algorithms. This phenomenon is quite opposite to the local dynamics, where dilution enhances critical slowing down.
Ren, Yihui; Eubank, Stephen; Nath, Madhurima
2016-10-01
Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a reliability property, Ising feasibility, for which the network reliability is the Ising model's partition function. As shown by Moore and Shannon, the network reliability can be separated into two factors: structural, solely determined by the network topology, and dynamical, determined by the underlying dynamics. In this case, the structural factor is known as the joint density of states. Using methods developed to approximate the structural factor for other reliability properties, we simulate the joint density of states, yielding an approximation for the partition function. Based on a detailed examination of why naïve Monte Carlo sampling gives a poor approximation, we introduce a parallel scheme for estimating the joint density of states using a Markov-chain Monte Carlo method with a spin-exchange random walk. This parallel scheme makes simulating the Ising model in the presence of an external field practical on small computer clusters for networks with arbitrary topology with ∼10^{6} energy levels and more than 10^{308} microstates.
NASA Astrophysics Data System (ADS)
Ren, Yihui; Eubank, Stephen; Nath, Madhurima
2016-10-01
Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a reliability property, Ising feasibility, for which the network reliability is the Ising model's partition function. As shown by Moore and Shannon, the network reliability can be separated into two factors: structural, solely determined by the network topology, and dynamical, determined by the underlying dynamics. In this case, the structural factor is known as the joint density of states. Using methods developed to approximate the structural factor for other reliability properties, we simulate the joint density of states, yielding an approximation for the partition function. Based on a detailed examination of why naïve Monte Carlo sampling gives a poor approximation, we introduce a parallel scheme for estimating the joint density of states using a Markov-chain Monte Carlo method with a spin-exchange random walk. This parallel scheme makes simulating the Ising model in the presence of an external field practical on small computer clusters for networks with arbitrary topology with ˜106 energy levels and more than 10308 microstates.
A simple 2-D inundation model for incorporating flood damage in urban drainage planning
NASA Astrophysics Data System (ADS)
Pathirana, A.; Tsegaye, S.; Gersonius, B.; Vairavamoorthy, K.
2008-11-01
In this paper a new inundation model code is developed and coupled with Storm Water Management Model, SWMM, to relate spatial information associated with urban drainage systems as criteria for planning of storm water drainage networks. The prime objective is to achive a model code that is simple and fast enough to be consistently be used in planning stages of urban drainage projects. The formulation for the two-dimensional (2-D) surface flow model algorithms is based on the Navier Stokes equation in two dimensions. An Alternating Direction Implicit (ADI) finite difference numerical scheme is applied to solve the governing equations. This numerical scheme is used to express the partial differential equations with time steps split into two halves. The model algorithm is written using C++ computer programming language. This 2-D surface flow model is then coupled with SWMM for simulation of both pipe flow component and surcharge induced inundation in urban areas. In addition, a damage calculation block is integrated within the inundation model code. The coupled model is shown to be capable of dealing with various flow conditions, as well as being able to simulate wetting and drying processes that will occur as the flood flows over an urban area. It has been applied under idealized and semi-hypothetical cases to determine detailed inundation zones, depths and velocities due to surcharged water on overland surface.
Model-based 3D/2D deformable registration of MR images.
Marami, Bahram; Sirouspour, Shahin; Capson, David W
2011-01-01
A method is proposed for automatic registration of 3D preoperative magnetic resonance images of deformable tissue to a sequence of its 2D intraoperative images. The algorithm employs a dynamic continuum mechanics model of the deformation and similarity (distance) measures such as correlation ratio, mutual information or sum of squared differences for registration. The registration is solely based on information present in the 3D preoperative and 2D intraoperative images and does not require fiducial markers, feature extraction or image segmentation. Results of experiments with a biopsy training breast phantom show that the proposed method can perform well in the presence of large deformations. This is particularly useful for clinical applications such as MR-based breast biopsy where large tissue deformations occur.
A new look on the two-dimensional Ising model: thermal artificial spins
NASA Astrophysics Data System (ADS)
Arnalds, Unnar B.; Chico, Jonathan; Stopfel, Henry; Kapaklis, Vassilios; Bärenbold, Oliver; Verschuuren, Marc A.; Wolff, Ulrike; Neu, Volker; Bergman, Anders; Hjörvarsson, Björgvin
2016-02-01
We present a direct experimental investigation of the thermal ordering in an artificial analogue of an asymmetric two-dimensional Ising system composed of a rectangular array of nano-fabricated magnetostatically interacting islands. During fabrication and below a critical thickness of the magnetic material the islands are thermally fluctuating and thus the system is able to explore its phase space. Above the critical thickness the islands freeze-in resulting in an arrested thermalized state for the array. Determining the magnetic state we demonstrate a genuine artificial two-dimensional Ising system which can be analyzed in the context of nearest neighbor interactions.
Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models
NASA Astrophysics Data System (ADS)
Labuhn, Henning; Barredo, Daniel; Ravets, Sylvain; de Léséleuc, Sylvain; Macrì, Tommaso; Lahaye, Thierry; Browaeys, Antoine
2016-06-01
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.
Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models.
Labuhn, Henning; Barredo, Daniel; Ravets, Sylvain; de Léséleuc, Sylvain; Macrì, Tommaso; Lahaye, Thierry; Browaeys, Antoine
2016-06-30
Spin models are the prime example of simplified many-body Hamiltonians used to model complex, strongly correlated real-world materials. However, despite the simplified character of such models, their dynamics often cannot be simulated exactly on classical computers when the number of particles exceeds a few tens. For this reason, quantum simulation of spin Hamiltonians using the tools of atomic and molecular physics has become a very active field over the past years, using ultracold atoms or molecules in optical lattices, or trapped ions. All of these approaches have their own strengths and limitations. Here we report an alternative platform for the study of spin systems, using individual atoms trapped in tunable two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100 per cent. When excited to high-energy Rydberg D states, the atoms undergo strong interactions whose anisotropic character opens the way to simulating exotic matter. We illustrate the versatility of our system by studying the dynamics of a quantum Ising-like spin-1/2 system in a transverse field with up to 30 spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects on the dynamics, we find excellent agreement with ab initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D states has a measurable influence. Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.
Microsommite: crystal chemistry, phase transitions, Ising model and Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Bonaccorsi, E.; Merlino, S.; Pasero, M.; Macedonio, G.
Microsommite, ideal formula [Na4K2(SO4)] [Ca2Cl2][Si6Al6O24], is a rare feldspathoid that occurs in volcanic products of Vesuvius. It belongs to the cancrinite-davyne group of minerals, presenting an ABAB... stacking sequence of layers that contain six-membered rings of tetrahedra, with Si and Al cations regularly alternating in the tetrahedral sites. The structure was refined in space group P63 to R=0.053 by means of single-crystal X-ray diffraction data. The cell parameters are a=22.161Å=√3adav, c=5.358Å=cdav Z=3. The superstructure arises due to the long-range ordering of extra-framework ions within the channels of the structure. This ordering progressively decreases with rising temperature until it is completely lost and microsommite transforms into davyne. The order-disorder transformation has been monitored in several crystals by means of X-ray superstructure reflections and the critical parameters Tc 750°C and β 0.12 were obtained. The kinetics of the ordering process were followed at different temperatures and the activation energy was determined to be about 125kJmol-1. The continuous order-disorder phase transition in microsommite has been discussed on the basis of a two-dimensional Ising model in a triangular lattice with nn (nearest neighbours) and nnn (next-nearest neighbours) interactions. Such a model was simulated using a Monte Carlo technique. The theoretical model well matches the experimental data; two phase transitions were indicated by the simulated runs: at low temperature only one of the three sublattices begins to disorder, whereas the second transition involves all three sublattices.
Nested 1D-2D approach for urban surface flood modeling
NASA Astrophysics Data System (ADS)
Murla, Damian; Willems, Patrick
2015-04-01
Floods in urban areas as a consequence of sewer capacity exceedance receive increased attention because of trends in urbanization (increased population density and impermeability of the surface) and climate change. Despite the strong recent developments in numerical modeling of water systems, urban surface flood modeling is still a major challenge. Whereas very advanced and accurate flood modeling systems are in place and operation by many river authorities in support of flood management along rivers, this is not yet the case in urban water management. Reasons include the small scale of the urban inundation processes, the need to have very high resolution topographical information available, and the huge computational demands. Urban drainage related inundation modeling requires a 1D full hydrodynamic model of the sewer network to be coupled with a 2D surface flood model. To reduce the computational times, 0D (flood cones), 1D/quasi-2D surface flood modeling approaches have been developed and applied in some case studies. In this research, a nested 1D/2D hydraulic model has been developed for an urban catchment at the city of Gent (Belgium), linking the underground sewer (minor system) with the overland surface (major system). For the overland surface flood modelling, comparison was made of 0D, 1D/quasi-2D and full 2D approaches. The approaches are advanced by considering nested 1D-2D approaches, including infiltration in the green city areas, and allowing the effects of surface storm water storage to be simulated. An optimal nested combination of three different mesh resolutions was identified; based on a compromise between precision and simulation time for further real-time flood forecasting, warning and control applications. Main streets as mesh zones together with buildings as void regions constitute one of these mesh resolution (3.75m2 - 15m2); they have been included since they channel most of the flood water from the manholes and they improve the accuracy of
ICF target 2D modeling using Monte Carlo SNB electron thermal transport in DRACO
NASA Astrophysics Data System (ADS)
Chenhall, Jeffrey; Cao, Duc; Moses, Gregory
2016-10-01
The iSNB (implicit Schurtz Nicolai Busquet multigroup diffusion electron thermal transport method is adapted into a Monte Carlo (MC) transport method to better model angular and long mean free path non-local effects. The MC model was first implemented in the 1D LILAC code to verify consistency with the iSNB model. Implementation of the MC SNB model in the 2D DRACO code enables higher fidelity non-local thermal transport modeling in 2D implosions such as polar drive experiments on NIF. The final step is to optimize the MC model by hybridizing it with a MC version of the iSNB diffusion method. The hybrid method will combine the efficiency of a diffusion method in intermediate mean free path regions with the accuracy of a transport method in long mean free path regions allowing for improved computational efficiency while maintaining accuracy. Work to date on the method will be presented. This work was supported by Sandia National Laboratories and the Univ. of Rochester Laboratory for Laser Energetics.
3D/2D Model-to-Image Registration for Quantitative Dietary Assessment.
Chen, Hsin-Chen; Jia, Wenyan; Li, Zhaoxin; Sun, Yung-Nien; Sun, Mingui
2012-12-31
Image-based dietary assessment is important for health monitoring and management because it can provide quantitative and objective information, such as food volume, nutrition type, and calorie intake. In this paper, a new framework, 3D/2D model-to-image registration, is presented for estimating food volume from a single-view 2D image containing a reference object (i.e., a circular dining plate). First, the food is segmented from the background image based on Otsu's thresholding and morphological operations. Next, the food volume is obtained from a user-selected, 3D shape model. The position, orientation and scale of the model are optimized by a model-to-image registration process. Then, the circular plate in the image is fitted and its spatial information is used as constraints for solving the registration problem. Our method takes the global contour information of the shape model into account to obtain a reliable food volume estimate. Experimental results using regularly shaped test objects and realistically shaped food models with known volumes both demonstrate the effectiveness of our method.
Uncertainties in modelling Mt. Pinatubo eruption with 2-D AER model and CCM SOCOL
NASA Astrophysics Data System (ADS)
Kenzelmann, P.; Weisenstein, D.; Peter, T.; Luo, B. P.; Rozanov, E.; Fueglistaler, S.; Thomason, L. W.
2009-04-01
Large volcanic eruptions may introduce a strong forcing on climate. They challenge the skills of climate models. In addition to the short time attenuation of solar light by ashes the formation of stratospheric sulphate aerosols, due to volcanic sulphur dioxide injection into the lower stratosphere, may lead to a significant enhancement of the global albedo. The sulphate aerosols have a residence time of about 2 years. As a consequence of the enhanced sulphate aerosol concentration both the stratospheric chemistry and dynamics are strongly affected. Due to absorption of longwave and near infrared radiation the temperature in the lower stratosphere increases. So far chemistry climate models overestimate this warming [Eyring et al. 2006]. We present an extensive validation of extinction measurements and model runs of the eruption of Mt. Pinatubo in 1991. Even if Mt. Pinatubo eruption has been the best quantified volcanic eruption of this magnitude, the measurements show considerable uncertainties. For instance the total amount of sulphur emitted to the stratosphere ranges from 5-12 Mt sulphur [e.g. Guo et al. 2004, McCormick, 1992]. The largest uncertainties are in the specification of the main aerosol cloud. SAGE II, for instance, could not measure the peak of the aerosol extinction for about 1.5 years, because optical termination was reached. The gap-filling of the SAGE II [Thomason and Peter, 2006] using lidar measurements underestimates the total extinctions in the tropics for the first half year after the eruption by 30% compared to AVHRR [Rusell et. al 1992]. The same applies to the optical dataset described by Stenchikov et al. [1998]. We compare these extinction data derived from measurements with extinctions derived from AER 2D aerosol model calculations [Weisenstein et al., 2007]. Full microphysical calculations with injections of 14, 17, 20 and 26 Mt SO2 in the lower stratosphere were performed. The optical aerosol properties derived from SAGE II
Nucleation dynamics in two-dimensional cylindrical Ising models and chemotaxis
NASA Astrophysics Data System (ADS)
Bosia, C.; Caselle, M.; Corá, D.
2010-02-01
The aim of our work is to study the effect of geometry variation on nucleation times and to address its role in the context of eukaryotic chemotaxis (i.e., the process which allows cells to identify and follow a gradient of chemical attractant). As a first step in this direction we study the nucleation dynamics of the two-dimensional Ising model defined on a cylindrical lattice whose radius changes as a function of time. Geometry variation is obtained by changing the relative value of the couplings between spins in the compactified (vertical) direction with respect to the horizontal one. This allows us to keep the lattice size unchanged and study in a single simulation the values of the compactification radius which change in time. We show both with theoretical arguments and numerical simulations that squeezing the geometry allows the system to speed up nucleation times even in presence of a very small energy gap between the stable and the metastable states. We then address the implications of our analysis for directional chemotaxis. The initial steps of chemotaxis can be modeled as a nucleation process occurring on the cell membrane as a consequence of the external chemical gradient (which plays the role of energy gap between the stable and metastable phases). In nature most of the cells modify their geometry by extending quasi-one-dimensional protrusions (filopodia) so as to enhance their sensitivity to chemoattractant. Our results show that this geometry variation has indeed the effect of greatly decreasing the time scale of the nucleation process even in presence of very small amounts of chemoattractants.
