Simulation of the 3-state Potts model with chemical potential
Mercado, Ydalia Delgado; Gattringer, Christof; Evertz, Hans Gerd
2011-05-23
The 3-state Potts model with chemical potential is mapped to a flux representation where the complex action problem is resolved. We perform a Monte Carlo simulation based on a worm algorithm to study the phase diagram of the model. Our results shed light on the role which center symmetry and its breaking play for the QCD phase diagram.
BTF Potts compound texture model
NASA Astrophysics Data System (ADS)
Haindl, Michal; Reměs, Václav; Havlíček, Vojtěch
2015-03-01
This paper introduces a method for modeling mosaic-like textures using a multispectral parametric Bidirectional Texture Function (BTF) compound Markov random field model (CMRF). The primary purpose of our synthetic texture approach is to reproduce, compress, and enlarge a given measured texture image so that ideally both natural and synthetic texture will be visually indiscernible, but the model can be easily applied for BFT material editing. The CMRF model consist of several sub-models each having different characteristics along with an underlying structure model which controls transitions between these sub models. The proposed model uses the Potts random field for distributing local texture models in the form of analytically solvable wide-sense BTF Markovian representation for single regions among the fields of a mosaic approximated by the Voronoi diagram. The control field of the BTF-CMRF is generated by the Potts random field model build on top of the adjacency graph of a measured mosaic. The compound random field synthesis combines the modified fast Swendsen- Wang Markov Chain Monte Carlo sampling of the hierarchical Potts MRF part with the fast and analytical synthesis of single regional BTF MRFs. The local texture regions (not necessarily continuous) are represented by an analytical BTF model which consists of single factors modeled by the adaptive 3D causal auto-regressive (3DCAR) random field model which can be analytically estimated as well as synthesized. The visual quality of the resulting complex synthetic textures generally surpasses the outputs of the previously published simpler non-compound BTF-MRF models.
Dilute Potts model in two dimensions.
Qian, Xiaofeng; Deng, Youjin; Blöte, Henk W J
2005-11-01
We study the two-dimensional dilute q-state Potts model by means of transfer-matrix and Monte Carlo methods. Using the random-cluster representation, we include noninteger values of q. We locate phase transitions in the three-dimensional parameter space of q, the Potts coupling K>0, and the chemical potential of the vacancies. The critical plane is found to contain a line of fixed points that divides into a critical branch and a tricritical one, just as predicted by the renormalization scenario formulated by Nienhuis et al for the dilute Potts model. The universal properties along the line of fixed points agree with the theoretical predictions. We also determine the density of the vacancies along these branches. For q=2-squareroot of 2 we obtain the phase diagram in a three-dimensional parameter space that also includes a coupling V> or = 0 between the vacancies. For q=2, the latter space contains the Blume-Capel model as a special case. We include a determination of the tricritical point of this model, as well as an analysis of percolation clusters constructed on tricritical Potts configurations for noninteger q. This percolation study is based on Monte Carlo algorithms that include local updates flipping between Potts sites and vacancies. The bond updates are performed locally for and by means of a cluster algorithm for q>1. The updates for q>1 use a number of operations per site independent of the system size. PMID:16383713
Dilute Potts model in two dimensions
NASA Astrophysics Data System (ADS)
Qian, Xiaofeng; Deng, Youjin; Blöte, Henk W. J.
2005-11-01
We study the two-dimensional dilute q -state Potts model by means of transfer-matrix and Monte Carlo methods. Using the random-cluster representation, we include noninteger values of q . We locate phase transitions in the three-dimensional parameter space of q , the Potts coupling K⩾0 , and the chemical potential of the vacancies. The critical plane is found to contain a line of fixed points that divides into a critical branch and a tricritical one, just as predicted by the renormalization scenario formulated by Nienhuis for the dilute Potts model. The universal properties along the line of fixed points agree with the theoretical predictions. We also determine the density of the vacancies along these branches. For q=2-2 we obtain the phase diagram in a three-dimensional parameter space that also includes a coupling V⩾0 between the vacancies. For q=2 , the latter space contains the Blume-Capel model as a special case. We include a determination of the tricritical point of this model, as well as an analysis of percolation clusters constructed on tricritical Potts configurations for noninteger q . This percolation study is based on Monte Carlo algorithms that include local updates flipping between Potts sites and vacancies. The bond updates are performed locally for q<1 and by means of a cluster algorithm for q>1 . The updates for q>1 use a number of operations per site independent of the system size.
Potts-model critical manifolds revisited
NASA Astrophysics Data System (ADS)
Scullard, Christian R.; Lykke Jacobsen, Jesper
2016-03-01
We compute critical polynomials for the q-state Potts model on the Archimedean lattices, using a parallel implementation of the algorithm of Jacobsen (2014 J. Phys. A: Math. Theor 47 135001) that gives us access to larger sizes than previously possible. The exact polynomials are computed for bases of size 6 × 6 unit cells, and the root in the temperature variable v={{{e}}}K-1 is determined numerically at q = 1 for bases of size 8 × 8. This leads to improved results for bond percolation thresholds, and for the Potts-model critical manifolds in the real (q, v) plane. In the two most favourable cases, we find now the kagome-lattice threshold to eleven digits and that of the (3,{12}2) lattice to thirteen. Our critical manifolds reveal many interesting features in the antiferromagnetic region of the Potts model, and determine accurately the extent of the Berker-Kadanoff phase for the lattices studied.
Phase Transitions in Delaunay Potts Models
NASA Astrophysics Data System (ADS)
Adams, Stefan; Eyers, Michael
2016-01-01
We establish phase transitions for certain classes of continuum Delaunay multi-type particle systems (continuum Potts models) with infinite range repulsive interaction between particles of different type. In one class of the Delaunay Potts models studied the repulsive interaction is a triangle (multi-body) interaction whereas in the second class the interaction is between pairs (edges) of the Delaunay graph. The result for the edge model is an extension of finite range results in Bertin et al. (J Stat Phys 114(1-2):79-100, 2004) for the Delaunay graph and in Georgii and Häggström (Commun Math Phys 181:507-528, 1996) for continuum Potts models to an infinite range repulsion decaying with the edge length. This is a proof of an old conjecture of Lebowitz and Lieb. The repulsive triangle interactions have infinite range as well and depend on the underlying geometry and thus are a first step towards studying phase transitions for geometry-dependent multi-body systems. Our approach involves a Delaunay random-cluster representation analogous to the Fortuin-Kasteleyn representation of the Potts model. The phase transitions manifest themselves in the percolation of the corresponding random-cluster model. Our proofs rely on recent studies (Dereudre et al. in Probab Theory Relat Fields 153:643-670, 2012) of Gibbs measures for geometry-dependent interactions.
Interplay between sign problem and Z3 symmetry in three-dimensional Potts models
NASA Astrophysics Data System (ADS)
Hirakida, Takehiro; Kouno, Hiroaki; Takahashi, Junichi; Yahiro, Masanobu
2016-07-01
We construct four kinds of Z3 -symmetric three-dimensional (3D) Potts models, each with a different number of states at each site on a 3D lattice, by extending the 3D 3-state Potts model. Comparing the ordinary Potts model with the four Z3-symmetric Potts models, we investigate how Z3 symmetry affects the sign problem and see how the deconfinement transition line changes in the μ -κ plane as the number of states increases, where μ (κ ) plays a role of chemical potential (temperature) in the models. We find that the sign problem is almost cured by imposing Z3 symmetry. This mechanism may happen in Z3-symmetric QCD-like theory. We also show that the deconfinement transition line has stronger μ dependence with respect to increasing the number of states.
Non compact continuum limit of two coupled Potts models
NASA Astrophysics Data System (ADS)
Vernier, Éric; Lykke Jacobsen, Jesper; Saleur, Hubert
2014-10-01
We study two Q-state Potts models coupled by the product of their energy operators, in the regime 2 < Q ⩽ 4 where the coupling is relevant. A particular choice of weights for the square lattice is shown to be equivalent to the integrable a_3(2) vertex model. It corresponds to a selfdual system of two antiferromagnetic Potts models, coupled ferromagnetically. We derive the Bethe ansatz equations and study them numerically for two arbitrary twist angles. The continuum limit is shown to involve two compact bosons and one non compact boson, with discrete states emerging from the continuum at appropriate twists. The non compact boson entails strong logarithmic corrections to the finite-size behaviour of the scaling levels, an understanding of which allows us to correct an earlier proposal for some of the critical exponents. In particular, we infer the full set of magnetic scaling dimensions (watermelon operators) of the Potts model.
Series analysis of Q-state checkerboard Potts models
Hansel, D.; Maillard, J.M.
1988-12-01
The series analysis of the low temperature expansion of the checkerboard q-state Potts model in a magnetic field initiated in two previous papers is continued. In particular algebraic varieties of the parameter space (corresponding or generalizing the so-called disorder solutions), the checkerboard Potts model and its Bethe approximation are indistinguishable as far as one is concerned with the partition function and its first order derivatives. The difference between the two models occurs for higher order derivatives. In particular one gives the exact expression of the (low temperature expansion of the) susceptibility of the checkerboard Ising model in zero magnetic field on one of these varieties.
Phenomenological theory of the Potts model evaporation-condensation transition
NASA Astrophysics Data System (ADS)
Ibáñez-Berganza, M.