A New Approach to Calculate Indirect GWPs using the UIUC 2-D CRT and RTM Model
NASA Astrophysics Data System (ADS)
Li, Y.; Youn, D.; Patten, K.; Wuebbles, D.
2006-12-01
Global warming potentials (GWPs) are defined to be the total impact over time of adding a unit mass of a greenhouse gas to the atmosphere. Indirect GWPs are due to ozone depletion effects in the stratosphere for a certain compound and therefore stand for the long-term global cooling effects. Previously, indirect GWPs were calculated using a box model, which was not able to consider the complex processes in the atmosphere. As a step towards obtaining indirect GWPs through a more robust approach, the UIUC 2-D CRT model was used as the computational tool to derive ozone changes. The 2-D model has more realistic chemical, physical, and dynamical processes in the atmosphere and a relatively complete transport system, which makes it useful for a more accurate analysis. Furthermore, the University of Illinois at Urbana-Champaign (UIUC) radiative transfer model (RTM) is employed to derive the corresponding time-dependent radiative forcings from the 2-D CRT outputs. Two Halon compounds, Halon-1211 and Halon-1301, were selected to be studied for their indirect GWPs. The results showed that instantaneous and stratospheric adjusted indirect GWPs for a 100-year horizon are -10004.8 and -10237.1 for Halon-1211, while for Halon-1301 they are -19218.0 and -19627.6. The indirect GWPs for Halon-1211 and -1301 presented here are two to three times smaller compared to the results in WMO (2006) draft. Further analysis on indirect GWPs will be carried out using our 3-D MOZART-3 model.
RVE Model with Porosity for 2D Woven CVI SiCf/SiC Composites
NASA Astrophysics Data System (ADS)
Shen, Xiuli; Gong, Longdong
2016-12-01
A representative volume element (RVE) model with porosity for 2D woven chemical vapor infiltration (CVI) SiCf/SiC composites is presented, and its mechanical properties are analyzed. Samples are divided after a tensile test, and their cross sections are scanned with a scanning electron microscope. The size of the feature structure of the RVE model is determined based on the measurement statistics of the feature structure parameters. In accordance with CVI technology, the deposition rates of the matrix in each direction along the surface of fiber bundles are assumed to be similar. The porosity structure is formed naturally when the RVE model is established. The RVE model conforms to the real structure and accurately shows the location and geometric shape of internal porosity. The relative error of the tensile modulus value estimated from the RVE model through the asymptotic expansion homogenization method and experimental data is 3.26%. Therefore, the RVE model is accurate and efficient.
Yue, Xiaoshan; Lukowski, Jessica K; Weaver, Eric M; Skube, Susan B; Hummon, Amanda B
2016-12-02
Cell cultures are widely used model systems. Some immortalized cell lines can be grown in either two-dimensional (2D) adherent monolayers or in three-dimensional (3D) multicellular aggregates, or spheroids. Here, the quantitative proteome and phosphoproteome of colon carcinoma HT29 cells cultures in 2D monolayers and 3D spheroids were compared with a stable isotope labeling of amino acids (SILAC) labeling strategy. Two biological replicates from each sample were examined, and notable differences in both the proteome and the phosphoproteome were determined by nanoliquid chromatography tandem mass spectrometry (LC-MS/MS) to assess how growth configuration affects molecular expression. A total of 5867 protein groups, including 2523 phosphoprotein groups and 8733 phosphopeptides were identified in the samples. The Gene Ontology analysis revealed enriched GO terms in the 3D samples for RNA binding, nucleic acid binding, enzyme binding, cytoskeletal protein binding, and histone binding for their molecular functions (MF) and in the process of cell cycle, cytoskeleton organization, and DNA metabolic process for the biological process (BP). The KEGG pathway analysis indicated that 3D cultures are enriched for oxidative phosphorylation pathways, metabolic pathways, peroxisome pathways, and biosynthesis of amino acids. In contrast, analysis of the phosphoproteomes indicated that 3D cultures have decreased phosphorylation correlating with slower growth rates and lower cell-to-extracellular matrix interactions. In sum, these results provide quantitative assessments of the effects on the proteome and phosphoproteome of culturing cells in 2D versus 3D cell culture configurations.
INTERACTIONS BETWEEN TOPOGRAPHY AND ROUGHNESS IN A 2D RASTER-BASED HYDRAULIC MODEL
NASA Astrophysics Data System (ADS)
Casas, M.; Yu, D.; Lane, S. N.; Benito-Ferrandez, G.
2009-12-01
Analysis of river flow using hydraulic modelling and its implications in derived environmental applications are inextricably connected with the way in which the river boundary shape is represented. This relationship is scale-dependent upon the modelling resolution which in turn determines the importance of a subscale performance of the model and the way subscale (surface and flow) processes are parameterised. This work aims to explore scaling effects associated with the parameterisation of topography and roughness (i.e. surface at different scales) and possible interactions between its components (mesh resolution, topographic content of the DEM and roughness parameterisation) within a 2D raster-based diffusion-wave model. A distributed roughness variable which is scale dependent on the mesh resolution and the surface roughness of the DEM is incorporated to the hydraulic model. The roughness parameterisation is carried out on the basis of a LiDAR-derived vegetation height model and applied in a raster based 2D diffusion wave model. Topographic models with different topographic contents and a constant mesh resolution are generated using LiDAR data and different vertical thresholds. Five DEMs are generated with different topographic contents (±Δz), (DEM±5cm, DEM±10cm, DEM±25cm, DEM±50cm) and four mesh resolutions (1, 2, 4 and 8m) are assessed. A sensitivity analysis on the model results to mesh resolution due to interpolation and resampling procedures of topographic data is performed. Interactions between topographic and roughness parameterisation are related to model results and finally, geostatistical methods are used to document scaling effects in hydraulic modelling results and model performance. This method explicitly recognises the three-way interaction between the discretised mesh resolution and the topographic content in the DEM with the roughness parameterisation. The work shows how the subscale behaviour of the 2D hydraulic model is not well
García-Usach, F; Ribes, J; Ferrer, J; Seco, A
2010-10-01
This paper presents the results of an experimental study for the modelling and calibration of denitrifying activity of polyphosphate accumulating organisms (PAOs) in full-scale WWTPs that incorporate simultaneous nitrogen and phosphorus removal. The convenience of using different yields under aerobic and anoxic conditions for modelling biological phosphorus removal processes with the ASM2d has been demonstrated. Thus, parameter η(PAO) in the model is given a physical meaning and represents the fraction of PAOs that are able to follow the DPAO metabolism. Using stoichiometric relationships, which are based on assumed biochemical pathways, the anoxic yields considered in the extended ASM2d can be obtained as a function of their respective aerobic yields. Thus, this modification does not mean an extra calibration effort to obtain the new parameters. In this work, an off-line calibration methodology has been applied to validate the model, where general relationships among stoichiometric parameters are proposed to avoid increasing the number of parameters to calibrate. The results have been validated through a UCT scheme pilot plant that is fed with municipal wastewater. The good concordance obtained between experimental and simulated values validates the use of anoxic yields as well as the calibration methodology. Deterministic modelling approaches, together with off-line calibration methodologies, are proposed to assist in decision-making about further process optimization in biological phosphate removal, since parameter values obtained by off-line calibration give valuable information about the activated sludge process such as the amount of DPAOs in the system.
Modeling the Elastic Modulus of 2D Woven CVI SiC Composites
NASA Technical Reports Server (NTRS)
Morscher, Gregory N.
2006-01-01
The use of fiber, interphase, CVI SiC minicomposites as structural elements for 2D-woven SiC fiber reinforced chemically vapor infiltrated (CVI) SiC matrix composites is demonstrated to be a viable approach to model the elastic modulus of these composite systems when tensile loaded in an orthogonal direction. The 0deg (loading direction) and 90deg (perpendicular to loading direction) oriented minicomposites as well as the open porosity and excess SiC associated with CVI SiC composites were all modeled as parallel elements using simple Rule of Mixtures techniques. Excellent agreement for a variety of 2D woven Hi-Nicalon(TradeMark) fiber-reinforced and Sylramic-iBN reinforced CVI SiC matrix composites that differed in numbers of plies, constituent content, thickness, density, and number of woven tows in either direction (i.e, balanced weaves versus unbalanced weaves) was achieved. It was found that elastic modulus was not only dependent on constituent content, but also the degree to which 90deg minicomposites carried load. This depended on the degree of interaction between 90deg and 0deg minicomposites which was quantified to some extent by composite density. The relationships developed here for elastic modulus only necessitated the knowledge of the fractional contents of fiber, interphase and CVI SiC as well as the tow size and shape. It was concluded that such relationships are fairly robust for orthogonally loaded 2D woven CVI SiC composite system and can be implemented by ceramic matrix composite component modelers and designers for modeling the local stiffness in simple or complex parts fabricated with variable constituent contents.
Using 2D and 3D Modeling to Infer the Depth of the Okavango Dyke Swarm
NASA Astrophysics Data System (ADS)
Dailey, M. K.; Mortimer, D.; Atekwana, E. A.
2009-12-01
The 179 Ma N110°-striking Okavango Dyke swarm (ODS) extends from southern Zimbabwe for approximately 1500 km northwest into Namibia. The emplacement of dyke swarms is typically associated with the initiation of continental breakup and has been suggested that ODS was emplaced during the breakup of Gondwana along an existing zone of weakness. However, the understanding of how these giant dyke swarms are emplaced over large distances for hundreds of kilometers is limited- do these giant dike swarms propagate from a single source for hundreds of kilometers or do they propagate from sub-crustal magma chambers along a zone of weakness? To address these questions we investigated the ODS in northern Botswana. The dyke swarm is exposed at the surface in the east close to its origin but is buried in the northwest within the Okavango Rift Zone. Using airborne magnetic and ground gravity survey data along with rock property data from the exposed sections, 2D and 3D models were created in order to determine the depth of the dyke swarm. Initially several 2D models were used to test hypothesis of varying depths and rock parameters. The 2D models were then used to ‘seed’ the 3D models with similar density, susceptibility, and depth parameters. The dykes appear to have relatively shallow and finite depths, in the range of 2 to 5 km deep. These results are consistent with a lateral emplacement stemming from the failed triple junction and thus ruling out an infinite depth extent which would have been the case if the dykes were propagated vertically from sub-crustal magma chambers.
An Implicit 2-D Depth-Averaged Finite-Volume Model of Flow and Sediment Transport in Coastal Waters
2010-01-01
Two-dimensional depth-averaged circulation model CMS- M2D : Version 3.0, Report 2: Sediment transport and morphology change, Technical Report ERDC/CHL TR...dimensional depth-averaged circulation model M2D : Version 2.0, Report 1, Technical documentation and user’s guide. ERDC/CHL TR-04-2, Coastal and Hydraulics
A solidification constitutive model for NIKE2D and NIKE3D
Raboin, P.J.
1994-03-17
This memo updates the current status of a solidification material model development which has been underway for more than a year. Significant modeling goals such as predicting cut-off stresses, thermo-elasto-plasticity, strain rate dependent plasticity and dynamic recovery have been completed. The model is called SOLMAT for solidification material model, and while developed for NIKE2D, it has already been implemented in NIKE3D and NIT03D by B. Maker. This memo details the future development strategy of SOLMAT including liquid and solid constitutive improvements, coupling of deviatoric and dilatational deformation and a plan to switch between constitutive theories. It explains some of the difficulties associated solidification modeling and proposes two experiments to measure properties for using SOLMAT. Due to the sensitive nature of these plans in relation to programmatic and CRADA concerns, this memo should be treated as confidential document.
An Integrative Model of Excitation Driven Fluid Flow in a 2D Uterine Channel
NASA Astrophysics Data System (ADS)
Maggio, Charles; Fauci, Lisa; Chrispell, John
2009-11-01
We present a model of intra-uterine fluid flow in a sagittal cross-section of the uterus by inducing peristalsis in a 2D channel. This is an integrative multiscale computational model that takes as input fluid viscosity, passive tissue properties of the uterine channel and a prescribed wave of membrane depolarization. This voltage pulse is coupled to a model of calcium dynamics inside a uterine smooth muscle cell, which in turn drives a kinetic model of myosin phosphorylation governing contractile muscle forces. Using the immersed boundary method, these muscle forces are communicated to a fluid domain to simulate the contractions which occur in a human uterus. An analysis of the effects of model parameters on the flow properties and emergent geometry of the peristaltic channel will be presented.
Adaptive multi-GPU Exchange Monte Carlo for the 3D Random Field Ising Model
NASA Astrophysics Data System (ADS)
Navarro, Cristóbal A.; Huang, Wei; Deng, Youjin
2016-08-01
This work presents an adaptive multi-GPU Exchange Monte Carlo approach for the simulation of the 3D Random Field Ising Model (RFIM). The design is based on a two-level parallelization. The first level, spin-level parallelism, maps the parallel computation as optimal 3D thread-blocks that simulate blocks of spins in shared memory with minimal halo surface, assuming a constant block volume. The second level, replica-level parallelism, uses multi-GPU computation to handle the simulation of an ensemble of replicas. CUDA's concurrent kernel execution feature is used in order to fill the occupancy of each GPU with many replicas, providing a performance boost that is more notorious at the smallest values of L. In addition to the two-level parallel design, the work proposes an adaptive multi-GPU approach that dynamically builds a proper temperature set free of exchange bottlenecks. The strategy is based on mid-point insertions at the temperature gaps where the exchange rate is most compromised. The extra work generated by the insertions is balanced across the GPUs independently of where the mid-point insertions were performed. Performance results show that spin-level performance is approximately two orders of magnitude faster than a single-core CPU version and one order of magnitude faster than a parallel multi-core CPU version running on 16-cores. Multi-GPU performance is highly convenient under a weak scaling setting, reaching up to 99 % efficiency as long as the number of GPUs and L increase together. The combination of the adaptive approach with the parallel multi-GPU design has extended our possibilities of simulation to sizes of L = 32 , 64 for a workstation with two GPUs. Sizes beyond L = 64 can eventually be studied using larger multi-GPU systems.
2D lattice model of a lipid bilayer: Microscopic derivation and thermodynamic exploration
NASA Astrophysics Data System (ADS)
Hakobyan, Davit; Heuer, Andreas
2017-02-01
Based on all-atom Molecular Dynamics (MD) simulations of a lipid bilayer we present a systematic mapping on a 2D lattice model. Keeping the lipid type and the chain order parameter as key variables we derive a free energy functional, containing the enthalpic interaction of adjacent lipids as well as the tail entropy. The functional form of both functions is explicitly determined for saturated and polyunsaturated lipids. By studying the lattice model via Monte Carlo simulations it is possible to reproduce the temperature dependence of the distribution of order parameters of the pure lipids, including the prediction of the gel transition. Furthermore, application to a mixture of saturated and polyunsaturated lipids yields the correct phase separation behavior at lower temperatures with a simulation time reduced by approximately 7 orders of magnitude as compared to the corresponding MD simulations. Even the time-dependence of the de-mixing is reproduced on a semi-quantitative level. Due to the generality of the approach we envisage a large number of further applications, ranging from modeling larger sets of lipids, sterols, and solvent proteins to predicting nucleation barriers for the melting of lipids. Particularly, from the properties of the 2D lattice model one can directly read off the enthalpy and entropy change of the 1,2-dipalmitoyl-sn-glycero-3-phosphocholine gel-to-liquid transition in excellent agreement with experimental and MD results.