2016-01-01
We present a phenomenological theory describing the finite-size evaporation-condensation transition of the q-state Potts model in the microcanonical ensemble. Our arguments rely on the existence of an exponent σ, relating the surface and the volume of the condensed phase droplet. The evaporation-condensation transition temperature and energy converge to their infinite-size values with the same power, a=(1-σ)/(2-σ) , of the inverse of the system size. For the 2D Potts model we show, by means of efficient simulations up to q = 24 and 10242 sites, that the exponent a is compatible with 1/4, assuming assymptotic finite-size convergence. While this value cannot be addressed by the evaporation-condensation theory developed for the Ising model, it is obtained in the present scheme if σ=2/3 , in agreement with previous theoretical guesses. The connection with the phenomenon of metastability in the canonical ensemble is also discussed.
The Potts model on a Bethe lattice with nonmagnetic impurities
Semkin, S. V. Smagin, V. P.
2015-10-15
We have obtained a solution for the Potts model on a Bethe lattice with mobile nonmagnetic impurities. A method is proposed for constructing a “pseudochaotic” impurity distribution by a vanishing correlation in the arrangement of impurity atoms for the nearest sites. For a pseudochaotic impurity distribution, we obtained the phase-transition temperature, magnetization, and spontaneous magnetization jumps at the phase-transition temperature.
A hybrid parallel framework for the cellular Potts model simulations
Jiang, Yi; He, Kejing; Dong, Shoubin
2009-01-01
The Cellular Potts Model (CPM) has been widely used for biological simulations. However, most current implementations are either sequential or approximated, which can't be used for large scale complex 3D simulation. In this paper we present a hybrid parallel framework for CPM simulations. The time-consuming POE solving, cell division, and cell reaction operation are distributed to clusters using the Message Passing Interface (MPI). The Monte Carlo lattice update is parallelized on shared-memory SMP system using OpenMP. Because the Monte Carlo lattice update is much faster than the POE solving and SMP systems are more and more common, this hybrid approach achieves good performance and high accuracy at the same time. Based on the parallel Cellular Potts Model, we studied the avascular tumor growth using a multiscale model. The application and performance analysis show that the hybrid parallel framework is quite efficient. The hybrid parallel CPM can be used for the large scale simulation ({approx}10{sup 8} sites) of complex collective behavior of numerous cells ({approx}10{sup 6}).
Exact Potts model partition functions on ladder graphs
NASA Astrophysics Data System (ADS)
Shrock, Robert
2000-08-01
We present exact calculations of the partition function Z of the q-state Potts model and its generalization to real q, for arbitrary temperature on n-vertex ladder graphs, i.e., strips of the square lattice with width Ly=2 and arbitrary length Lx, with free, cyclic, and Möbius longitudinal boundary conditions. These partition functions are equivalent to Tutte/Whitney polynomials for these graphs. The free energy is calculated exactly for the infinite-length limit of these ladder graphs and the thermodynamics is discussed. By comparison with strip graphs of other widths, we analyze how the singularities at the zero-temperature critical point of the ferromagnet on infinite-length, finite-width strips depend on the width. We point out and study the following noncommutativity at certain special values q s: lim n→∞ limq→q s Z 1/n≠ limq→q s limn→∞ Z 1/n. It is shown that the Potts antiferromagnet on both the infinite-length line and ladder graphs with cyclic or Möbius boundary conditions exhibits a phase transition at finite temperature if 0< q<2, but with unphysical properties, including negative specific heat and non-existence, in the low-temperature phase, of an n→∞ limit for thermodynamic functions that is independent of boundary conditions. Considering the full generalization to arbitrary complex q and temperature, we determine the singular locus B in the corresponding C2 space, arising as the accumulation set of partition function zeros as n→∞. In particular, we study the connection with the T=0 limit of the Potts antiferromagnet where B reduces to the accumulation set of chromatic zeros. Certain properties of the complex-temperature phase diagrams are shown to exhibit close connections with those of the model on the square lattice, showing that exact solutions on infinite-length strips provide a way of gaining insight into these complex-temperature phase diagrams.
Hexagon and pentagon identities for the Z sub 3 Potts model
Ryang, S. )
1991-04-15
Investigating the transformation properties of the conformal blocks in the {ital Z}{sub 3} Potts model we derive some braid matrices. From the obtained braid matrices we explicitly show how the hexagon and pentagon identities are satisfied.
Multiscale Model of Colorectal Cancer Using the Cellular Potts Framework
Osborne, James M
2015-01-01
Colorectal cancer (CRC) is one of the major causes of death in the developed world and forms a canonical example of tumorigenesis. CRC arises from a string of mutations of individual cells in the colorectal crypt, making it particularly suited for multiscale multicellular modeling, where mutations of individual cells can be clearly represented and their effects readily tracked. In this paper, we present a multicellular model of the onset of colorectal cancer, utilizing the cellular Potts model (CPM). We use the model to investigate how, through the modification of their mechanical properties, mutant cells colonize the crypt. Moreover, we study the influence of mutations on the shape of cells in the crypt, suggesting possible cell- and tissue-level indicators for identifying early-stage cancerous crypts. Crucially, we discuss the effect that the motility parameters of the model (key factors in the behavior of the CPM) have on the distribution of cells within a homeostatic crypt, resulting in an optimal parameter regime that accurately reflects biological assumptions. In summary, the key results of this paper are 1) how to couple the CPM with processes occurring on other spatial scales, using the example of the crypt to motivate suitable motility parameters; 2) modeling mutant cells with the CPM; 3) and investigating how mutations influence the shape of cells in the crypt. PMID:26461973
A node-based version of the cellular Potts model.
Scianna, Marco; Preziosi, Luigi
2016-09-01
The cellular Potts model (CPM) is a lattice-based Monte Carlo method that uses an energetic formalism to describe the phenomenological mechanisms underlying the biophysical problem of interest. We here propose a CPM-derived framework that relies on a node-based representation of cell-scale elements. This feature has relevant consequences on the overall simulation environment. First, our model can be implemented on any given domain, provided a proper discretization (which can be regular or irregular, fixed or time evolving). Then, it allowed an explicit representation of cell membranes, whose displacements realistically result in cell movement. Finally, our node-based approach can be easily interfaced with continuous mechanics or fluid dynamics models. The proposed computational environment is here applied to some simple biological phenomena, such as cell sorting and chemotactic migration, also in order to achieve an analysis of the performance of the underlying algorithm. This work is finally equipped with a critical comparison between the advantages and disadvantages of our model with respect to the traditional CPM and to some similar vertex-based approaches. PMID:27416549
Potts models with magnetic field: Arithmetic, geometry, and computation
NASA Astrophysics Data System (ADS)
Dasu, Shival; Marcolli, Matilde
2015-11-01
We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.
Jason D. Hales; Veena Tikare
2014-04-01
The Used Fuel Disposition (UFD) program has initiated a project to develop a hydride formation modeling tool using a hybrid Pottsphase field approach. The Potts model is incorporated in the SPPARKS code from Sandia National Laboratories. The phase field model is provided through MARMOT from Idaho National Laboratory.
Marginal dimensions of the Potts model with invisible states
NASA Astrophysics Data System (ADS)
Krasnytska, M.; Sarkanych, P.; Berche, B.; Holovatch, Yu; Kenna, R.
2016-06-01
We reconsider the mean-field Potts model with q interacting and r non-interacting (invisible) states. The model was recently introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where the Z q -symmetry is spontaneously broken. We analyse the marginal dimensions of the model, i.e., the value of r at which the order of the phase transition changes. In the q = 2 case, we determine that value to be {r}{{c}}=3.65(5); there is a second-order phase transition there when r\\lt {r}{{c}} and a first-order one at r\\gt {r}{{c}}. We also analyse the region 1≤slant q\\lt 2 and show that the change from second to first order there is manifest through a new mechanism involving two marginal values of r. The q = 1 limit gives bond percolation. Above the lower value r c1, the order parameters exhibit discontinuities at temperature \\tilde{t} below a critical value t c. The larger value r c2 marks the point at which the phase transition at t c changes from second to first order. Thus, for {r}{{c}1}\\lt r\\lt {r}{{c}2}, the transition at t c remains second order while at \\tilde{t} the system undergoes a first order phase transition. As r increases further, \\tilde{t} increases, bringing the discontinuity closer to t c. Finally, when r exceeds r c2 \\tilde{t} coincides with t c and the phase transition becomes first order. This new mechanism indicates how the discontinuity characteristic of first order phase transitions emerges.
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.
Duality and Fisher zeros in the two-dimensional Potts model on a square lattice
NASA Astrophysics Data System (ADS)
Astorino, Marco; Canfora, Fabrizio
2010-05-01
A phenomenological approach to the ferromagnetic two-dimensional (2D) Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the q -state Potts model. The duality symmetry of the 2D Potts model together with the known results on its critical exponent α allows us to fix consistently the details of the proposed expression for the free energy. The agreement of the analytic ansatz with numerical data in the q=3 case is very good at high and low temperatures as well as at the critical point. It is shown that the q>4 cases naturally fit into the same scheme and that one should also expect a good agreement with numerical data. The limiting q=4 case is shortly discussed.
A Bayesian non-parametric Potts model with application to pre-surgical FMRI data.