Evaluation of Hydrus-2D model for solute distribution in subsurface drip
NASA Astrophysics Data System (ADS)
Souza, Claudinei; Bizari, Douglas; Grecco, Katarina
2015-04-01
The competition for water use between agriculture, industry and population has become intense over the years, requiring a rational use of this resource for food production. The subsurface drip irrigation can help producers with the optimization of operating parameters such as frequency and duration of irrigation, flow, spacing and depth of the dripper installation. This information can be obtained by numerical simulations using mathematical models, thus the aim of this study was to evaluate the HYDRUS-2D model from experimental data to predict the size of the wet bulbs generated by emitters of different application rates (1.0 and 1.6 L h-1). The results showed that horizontal displacement (bulb diameter) remained the largest in all the bulbs, observed both in experimental trials and estimated by the model and the correlation between them was high, above 0.90 to below 16% error. We conclude that the HYDRUS-2D model can be used to estimate the dimensions of the wet bulb getting new information on the sizing of the irrigation system.
NASA Astrophysics Data System (ADS)
Mendoza-Torres, F.; Diaz-Viera, M. A.
2015-12-01
In many natural fractured porous media, such as aquifers, soils, oil and geothermal reservoirs, fractures play a crucial role in their flow and transport properties. An approach that has recently gained popularity for modeling fracture systems is the Discrete Fracture Network (DFN) model. This approach consists in applying a stochastic boolean simulation method, also known as object simulation method, where fractures are represented as simplified geometric objects (line segments in 2D and polygons in 3D). One of the shortcomings of this approach is that it usually does not consider the dependency relationships that may exist between the geometric properties of fractures (direction, length, aperture, etc), that is, each property is simulated independently. In this work a method for modeling such dependencies by copula theory is introduced. In particular, a nonparametric model using Bernstein copulas for direction-length fracture dependency in 2D is presented. The application of this method is illustrated in a case study for a fractured rock sample from a carbonate reservoir outcrop.
Momentum Transport: 2D and 3D Cloud Resolving Model Simulations
NASA Technical Reports Server (NTRS)
Tao, Wei-Kuo
2001-01-01
The major objective of this study is to investigate the momentum budgets associated with several convective systems that developed during the TOGA COARE IOP (west Pacific warm pool region) and GATE (east Atlantic region). The tool for this study is the improved Goddard Cumulas Ensemble (GCE) model which includes a 3-class ice-phase microphysical scheme, explicit cloud radiative interactive processes and air-sea interactive surface processes. The model domain contains 256 x 256 grid points (with 2 km resolution) in the horizontal and 38 grid points (to a depth of 22 km) in the vertical. The 2D domain has 1024 grid points. The simulations were performed over a 7-day time period (December 19-26, 1992, for TOGA COARE and September 1-7, 1994 for GATE). Cyclic literal boundary conditions are required for this type of long-term integration. Two well organized squall systems (TOGA, COARE February 22, 1993, and GATE September 12, 1994) were also simulated using the 3D GCE model. Only 9 h simulations were required to cover the life time of the squall systems. the lateral boundary conditions were open for these two squall systems simulations. the following will be examined: (1) the momentum budgets in the convective and stratiform regions, (2) the relationship between momentum transport and cloud organization (i.e., well organized squall lines versus less organized convective), (3) the differences and similarities in momentum transport between 2D and 3D simulated convective systems, and (4) the differences and similarities in momentum budgets between cloud systems simulated with open and cyclic lateral boundary conditions. Preliminary results indicate that there are only small differences between 2D and 3D simulated momentum budgets. Major differences occur, however, between momentum budgets associated with squall systems simulated using different lateral boundary conditions.
An interactive 2-D power-line modeling and simulation tool
NASA Astrophysics Data System (ADS)
Hull, David; Adelman, Ross
2012-06-01
The U.S. Army Research Laboratory's Power-Line unmanned aerial vehicle (UAV) Modeling and Simulation (ARL-PLUMS) is a tool for estimating and analyzing quasi-static electric and magnetic fields due to power lines. This tool consists of an interactive 2-D graphical user interface (GUI) and a compute engine that can be used to calculate and visualize the E-Field and H-Field due to as many as seven conductors (two 3-phase circuits and a ground wire). ARL-PLUMS allows the user to set the geometry of the lines and the load conditions on those lines, and then calculate Ey, Ez, Hy, or Hz along a linear path or cutting plane, or in the form of a movie. The path can be along the ground or in the air to simulate the fields that might be observed, for example, by a robotic vehicle or a UAV. ARL-PLUMS makes several simplifying assumptions in order to allow simulations to be completed on a laptop PC interactively. In most cases, the results are excellent, providing a "90% solution" in just a few minutes of total modeling and simulation time. This paper describes the physics used by ARL-PLUMS, including the simplifying assumptions and the 2-D Method of Moments solver. Examples of electric and magnetic fields for different wire configurations, including typical 3-phase distribution and transmissions lines, are provided. Comparisons to similar results using a full 3-D model are also shown, and a discussion of errors that may be expected from the 2-D simulations is provided.
JetCurry: Modeling 3D geometry of AGN jets from 2D images
NASA Astrophysics Data System (ADS)
Kosak, Katie; Li, KunYang; Avachat, Sayali S.; Perlman, Eric S.
2017-02-01
Written in Python, JetCurry models the 3D geometry of jets from 2-D images. JetCurry requires NumPy and SciPy and incorporates emcee (ascl:1303.002) and AstroPy (ascl:1304.002), and optionally uses VPython. From a defined initial part of the jet that serves as a reference point, JetCurry finds the position of highest flux within a bin of data in the image matrix and fits along the x axis for the general location of the bends in the jet. A spline fitting is used to smooth out the resulted jet stream.
JetCurry: Modeling 3D geometry of AGN jets from 2D images
NASA Astrophysics Data System (ADS)
Li, Kunyang; Kosak, Katie; Avachat, Sayali S.; Perlman, Eric S.
2017-02-01
Written in Python, JetCurry models the 3D geometry of AGN jets from 2-D images. JetCurry requires NumPy and SciPy and incorporates emcee (ascl:1303.002) and AstroPy (ascl:1304.002), and optionally uses VPython. From a defined initial part of the jet that serves as a reference point, JetCurry finds the position of highest flux within a bin of data in the image matrix and fits along the x axis for the general location of the bends in the jet. A spline fitting is used to smooth out the resulted jet stream.
A 2D Axisymmetric Mixture Multiphase Model for Bottom Stirring in a BOF Converter
NASA Astrophysics Data System (ADS)
Kruskopf, Ari
2017-02-01
A process model for basic oxygen furnace (BOF) steel converter is in development. The model will take into account all the essential physical and chemical phenomena, while achieving real-time calculation of the process. The complete model will include a 2D axisymmetric turbulent multiphase flow model for iron melt and argon gas mixture, a steel scrap melting model, and a chemical reaction model. A novel liquid mass conserving mixture multiphase model for bubbling gas jet is introduced in this paper. In-house implementation of the model is tested and validated in this article independently from the other parts of the full process model. Validation data comprise three different water models with different volume flow rates of air blown through a regular nozzle and a porous plug. The water models cover a wide range of dimensionless number R_{{p}} , which include values that are similar for industrial-scale steel converter. The k- ɛ turbulence model is used with wall functions so that a coarse grid can be utilized. The model calculates a steady-state flow field for gas/liquid mixture using control volume method with staggered SIMPLE algorithm.
Modeling of lamps through a diffuser with 2D and 3D picket-fence backlight models
NASA Astrophysics Data System (ADS)
Belshaw, Richard J.; Wilmott, Roger; Thomas, John T.
2002-08-01
Laboratory photometric measurements are taken of a display backlight one metre away from the emission surface (diffuser) with a whole acceptance angle on the photometer of about 0.125 degrees (2.182mm spot size at emission surface). A simulation method was sought to be able to obtain the brightness uniformity (luminance peak to trough ratio from above one lamp to the null between lamps in a picket-fence backlight). A 3D raytrace BackLight model in TracePro and a 2D Mathematical model in Matlab have been developed. With a specimen backlight in the laboratory, a smooth luminance profile was measured by the photometer on the diffuser surface. Ray Trace models in both 3D and 2D take too long to produce smooth 'continuous filled' distributions. The Mathematical 2D approach, although with limitations, yielded smooth solutions in a very reasonable time frame.
A mathematical model incorporating the effects of detector width in 2D PET
NASA Astrophysics Data System (ADS)
Mair, B. A.
2000-02-01
For decades, the Radon transform has been used as an approximate model for two-dimensional (2D) positron emission tomography (PET). Since this model assumes that detector tubes are represented by lines (hence have no area), PET reconstruction algorithms need to be modified to account for the nonzero width of detectors. To date, these modifications have been obtained by computational methods, so fail to exhibit any inherent mathematical structure of the PET transform which takes emission intensity to detector tube means. This paper contains a precise mathematical representation of this PET transform and exploits this representation to propose a new method for reconstructing PET images. This representation is achieved by expressing the probability that an emission at a point is detected in a detector tube, in terms of the Green function and Poisson kernel for Laplace's equation on the unit disc. This new PET transform involves four weighted line integrals of the emission intensity function, instead of the single unweighted line integral defining the 2D Radon transform. Despite the complexity of this model, a reconstruction method is obtained by using classical orthogonal series representations of the emission intensity and detection means in terms of circular harmonics, Bessel functions and Chebyshev polynomials.
Self-Organization in 2D Traffic Flow Model with Jam-Avoiding Drive
NASA Astrophysics Data System (ADS)
Nagatani, Takashi
1995-04-01
A stochastic cellular automaton (CA) model is presented to investigate the traffic jam by self-organization in the two-dimensional (2D) traffic flow. The CA model is the extended version of the 2D asymmetric exclusion model to take into account jam-avoiding drive. Each site contains either a car moving to the up, a car moving to the right, or is empty. A up car can shift right with probability p ja if it is blocked ahead by other cars. It is shown that the three phases (the low-density phase, the intermediate-density phase and the high-density phase) appear in the traffic flow. The intermediate-density phase is characterized by the right moving of up cars. The jamming transition to the high-density jamming phase occurs with higher density of cars than that without jam-avoiding drive. The jamming transition point p 2c increases with the shifting probability p ja. In the deterministic limit of p ja=1, it is found that a new jamming transition occurs from the low-density synchronized-shifting phase to the high-density moving phase with increasing density of cars. In the synchronized-shifting phase, all up cars do not move to the up but shift to the right by synchronizing with the move of right cars. We show that the jam-avoiding drive has an important effect on the dynamical jamming transition.
NASA Astrophysics Data System (ADS)
Bouttier, J.; Di Francesco, P.; Guitter, E.
2007-07-01
We introduce Eulerian maps with blocked edges as a general way to implement statistical matter models on random maps by a modification of intrinsic distances. We show how to code these dressed maps by means of mobiles, i.e. decorated trees with labelled vertices, leading to a closed system of recursion relations for their generating functions. We discuss particular solvable cases in detail, as well as various applications of our method to several statistical systems such as spanning trees on quadrangulations, mutually excluding particles on Eulerian triangulations or the Ising model on quadrangulations.
Fytas, Nikolaos G; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas
2016-06-03
By performing a high-statistics simulation of the D=4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.
NASA Astrophysics Data System (ADS)
Janke, W.; Kenna, R.
2002-03-01
The two-dimensional Ising model with Brascamp-Kunz boundary conditions has a partition function more amenable to analysis than its counterpart on a torus. This fact is exploited to exactly determine the full finite-size scaling behaviour of the Fisher zeroes of the model. Moreover, exact results are also determined for the scaling of the specific heat at criticality, for the specific-heat peak and for the pseudocritical points. All corrections to scaling are found to be analytic and the shift exponent λ does not coincide with the inverse of the correlation length exponent 1/ν.
NASA Astrophysics Data System (ADS)
Janke, W.; Kenna, R.
The two-dimensional Ising model with Brascamp-Kunz boundary conditions has a partition function more amenable to analysis than its counterpart on a torus. This fact is exploited to exactly determine the full finite-size scaling behaviour of the Fisher zeroes of the model. Moreover, exact results are also determined for the scaling of the specific heat at criticality, for the specific-heat peak and for the pseudocritical points. All corrections to scaling are found to be analytic and the shift exponent λ does not coincide with the inverse of the correlation length exponent 1/ν.
A model of the near-earth plasma environment and application to the ISEE-A and -B orbit
NASA Technical Reports Server (NTRS)
Chan, K. W.; Sawyer, K. W.; Vette, J. I.
1977-01-01
A model of the near-earth environment to obtain a best estimate of the average flux of protons and electrons in the energy range from 0.1 to 100 keV for the International Sun-Earth Explorer (ISEE)-A and -B spacecraft. The possible radiation damage to the thermal coating on these spinning spacecraft is also studied. Applications of the model to other high-altitude satellites can be obtained with the appropriate orbit averaging. This study is the first attempt to synthesize an overall quantitative environment of low-energy particles for high altitude spacecraft, using data from in situ measurements.
NASA Astrophysics Data System (ADS)
Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas
2016-06-01
By performing a high-statistics simulation of the D =4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.
A comparative 2D modeling of debris-flow propagation and outcomes for end-users
NASA Astrophysics Data System (ADS)
Bettella, F.; Bertoldi, G.; Pozza, E.; McArdell, B. W.; D'Agostino, V.
2012-04-01
In Alpine regions gravity-driven natural hazards, in particular debris flows, endanger settlements and human life. Mitigation strategies based on hazard maps are necessary tools for land planning. These maps can be made more precise by using numerical models to forecasting the inundated areas after a careful setting of those 'key parameters' (K-P) which directly affect the flow motion and its interaction with the ground surface. Several physically based 2D models are available for practitioners and governmental agencies, but the selection criteria of model type and of the related K-P remain flexible and partly subjective. This remark has driven us to investigate how different models simulate different types of debris flows (from granular to muddy debris flows, going through intermediate types), in particular when the flow is influenced by the presence of deposition basins. Two commercial 2D physical models (RAMMS and FLO-2D) have been tested for five well-documented debris flows events from five Italian catchments were different geology and flow dynamics are observed: 1) a viscous debris flow occurred in 2009 in a catchment with a metamorphic geology (Gadria torrent, Bolzano Province); 2) the 2009 granular debris flow in an granitic geological setting (Rio Dosson, Trento Province); 3-4) two events occurred in the 'rio Val del Lago' and 'rio Molinara' (Trento Province) in 2010 where porphyritic lithology prevails (intermediate granular debris flow); 5) the Rotolon torrent (Vicenza Province) 2009 debris flow containing sedimentary rocks enclosed in an abundant clay-rich matrix (intermediate viscous case). Event volumes range from 5.000 to 50.000 cubic meters. The Gadria, Rotolon and Val del Lago events are also influenced by artificial retention basins. Case study simulations allowed delineation of some practical end-user suggestions and good practices in order to guide the model choice and the K-P setting, particularly related to different flow dynamics. The
Kinetic parameter estimation in N. europaea biofilms using a 2-D reactive transport model.
Lauchnor, Ellen G; Semprini, Lewis; Wood, Brian D
2015-06-01
Biofilms of the ammonia oxidizing bacterium Nitrosomonas europaea were cultivated to study microbial processes associated with ammonia oxidation in pure culture. We explored the hypothesis that the kinetic parameters of ammonia oxidation in N. europaea biofilms were in the range of those determined with batch suspended cells. Oxygen and pH microelectrodes were used to measure dissolved oxygen (DO) concentrations and pH above and inside biofilms and reactive transport modeling was performed to simulate the measured DO and pH profiles. A two dimensional (2-D) model was used to simulate advection parallel to the biofilm surface and diffusion through the overlying fluid while reaction and diffusion were simulated in the biofilm. Three experimental studies of microsensor measurements were performed with biofilms: i) NH3 concentrations near the Ksn value of 40 μM determined in suspended cell tests ii) Limited buffering capacity which resulted in a pH gradient within the biofilms and iii) NH3 concentrations well below the Ksn value. Very good fits to the DO concentration profiles both in the fluid above and in the biofilms were achieved using the 2-D model. The modeling study revealed that the half-saturation coefficient for NH3 in N. europaea biofilms was close to the value measured in suspended cells. However, the third study of biofilms with low availability of NH3 deviated from the model prediction. The model also predicted shifts in the DO profiles and the gradient in pH that resulted for the case of limited buffering capacity. The results illustrate the importance of incorporating both key transport and chemical processes in a biofilm reactive transport model.
NASA Astrophysics Data System (ADS)
Richwalski, S. M.; Parolai, S.; Wang, R.; Roth, F.
The effect of sedimentary basins on the seismic wavefield is mainly twofold: The shaking at resonance frequencies is amplified and the shaking duration is increased. We study these effects for the area of Cologne (Germany), which is situated in the Lower Rhine Embayment. This is an active tectonic region with a horst/graben struc- ture where moderate sized earthquakes occur along the fault systems. The Erft fault system for example, with the closest surface exposure only 15 km West of the city of Cologne and its high concentration of industrial facilities, is the most important po- tential fault (Ahorner, 2001, DGG Mittlg., 2, p 3). This research is part of the German Research Network for Natural Disasters (DFNK) which aims at an integrated approach for assessing the seismic hazard in this region. Seismic modelling may aid the mitigation of earthquake risk by providing shaking sce- narios for possible source locations and parameters. For modelling, we use a hybrid technique, which combines an improved Thomson-Haskell algorithm (Wang, 1999, BSSA, p 733) with a 2D finite-difference algorithm (Zahradník and Moczo, 1996, PAGEOPH, p 21). This allows for including realistic sources, a regional background model, and a detailed near surface model for the basin. The increase in the shaking duration is already visible in the seismograms but bet- ter visualised by sonograms that show the distribution of the spectral energy in time. Resonance frequencies can be identified using the classical spectral ratio method. The necessary reference site can be created by repeating the modelling using only the re- gional background model but not the basin structure. We also compare the results of 1D and 2D modelling.
Assessing soil fluxes using meteoric 10Be: development and application of the Be2D model
NASA Astrophysics Data System (ADS)
Campforts, Benjamin; Govers, Gerard; Vanacker, Veerle; Baken, Stijn; Smolders, Erik; Vanderborght, Jan
2015-04-01
Meteoric 10Be is a promising and increasingly popular tool to better understand soil fluxes at different timescales. Unlike other, more classical, methods such as the study of sedimentary archives it enables a direct coupling between eroding and deposition sites. However, meteoric 10Be can be mobilized within the soil. Therefore, spatial variations in meteoric 10Be inventories cannot directly be translated into spatial variations in erosion and sedimentation rates: a correct interpretation of measured 10Be inventories requires that both lateral and vertical movement of meteoric 10Be are accounted for. Here, we present a spatially explicit 2D model that allows to simulate the behaviour of meteoric 10Be in the soil system over timescales of up to 1 million year and use the model to investigate the impact of accelerated erosion on meteoric 10Be inventories. The model consists of two parts. A first component deals with advective and diffusive mobility within the soil profile, whereas a second component describes lateral soil (and meteoric 10Be) fluxes over the hillslope. Soil depth is calculated dynamically, accounting for soil production through weathering and lateral soil fluxes. Different types of erosion such as creep, water and tillage erosion are supported. Model runs show that natural soil fluxes can be well reconstructed based on meteoric 10Be inventories, and this for a wide range of geomorphological and pedological conditions. However, extracting signals of human impact and distinguishing them from natural soil fluxes is only feasible when the soil has a rather high retention capacity so that meteoric 10Be is retained in the top soil layer. Application of the Be2D model to an existing data set in the Appalachian Mountains [West et al.,2013] using realistic parameter values for the soil retention capacity as well as for vertical advection resulted in a good agreement between simulated and observed 10Be inventories. This confirms the robustness of the model. We
Well-posedness and generalized plane waves simulations of a 2D mode conversion model
Imbert-Gérard, Lise-Marie
2015-12-15
Certain types of electro-magnetic waves propagating in a plasma can undergo a mode conversion process. In magnetic confinement fusion, this phenomenon is very useful to heat the plasma, since it permits to transfer the heat at or near the plasma center. This work focuses on a mathematical model of wave propagation around the mode conversion region, from both theoretical and numerical points of view. It aims at developing, for a well-posed equation, specific basis functions to study a wave mode conversion process. These basis functions, called generalized plane waves, are intrinsically based on variable coefficients. As such, they are particularly adapted to the mode conversion problem. The design of generalized plane waves for the proposed model is described in detail. Their implementation within a discontinuous Galerkin method then provides numerical simulations of the process. These first 2D simulations for this model agree with qualitative aspects studied in previous works.
The concept models and implementations of multiport neural net associative memory for 2D patterns
NASA Astrophysics Data System (ADS)
Krasilenko, Vladimir G.; Nikolskyy, Aleksandr I.; Yatskovskaya, Rimma A.; Yatskovsky, Victor I.
2011-04-01
The paper considers neural net models and training and recognizing algorithms with base neurobiologic operations: p-step autoequivalence and non-equivalenc The Modified equivalently models (MEMs) of multiport neural net associative memory (MNNAM) are offered with double adaptive - equivalently weighing (DAEW) for recognition of 2D-patterns (images). It is shown, the computing process in MNNAM under using the proposed MEMs, is reduced to two-step and multi-step algorithms and step-by-step matrix-matrix (tensor-tensor) procedures. The given results of computer simulations confirmed the perspective of such models. Besides the result was received when MNNAM capacity on base of MEMs exceeded the amount of neurons.
Analysis of stochastic phenomena in 2D Hindmarsh-Rose neuron model
NASA Astrophysics Data System (ADS)
Bashkirtseva, I.; Ryashko, L.; Slepukhina, E.
2016-10-01
In mathematical research of neuronal activity, conceptual models play an important role. We consider 2D Hindmarsh-Rose model, which exhibits the fundamental property of neuron, the excitability. We study how random disturbances affect this property. The effects of noise are analysed in the parametric zone where the deterministic model is characterized by the coexistence of two stable equilibria. We show that under random disturbances, noise-induced transitions between the attractors occur, forming a new complex dynamic regime of stochastic bursting. It is confirmed by changes of distribution of random trajectories and interspike intervals. For the analysis of this noise-induced phenomenon, we apply the stochastic sensitivity technique and confidence domains method. We suggest a method for estimation of threshold noise intensity corresponding to the onset of noise-induced bursting. We show that the obtained values are in a good agreement with direct numerical simulations.
Longtime Well-posedness for the 2D Groma-Balogh Model
NASA Astrophysics Data System (ADS)
Wan, Renhui; Chen, Jiecheng
2016-12-01
In this paper, we consider the cauchy problem for the 2D Groma-Balogh model (Acta Mater 47:3647-3654, 1999). From the works Cannone et al. (Arch Ration Mech Anal 196:71-96, 2010) and El Hajj (Ann Inst Henri Poincaré Anal Nonlinéaire 27:21-35, 2010), one can see global well-posedness for this model is an open question. However, we can prove longtime well-posedness. In particular, we show that this model admits a unique solution with the lifespan T^star satisfying T^star log ^2(1+T^star )≳ ɛ ^{-2} if the initial data is of size ɛ . To achieve this, we first establish some new decay estimates concerning the operator e^{-{R}_{12}^2t}. Then, we prove the longtime well-posedness by utilizing the weak dissipation to deal with the nonlinear terms.
Partitioning of crustal shortening during continental collision: 2-D thermomechanical modeling
NASA Astrophysics Data System (ADS)
Liao, Jie; Gerya, Taras
2017-01-01
Partitioning of crustal shortening between the colliding continental plates is highly variable in nature. Physical controls of such variability remain largely enigmatic and require quantitative understanding. In this study, we employ 2-D thermomechanical numerical modeling to investigate the influence of the rheological properties of the continental crust on the dynamics and distribution of crustal shortening during continental collision. Three major physical parameters, (i) the mechanical strength of the upper crust, (ii) the Moho temperature, and (iii) the convergence rate, are investigated, and their influences on crustal shortening partitioning between the lower and upper plates are systematically documented. Numerical modeling results suggest that a strong upper crust of the lower plate, high Moho temperature, and slow convergence rate favor migration of crustal shortening from the lower to the upper plate. Our numerical modeling results compare well with natural observations from the Alpine orogenic system where variable partitioning of crustal deformation between the plates is documented.
da Silva, Roberto; Alves, Nelson; Drugowich de Felício, Jose Roberto
2013-01-01
In this work, we study the critical behavior of second-order points, specifically the Lifshitz point (LP) of a three-dimensional Ising model with axial competing interactions [the axial-next-nearest-neighbor Ising (ANNNI) model], using time-dependent Monte Carlo simulations. We use a recently developed technique that helps us localize the critical temperature corresponding to the best power law for magnetization decay over time:
Efficient finite element modeling of scattering for 2D and 3D problems
NASA Astrophysics Data System (ADS)
Wilcox, Paul D.; Velichko, Alexander
2010-03-01
The scattering of waves by defects is central to ultrasonic NDE and SHM. In general, scattering problems must be modeled using direct numerical methods such as finite elements (FE), which is very computationally demanding. The most efficient way is to only model the scatterer itself and a minimal region of the surrounding host medium, and this was previously demonstrated for 2-dimensional (2D) bulk wave scattering problems in isotropic media. An encircling array of monopole and dipole sources is used to inject an arbitrary wavefront onto the scatterer and the scattered field is monitored by a second encircling array of monitoring points. From this data, the scattered field can be projected out to any point in space. If the incident wave is chosen to be a plane wave incident from a given angle and the scattered field is projected to distant points in the far-field of the scatterer, the far-field scattering or S-matrix may be obtained, which encodes all the available scattering information. In this paper, the technique is generalized to any elastic wave geometry in both 2D and 3D, where the latter can include guided wave scattering problems. A further refinement enables the technique to be employed with free FE meshes of triangular or tetrahedral elements.
Laser irradiated fluorescent perfluorocarbon microparticles in 2-D and 3-D breast cancer cell models
Niu, Chengcheng; Wang, Long; Wang, Zhigang; Xu, Yan; Hu, Yihe; Peng, Qinghai
2017-01-01
Perfluorocarbon (PFC) droplets were studied as new generation ultrasound contrast agents via acoustic or optical droplet vaporization (ADV or ODV). Little is known about the ODV irradiated vaporization mechanisms of PFC-microparticle complexs and the stability of the new bubbles produced. In this study, fluorescent perfluorohexane (PFH) poly(lactic-co-glycolic acid) (PLGA) particles were used as a model to study the process of particle vaporization and bubble stability following excitation in two-dimensional (2-D) and three-dimensional (3-D) cell models. We observed localization of the fluorescent agent on the microparticle coating material initially and after vaporization under fluorescence microscopy. Furthermore, the stability and growth dynamics of the newly created bubbles were observed for 11 min following vaporization. The particles were co-cultured with 2-D cells to form 3-D spheroids and could be vaporized even when encapsulated within the spheroids via laser irradiation, which provides an effective basis for further work. PMID:28262671
Modeling and 2-D discrete simulation of dislocation dynamics for plastic deformation of metal
NASA Astrophysics Data System (ADS)
Liu, Juan; Cui, Zhenshan; Ou, Hengan; Ruan, Liqun
2013-05-01
Two methods are employed in this paper to investigate the dislocation evolution during plastic deformation of metal. One method is dislocation dynamic simulation of two-dimensional discrete dislocation dynamics (2D-DDD), and the other is dislocation dynamics modeling by means of nonlinear analysis. As screw dislocation is prone to disappear by cross-slip, only edge dislocation is taken into account in simulation. First, an approach of 2D-DDD is used to graphically simulate and exhibit the collective motion of a large number of discrete dislocations. In the beginning, initial grains are generated in the simulation cells according to the mechanism of grain growth and the initial dislocation is randomly distributed in grains and relaxed under the internal stress. During the simulation process, the externally imposed stress, the long range stress contribution of all dislocations and the short range stress caused by the grain boundaries are calculated. Under the action of these forces, dislocations begin to glide, climb, multiply, annihilate and react with each other. Besides, thermal activation process is included. Through the simulation, the distribution of dislocation and the stress-strain curves can be obtained. On the other hand, based on the classic dislocation theory, the variation of the dislocation density with time is described by nonlinear differential equations. Finite difference method (FDM) is used to solve the built differential equations. The dislocation evolution at a constant strain rate is taken as an example to verify the rationality of the model.
A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method
Brocklehurst, Paul; Adeniran, Ismail; Yang, Dongmin; Sheng, Yong; Zhang, Henggui; Ye, Jianqiao
2015-01-01
Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM). In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca2+ concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue's corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart. PMID:26583141
Tropical Oceanic Precipitation Processes over Warm Pool: 2D and 3D Cloud Resolving Model Simulations
NASA Technical Reports Server (NTRS)
Tao, W.- K.; Johnson, D.