Johnson, Timothy D; Liu, Zhuqing; Bartsch, Andreas J; Nichols, Thomas E
2013-08-01
The Potts model has enjoyed much success as a prior model for image segmentation. Given the individual classes in the model, the data are typically modeled as Gaussian random variates or as random variates from some other parametric distribution. In this article, we present a non-parametric Potts model and apply it to a functional magnetic resonance imaging study for the pre-surgical assessment of peritumoral brain activation. In our model, we assume that the Z-score image from a patient can be segmented into activated, deactivated, and null classes, or states. Conditional on the class, or state, the Z-scores are assumed to come from some generic distribution which we model non-parametrically using a mixture of Dirichlet process priors within the Bayesian framework. The posterior distribution of the model parameters is estimated with a Markov chain Monte Carlo algorithm, and Bayesian decision theory is used to make the final classifications. Our Potts prior model includes two parameters, the standard spatial regularization parameter and a parameter that can be interpreted as the a priori probability that each voxel belongs to the null, or background state, conditional on the lack of spatial regularization. We assume that both of these parameters are unknown, and jointly estimate them along with other model parameters. We show through simulation studies that our model performs on par, in terms of posterior expected loss, with parametric Potts models when the parametric model is correctly specified and outperforms parametric models when the parametric model in misspecified. PMID:22627277
Critical behavior of the q = 3 , 4-Potts model on quasiperiodic decagonal lattices
NASA Astrophysics Data System (ADS)
Ferraz, Carlos Handrey Araujo
2015-12-01
In this study, we performed Monte Carlo simulations of the q = 3 , 4-Potts model on quasiperiodic decagonal lattices (QDL) to assess the critical behavior of these systems. Using the single histogram technique in conjunction with the finite-size scaling analysis, we estimate the infinite lattice critical temperatures and the leading critical exponents for q = 3 and q = 4 states. Our estimates for the critical exponents on QDL are in good agreement with the exact values on 2D periodic lattices, supporting the claim that both the q = 3 and q = 4 Potts model on quasiperiodic lattices belong to the same universality class as those on 2D periodic lattices.
Potts model on directed small-world Voronoi-Delaunay lattices
NASA Astrophysics Data System (ADS)
Marques, R. M.; Lima, F. W. S.; Costa Filho, Raimundo N.
2016-06-01
The critical properties of the Potts model with q = 3 and 4 states in two-dimensions on directed small-world Voronoi-Delaunay random lattices with quenched connectivity disorder are investigated. This disordered system is simulated by applying the Monte Carlo update heat bath algorithm. The Potts model on these directed small-world random lattices presents in fact a second-order phase transition with new critical exponents for q = 3 and value of the rewiring probability p = 0.01, but for q = 4 the system exhibits only a first-order phase transition independent of p (0 < p < 1).
Parallel family trees for transfer matrices in the Potts model
NASA Astrophysics Data System (ADS)
Navarro, Cristobal A.; Canfora, Fabrizio; Hitschfeld, Nancy; Navarro, Gonzalo
2015-02-01
The computational cost of transfer matrix methods for the Potts model is related to the question in how many ways can two layers of a lattice be connected? Answering the question leads to the generation of a combinatorial set of lattice configurations. This set defines the configuration space of the problem, and the smaller it is, the faster the transfer matrix can be computed. The configuration space of generic (q , v) transfer matrix methods for strips is in the order of the Catalan numbers, which grows asymptotically as O(4m) where m is the width of the strip. Other transfer matrix methods with a smaller configuration space indeed exist but they make assumptions on the temperature, number of spin states, or restrict the structure of the lattice. In this paper we propose a parallel algorithm that uses a sub-Catalan configuration space of O(3m) to build the generic (q , v) transfer matrix in a compressed form. The improvement is achieved by grouping the original set of Catalan configurations into a forest of family trees, in such a way that the solution to the problem is now computed by solving the root node of each family. As a result, the algorithm becomes exponentially faster than the Catalan approach while still highly parallel. The resulting matrix is stored in a compressed form using O(3m ×4m) of space, making numerical evaluation and decompression to be faster than evaluating the matrix in its O(4m ×4m) uncompressed form. Experimental results for different sizes of strip lattices show that the parallel family trees (PFT) strategy indeed runs exponentially faster than the Catalan Parallel Method (CPM), especially when dealing with dense transfer matrices. In terms of parallel performance, we report strong-scaling speedups of up to 5.7 × when running on an 8-core shared memory machine and 28 × for a 32-core cluster. The best balance of speedup and efficiency for the multi-core machine was achieved when using p = 4 processors, while for the cluster
An improvement of extremality regions for Gibbs measures of the Potts model on a Cayley tree
NASA Astrophysics Data System (ADS)
Haydarov, Farhod; Khakimov, Rustam
2016-03-01
We give a condition of extemelity for translation-invariant Gibbs measures of q—state Potts model on a Cayley tree. We'll improve the regions of extremality for some measures considered in [14]. Moreover, some results in [14] are generalized.
Phase transitions of the q-state Potts model on multiply-laced Sierpinski gaskets
NASA Astrophysics Data System (ADS)
Tian, Liang; Ma, Hui; Guo, Wenan; Tang, Lei-Han
2013-05-01
We present an exact solution of the q-state Potts model on a class of generalized Sierpinski fractal lattices. The model is shown to possess an ordered phase at low temperatures and a continuous transition to the high temperature disordered phase at any q ≥ 1. Multicriticality is observed in the presence of a symmetry-breaking field. Exact renormalization group analysis yields the phase diagram of the model and a complete set of critical exponents at various transitions.
Fluctuation complexity of agent-based financial time series model by stochastic Potts system
NASA Astrophysics Data System (ADS)
Hong, Weijia; Wang, Jun
2015-03-01
Financial market is a complex evolved dynamic system with high volatilities and noises, and the modeling and analyzing of financial time series are regarded as the rather challenging tasks in financial research. In this work, by applying the Potts dynamic system, a random agent-based financial time series model is developed in an attempt to uncover the empirical laws in finance, where the Potts model is introduced to imitate the trading interactions among the investing agents. Based on the computer simulation in conjunction with the statistical analysis and the nonlinear analysis, we present numerical research to investigate the fluctuation behaviors of the proposed time series model. Furthermore, in order to get a robust conclusion, we consider the daily returns of Shanghai Composite Index and Shenzhen Component Index, and the comparison analysis of return behaviors between the simulation data and the actual data is exhibited.
Graphical Representations for Ising and Potts Models in General External Fields
NASA Astrophysics Data System (ADS)
Cioletti, Leandro; Vila, Roberto
2016-01-01
This work is concerned with the theory of graphical representation for the Ising and Potts models over general lattices with non-translation invariant external field. We explicitly describe in terms of the random-cluster representation the distribution function and, consequently, the expected value of a single spin for the Ising and q-state Potts models with general external fields. We also consider the Gibbs states for the Edwards-Sokal representation of the Potts model with non-translation invariant magnetic field and prove a version of the FKG inequality for the so called general random-cluster model (GRC model) with free and wired boundary conditions in the non-translation invariant case. Adding the amenability hypothesis on the lattice, we obtain the uniqueness of the infinite connected component and the almost sure quasilocality of the Gibbs measures for the GRC model with such general magnetic fields. As a final application of the theory developed, we show the uniqueness of the Gibbs measures for the ferromagnetic Ising model with a positive power-law decay magnetic field with small enough power, as conjectured in Bissacot et al. (Commun Math Phys 337: 41-53, 2015).
Lattice models of glasses and Potts models for community detection
NASA Astrophysics Data System (ADS)
Darst, Richard K.
In Part I, we construct a configurationally constrained lattice glass model following the example of Biroli and Mézard (Phys. Rev. Lett., 82, 025501 (2001)), which we denote t154. By examining the relaxation, atomic motion, Stokes-Einstein relationship violation, time-dependent displacement (van Hove function), wavevector-dependent relaxation, and multi-point correlations S4 and χ4 , we can show that this new model satisfies all minimal requirements set by the observed phenomena of dynamical heterogeneity of supercooled liquids, though with a drastically different theoretical basis from existing lattice models of glasses based on kinetic facilitation. We then proceed to perform a more detailed comparison between lattice glass models, including t154 and a model by Ciamarra et. al. (Phys. Rev. E 68 066111 (2003)), with traditional facilitated models. We study two forms of dynamical sensitivity: sensitivity to boundary conditions, and a sensitivity to initial conditions. By comparison to atomistic computer simulation, we find evidence that the lattice glass models better describe glassy behavior. We conclude by discussing the implications of our findings for contrasting theories of the glass transition. In Part II, we change our focus and examine community detection in graphs from a theoretical standpoint. Many disparate community definitions have been proposed, however except for one, few have been analyzed in any great detail. In this work, we, for the first time, formally study a definition based on internal edge density. Using the concept that internal edge density is the fraction of intra-community edges relative to the maximal number of intra-community edges, we produce a rich framework to use as the basis of community detection. We discuss its use in local and global community detection algorithms, and how our methods can extend to overlapping and hierarchical communities, and weighted, directed, and multi-graphs. In order to validate our definition, we use
CSOS models descending from chiral Potts models: degeneracy of the eigenspace and loop algebra
NASA Astrophysics Data System (ADS)
Au-Yang, Helen; Perk, Jacques H. H.