1998-01-01
Rainfall is a key link in the hydrologic cycle as well as the primary heat source for the atmosphere, The vertical distribution of convective latent-heat release modulates the large-scale circulations of the tropics, Furthermore, changes in the moisture distribution at middle and upper levels of the troposphere can affect cloud distributions and cloud liquid water and ice contents. How the incoming solar and outgoing longwave radiation respond to these changes in clouds is a major factor in assessing climate change. Present large-scale weather and climate models simulate cloud processes only crudely, reducing confidence in their predictions on both global and regional scales. One of the most promising methods to test physical parameterizations used in General Circulation Models (GCMS) and climate models is to use field observations together with Cloud Resolving Models (CRMs). The CRMs use more sophisticated and physically realistic parameterizations of cloud microphysical processes, and allow for their complex interactions with solar and infrared radiative transfer processes. The CRMs can reasonably well resolve the evolution, structure, and life cycles of individual clouds and cloud systems, The major objective of this paper is to investigate the latent heating, moisture and momenti,im budgets associated with several convective systems developed during the TOGA COARE IFA - westerly wind burst event (late December, 1992). The tool for this study is the Goddard Cumulus Ensemble (CCE) model which includes a 3-class ice-phase microphysical scheme, The model domain contains 256 x 256 grid points (using 2 km resolution) in the horizontal and 38 grid points (to a depth of 22 km depth) in the vertical, The 2D domain has 1024 grid points. The simulations are performed over a 7 day time period. We will examine (1) the precipitation processes (i.e., condensation/evaporation) and their interaction with warm pool; (2) the heating and moisture budgets in the convective and
LeVine, Michael V; Weinstein, Harel
2015-05-01
In performing their biological functions, molecular machines must process and transmit information with high fidelity. Information transmission requires dynamic coupling between the conformations of discrete structural components within the protein positioned far from one another on the molecular scale. This type of biomolecular "action at a distance" is termed allostery. Although allostery is ubiquitous in biological regulation and signal transduction, its treatment in theoretical models has mostly eschewed quantitative descriptions involving the system's underlying structural components and their interactions. Here, we show how Ising models can be used to formulate an approach to allostery in a structural context of interactions between the constitutive components by building simple allosteric constructs we termed Allosteric Ising Models (AIMs). We introduce the use of AIMs in analytical and numerical calculations that relate thermodynamic descriptions of allostery to the structural context, and then show that many fundamental properties of allostery, such as the multiplicative property of parallel allosteric channels, are revealed from the analysis of such models. The power of exploring mechanistic structural models of allosteric function in more complex systems by using AIMs is demonstrated by building a model of allosteric signaling for an experimentally well-characterized asymmetric homodimer of the dopamine D2 receptor.
Dynamical modeling of sub-grid scales in 2D turbulence
NASA Astrophysics Data System (ADS)
Laval, Jean-Philippe; Dubrulle, Bérengère; Nazarenko, Sergey
2000-08-01
We develop a new numerical method which treats resolved and sub-grid scales as two different fluid components evolving according to their own dynamical equations. These two fluids are nonlinearly interacting and can be transformed one into another when their scale becomes comparable to the grid size. Equations describing the two-fluid dynamics were rigorously derived from Euler equations [B. Dubrulle, S. Nazarenko, Physica D 110 (1997) 123-138] and they do not involve any adjustable parameters. The main assumption of such a derivation is that the large-scale vortices are so strong that they advect the sub-grid scales as a passive scalar, and the interactions of small scales with small and intermediate scales can be neglected. As a test for our numerical method, we performed numerical simulations of 2D turbulence with a spectral gap, and we found a good agreement with analytical results obtained for this case by Nazarenko and Laval [Non-local 2D turbulence and passive scalars in Batchelor’s regime, J. Fluid Mech., in press]. We used the two-fluid method to study three typical problems in 2D dynamics of incompressible fluids: decaying turbulence, vortex merger and forced turbulence. The two-fluid simulations performed on at 128 2 and 256 2 resolution were compared with pseudo-spectral simulations using hyperviscosity performed at the same and at much higher resolution. This comparison shows that performance of the two-fluid method is much better than one of the pseudo-spectral method at the same resolution and comparable computational cost. The most significant improvement is observed in modeling of the small-scale component, so that effective inertial interval increases by about two decades compared to the high-resolution pseudo-spectral method. Using the two-fluid method, we demonstrated that the k-3 tail always exists for the energy spectrum, although its amplitude is slowly decreasing in decaying turbulence.
Locally adaptive 2D-3D registration using vascular structure model for liver catheterization.
Kim, Jihye; Lee, Jeongjin; Chung, Jin Wook; Shin, Yeong-Gil
2016-03-01
Two-dimensional-three-dimensional (2D-3D) registration between intra-operative 2D digital subtraction angiography (DSA) and pre-operative 3D computed tomography angiography (CTA) can be used for roadmapping purposes. However, through the projection of 3D vessels, incorrect intersections and overlaps between vessels are produced because of the complex vascular structure, which makes it difficult to obtain the correct solution of 2D-3D registration. To overcome these problems, we propose a registration method that selects a suitable part of a 3D vascular structure for a given DSA image and finds the optimized solution to the partial 3D structure. The proposed algorithm can reduce the registration errors because it restricts the range of the 3D vascular structure for the registration by using only the relevant 3D vessels with the given DSA. To search for the appropriate 3D partial structure, we first construct a tree model of the 3D vascular structure and divide it into several subtrees in accordance with the connectivity. Then, the best matched subtree with the given DSA image is selected using the results from the coarse registration between each subtree and the vessels in the DSA image. Finally, a fine registration is conducted to minimize the difference between the selected subtree and the vessels of the DSA image. In experimental results obtained using 10 clinical datasets, the average distance errors in the case of the proposed method were 2.34±1.94mm. The proposed algorithm converges faster and produces more correct results than the conventional method in evaluations on patient datasets.
2-D Modeling of Nanoscale MOSFETs: Non-Equilibrium Green's Function Approach
NASA Technical Reports Server (NTRS)
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan
2001-01-01
We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions and oxide tunneling are treated on an equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Electron-electron interaction is treated within Hartree approximation by solving NEGF and Poisson equations self-consistently. For the calculations presented here, parallelization is performed by distributing the solution of NEGF equations to various processors, energy wise. We present simulation of the "benchmark" MIT 25nm and 90nm MOSFETs and compare our results to those from the drift-diffusion simulator and the quantum-corrected results available. In the 25nm MOSFET, the channel length is less than ten times the electron wavelength, and the electron scattering time is comparable to its transit time. Our main results are: (1) Simulated drain subthreshold current characteristics are shown, where the potential profiles are calculated self-consistently by the corresponding simulation methods. The current predicted by our quantum simulation has smaller subthreshold slope of the Vg dependence which results in higher threshold voltage. (2) When gate oxide thickness is less than 2 nm, gate oxide leakage is a primary factor which determines off-current of a MOSFET (3) Using our 2-D NEGF simulator, we found several ways to drastically decrease oxide leakage current without compromising drive current. (4) Quantum mechanically calculated electron density is much smaller than the background doping density in the poly silicon gate region near oxide interface. This creates an additional effective gate voltage. Different ways to. include this effect approximately will be discussed.
Be2D: A model to understand the distribution of meteoric 10Be in soilscapes
NASA Astrophysics Data System (ADS)
Campforts, Benjamin; Vanacker, Veerle; Vanderborght, Jan; Govers, Gerard
2016-04-01
Cosmogenic nuclides have revolutionised our understanding of earth surface process rates. They have become one of the standard tools to quantify soil production by weathering, soil redistribution and erosion. Especially Beryllium-10 has gained much attention due to its long half-live and propensity to be relatively conservative in the landscape. The latter makes 10Be an excellent tool to assess denudation rates over the last 1000 to 100 × 103 years, bridging the anthropogenic and geological time scale. Nevertheless, the mobility of meteoric 10Be in soil systems makes translation of meteoric 10Be inventories into erosion and deposition rates difficult. Here we present a coupled soil hillslope model, Be2D, that is applied to synthetic and real topography to address the following three research questions. (i) What is the influence of vertical meteoric Be10 mobility, caused by chemical mobility, clay translocation and bioturbation, on its lateral redistribution over the soilscape, (ii) How does vertical mobility influence erosion rates and soil residence times inferred from meteoric 10Be inventories and (iii) To what extent can a tracer with a half-life of 1.36 Myr be used to distinguish between natural and human-disturbed soil redistribution rates? The model architecture of Be2D is designed to answer these research questions. Be2D is a dynamic model including physical processes such as soil formation, physical weathering, clay migration, bioturbation, creep, overland flow and tillage erosion. Pathways of meteoric 10Be mobility are simulated using a two step approach which is updated each timestep. First, advective and diffusive mobility of meteoric 10Be is simulated within the soil profile and second, lateral redistribution because of lateral soil fluxes is calculated. The performance and functionality of the model is demonstrated through a number of synthetic and real model runs using existing datasets of meteoric 10Be from case-studies in southeastern US. Brute
Estimating nitrogen losses in furrow irrigated soil amended by compost using HYDRUS-2D model
NASA Astrophysics Data System (ADS)
Iqbal, Shahid; Guber, Andrey; Zaman Khan, Haroon; ullah, Ehsan
2014-05-01
Furrow irrigation commonly results in high nitrogen (N) losses from soil profile via deep infiltration. Estimation of such losses and their reduction is not a trivial task because furrow irrigation creates highly nonuniform distribution of soil water that leads to preferential water and N fluxes in soil profile. Direct measurements of such fluxes are impractical. The objective of this study was to assess applicability of HYDRUS-2D model for estimating nitrogen balance in manure amended soil under furrow irrigation. Field experiments were conducted in a sandy loam soil amended by poultry manure compost (PMC) and pressmud compost (PrMC) fertilizers. The PMC and PrMC contained 2.5% and 0.9% N and were applied at 5 rates: 2, 4, 6, 8 and 10 ton/ha. Plots were irrigated starting from 26th day from planting using furrows with 1x1 ridge to furrow aspect ratio. Irrigation depths were 7.5 cm and time interval between irrigations varied from 8 to 15 days. Results of the field experiments showed that approximately the same corn yield was obtained with considerably higher N application rates using PMC than using PrMC as a fertilizer. HYDRUS-2D model was implemented to evaluate N fluxes in soil amended by PMC and PrMC fertilizers. Nitrogen exchange between two pools of organic N (compost and soil) and two pools of mineral N (soil NH4-N and soil NO3-N) was modeled using mineralization and nitrification reactions. Sources of mineral N losses from soil profile included denitrification, root N uptake and leaching with deep infiltration of water. HYDRUS-2D simulations showed that the observed increases in N root water uptake and corn yields associated with compost application could not be explained by the amount of N added to soil profile with the compost. Predicted N uptake by roots significantly underestimated the field data. Good agreement between simulated and field-estimated values of N root uptake was achieved when the rate of organic N mineralization was increased
Destabilization of survival factor MEF2D mRNA by neurotoxin in models of Parkinson's disease.
Wang, Bao; Cai, Zhibiao; Lu, Fangfang; Li, Chen; Zhu, Xiaofei; Su, Linna; Gao, Guodong; Yang, Qian
2014-09-01
Progressive loss of dopaminergic (DA) neurons in the substantial nigra pars compacta (SNc) is an important pathological feature in Parkinson's disease (PD). Loss of transcription factor myocyte enhancer factor 2D (MEF2D), a key neuronal survival factor, has been shown to underlie the loss of DA neurons in SNc and the pathogenic process of PD. It is known that PD-associated neurotoxins reduce the level of MEF2D protein to trigger neuronal death. Although neurotoxins clearly destabilize MEF2D by post-translational mechanisms, it is not known whether regulation of MEF2D mRNA contributes to neurotoxin-induced decrease in MEF2D protein. In this work, we showed that MPP(+), the toxic metabolite of MPTP, caused a significant decrease in the half-life and total level of MEF2D mRNA in a DA neuronal cell line, SN4741 cells. Quantitative PCR analysis of the SNc DA neurons captured by immune-laser capture microdissection showed that exposure to MPTP led to a marked reduction in the level of MEF2D mRNA in SNc DA neurons compared to controls. Down-regulation of MEF2D mRNA alone reduced the viability of SN4741 cells and sensitized the cells to MPP(+)-induced toxicity. These results suggest that destabilization and reduction in MEF2D mRNA is in part responsible for neurotoxin-induced decrease in MEF2D protein and neuronal viability. Myocyte enhancer factor 2D (MEF2D) plays an important role in neuronal survival. How MEF2D mRNA is deregulated under toxic stress is unclear. We found that PD-associated neurotoxins destabilize MEF2D mRNA and reduce its level in vitro and in vivo. Reduction in MEF2D mRNA is sufficient to sensitize model cells to neurotoxin-induced toxicity, suggesting that destabilization of MEF2D mRNA is part of the mechanism by which neurotoxins trigger deregulation of neuronal survival.
A New Proof of the Sharpness of the Phase Transition for Bernoulli Percolation and the Ising Model
NASA Astrophysics Data System (ADS)
Duminil-Copin, Hugo; Tassion, Vincent
2016-04-01
We provide a new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model. The proof applies to infinite-range models on arbitrary locally finite transitive infinite graphs. For Bernoulli percolation, we prove finiteness of the susceptibility in the subcritical regime {β < β_c}, and the mean-field lower bound {{P}_β[0longleftrightarrow infty ]ge (β-β_c)/β} for {β > β_c}. For finite-range models, we also prove that for any {β < β_c}, the probability of an open path from the origin to distance n decays exponentially fast in n. For the Ising model, we prove finiteness of the susceptibility for {β < β_c}, and the mean-field lower bound {< σ_0rangle_β^+ge sqrt{(β^2-β_c^2)/β^2}} for {β > β_c}. For finite-range models, we also prove that the two-point correlation functions decay exponentially fast in the distance for {β < β_c}.
A computationally efficient 2D hydraulic approach for global flood hazard modeling
NASA Astrophysics Data System (ADS)
Begnudelli, L.; Kaheil, Y.; Sanders, B. F.