2016-04-01
Monodromy matrices of the {{\\boldsymbol{τ }}}2\\phantom{^{\\prime }} model are known to satisfy a Yang-Baxter equation with a six-vertex R-matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this R-matrix. We show the reason why in the superintegrable case the eigenspace is degenerate, but not in the general case. We then show that the eigenspaces of special CSOS models descending from the chiral Potts model are also degenerate. The existence of an L({{sl}}2) quantum loop algebra (or subalgebra) in these models is established by showing that the Serre relations hold for the generators. The highest weight polynomial (or the Drinfeld polynomial) of the representation is obtained by using the method of Baxter for the superintegrable case. As a byproduct, the eigenvalues of all such CSOS models are given explicitly.
Sums of random matrices and the Potts model on random planar maps
NASA Astrophysics Data System (ADS)
Atkin, Max R.; Niedner, Benjamin; Wheater, John F.
2016-05-01
We compute the partition function of the q-states Potts model on a random planar lattice with p≤slant q allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit, generalising a result by Voiculescu for the addition of random matrices to a situation beyond free probability theory. We show that the partition functions with p and q - p colours on the boundary are related algebraically. Finally, we investigate the phase diagram of the model when 0≤slant q≤slant 4 and comment on the conformal field theory description of the critical points.
Shaken, but not stirred—Potts model coupled to quantum gravity
NASA Astrophysics Data System (ADS)
Ambjørn, J. A.; Anagnostopoulos, K. N.; Loll, R.; Pushkina, I.
2009-01-01
We investigate the critical behaviour of both matter and geometry of the three-state Potts model coupled to two-dimensional Lorentzian quantum gravity in the framework of causal dynamical triangulations. Contrary to what general arguments on the effects of disorder suggest, we find strong numerical evidence that the critical exponents of the matter are not changed under the influence of quantum fluctuations in the geometry, compared to their values on fixed, regular lattices. This lends further support to previous findings that quantum gravity models based on causal dynamical triangulations are in many ways better behaved than their Euclidean counterparts.
The early history of the integrable chiral Potts model and the odd-even problem
NASA Astrophysics Data System (ADS)
Perk, Jacques H. H.
2016-04-01
In the first part of this paper I shall discuss the round-about way of how the integrable chiral Potts model was discovered about 30 years ago. As there should be more higher-genus models to be discovered, this might be of interest. In the second part I shall discuss some quantum group aspects, especially issues of odd versus even N related to the Serre relations conjecture in our quantum loop subalgebra paper of 5 years ago and how we can make good use of coproducts, also borrowing ideas of Drinfeld, Jimbo, Deguchi, Fabricius, McCoy and Nishino.
Potts model simulation of grain size distributions during final stage sintering
Zeng, P.; Tikare, V.
1998-09-01
The Potts Monte Carlo model was used to simulate microstructural evolution and characterize grain size distribution during the final stages of sintering. Simultaneous grain growth, pore migration and pore shrinkage were simulated in a system with an initial porosity of 10% with varying ratios of grain boundary mobility to pore shrinkage rates. This investigation shows that the presence of pores changes the grain size distribution and the topological characteristics due to pinning of grains by pores. As pores shrink away, their pinning effect decreases. Once pore shrinkage is complete, normal grain growth is achieved.
Dynamics of Cell Shape and Forces on Micropatterned Substrates Predicted by a Cellular Potts Model
Albert, Philipp J.; Schwarz, Ulrich S.
2014-01-01
Micropatterned substrates are often used to standardize cell experiments and to quantitatively study the relation between cell shape and function. Moreover, they are increasingly used in combination with traction force microscopy on soft elastic substrates. To predict the dynamics and steady states of cell shape and forces without any a priori knowledge of how the cell will spread on a given micropattern, here we extend earlier formulations of the two-dimensional cellular Potts model. The third dimension is treated as an area reservoir for spreading. To account for local contour reinforcement by peripheral bundles, we augment the cellular Potts model by elements of the tension-elasticity model. We first parameterize our model and show that it accounts for momentum conservation. We then demonstrate that it is in good agreement with experimental data for shape, spreading dynamics, and traction force patterns of cells on micropatterned substrates. We finally predict shapes and forces for micropatterns that have not yet been experimentally studied. PMID:24896113
NASA Astrophysics Data System (ADS)
Hu, Zhan-Ning
In this letter, the connection is found between the "star-square" relation in the Baxter-Bazhanov model and the "star-triangle" relation in the chiral Potts model, which means that the tetrahedron equation of the Baxter-Bazhanov model is a consequence of the latter. The four additional constraints in the tetrahedron equation given by Kashaev et al. hold naturally in respect to the spherical trigonometry parametrizations.
Structural propensities of kinase family proteins from a Potts model of residue co-variation.
Haldane, Allan; Flynn, William F; He, Peng; Vijayan, R S K; Levy, Ronald M
2016-08-01
Understanding the conformational propensities of proteins is key to solving many problems in structural biology and biophysics. The co-variation of pairs of mutations contained in multiple sequence alignments of protein families can be used to build a Potts Hamiltonian model of the sequence patterns which accurately predicts structural contacts. This observation paves the way to develop deeper connections between evolutionary fitness landscapes of entire protein families and the corresponding free energy landscapes which determine the conformational propensities of individual proteins. Using statistical energies determined from the Potts model and an alignment of 2896 PDB structures, we predict the propensity for particular kinase family proteins to assume a "DFG-out" conformation implicated in the susceptibility of some kinases to type-II inhibitors, and validate the predictions by comparison with the observed structural propensities of the corresponding proteins and experimental binding affinity data. We decompose the statistical energies to investigate which interactions contribute the most to the conformational preference for particular sequences and the corresponding proteins. We find that interactions involving the activation loop and the C-helix and HRD motif are primarily responsible for stabilizing the DFG-in state. This work illustrates how structural free energy landscapes and fitness landscapes of proteins can be used in an integrated way, and in the context of kinase family proteins, can potentially impact therapeutic design strategies. PMID:27241634
Multi-Scale Modeling in Morphogenesis: A Critical Analysis of the Cellular Potts Model
Voss-Böhme, Anja
2012-01-01
Cellular Potts models (CPMs) are used as a modeling framework to elucidate mechanisms of biological development. They allow a spatial resolution below the cellular scale and are applied particularly when problems are studied where multiple spatial and temporal scales are involved. Despite the increasing usage of CPMs in theoretical biology, this model class has received little attention from mathematical theory. To narrow this gap, the CPMs are subjected to a theoretical study here. It is asked to which extent the updating rules establish an appropriate dynamical model of intercellular interactions and what the principal behavior at different time scales characterizes. It is shown that the longtime behavior of a CPM is degenerate in the sense that the cells consecutively die out, independent of the specific interdependence structure that characterizes the model. While CPMs are naturally defined on finite, spatially bounded lattices, possible extensions to spatially unbounded systems are explored to assess to which extent spatio-temporal limit procedures can be applied to describe the emergent behavior at the tissue scale. To elucidate the mechanistic structure of CPMs, the model class is integrated into a general multiscale framework. It is shown that the central role of the surface fluctuations, which subsume several cellular and intercellular factors, entails substantial limitations for a CPM's exploitation both as a mechanistic and as a phenomenological model. PMID:22984409
A study of perfect wetting for Potts and Blume-Capel models with correlation inequalities
De Coninck, J.; Messager, A.; Miracle-Sole, S.; Ruiz, J. )
1988-07-01
The so-called perfect wetting phenomenon is studied for the q-state, d {>=} 2 Potts model. Using a new correlation inequality, a general inequality is established for the surface tension between ordered phases ({sigma}{sup a,b}) and the surface tension between an ordered and the disordered phases ({sigma}{sup a,f}) for any even value of q. This result implies in particular {sigma}{sub {beta}{sub t}}{sup a,b} {>=} {sigma}{sub {beta}{sub t}}{sup a,f} + {sigma}{sub {beta}{sub t}}{sup b,f} > 0 at the transition point {beta}{sub t} where the previous phases coexist for q large. This inequality is connected to perfect wetting at the transition point using thermodynamic considerations. The same kinds of results are derived for the Blume-Capel model.
High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials
NASA Astrophysics Data System (ADS)
>Jesper Lykke Jacobsen,
2014-04-01
The critical curves of the q-state Potts model can be determined exactly for regular two-dimensional lattices G that are of the three-terminal type. This comprises the square, triangular, hexagonal and bow-tie lattices. Jacobsen and Scullard have defined a graph polynomial PB(q, v) that gives access to the critical manifold for general lattices. It depends on a finite repeating part of the lattice, called the basis B, and its real roots in the temperature variable v = eK - 1 provide increasingly accurate approximations to the critical manifolds upon increasing the size of B. Using transfer matrix techniques, these authors computed PB(q, v) for large bases (up to 243 edges), obtaining determinations of the ferromagnetic critical point vc > 0 for the (4, 82), kagome, and (3, 122) lattices to a precision (of the order 10-8) slightly superior to that of the best available Monte Carlo simulations. In this paper we describe a more efficient transfer matrix approach to the computation of PB(q, v) that relies on a formulation within the periodic Temperley-Lieb algebra. This makes possible computations for substantially larger bases (up to 882 edges), and the precision on vc is hence taken to the range 10-13. We further show that a large variety of regular lattices can be cast in a form suitable for this approach. This includes all Archimedean lattices, their duals and their medials. For all these lattices we tabulate high-precision estimates of the bond percolation thresholds pc and Potts critical points vc. We also trace and discuss the full Potts critical manifold in the (q, v) plane, paying special attention to the antiferromagnetic region v < 0. Finally, we adapt the technique to site percolation as well, and compute the polynomials PB(p) for certain Archimedean and dual lattices (those having only cubic and quartic vertices), using very large bases (up to 243 vertices). This produces the site percolation thresholds pc to a precision of the order of 10-9.
Spanning Forests and the q-State Potts Model in the Limit q →0
NASA Astrophysics Data System (ADS)
Jacobsen, Jesper Lykke; Salas, Jesús; Sokal, Alan D.
2005-06-01
We study the q-state Potts model with nearest-neighbor coupling v=eβJ-1 in the limit q,v → 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2≤ L ≤ 10, as well as the limiting curves B of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w= w 0, where w0 =-1/4 (resp. w0=-0.1753 ± 0.0002) for the square (resp. triangular) lattice. For w>w0 we find a non-critical disordered phase that is compatible with the predicted asymptotic freedom as w → +∞. For w
FAST TRACK COMMUNICATION Critical exponents of domain walls in the two-dimensional Potts model
NASA Astrophysics Data System (ADS)
Dubail, Jérôme; Lykke Jacobsen, Jesper; Saleur, Hubert
2010-12-01
We address the geometrical critical behavior of the two-dimensional Q-state Potts model in terms of the spin clusters (i.e. connected domains where the spin takes a constant value). These clusters are different from the usual Fortuin-Kasteleyn clusters, and are separated by domain walls that can cross and branch. We develop a transfer matrix technique enabling the formulation and numerical study of spin clusters even when Q is not an integer. We further identify geometrically the crossing events which give rise to conformal correlation functions. This leads to an infinite series of fundamental critical exponents h_{\\ell _1-\\ell _2,2\\ell _1}, valid for 0 <= Q <= 4, that describe the insertion of ell1 thin and ell2 thick domain walls.
A parallel implementation of the Cellular Potts Model for simulation of cell-based morphogenesis
Chen, Nan; Glazier, James A.; Izaguirre, Jesús A.; Alber, Mark S.
2007-01-01
The Cellular Potts Model (CPM) has been used in a wide variety of biological simulations. However, most current CPM implementations use a sequential modified Metropolis algorithm which restricts the size of simulations. In this paper we present a parallel CPM algorithm for simulations of morphogenesis, which includes cell–cell adhesion, a cell volume constraint, and cell haptotaxis. The algorithm uses appropriate data structures and checkerboard subgrids for parallelization. Communication and updating algorithms synchronize properties of cells simulated on different processor nodes. Tests show that the parallel algorithm has good scalability, permitting large-scale simulations of cell morphogenesis (107 or more cells) and broadening the scope of CPM applications. The new algorithm satisfies the balance condition, which is sufficient for convergence of the underlying Markov chain. PMID:18084624
A Cellular Potts Model of single cell migration in presence of durotaxis.
Allena, R; Scianna, M; Preziosi, L
2016-05-01
Cell migration is a fundamental biological phenomenon during which cells sense their surroundings and respond to different types of signals. In presence of durotaxis, cells preferentially crawl from soft to stiff substrates by reorganizing their cytoskeleton from an isotropic to an anisotropic distribution of actin filaments. In the present paper, we propose a Cellular Potts Model to simulate single cell migration over flat substrates with variable stiffness. We have tested five configurations: (i) a substrate including a soft and a stiff region, (ii) a soft substrate including two parallel stiff stripes, (iii) a substrate made of successive stripes with increasing stiffness to create a gradient and (iv) a stiff substrate with four embedded soft squares. For each simulation, we have evaluated the morphology of the cell, the distance covered, the spreading area and the migration speed. We have then compared the numerical results to specific experimental observations showing a consistent agreement. PMID:26968932
Transfer matrix computation of critical polynomials for two-dimensional Potts models
Jacobsen, Jesper Lykke; Scullard, Christian R.
2013-02-04
We showed, In our previous work, that critical manifolds of the q-state Potts model can be studied by means of a graph polynomial PB(q, v), henceforth referred to as the critical polynomial. This polynomial may be defined on any periodic two-dimensional lattice. It depends on a finite subgraph B, called the basis, and the manner in which B is tiled to construct the lattice. The real roots v = eK — 1 of PB(q, v) either give the exact critical points for the lattice, or provide approximations that, in principle, can be made arbitrarily accurate by increasing the size ofmore » B in an appropriate way. In earlier work, PB(q, v) was defined by a contraction-deletion identity, similar to that satisfied by the Tutte polynomial. Here, we give a probabilistic definition of PB(q, v), which facilitates its computation, using the transfer matrix, on much larger B than was previously possible.We present results for the critical polynomial on the (4, 82), kagome, and (3, 122) lattices for bases of up to respectively 96, 162, and 243 edges, compared to the limit of 36 edges with contraction-deletion. We discuss in detail the role of the symmetries and the embedding of B. The critical temperatures vc obtained for ferromagnetic (v > 0) Potts models are at least as precise as the best available results from Monte Carlo simulations or series expansions. For instance, with q = 3 we obtain vc(4, 82) = 3.742 489 (4), vc(kagome) = 1.876 459 7 (2), and vc(3, 122) = 5.033 078 49 (4), the precision being comparable or superior to the best simulation results. More generally, we trace the critical manifolds in the real (q, v) plane and discuss the intricate structure of the phase diagram in the antiferromagnetic (v < 0) region.« less
Šimėnas, Mantas; Balčiūnas, Sergejus; Ma Combining Cedilla Czka, Mirosław; Banys, Jūras; Tornau, Evaldas E
2016-07-21
We propose a combined experimental and numerical study to describe an order-disorder structural phase transition in perovskite-based [(CH3)2NH2][M(HCOO)3] (M = Zn(2+), Mn(2+), Fe(2+), Co(2+) and Ni(2+)) dense metal-organic frameworks (MOFs). The three-fold degenerate orientation of the molecular (CH3)2NH2(+) (DMA(+)) cation implies a selection of the statistical three-state model of the Potts type. It is constructed on a simple cubic lattice where each lattice point can be occupied by a DMA(+) cation in one of the available states. In our model the main interaction is the nearest-neighbor Potts-type interaction, which effectively accounts for the H-bonding between DMA(+) cations and M(HCOO)3(-) cages. The model is modified by accounting for the dipolar interactions which are evaluated for the real monoclinic lattice using density functional theory. We employ the Monte Carlo method to numerically study the model. The calculations are supplemented with the experimental measurements of electric polarization. The obtained results indicate that the three-state Potts model correctly describes the phase transition order in these MOFs, while dipolar interactions are necessary to obtain better agreement with the experimental polarization. We show that in our model with substantial dipolar interactions the ground state changes from uniform to the layers with alternating polarization directions. PMID:27341447
Chair, Noureddine
2014-02-15
We have recently developed methods for obtaining exact two-point resistance of the complete graph minus N edges. We use these methods to obtain closed formulas of certain trigonometrical sums that arise in connection with one-dimensional lattice, in proving Scott’s conjecture on permanent of Cauchy matrix, and in the perturbative chiral Potts model. The generalized trigonometrical sums of the chiral Potts model are shown to satisfy recursion formulas that are transparent and direct, and differ from those of Gervois and Mehta. By making a change of variables in these recursion formulas, the dimension of the space of conformal blocks of SU(2) and SO(3) WZW models may be computed recursively. Our methods are then extended to compute the corner-to-corner resistance, and the Kirchhoff index of the first non-trivial two-dimensional resistor network, 2×N. Finally, we obtain new closed formulas for variant of trigonometrical sums, some of which appear in connection with number theory. -- Highlights: • Alternative derivation of certain trigonometrical sums of the chiral Potts model are given. • Generalization of these trigonometrical sums satisfy recursion formulas. • The dimension of the space of conformal blocks may be computed from these recursions. • Exact corner-to-corner resistance, the Kirchhoff index of 2×N are given.
Fraction of uninfected walkers in the one-dimensional Potts model
NASA Astrophysics Data System (ADS)
O'Donoghue, S. J.; Bray, A. J.
2002-05-01
The dynamics of the one-dimensional q-state Potts model, in the zero-temperature limit, can be formulated through the motion of random walkers which either annihilate (A+A-->∅) or coalesce (A+A-->A) with a q-dependent probability. We consider all of the walkers in this model to be mutually infectious. Whenever two walkers meet, they experience mutual contamination. Walkers which avoid an encounter with another random walker up to time t remain uninfected. The fraction of uninfected walkers is known to obey a power-law decay U(t)~t-φ(q), with a nontrivial exponent φ(q) [C. Monthus, Phys. Rev. E 54, 4844 (1996); S. N. Majumdar and S. J. Cornell, ibid. 57, 3757 (1998)]. We probe the numerical values of φ(q) to a higher degree of accuracy than previous simulations and relate the exponent φ(q) to the persistence exponent θ(q) [B. Derrida, V. Hakim, and V. Pasquier, Phys. Rev. Lett. 75, 751 (1995)], through the relation φ(q)=γ(q)θ(q) where γ is an exponent introduced in [S. J. O'Donoghue and A. J. Bray, preceding paper, Phys. Rev. E 65, XXXX (2002)]. Our study is extended to include the coupled diffusion-limited reaction A+A-->B, B+B-->A in one dimension with equal initial densities of A and B particles. We find that the density of walkers decays in this model as ρ(t)~t-1/2. The fraction of sites unvisited by either an A or a B particle is found to obey a power law, P(t)~t-θ with θ~=1.33. We discuss these exponents within the context of the q-state Potts model and present numerical evidence that the fraction of walkers which remain uninfected decays as U(t)~t-φ, where φ~=1.13 when infection occurs between like particles only, and φ~=1.93 when we also include cross-species contamination. We find that the relation between φ and θ in this model can also be characterized by an exponent γ, where similarly, φ=γθ.