2014-12-01
We present a physically-based flood hazard model that incorporates two main components: a hydrologic model and a hydraulic model. For hydrology we use TOPNET, a more comprehensive version of the original TOPMODEL. To simulate flood propagation, we use a 2D Godunov-type finite volume shallow water model. Physically-based global flood hazard simulation poses enormous computational challenges stemming from the increasingly fine resolution of available topographic data which represents the key input. Parallel computing helps to distribute the computational cost, but the computationally-intensive hydraulic model must be made far faster and agile for global-scale feasibility. Here we present a novel technique for hydraulic modeling whereby the computational grid is much coarser (e.g., 5-50 times) than the available topographic data, but the coarse grid retains the storage and conveyance (cross-sectional area) of the fine resolution data. This allows the 2D hydraulic model to be run on extremely large domains (e.g. thousands km2) with a single computational processor, and opens the door to global coverage with parallel computing. The model also downscales the coarse grid results onto the high-resolution topographic data to produce fine-scale predictions of flood depths and velocities. The model achieves computational speeds typical of very coarse grids while achieving an accuracy expected of a much finer resolution. In addition, the model has potential for assimilation of remotely sensed water elevations, to define boundary conditions based on water levels or river discharges and to improve model results. The model is applied to two river basins: the Susquehanna River in Pennsylvania, and the Ogeechee River in Florida. The two rivers represent different scales and span a wide range of topographic characteristics. Comparing spatial resolutions ranging between 30 m to 500 m in both river basins, the new technique was able to reduce simulation runtime by at least 25 fold
Tsai, Shan-Ho; Wang, Fugao; Landau, D P
2007-06-01
Using the Wang-Landau sampling method with a two-dimensional random walk we determine the density of states for an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. With an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite-size analyses at, and away from, the critical endpoint. We observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint, and the exponents for both divergences agree well with previous theoretical predictions.
NASA Astrophysics Data System (ADS)
Tsai, Shan-Ho; Wang, Fugao; Landau, D. P.
2007-06-01
Using the Wang-Landau sampling method with a two-dimensional random walk we determine the density of states for an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. With an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite-size analyses at, and away from, the critical endpoint. We observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint, and the exponents for both divergences agree well with previous theoretical predictions.
Cardozo, David Lopes; Holdsworth, Peter C W
2016-04-27
The magnetization probability density in d = 2 and 3 dimensional Ising models in slab geometry of volume [Formula: see text] is computed through Monte-Carlo simulation at the critical temperature and zero magnetic field. The finite-size scaling of this distribution and its dependence on the system aspect-ratio [Formula: see text]and boundary conditions are discussed. In the limiting case [Formula: see text] of a macroscopically large slab ([Formula: see text]) the distribution is found to scale as a Gaussian function for all tested system sizes and boundary conditions.
NASA Astrophysics Data System (ADS)
Liang, Ya-Qiu; Wei, Guo-Zhu; Xu, Xiao-Juan; Song, Guo-Li
2010-05-01
The longitudinal-random-field mixed Ising model consisting of arbitrary spin values has been studied by the use of an effective field theory with correlations (EFT). The phase diagrams of systems with mixed spins: σ = 1/2, S = 1; σ = 1/2, S = 3/2 are plotted. Not only the discontinuity at T = 0 K, is found when both longitudinal fields are trimodal distributed, but also the tricritical behavior is observed in these phase diagrams between the bimodal and trimodal distributions of longitudinal fields, which is different from the single-spin one. The appearance of tricritical point is independent of the coordination number and spin values.
Magnetic properties of the spin-3/2 Blume-Capel model on a hexagonal Ising nanowire
Kocakaplan, Y.; Ertaş, M.
2015-10-15
Magnetic properties, such as magnetizations, internal energy, specific heat, entropy, Helmholtz free energy, and phase diagrams of the spin-3/2 Blume-Capel model on a hexagonal Ising nanowire with core-shell structure are studied by using the effective-field theory with correlations. The hysteresis behaviors of the system are also investigated and the effects of Hamiltonian parameters on hysteresis behaviors are discussed in detail. The obtained results are compared with some theoretical results and a qualitatively good agreement is found.
NASA Astrophysics Data System (ADS)
Krawczyk, Małgorzata J.
2010-05-01
Topology of the space of periodic ground states in the antiferromagnetic Ising and Potts (3-state) models is analysed in selected spatial structures. The states are treated as graph nodes, connected by one-spin-flip transitions. The spatial structures are the triangular lattice, the Archimedean ( 3,12) lattice and the cubic Laves C15 lattice with the periodic boundary conditions. In most cases the ground states are isolated nodes, but for selected systems we obtain connected graphs. The latter means that the magnetisation can vary in time with zero energy cost. The ground states are classified according to their degree and type of neighbours.
NASA Astrophysics Data System (ADS)
Yamaguchi, K.; Okumura, M.; Mori, W.; Maki, J.; Takada, K.; Noro, T.; Tanaka, K.
1993-07-01
Spin-restricted and unrestricted post-Hartree—Fock calculations were carried out for clusters of triplet methylene and nitroxide radicals. The UHF-based methods such as UMP and QCISD followed by approximate spin projection provide reasonable energy differences between the high-and low-spin states of these species. They are close to the corresponding values from spin-restricted multi-reference (MR) approaches such as CASSCF and second-order (SO) CI. Implications of SOCI and MRSDCI results are discussed in relation to the size inconsistency erros involved in ab initio calculations of weak interaction energies, such as the effective exchange integrals in Ising and Heisenberg models.
del Campo, Adolfo; Rams, Marek M; Zurek, Wojciech H
2012-09-14
The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point, allowing one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter. The method is illustrated in the one-dimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.
NASA Astrophysics Data System (ADS)
Lopes Cardozo, David; Holdsworth, Peter C. W.
2016-04-01
The magnetization probability density in d = 2 and 3 dimensional Ising models in slab geometry of volume L\\paralleld-1× {{L}\\bot} is computed through Monte-Carlo simulation at the critical temperature and zero magnetic field. The finite-size scaling of this distribution and its dependence on the system aspect-ratio ρ =\\frac{{{L}\\bot}}{{{L}\\parallel}} and boundary conditions are discussed. In the limiting case ρ \\to 0 of a macroscopically large slab ({{L}\\parallel}\\gg {{L}\\bot} ) the distribution is found to scale as a Gaussian function for all tested system sizes and boundary conditions.
Dynamics of a 2D Piecewise Linear Braess Paradox Model: Effect of the Third Partition
NASA Astrophysics Data System (ADS)
Avrutin, Viktor; Dibak, Christoph; Dal Forno, Arianna; Merlone, Ugo
In this work, we investigate the dynamics of a piecewise linear 2D discontinuous map modeling a simple network showing the Braess paradox. This paradox represents an example in which adding a new route to a specific congested transportation network makes all the travelers worse off in terms of their individual travel time. In the particular case in which the modeled network corresponds to a binary choice situation, the map is defined on two partitions and its dynamics has already been described. In the general case corresponding to a ternary choice, a third partition appears leading to significantly more complex bifurcation structures formed by border collision bifurcations of stable cycles with points located in all three partitions. Considering a map taking a constant value on one of the partitions, we provide a first systematic description of possible dynamics for this case.
An investigation of DTNS2D for use as an incompressible turbulence modelling test-bed
NASA Technical Reports Server (NTRS)
Steffen, Christopher J., Jr.
1992-01-01
This paper documents an investigation of a two dimensional, incompressible Navier-Stokes solver for use as a test-bed for turbulence modelling. DTNS2D is the code under consideration for use at the Center for Modelling of Turbulence and Transition (CMOTT). This code was created by Gorski at the David Taylor Research Center and incorporates the pseudo compressibility method. Two laminar benchmark flows are used to measure the performance and implementation of the method. The classical solution of the Blasius boundary layer is used for validating the flat plate flow, while experimental data is incorporated in the validation of backward facing step flow. Velocity profiles, convergence histories, and reattachment lengths are used to quantify these calculations. The organization and adaptability of the code are also examined in light of the role as a numerical test-bed.
NASA Astrophysics Data System (ADS)
Bezzeccheri, E.; Colasanti, S.; Falco, A.; Liguori, R.; Rubino, A.; Lugli, P.
2016-05-01
Vertical Organic Transistors and Phototransistors have been proven to be promising technologies due to the advantages of reduced channel length and larger sensitive area with respect to planar devices. Nevertheless, a real improvement of their performance is subordinate to the quantitative description of their operation mechanisms. In this work, we present a comparative study on the modeling of vertical and planar Organic Phototransistor (OPT) structures. Computer-based simulations of the devices have been carried out with Synopsys Sentaurus TCAD in a 2D Drift-Diffusion framework. The photoactive semiconductor material has been modeled using the virtual semiconductor approach as the archetypal P3HT:PC61BM bulk heterojunction. It has been found that both simulated devices have comparable electrical and optical characteristics, accordingly to recent experimental reports on the subject.
Brief Communication: 2-D numerical modeling of the transformation mechanism of a braided channel
NASA Astrophysics Data System (ADS)
Xiao, Y.; Yang, S. F.; Shao, X.; Chen, W. X.; Xu, X. M.
2014-05-01
This paper investigates the controls on the transformation mechanism among different channel patterns. A 2-D depth-averaged numerical model is applied to produce the evolution of channel patterns with complex interactions among water flow, sediment transport, and bank erosion. Changes of the variables as discharge, sediment supply, and vegetation are considered in the numerical experiments, leading to the transformation from a braided pattern into a meandering one. What controls the transformation is discussed with the numerical results: vegetation helps stabilize the cut bank and bar surface, but is not a key in the transition; a decrease in discharge and sediment supply could lead a braided pattern to a meandering one. The conclusion is in agreement with various previous field work, confirming the two dimensional model's potential in predicting the transition between different rivers and improving understanding of patterning processes.
Saraceno, Marilena; Massarelli, Ilaria; Imbriani, Marcello; James, Thomas L; Bianucci, Anna M
2011-08-01
The cytochrome P450 isozyme CYP2D6 binds a large variety of drugs, oxidizing many of them, and plays a crucial role in establishing in vivo drug levels, especially in multidrug regimens. The current study aimed to develop reliable predictive models for estimating the CYP2D6 inhibition properties of drug candidates. Quantitative structure-activity relationship (QSAR) studies utilizing 51 known CYP2D6 inhibitors were carried out. Performance achieved using models based on two-dimensional (2D) molecular descriptors was compared with performance using models entailing additional molecular descriptors that depend upon the three-dimensional (3D) structure of ligands. To properly compute the descriptors, all the 3D inhibitor structures were optimized such that induced-fit binding of the ligand to the active site was accommodated. CODESSA software was used to obtain equations for correlating the structural features of the ligands to their pharmacological effects on CYP2D6 (inhibition). The predictive power of all the QSAR models obtained was estimated by applying rigorous statistical criteria. To assess the robustness and predictability of the models, predictions were carried out on an additional set of known molecules (prediction set). The results showed that only models incorporating 3D descriptors in addition to 2D molecular descriptors possessed the requisite high predictive power for CYP2D6 inhibition.
Cağlar, Tolga; Berker, A Nihat
2011-11-01
The roughening phase diagram of the d=3 Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, from decoupled planes to the isotropic model to the solid-on-solid model, using hard-spin mean-field theory. The phase diagram contains the line of ordering phase transitions and, at lower temperatures, the line of roughening phase transitions, where the interface between ordered domains roughens. Upon increasing the anisotropy, roughening transition temperatures settle after the isotropic case, whereas the ordering transition temperature increases to infinity. The calculation is repeated for the d=2 Ising model for the full range of anisotropy, yielding no roughening transition.
Finite-size scaling relations for a four-dimensional Ising model on Creutz cellular automatons
NASA Astrophysics Data System (ADS)
Merdan, Z.; Güzelsoy, E.
2011-06-01
The four-dimensional Ising model is simulated on Creutz cellular automatons using finite lattices with linear dimensions 4 ≤ L ≤ 8. The temperature variations and finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature for 7, 14, and 21 independent simulations. Approximate values for the critical temperature of the infinite lattice of Tc(∞) = 6.6965(35), 6.6961(30), 6.6960(12), 6.6800(3), 6.6801(2), 6.6802(1) and 6.6925(22) (without the logarithmic factor), 6.6921(22) (without the logarithmic factor), 6.6909(2) (without the logarithmic factor), 6.6822(13) (with the logarithmic factor), 6.6819(11) (with the logarithmic factor), and 6.6808(8) (with the logarithmic factor) are obtained from the intersection points of the specific heat curves, the Binder parameter curves, and straight line fits of specific heat maxima for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the results, 6.6802(1) and 6.6808(8), are in very good agreement with the results of a series expansion of Tc(∞), 6.6817(15) and 6.6802(2), the dynamic Monte Carlo value Tc(∞) = 6.6803(1), the cluster Monte Carlo value Tc(∞) = 6.680(1), and the Monte Carlo value using the Metropolis-Wolff cluster algorithm Tc(∞) = 6.6802632 ± 5 . 10-5. The average values calculated for the critical exponent of the specific heat are α =- 0.0402(15), - 0.0393(12), - 0.0391(11) with 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the result, α =- 0.0391(11), agrees with the series expansions result, α =- 0.12 ± 0.03 and the Monte Carlo result using the Metropolis-Wolff cluster algorithm, α ≥ 0 ± 0.04. However, α =- 0.0391(11) is inconsistent with the renormalization group prediction of α = 0.
Ye, Hong-Zhou; Sun, Chong; Jiang, Hong
2015-03-14
Materials with spin-crossover (SCO) properties hold great potential in information storage and therefore have received a lot of concerns in recent decades. The hysteresis phenomena accompanying SCO are attributed to the intermolecular cooperativity whose underlying mechanism may have a vibronic origin. In this work, a new vibronic Ising-like model in which the elastic coupling between SCO centers is included by considering harmonic stretching and bending (SAB) interactions is proposed and solved by Monte Carlo (MC) simulations. The key parameters in the new model, k1 and k2, corresponding to the elastic constant of the stretching and bending mode, respectively, can be directly related to the macroscopic bulk and shear modulus of the material of study, which can be readily estimated either based on experimental measurements or first-principles calculations. Using realistic parameters estimated based on density-functional theory calculations of a specific polymeric coordination SCO compound, [Fe(pz)Pt(CN)4]·2H2O (pz = pyrazine), temperature-induced hysteresis and pressure effects on SCO phenomena are simulated successfully. Our MC simulations shed light on the role of the vibronic couplings in the thermal hysteresis of SCO systems, and also point out the limitations of highly simplified Ising-like models for quantitative description of real SCO systems, which will be of great value for the development of more realistic SCO models.
NASA Astrophysics Data System (ADS)
Barton, J. P.; Cocco, S.; De Leonardis, E.; Monasson, R.
2014-07-01
The mean-field (MF) approximation offers a simple, fast way to infer direct interactions between elements in a network of correlated variables, a common, computationally challenging problem with practical applications in fields ranging from physics and biology to the social sciences. However, MF methods achieve their best performance with strong regularization, well beyond Bayesian expectations, an empirical fact that is poorly understood. In this work, we study the influence of pseudocount and L2-norm regularization schemes on the quality of inferred Ising or Potts interaction networks from correlation data within the MF approximation. We argue, based on the analysis of small systems, that the optimal value of the regularization strength remains finite even if the sampling noise tends to zero, in order to correct for systematic biases introduced by the MF approximation. Our claim is corroborated by extensive numerical studies of diverse model systems and by the analytical study of the m-component spin model for large but finite m. Additionally, we find that pseudocount regularization is robust against sampling noise and often outperforms L2-norm regularization, particularly when the underlying network of interactions is strongly heterogeneous. Much better performances are generally obtained for the Ising model than for the Potts model, for which only couplings incoming onto medium-frequency symbols are reliably inferred.