Nature of phase transitions in Axelrod-like coupled Potts models in two dimensions
NASA Astrophysics Data System (ADS)
Gandica, Yerali; Chiacchiera, Silvia
2016-03-01
We study F coupled q -state Potts models in a two-dimensional square lattice. The interaction between the different layers is attractive to favor a simultaneous alignment in all of them, and its strength is fixed. The nature of the phase transition for zero field is numerically determined for F =2 ,3 . Using the Lee-Kosterlitz method, we find that it is continuous for F =2 and q =2 , whereas it is abrupt for higher values of q and/or F . When a continuous or a weakly first-order phase transition takes place, we also analyze the properties of the geometrical clusters. This allows us to determine the fractal dimension D of the incipient infinite cluster and to examine the finite-size scaling of the cluster number density via data collapse. A mean-field approximation of the model, from which some general trends can be determined, is presented too. Finally, since this lattice model has been recently considered as a thermodynamic counterpart of the Axelrod model of social dynamics, we discuss our results in connection with this one.
Cluster-size distribution and the magnetic property of a Potts model
NASA Astrophysics Data System (ADS)
Hu, Chin-Kun
1986-11-01
Based on the connection between a q-state Potts model (QPM) and a q-state bond-correlated percolation model (QBCPM), we propose that in the calculation of the free energy and a physical quantity, e.g., the magnetic susceptibility, we need only to retain the terms of the most probable cluster-size distribution (MPCSD) defined in the text. For the one-dimensional model, the MPCSD may be calculated exactly. The free energy and the magnetic susceptibility determined by such MPCSD are the same as those calculated exactly by the transfer-matrix method. For the QPM on the lattice with dimensions d>=2, the above assumption about the MPCSD implies that the magnetic susceptibility of the QPM is proportional to the mean cluster sizes of the QBCPM for both T>Tc and T
Transfer matrix computation of critical polynomials for two-dimensional Potts models
Jacobsen, Jesper Lykke; Scullard, Christian R.
2013-02-04
We showed, In our previous work, that critical manifolds of the q-state Potts model can be studied by means of a graph polynomial P_{B}(q, v), henceforth referred to as the critical polynomial. This polynomial may be defined on any periodic two-dimensional lattice. It depends on a finite subgraph B, called the basis, and the manner in which B is tiled to construct the lattice. The real roots v = e^{K} — 1 of P_{B}(q, v) either give the exact critical points for the lattice, or provide approximations that, in principle, can be made arbitrarily accurate by increasing the size of B in an appropriate way. In earlier work, P_{B}(q, v) was defined by a contraction-deletion identity, similar to that satisfied by the Tutte polynomial. Here, we give a probabilistic definition of P_{B}(q, v), which facilitates its computation, using the transfer matrix, on much larger B than was previously possible.We present results for the critical polynomial on the (4, 8^{2}), kagome, and (3, 12^{2}) lattices for bases of up to respectively 96, 162, and 243 edges, compared to the limit of 36 edges with contraction-deletion. We discuss in detail the role of the symmetries and the embedding of B. The critical temperatures v_{c }obtained for ferromagnetic (v > 0) Potts models are at least as precise as the best available results from Monte Carlo simulations or series expansions. For instance, with q = 3 we obtain v_{c}(4, 8^{2}) = 3.742 489 (4), v_{c}(kagome) = 1.876 459 7 (2), and v_{c}(3, 12^{2}) = 5.033 078 49 (4), the precision being comparable or superior to the best simulation results. More generally, we trace the critical manifolds in the real (q, v) plane and discuss the intricate structure of the phase diagram in the antiferromagnetic (v < 0) region.
NASA Astrophysics Data System (ADS)
Chang, Shu-Chiuan; Shrock, Robert
2001-07-01
The q-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width Ly and arbitrary length Lx has the form Z(G,q,v)=∑ j=1N Z,G,λ c Z,G,j(λ Z,G,j) L x, where v is a temperature-dependent variable. The special case of the zero-temperature antiferromagnet ( v=-1) is the chromatic polynomial P( G, q). Using coloring and transfer matrix methods, we give general formulas for C X,G=∑ j=1N X,G,λ c X,G,j for X= Z, P on cyclic and Möbius strip graphs of the square and triangular lattice. Combining these with a general expression for the (unique) coefficient cZ, G, j of degree d in q: c (d)=U 2d( q/2) , where Un( x) is the Chebyshev polynomial of the second kind, we determine the number of λZ, G, j's with coefficient c( d) in Z( G, q, v) for these cyclic strips of width Ly to be n Z(L y,d)=(2d+1)(L y+d+1) -1{2L y}/{L y-d } for 0⩽ d⩽ Ly and zero otherwise. For both cyclic and Möbius strips of these lattices, the total number of distinct eigenvalues λZ, G, j is calculated to be N Z,L y,λ = {2L y}/{L y}. Results are also presented for the analogous numbers nP( Ly, d) and NP, Ly, λ for P( G, q). We find that nP( Ly,0)= nP( Ly-1,1)= MLy-1 (Motzkin number), nZ( Ly,0)= CLy (the Catalan number), and give an exact expression for NP, Ly, λ. Our results for NZ, Ly, λ and NP, Ly, λ apply for both the cyclic and Möbius strips of both the square and triangular lattices; we also point out the interesting relations NZ, Ly, λ=2 NDA, tri, Ly and NP, Ly, λ=2 NDA, sq, Ly, where NDA, Λ, n denotes the number of directed lattice animals on the lattice Λ. We find the asymptotic growths NZ, Ly, λ∼ Ly-1/24 Ly and NP, Ly, λ∼ Ly-1/23 Ly as Ly→∞. Some general geometric identities for Potts model partition functions are also presented.
Reconstruction of a Real World Social Network using the Potts Model and Loopy Belief Propagation
Bisconti, Cristian; Corallo, Angelo; Fortunato, Laura; Gentile, Antonio A.; Massafra, Andrea; Pellè, Piergiuseppe
2015-01-01
The scope of this paper is to test the adoption of a statistical model derived from Condensed Matter Physics, for the reconstruction of the structure of a social network. The inverse Potts model, traditionally applied to recursive observations of quantum states in an ensemble of particles, is here addressed to observations of the members' states in an organization and their (anti)correlations, thus inferring interactions as links among the members. Adopting proper (Bethe) approximations, such an inverse problem is showed to be tractable. Within an operational framework, this network-reconstruction method is tested for a small real-world social network, the Italian parliament. In this study case, it is easy to track statuses of the parliament members, using (co)sponsorships of law proposals as the initial dataset. In previous studies of similar activity-based networks, the graph structure was inferred directly from activity co-occurrences: here we compare our statistical reconstruction with such standard methods, outlining discrepancies and advantages. PMID:26617539
Improved contact prediction in proteins: using pseudolikelihoods to infer Potts models.
Ekeberg, Magnus; Lövkvist, Cecilia; Lan, Yueheng; Weigt, Martin; Aurell, Erik
2013-01-01
Spatially proximate amino acids in a protein tend to coevolve. A protein's three-dimensional (3D) structure hence leaves an echo of correlations in the evolutionary record. Reverse engineering 3D structures from such correlations is an open problem in structural biology, pursued with increasing vigor as more and more protein sequences continue to fill the data banks. Within this task lies a statistical inference problem, rooted in the following: correlation between two sites in a protein sequence can arise from firsthand interaction but can also be network-propagated via intermediate sites; observed correlation is not enough to guarantee proximity. To separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics, where the task is to learn model parameters (fields, couplings) from observables (magnetizations, correlations, samples) in large systems. In the context of protein sequences, the approach has been referred to as direct-coupling analysis. Here we show that the pseudolikelihood method, applied to 21-state Potts models describing the statistical properties of families of evolutionarily related proteins, significantly outperforms existing approaches to the direct-coupling analysis, the latter being based on standard mean-field techniques. This improved performance also relies on a modified score for the coupling strength. The results are verified using known crystal structures of specific sequence instances of various protein families. Code implementing the new method can be found at http://plmdca.csc.kth.se/. PMID:23410359
Improved contact prediction in proteins: Using pseudolikelihoods to infer Potts models
NASA Astrophysics Data System (ADS)
Ekeberg, Magnus; Lövkvist, Cecilia; Lan, Yueheng; Weigt, Martin; Aurell, Erik
2013-01-01
Spatially proximate amino acids in a protein tend to coevolve. A protein's three-dimensional (3D) structure hence leaves an echo of correlations in the evolutionary record. Reverse engineering 3D structures from such correlations is an open problem in structural biology, pursued with increasing vigor as more and more protein sequences continue to fill the data banks. Within this task lies a statistical inference problem, rooted in the following: correlation between two sites in a protein sequence can arise from firsthand interaction but can also be network-propagated via intermediate sites; observed correlation is not enough to guarantee proximity. To separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics, where the task is to learn model parameters (fields, couplings) from observables (magnetizations, correlations, samples) in large systems. In the context of protein sequences, the approach has been referred to as direct-coupling analysis. Here we show that the pseudolikelihood method, applied to 21-state Potts models describing the statistical properties of families of evolutionarily related proteins, significantly outperforms existing approaches to the direct-coupling analysis, the latter being based on standard mean-field techniques. This improved performance also relies on a modified score for the coupling strength. The results are verified using known crystal structures of specific sequence instances of various protein families. Code implementing the new method can be found at http://plmdca.csc.kth.se/.
Cellular Potts Modeling of Tumor Growth, Tumor Invasion, and Tumor Evolution
Szabó, András; Merks, Roeland M. H.
2013-01-01
Despite a growing wealth of available molecular data, the growth of tumors, invasion of tumors into healthy tissue, and response of tumors to therapies are still poorly understood. Although genetic mutations are in general the first step in the development of a cancer, for the mutated cell to persist in a tissue, it must compete against the other, healthy or diseased cells, for example by becoming more motile, adhesive, or multiplying faster. Thus, the cellular phenotype determines the success of a cancer cell in competition with its neighbors, irrespective of the genetic mutations or physiological alterations that gave rise to the altered phenotype. What phenotypes can make a cell “successful” in an environment of healthy and cancerous cells, and how? A widely used tool for getting more insight into that question is cell-based modeling. Cell-based models constitute a class of computational, agent-based models that mimic biophysical and molecular interactions between cells. One of the most widely used cell-based modeling formalisms is the cellular Potts model (CPM), a lattice-based, multi particle cell-based modeling approach. The CPM has become a popular and accessible method for modeling mechanisms of multicellular processes including cell sorting, gastrulation, or angiogenesis. The CPM accounts for biophysical cellular properties, including cell proliferation, cell motility, and cell adhesion, which play a key role in cancer. Multiscale models are constructed by extending the agents with intracellular processes including metabolism, growth, and signaling. Here we review the use of the CPM for modeling tumor growth, tumor invasion, and tumor progression. We argue that the accessibility and flexibility of the CPM, and its accurate, yet coarse-grained and computationally efficient representation of cell and tissue biophysics, make the CPM the method of choice for modeling cellular processes in tumor development. PMID:23596570
Competitive heterogeneous nucleation onto a microscopic impurity in a Potts model
NASA Astrophysics Data System (ADS)
Asuquo, Cletus C.; McArthur, Danielle; Bowles, Richard K.
2016-08-01
Many metastable systems can nucleate to multiple competing stable or intermediate metastable states. In this work, a Potts model, subject to external fields, is used to study the competitive nucleation of two phases attempting to grow on a microscopic impurity. Monte Carlo simulations are used to calculate the free energy surfaces for the system under different conditions, where the relative stability of the phases is adjusted by changing the interaction parameters, and the nucleation rates obtained using multicomponent transition state theory (TST) are compared with the rates measured using the survival probability method. We find that the two methods predict similar nucleation rates when the free energy barrier used in the transition state theory is defined as the work required to form a critical embryo from the metastable phase. An analysis of the free energy surfaces also reveals that the competition between the nucleating phases leads to an effective drying of the impurity which slows down the nucleation rate compared to the single phase case.
Implications of lack-of-ergodicity in 2D Potts model
NASA Astrophysics Data System (ADS)
Ota, Smita
2015-03-01
Microcanonical Monte Carlo simulation is used to study two dimensional (2D) q state Potts model. We consider a 2D square lattice having NxN spins with periodic boundary condition and simulated the system with N =15 and q =10. The demon energy distribution is found to be exponential for high system energy and large system size. For smaller system size and above the first order transition the demon energy distribution is found to deviate from exp(- βED) and has the form exp(- βED + γ ED2). Here β = 1/kBT and kB is the Boltzmann constant. It is found that γ is finite at higher temperatures. As the system energy is reduced γ becomes zero near the first order transition. It is found that during cooling γ changes sign from negative to positive and then to negative again near the 1st order transition. Therefore the demon energy distribution becomes exp(- βED) (or ergodic) at two values of system energy near the 1st order transition. Further cooling or at still lower temperatures the system shows lack of ergodicity. However, difference in heating cooling curves are apparent in E vs γ. The system energies for which γ is zero during cooling can represent the 'ergodic' states. This can be related to the two-level systems observed in glasses at low temperatures.
Potts model partition functions for self-dual families of strip graphs
NASA Astrophysics Data System (ADS)
Chang, Shu-Chiuan; Shrock, Robert
2001-12-01
We consider the q-state Potts model on families of self-dual strip graphs GD of the square lattice of width Ly and arbitrarily great length Lx, with periodic longitudinal boundary conditions. The general partition function Z and the T=0 antiferromagnetic special case P (chromatic polynomial) have the respective forms ∑ j=1 NF, Ly, λcF, Ly, j( λF, Ly, j) Lx, with F= Z, P. For arbitrary Ly, we determine (i) the general coefficient cF, Ly, j in terms of Chebyshev polynomials, (ii) the number nF( Ly, d) of terms with each type of coefficient, and (iii) the total number of terms NF, Ly, λ. We point out interesting connections between the nZ( Ly, d) and Temperley-Lieb algebras, and between the NF, Ly, λ and enumerations of directed lattice animals. Exact calculations of P are presented for 2⩽ Ly⩽4. In the limit of infinite length, we calculate the ground state degeneracy per site (exponent of the ground state entropy), W( q). Generalizing q from Z+ to C, we determine the continuous locus B in the complex q plane where W( q) is singular. We find the interesting result that for all Ly values considered, the maximal point at which B crosses the real q-axis, denoted qc, is the same, and is equal to the value for the infinite square lattice, qc=3. This is the first family of strip graphs of which we are aware that exhibits this type of universality of qc.
Jacobsen, J L; Saleur, H
2008-02-29
We determine exactly the probability distribution of the number N_(c) of valence bonds connecting a subsystem of length L>1 to the rest of the system in the ground state of the XXX antiferromagnetic spin chain. This provides, in particular, the asymptotic behavior of the valence-bond entanglement entropy S_(VB)=N_(c)ln2=4ln2/pi(2)lnL disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/3lnL. Our results generalize to the Q-state Potts model. PMID:18352661
NASA Astrophysics Data System (ADS)
Murtazaev, A. K.; Babaev, A. B.; Ataeva, G. Ya.
2015-07-01
The effect of quenched-in nonmagnetic impurities on phase transitions in a two-dimensional diluted antiferromagnetic three-vertex Potts model on a triangular lattice has been investigated using the Monte Carlo method. The systems with linear dimensions L × L = N and L = 9-144 have been considered. It has been shown using the fourth-order Binder cumulant method that the introduction of a quenched-in disorder into a spin system described by the two-dimensional antiferromagnetic Potts model leads to a change from the first-order phase transition to the second-order phase transition.
NASA Astrophysics Data System (ADS)
Babaev, A. B.; Magomedov, M. A.; Murtazaev, A. K.; Kassan-Ogly, F. A.; Proshkin, A. I.
2016-02-01
Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J 1 and J 2, respectively. PTs in these models are analyzed for the ratio r = J 2/ J 1 of next-nearest to nearest exchange interaction constants in the interval | r| = 0-1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J 1 < 0 and J 2 < 0 exhibits a first-order PT in the range of 0 ⩽ r < 0.2, whereas, in the interval 0.2 ⩽ r ⩽ 1.0, frustrations arise in the system. At the same time, for J 1 > 0 and J 2 < 0, frustrations arise in the range 0.5 < | r| < 1.0, while, in the interval 0 ⩽ | r| ⩽ 1/3, the model exhibits a second-order PT.
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.
Quasi-Long-Range Order and Vortex Lattice in the Three-State Potts Model
NASA Astrophysics Data System (ADS)
Bhattacharya, Soumyadeep; Ray, Purusattam
2016-03-01
We show that the order-disorder phase transition in the three-state Potts ferromagnet on a square lattice is driven by a coupled proliferation of domain walls and vortices. Raising the vortex core energy above a threshold value decouples the proliferation and splits the transition into two. The phase between the two transitions exhibits an emergent U(1) symmetry and quasi-long-range order. Lowering the core energy below a threshold value also splits the order-disorder transition but the system forms a vortex lattice in the intermediate phase.
Ding, Chengxiang; Fu, Zhe; Guo, Wenan; Wu, F Y
2010-06-01
In the preceding paper, one of us (F. Y. Wu) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu's result is exact, and for the kagome-type lattices Wu's expression is under a homogeneity assumption. The purpose of the present paper is twofold: First, an essential step in Wu's analysis is the derivation of lattice-dependent constants A,B,C for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Second, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the q -state Potts model and the bond percolation on the 3-12 and kagome-type subnet lattices (n×n):(n×n) , n≤4 , for which the exact solution is not known. Our numerical determination of critical properties such as conformal anomaly and magnetic correlation length verifies that the universality principle holds. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical values are correct within errors of our finite-size analysis, which correspond to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices (1×1):(n×n) for 1≤n≤6 . PMID:20866382
Kauffman knot invariant from SO(N) or Sp(N) Chern-Simons theory and the Potts model
Astorino, Marco
2010-06-15
The expectation value of Wilson loop operators in three-dimensional SO(N) Chern-Simons gauge theory gives a known knot invariant: the Kauffman polynomial. Here this result is derived, at the first order, via a simple variational method. With the same procedure the skein relation for Sp(N) are also obtained. Jones polynomial arises as special cases: Sp(2), SO(-2), and SL(2,R). These results are confirmed and extended up to the second order, by means of perturbation theory, which moreover let us establish a duality relation between SO({+-}N) and Sp({+-}N) invariants. A correspondence between the first orders in perturbation theory of SO(-2), Sp(2) or SU(2) Chern-Simons quantum holonomy's traces and the partition function of the Q=4 Potts model is built.