Preliminary results for model identification in characterizing 2-D topographic road profiles
NASA Astrophysics Data System (ADS)
Kern, Joshua V.; Ferris, John B.
2006-05-01
Load data representing severe customer usage is needed throughout a chassis development program; the majority of these chassis loads originate with the excitation from the road. These chassis loads are increasingly derived from vehicle simulations. Simulating a vehicle traversing long roads is simply impractical, however, and a greatly reduced set of characteristic roads must be found. In order to characterize a road, certain modeling assumptions must be made. Several models have been proposed making various assumptions about the properties that road profiles possess. The literature in this field is reviewed before focusing on two modeling assumptions of particular interest: the stationarity of the signal (homogeneity of the road) and the corresponding interval over which previous data points are correlated to the current data point. In this work, 2-D topographic road profiles are considered to be signals that are realizations of a stochastic process. The objective of this work is to investigate the stationarity assumption and the interval of influence for several carefully controlled sections of highway pavement in the United States. Two statistical techniques are used in analyzing these data: the autocorrelation and the partial autocorrelation. It is shown that the road profile signals in their original form are not stationary and have an extremely long interval of influence on the order of 25m. By differencing the data, however, it is often possible to generate stationary residuals and a very short interval of influence on the order of 250mm. By examining the autocorrelation and the partial autocorrelation, various versions of ARIMA models appear to be appropriate for further modeling. Implications to modeling the signals as Markov Chains are also discussed. In this way, roads can be characterized by the model architecture and the particular parameterization of the model. Any synthetic road realized from a particular model represents all profiles in this set
NASA Astrophysics Data System (ADS)
Mo, Yike; Greenhalgh, Stewart A.; Robertsson, Johan O. A.; Karaman, Hakki
2015-05-01
Lateral velocity variations and low velocity near-surface layers can produce strong scattered and guided waves which interfere with reflections and lead to severe imaging problems in seismic exploration. In order to investigate these specific problems by laboratory seismic modelling, a simple 2D ultrasonic model facility has been recently assembled within the Wave Propagation Lab at ETH Zurich. The simulated geological structures are constructed from 2 mm thick metal and plastic sheets, cut and bonded together. The experiments entail the use of a piezoelectric source driven by a pulse amplifier at ultrasonic frequencies to generate Lamb waves in the plate, which are detected by piezoelectric receivers and recorded digitally on a National Instruments recording system, under LabVIEW software control. The 2D models employed were constructed in-house in full recognition of the similitude relations. The first heterogeneous model features a flat uniform low velocity near-surface layer and deeper dipping and flat interfaces separating different materials. The second model is comparable but also incorporates two rectangular shaped inserts, one of low velocity, the other of high velocity. The third model is identical to the second other than it has an irregular low velocity surface layer of variable thickness. Reflection as well as transmission experiments (crosshole & vertical seismic profiling) were performed on each model. The two dominant Lamb waves recorded are the fundamental symmetric mode (non-dispersive) and the fundamental antisymmetric (flexural) dispersive mode, the latter normally being absent when the source transducer is located on a model edge but dominant when it is on the flat planar surface of the plate. Experimental group and phase velocity dispersion curves were determined and plotted for both modes in a uniform aluminium plate. For the reflection seismic data, various processing techniques were applied, as far as pre-stack Kirchhoff migration. The
Turbulence modeling for subsonic separated flows over 2-D airfoils and 3-D wings
NASA Astrophysics Data System (ADS)
Rosen, Aaron M.
Accurate predictions of turbulent boundary layers and flow separation through computational fluid dynamics (CFD) are becoming more and more essential for the prediction of loads in the design of aerodynamic flight components. Standard eddy viscosity models used in many commercial codes today do not capture the nonequilibrium effects seen in a separated flow and thus do not generally make accurate separation predictions. Part of the reason for this is that under nonequilibrium conditions such as a strong adverse pressure gradient, the history effects of the flow play an important role in the growth and decay of turbulence. More recent turbulence models such as Olsen and Coakley's Lag model and Lillard's lagRST model seek to simulate these effects by lagging the turbulent variables when nonequilibrium effects become important. The purpose of the current research is to assess how these nonequilibrium turbulence models capture the separated regions on various 2-D airfoils and 3-D wings. Nonequilibrium models including the Lag model and the lagRST model are evaluated in comparison with three baseline models (Spalart-Allmaras, Wilcox's k-omega, and Menter's SST) using a modified version of the OVERFLOW code. Tuning the model coefficients of the Lag and lagRST models is also explored. Results show that the various lagRST formulations display an improvement in velocity profile predictions over the standard RANS models, but have trouble capturing the edge of the boundary layer. Experimental separation location measurements were not available, but several trends are noted which may be useful to tuning the model coefficients in the future.
2D-photochemical modeling of Saturn’s stratosphere: hydrocarbon and water distributions
NASA Astrophysics Data System (ADS)
Hue, Vincent; Cavalié, Thibault; Hersant, Franck; Dobrijevic, Michel; Greathouse, Thomas; Lellouch, Emmanuel; Hartogh, Paul; Cassidy, Timothy; Spiga, Aymeric; Guerlet, Sandrine; Sylvestre, Melody
2014-11-01
Saturn’s axial tilt of 27° produces seasons in a similar way as on Earth. The seasonal forcing over Saturn’s 30 years period influences the production/loss of the major atmospheric absorbers and coolants through photochemistry, and influences therefore Saturn’s stratospheric temperatures. We have developed a 2D time-dependent photochemical model of Saturn’s atmosphere [Hue et al., in prep.], coupled to a radiative-climate model [Greathouse et al., 2008] to study seasonal effects on its atmospheric composition. Cassini spacecraft has revealed that the distribution of hydrocarbons in Saturn’s stratosphere [Guerlet et al., 2009] differs from pure photochemical predictions, i.e. without meridional transport [Moses et al., 2005]. Differences between the observed distribution of hydrocarbons and 2D-photochemical predictions are likely to be an indicator of dynamical forcing.Disentangling the origin of water in the stratosphere of this planet has been a long-term issue. Due to Saturn’s cold tropopause trap, which acts as a transport barrier, the water vapor observed by the Infrared Space Observatory (ISO) [Feuchtgruber et al., 1997] has an external origin. Three external sources have been identified: (i) permanent flux from interplanetary dust particles, (ii) local sources form planetary environments (rings, satellites), (iii) large cometary impacts, similar to Shoemaker-Levy 9 on Jupiter. Previous observations of Saturn with Herschel’s Hsso program [Hartogh et al., 2009] led to the detection of a water torus around Saturn [Hartogh et al., 2011], fed by Enceladus’ geysers. A substantial fraction of this torus is predicted to be a local source of water for Saturn’s and its satellites, as it will spread in this system [Cassidy et al., 2010]. Using the new 2D-photochemical model, we test here the validity of Enceladus’ torus as the source of Saturn’s stratospheric water.References : Hue et al., in prep. Greathouse et al., 2008. AGU Fall Meeting
The combined effect of attraction and orientation zones in 2D flocking models
NASA Astrophysics Data System (ADS)
Iliass, Tarras; Cambui, Dorilson
2016-01-01
In nature, many animal groups, such as fish schools or bird flocks, clearly display structural order and appear to move as a single coherent entity. In order to understand the complex motion of these systems, we study the Vicsek model of self-propelled particles (SPP) which is an important tool to investigate the behavior of collective motion of live organisms. This model reproduces the biological behavior patterns in the two-dimensional (2D) space. Within the framework of this model, the particles move with the same absolute velocity and interact locally in the zone of orientation by trying to align their direction with that of the neighbors. In this paper, we model the collective movement of SPP using an agent-based model which follows biologically motivated behavioral rules, by adding a second region called the attraction zone, where each particles move towards each other avoiding being isolated. Our main goal is to present a detailed numerical study on the effect of the zone of attraction on the kinetic phase transition of our system. In our study, the consideration of this zone seems to play an important role in the cohesion. Consequently, in the directional orientation, the zone that we added forms the compact particle group. In our simulation, we show clearly that the model proposed here can produce two collective behavior patterns: torus and dynamic parallel group. Implications of these findings are discussed.
Coronary arteries motion modeling on 2D x-ray images
NASA Astrophysics Data System (ADS)
Gao, Yang; Sundar, Hari
2012-02-01
During interventional procedures, 3D imaging modalities like CT and MRI are not commonly used due to interference with the surgery and radiation exposure concerns. Therefore, real-time information is usually limited and building models of cardiac motion are difficult. In such case, vessel motion modeling based on 2-D angiography images become indispensable. Due to issues with existing vessel segmentation algorithms and the lack of contrast in occluded vessels, manual segmentation of certain branches is usually necessary. In addition, such occluded branches are the most important vessels during coronary interventions and obtaining motion models for these can greatly help in reducing the procedure time and radiation exposure. Segmenting different cardiac phases independently does not guarantee temporal consistency and is not efficient for occluded branches required manual segmentation. In this paper, we propose a coronary motion modeling system which extracts the coronary tree for every cardiac phase, maintaining the segmentation by tracking the coronary tree during the cardiac cycle. It is able to map every frame to the specific cardiac phase, thereby inferring the shape information of the coronary arteries using the model corresponding to its phase. Our experiments show that our motion modeling system can achieve promising results with real-time performance.
NASA Astrophysics Data System (ADS)
Ananikian, N.; Hovhannisyan, V.
2013-05-01
The exactly solvable spin-{1}/{2} Ising-Heisenberg model on a diamond chain has been considered. We have found the exact results for the magnetization using the recursion relation method. The existence of the magnetization plateau has been observed at one third of the saturation magnetization in the antiferromagnetic case. Some ground-state properties of the model are examined. At low temperatures, the system has two ferrimagnetic (FRI1 and FRI2) phases and one paramagnetic (PRM) phase. Lyapunov exponents for the various values of the exchange parameters and temperatures have been analyzed. It has also been shown that the maximal Lyapunov exponent exhibits plateau. Lyapunov exponents exhibit different behavior for two ferrimagnetic phases. We have found the existence of the supercritical point for the multi-dimensional rational mapping of the spin-{1}/{2} Ising-Heisenberg model on a diamond chain for the first time in the absence of the external magnetic field and T→0 in the antiferromagnetic case.
NASA Astrophysics Data System (ADS)
Zhao, Hongbo; Engelbrecht, Jan R.
2000-03-01
At the Mean Field level (G. Murthy and R. Shankar, J. Phys. Condens. Matter, 7) (1995), the frustration due to an external field first makes the uniform BCS ground state unstable to an incommensurate (qne0) superconducting state and then to a spin-polarized Fermi Liquid state. Our interest is how fluctuations modify this picture, as well as the normal state of this system which has a quantum critical point. We use the Fluctuation-Exchange Approximation for the 2D Attractive Hubbard Model, to study this system beyond the Mean-Field level. Earlier work in zero field has shown that this numerical method successfully captures the critical scaling of the KT superconducting transition upon cooling in the normal state. Here we investigate how the pair-breaking external field modifies this picture, and the development of incommensurate pairing.
Calibration Of 2D Hydraulic Inundation Models In The Floodplain Region Of The Lower Tagus River
NASA Astrophysics Data System (ADS)
Pestanana, R.; Matias, M.; Canelas, R.; Araujo, A.; Roque, D.; Van Zeller, E.; Trigo-Teixeira, A.; Ferreira, R.; Oliveira, R.; Heleno, S.
2013-12-01
In terms of inundated area, the largest floods in Portugal occur in the Lower Tagus River. On average, the river overflows every 2.5 years, at times blocking roads and causing important agricultural damages. This paper focus on the calibration of 2D-horizontal flood simulation models for the floods of 2001 and 2006 on a 70-km stretch of the Lower Tagus River. Flood extent maps, derived from ERS SAR and ENVISAT ASAR imagery were compared with the flood extent maps obtained for each simulation, to calibrate roughness coefficients. The combination of the calibration results from the 2001 and 2006 floods provided a preliminary Manning coefficient map of the study area.
NASA Astrophysics Data System (ADS)
Albella, P.; Moreno, F.; Saiz, J. M.; González, F.
2007-07-01
An interaction model developed in previous research [de la Peña JL, González F, Saiz JM, Moreno F, Valle PJ. Sizing particles on substrates. A general method for oblique incidence. J Appl Phys 1999; 85:432] is extended to the study of two-scaled systems consisting of particles located on larger structures. Far-field scattering patterns produced by these systems can be obtained by coherent addition of different electromagnetic contributions, each one obtained from an independent isolated particle calculation. Results are performed on a 2D scheme, where they can be easily compared with those given by an exact method. This analysis shows some features of the scattering patterns that can be obtained with high reliability. Research on this kind of systems can be applied to 3D situations like particle substrate contamination and particle particle contamination.
Robust autonomous model learning from 2D and 3D data sets.
Langs, Georg; Donner, René; Peloschek, Philipp; Bischof, Horst
2007-01-01
In this paper we propose a weakly supervised learning algorithm for appearance models based on the minimum description length (MDL) principle. From a set of training images or volumes depicting examples of an anatomical structure, correspondences for a set of landmarks are established by group-wise registration. The approach does not require any annotation. In contrast to existing methods no assumptions about the topology of the data are made, and the topology can change throughout the data set. Instead of a continuous representation of the volumes or images, only sparse finite sets of interest points are used to represent the examples during optimization. This enables the algorithm to efficiently use distinctive points, and to handle texture variations robustly. In contrast to standard elasticity based deformation constraints the MDL criterion accounts for systematic deformations typical for training sets stemming from medical image data. Experimental results are reported for five different 2D and 3D data sets.
Strečka, Jozef; Ekiz, Cesur
2015-05-01
The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three interconnected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes upon increasing the coordination number of the underlying Husimi lattice.
An application of the distributed hydrologic model CASC2D to a tropical montane watershed
NASA Astrophysics Data System (ADS)
Marsik, Matt; Waylen, Peter
2006-11-01
SummaryIncreased stormflow in the Quebrada Estero watershed (2.5 km 2), in the northwestern Central Valley tectonic depression of Costa Rica, reportedly has caused flooding of the city of San Ramón in recent decades. Although scientifically untested, urban expansion was deemed the cause and remedial measures were recommended by the Programa de Investigación en Desarrollo Humano Sostenible (ProDUS). CASC2D, a physically-based, spatially explicit hydrologic model, was constructed and calibrated to a June 10th 2002 storm that delivered 110.5 mm of precipitation in 4.5 h visibly exceeded the bankfull stage (0.9 m) of the Quebrada flooding portions of San Ramón. The calibrated hydrograph showed a peak discharge 16.68% (2.5 m 3 s -1) higher, an above flood stage duration 20% shorter, and time to peak discharge 11 min later than the same observed discharge hydrograph characteristics. Simulations of changing land cover conditions from 1979 to 1999 showed an increase also in the peak discharge, above flood stage duration, and time to peak discharge. Analysis using a modified location quotient identified increased urbanization in lower portions of the watershed over the time period studied. These results suggest that increased urbanization in the Quebrada Estero watershed have increased flooding peaks, and durations above threshold, confirming the ProDUS report. These results and the CASC2D model offer an easy-to-use, pragmatic planning tool for policymakers in San Ramón to assess future development scenarios and their potential flooding impacts to San Ramón.
Field Evaluation of a Novel 2D Preferential Flow Snowpack Hydrology Model
NASA Astrophysics Data System (ADS)
Leroux, N.; Pomeroy, J. W.; Kinar, N. J.
2015-12-01
Accurate estimation of snowmelt flux is of primary importance for runoff hydrograph prediction, which is used for water management and flood forecasting. Lateral flows and preferential flow pathways in porous media flow have proven critical for improving soil and groundwater flow models, but though many physically-based layered snowmelt models have been developed, only 1D matrix flow is accounted for in these models. Therefore, there is a need for snowmelt models that include these processes so as to examine the potential to improve snowmelt hydrological modelling. A 2D model is proposed that enables an improved understanding of energy and water flows within deep heterogeneous snowpacks, including those on slopes. A dual pathway theory is presented that simulates the formation of preferential flow paths, vertical and lateral water flows through the snow matrix and flow fingers, internal energy fluxes, melt, wet snow metamorphism, and internal refreezing. The dual pathway model utilizes an explicit finite volume method to solve for the energy and water flux equations over a non-orthogonal grid. It was run and evaluated using in-situ data collected from snowpit - accessed gravimetric, thermometric, photographic, and dielectric observations and novel non-invasive acoustic observations of layering, temperature, flowpath geometry, density and wetness at the Fortress Mountain Snow Laboratory, Alberta, Canada. The melt of a natural snowpack was artificially generated after detailed observation of snowpack initial conditions such as snow layer properties, temperature, and liquid water content. Snowpack ablation and liquid water content distribution over time were then measured and used for model parameterization and validation. Energy available at the snow surface and soil slope angle were set as mondel inputs. Model verification was based on snowpack property evolution. The heterogeneous flow model can be an important tool to help understand snowmelt flow processes, how
Thermochemical Nonequilibrium 2D Modeling of Nitrogen Inductively Coupled Plasma Flow
NASA Astrophysics Data System (ADS)
Yu, Minghao; Yusuke, Takahashi; Hisashi, Kihara; Ken-ichi, Abe; Kazuhiko, Yamada; Takashi, Abe; Satoshi, Miyatani
2015-09-01
Two-dimensional (2D) numerical simulations of thermochemical nonequilibrium inductively coupled plasma (ICP) flows inside a 10-kW inductively coupled plasma wind tunnel (ICPWT) were carried out with nitrogen as the working gas. Compressible axisymmetric Navier-Stokes (N-S) equations coupled with magnetic vector potential equations were solved. A four-temperature model including an improved electron-vibration relaxation time was used to model the internal energy exchange between electron and heavy particles. The third-order accuracy electron transport properties (3rd AETP) were applied to the simulations. A hybrid chemical kinetic model was adopted to model the chemical nonequilibrium process. The flow characteristics such as thermal nonequilibrium, inductive discharge, effects of Lorentz force were made clear through the present study. It was clarified that the thermal nonequilibrium model played an important role in properly predicting the temperature field. The prediction accuracy can be improved by applying the 3rd AETP to the simulation for this ICPWT. supported by Grant-in-Aid for Scientific Research (No. 23560954), sponsored by the Japan Society for the Promotion of Science
Spin Circuit Model for 2D Channels with Spin-Orbit Coupling.
Hong, Seokmin; Sayed, Shehrin; Datta, Supriyo
2016-03-02
In this paper we present a general theory for an arbitrary 2D channel with "spin momentum locking" due to spin-orbit coupling. It is based on a semiclassical model that classifies all the channel electronic states into four groups based on the sign of the z-component of the spin (up (U), down (D)) and the sign of the x-component of the velocity (+, -). This could be viewed as an extension of the standard spin diffusion model which uses two separate electrochemical potentials for U and D states. Our model uses four: U+, D+, U-, and D-. We use this formulation to develop an equivalent spin circuit that is also benchmarked against a full non-equilibrium Green's function (NEGF) model. The circuit representation can be used to interpret experiments and estimate important quantities of interest like the charge to spin conversion ratio or the maximum spin current that can be extracted. The model should be applicable to topological insulator surface states with parallel channels as well as to other layered structures with interfacial spin-orbit coupling.
NASA Astrophysics Data System (ADS)
Wörz, Stefan; Heinzer, Stephan; Weiss, Matthias; Rohr, Karl
2008-03-01
We introduce a model-based approach for segmenting and quantifying GFP-tagged subcellular structures of the Golgi apparatus in 2D and 3D microscopy images. The approach is based on 2D and 3D intensity models, which are directly fitted to an image within 2D circular or 3D spherical regions-of-interest (ROIs). We also propose automatic approaches for the detection of candidates, for the initialization of the model parameters, and for adapting the size of the ROI used for model fitting. Based on the fitting results, we determine statistical information about the spatial distribution and the total amount of intensity (fluorescence) of the subcellular structures. We demonstrate the applicability of our new approach based on 2D and 3D microscopy images.
Decelle, Aurélien; Ricci-Tersenghi, Federico
2014-02-21
In this Letter we propose a new method to infer the topology of the interaction network in pairwise models with Ising variables. By using the pseudolikelihood method (PLM) at high temperature, it is generally possible to distinguish between zero and nonzero couplings because a clear gap separate the two groups. However at lower temperatures the PLM is much less effective and the result depends on subjective choices, such as the value of the ℓ1 regularizer and that of the threshold to separate nonzero couplings from null ones. We introduce a decimation procedure based on the PLM that recursively sets to zero the less significant couplings, until the variation of the pseudolikelihood signals that relevant couplings are being removed. The new method is fully automated and does not require any subjective choice by the user. Numerical tests have been performed on a wide class of Ising models, having different topologies (from random graphs to finite dimensional lattices) and different couplings (both diluted ferromagnets in a field and spin glasses). These numerical results show that the new algorithm performs better than standard PLM.
NASA Astrophysics Data System (ADS)
Decelle, Aurélien; Ricci-Tersenghi, Federico
2014-02-01
In this Letter we propose a new method to infer the topology of the interaction network in pairwise models with Ising variables. By using the pseudolikelihood method (PLM) at high temperature, it is generally possible to distinguish between zero and nonzero couplings because a clear gap separate the two groups. However at lower temperatures the PLM is much less effective and the result depends on subjective choices, such as the value of the ℓ1 regularizer and that of the threshold to separate nonzero couplings from null ones. We introduce a decimation procedure based on the PLM that recursively sets to zero the less significant couplings, until the variation of the pseudolikelihood signals that relevant couplings are being removed. The new method is fully automated and does not require any subjective choice by the user. Numerical tests have been performed on a wide class of Ising models, having different topologies (from random graphs to finite dimensional lattices) and different couplings (both diluted ferromagnets in a field and spin glasses). These numerical results show that the new algorithm performs better than standard PLM.
A new model for two-dimensional numerical simulation of pseudo-2D gas-solids fluidized beds
Li, Tingwen; Zhang, Yongmin
2013-10-11
Pseudo-two dimensional (pseudo-2D) fluidized beds, for which the thickness of the system is much smaller than the other two dimensions, is widely used to perform fundamental studies on bubble behavior, solids mixing, or clustering phenomenon in different gas-solids fluidization systems. The abundant data from such experimental systems are very useful for numerical model development and validation. However, it has been reported that two-dimensional (2D) computational fluid dynamic (CFD) simulations of pseudo-2D gas-solids fluidized beds usually predict poor quantitative agreement with the experimental data, especially for the solids velocity field. In this paper, a new model is proposed to improve the 2D numerical simulations of pseudo-2D gas-solids fluidized beds by properly accounting for the frictional effect of the front and back walls. Two previously reported pseudo-2D experimental systems were simulated with this model. Compared to the traditional 2D simulations, significant improvements in the numerical predictions have been observed and the predicted results are in better agreement with the available experimental data.
Unusual Yang-Lee edge singularity in the one-dimensional axial-next-to-nearest-neighbor Ising model.
Dalmazi, D; Sá, F L
2010-11-01
We show here for the one-dimensional spin-1/2 axial-next-to-nearest-neighbor Ising model in an external magnetic field that the linear density of Yang-Lee zeros may diverge with critical exponent σ=-2/3 at the Yang-Lee edge singularity. The necessary condition for this unusual behavior is the triple degeneracy of the transfer-matrix eigenvalues. If this condition is absent we have the usual value σ=-1/2 . Analogous results have been found in the literature in the spin-1 Blume-Emery-Griffths model and in the three-state Potts model in a magnetic field with two complex components. Our results support the universality of σ=-2/3 which might be a one-dimensional footprint of a tricritical version of the Yang-Lee edge singularity possibly present also in higher-dimensional spin models.
NASA Astrophysics Data System (ADS)
Jurčišinová, E.; Jurčišin, M.
2016-09-01
The antiferromagnetic spin-1 Ising model is studied on the Husimi lattice constructed from elementary triangles with coordination number z = 4. It is found that the model has a unique solution for arbitrary values of the magnetic field as well as for all temperatures. A detailed analysis of the magnetization is performed and it is shown that in addition to the standard plateau-like ground states, the model also contains well-defined single-point ground states related to definite values of the magnetic field. Exact values of the residual entropies for all ground states are found. The properties of the susceptibility and the specific heat of the model are also discussed. The existence of the Schottky-type behavior of the specific heat and the strong magnetocaloric effect for low enough temperatures and for the external magnetic field close to the values at which the single-point ground states exist are identified.
Transectional heat transfer in thermoregulating bigeye tuna (Thunnus obesus) - a 2D heat flux model.
Boye, Jess; Musyl, Michael; Brill, Richard; Malte, Hans
2009-11-01
We developed a 2D heat flux model to elucidate routes and rates of heat transfer within bigeye tuna Thunnus obesus Lowe 1839 in both steady-state and time-dependent settings. In modeling the former situation, we adjusted the efficiencies of heat conservation in the red and the white muscle so as to make the output of the model agree as closely as possible with observed cross-sectional isotherms. In modeling the latter situation, we applied the heat exchanger efficiencies from the steady-state model to predict the distribution of temperature and heat fluxes in bigeye tuna during their extensive daily vertical excursions. The simulations yielded a close match to the data recorded in free-swimming fish and strongly point to the importance of the heat-producing and heat-conserving properties of the white muscle. The best correspondence between model output and observed data was obtained when the countercurrent heat exchangers in the blood flow pathways to the red and white muscle retained 99% and 96% (respectively) of the heat produced in these tissues. Our model confirms that the ability of bigeye tuna to maintain elevated muscle temperatures during their extensive daily vertical movements depends on their ability to rapidly modulate heating and cooling rates. This study shows that the differential cooling and heating rates could be fully accounted for by a mechanism where blood flow to the swimming muscles is either exclusively through the heat exchangers or completely shunted around them, depending on the ambient temperature relative to the body temperature. Our results therefore strongly suggest that such a mechanism is involved in the extensive physiological thermoregulatory abilities of endothermic bigeye tuna.
Wuebbles, D.J.; Connell, P.S.; Grant, K.E.; Tarp, R.; Taylor, K.E.
1987-09-01
Significant progress has been made at LLNL in the development of a zonally averaged (two-dimensional) chemical-radiative-transport model of the troposphere and stratosphere. Although further model development and refinement is being planned the LLNL 2-D model is currently ready to be applied to appropriately designed research studies of stratospheric chemical processes and interactions. Several such studies are now underway. This paper provides a description of the existing 2-D model and discusses some of the pertinent results for evaluating the capabilities of the model. Special attempts at improving the timing of the model are also discussed. 6 figs.
Simulation of abrasive flow machining process for 2D and 3D mixture models
NASA Astrophysics Data System (ADS)
Dash, Rupalika; Maity, Kalipada
2015-12-01
Improvement of surface finish and material removal has been quite a challenge in a finishing operation such as abrasive flow machining (AFM). Factors that affect the surface finish and material removal are media viscosity, extrusion pressure, piston velocity, and particle size in abrasive flow machining process. Performing experiments for all the parameters and accurately obtaining an optimized parameter in a short time are difficult to accomplish because the operation requires a precise finish. Computational fluid dynamics (CFD) simulation was employed to accurately determine optimum parameters. In the current work, a 2D model was designed, and the flow analysis, force calculation, and material removal prediction were performed and compared with the available experimental data. Another 3D model for a swaging die finishing using AFM was simulated at different viscosities of the media to study the effects on the controlling parameters. A CFD simulation was performed by using commercially available ANSYS FLUENT. Two phases were considered for the flow analysis, and multiphase mixture model was taken into account. The fluid was considered to be a
Model-guided respiratory organ motion prediction of the liver from 2D ultrasound.
Preiswerk, Frank; De Luca, Valeria; Arnold, Patrik; Celicanin, Zarko; Petrusca, Lorena; Tanner, Christine; Bieri, Oliver; Salomir, Rares; Cattin, Philippe C
2014-07-01
With the availability of new and more accurate tumour treatment modalities such as high-intensity focused ultrasound or proton therapy, accurate target location prediction has become a key issue. Various approaches for diverse application scenarios have been proposed over the last decade. Whereas external surrogate markers such as a breathing belt work to some extent, knowledge about the internal motion of the organs inherently provides more accurate results. In this paper, we combine a population-based statistical motion model and information from 2d ultrasound sequences in order to predict the respiratory motion of the right liver lobe. For this, the motion model is fitted to a 3d exhalation breath-hold scan of the liver acquired before prediction. Anatomical landmarks tracked in the ultrasound images together with the model are then used to reconstruct the complete organ position over time. The prediction is both spatial and temporal, can be computed in real-time and is evaluated on ground truth over long time scales (5.5 min). The method is quantitatively validated on eight volunteers where the ultrasound images are synchronously acquired with 4D-MRI, which provides ground-truth motion. With an average spatial prediction accuracy of 2.4 mm, we can predict tumour locations within clinically acceptable margins.