NASA Astrophysics Data System (ADS)
Salas, Jesús; Sokal, Alan D.
2011-09-01
We study, using transfer-matrix methods, the partition-function zeros of the square-lattice q-state Potts antiferromagnet at zero temperature (= square-lattice chromatic polynomial) for the boundary conditions that are obtained from an m× n grid with free boundary conditions by adjoining one new vertex adjacent to all the sites in the leftmost column and a second new vertex adjacent to all the sites in the rightmost column. We provide numerical evidence that the partition-function zeros are becoming dense everywhere in the complex q-plane outside the limiting curve {B}_{infty}(sq) for this model with ordinary (e.g. free or cylindrical) boundary conditions. Despite this, the infinite-volume free energy is perfectly analytic in this region.
NASA Astrophysics Data System (ADS)
Saburov, Mansoor; Khameini Ahmad, Mohd Ali
2015-12-01
Unlike the real number field, a set of p-adic Gibbs measures of p-adic lattice models of statistical mechanics has a complex structure in a sense that it is strongly tied up with a Diophantine problem over p-adic fields. Recently, all translation-invariant p-adic Gibbs measures of the p-adic Potts model on the Cayley tree of order two were described by means of roots of a certain quadratic equation over some domain of the p-adic field. In this paper, we consider the same problem on the Cayley tree of order three. In this case, we show that all translation-invariant p-adic Gibbs measures of the p-adic Potts model can be described in terms of roots of some cubic equation over Zpsetminus Zp^{*}. In own its turn, we also provide a solvability criterion of a general cubic equation over Zpsetminus Zp^{*} for p > 3.
NASA Astrophysics Data System (ADS)
Ding, Chengxiang; Fu, Zhe; Guo, Wenan; Wu, F. Y.
2010-06-01
In the preceding paper, one of us (F. Y. Wu) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu’s result is exact, and for the kagome-type lattices Wu’s expression is under a homogeneity assumption. The purpose of the present paper is twofold: First, an essential step in Wu’s analysis is the derivation of lattice-dependent constants A,B,C for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Second, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the q -state Potts model and the bond percolation on the 3-12 and kagome-type subnet lattices (n×n):(n×n) , n≤4 , for which the exact solution is not known. Our numerical determination of critical properties such as conformal anomaly and magnetic correlation length verifies that the universality principle holds. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical values are correct within errors of our finite-size analysis, which correspond to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices (1×1):(n×n) for 1≤n≤6 .
Okamoto, Atsushi; Kuwatani, Tatsu; Omori, Toshiaki; Hukushima, Koji
2015-10-01
Metastable minerals commonly form during reactions between water and rock. The nucleation mechanism of polymorphic phases from solution are explored here using a two-dimensional Potts model. The model system is composed of a solvent and three polymorphic solid phases. The local state and position of the solid phase are updated by Metropolis dynamics. Below the critical temperature, a large cluster of the least stable solid phase initially forms in the solution before transitioning into more-stable phases following the Ostwald step rule. The free-energy landscape as a function of the modal abundance of each solid phase clearly reveals that before cluster formation, the least stable phase has an energetic advantage because of its low interfacial energy with the solution, and after cluster formation, phase transformation occurs along the valley of the free-energy landscape, which contains several minima for the regions of three phases. Our results indicate that the solid-solid and solid-liquid interfacial energy contribute to the formation of the complex free-energy landscape and nucleation pathways following the Ostwald step rule. PMID:26565191
NASA Astrophysics Data System (ADS)
Okamoto, Atsushi; Kuwatani, Tatsu; Omori, Toshiaki; Hukushima, Koji
2015-10-01
Metastable minerals commonly form during reactions between water and rock. The nucleation mechanism of polymorphic phases from solution are explored here using a two-dimensional Potts model. The model system is composed of a solvent and three polymorphic solid phases. The local state and position of the solid phase are updated by Metropolis dynamics. Below the critical temperature, a large cluster of the least stable solid phase initially forms in the solution before transitioning into more-stable phases following the Ostwald step rule. The free-energy landscape as a function of the modal abundance of each solid phase clearly reveals that before cluster formation, the least stable phase has an energetic advantage because of its low interfacial energy with the solution, and after cluster formation, phase transformation occurs along the valley of the free-energy landscape, which contains several minima for the regions of three phases. Our results indicate that the solid-solid and solid-liquid interfacial energy contribute to the formation of the complex free-energy landscape and nucleation pathways following the Ostwald step rule.
Praveen, E. Satyanarayana, S. V. M.
2014-04-24
Traditional definition of phase transition involves an infinitely large system in thermodynamic limit. Finite systems such as biological proteins exhibit cooperative behavior similar to phase transitions. We employ recently discovered analysis of inflection points of microcanonical entropy to estimate the transition temperature of the phase transition in q state Potts model on a finite two dimensional square lattice for q=3 (second order) and q=8 (first order). The difference of energy density of states (DOS) Δ ln g(E) = ln g(E+ ΔE) −ln g(E) exhibits a point of inflexion at a value corresponding to inverse transition temperature. This feature is common to systems exhibiting both first as well as second order transitions. While the difference of DOS registers a monotonic variation around the point of inflexion for systems exhibiting second order transition, it has an S-shape with a minimum and maximum around the point of inflexion for the case of first order transition.
NASA Astrophysics Data System (ADS)
Liberty, Joshua W.
This dissertation uses the hierarchical q-state Potts model at the critical point to develop a new random number generator test. We start with an exposition of renormalization group approach by means of which one can numerically exactly compute the free energy, specific heat and susceptibility of large, but finite lattices. We then show that generalization of these standard techniques allows one to also compute probability distributions related to the energy and the order parameter. The various computed quantities can be compared with Monte Carlo estimates of the same quantities. We demonstrate that the structure of the hierarchical lattices used allows one to perform the Monte Carlo calculations by direct sampling. This avoids the usual critical slowing down that plagues Monte Carlo calculations at the critical point. As is well known, critical behavior is highly susceptible to perturbations. We expect that flaws of the pseudo random number generator, such as correlations, will cause statistically significant discrepancies between the results of the simulations and the numerically exactly computed results. Details of the computer code generated for these tests are included.
Statics and dynamics of the ten-state mean-field Potts glass model: a Monte Carlo study
NASA Astrophysics Data System (ADS)
Brangian, Claudio; Kob, Walter; Binder, Kurt
2002-01-01
We investigate by means of Monte Carlo simulations the fully connected p-state Potts model for different system sizes in order to see how the static and dynamic properties of a finite model compare with the, exactly known, behaviour of the system in the thermodynamic limit. Using p = 10 we are able to study the equilibrium dynamics for system sizes as large as N = 2560. We find that the static quantities, such as the energy, the entropy, the spin glass susceptibility as well as the distribution of the order parameter P(q) show very strong finite-size effects. From P(q) we calculate the fourth-order cumulant g4(N,T) and the Guerra parameter G(N,T) and show that these quantities cannot be used to locate the static transition temperature for the system sizes investigated. Also the spin-autocorrelation function C(t) shows strong finite-size effects in that it does not show a plateau even for temperatures around the dynamical critical temperature TD. We show that the dependence on N and T of the α-relaxation time can be understood by means of a dynamical finite-size scaling ansatz. C(t) does not obey the time-temperature superposition principle for temperatures around TD, but does so for significantly lower T. Finally we study the relaxation dynamics of the individual spins and show that their dependence on time depends strongly on the chosen spin, i.e. that the system is dynamically very heterogeneous, which explains the non-exponentiality of C(t).
NASA Astrophysics Data System (ADS)
Scianna, Marco; Preziosi, Luigi
2014-03-01
Cell migration is fundamental in a wide variety of physiological and pathological phenomena, among other in cancer invasion and development. In particular, the migratory/invasive capability of single metastatic cells is fundamental in determining the malignancy of a solid tumor. Specific cell migration phenotypes result for instance from the reciprocal interplay between the biophysical and biochemical properties of both the malignant cells themselves and of the surrounding environment. In particular, the extracellular matrices (ECMs) forming connective tissues can provide both loosely organized zones and densely packed barriers, which may impact cell invasion mode and efficiency. The critical processes involved in cell movement within confined spaces are (i) the proteolytic activity of matrix metalloproteinases (MMPs) and (ii) the deformation of the entire cell body, and in particular of the nucleus. We here present an extended cellular Potts model (CPM) to simulate a bio-engineered matrix system, which tests the active motile behavior of a single cancer cell into narrow channels of different widths. As distinct features of our approach, the cell is modeled as a compartmentalized discrete element, differentiated in the nucleus and in the cytosolic region, while a directional shape-dependent movement is explicitly driven by the evolution of its polarity vector. As outcomes, we find that, in a large track, the tumor cell is not able to maintain a directional movement. On the contrary, a structure of subcellular width behaves as a contact guidance sustaining cell persistent locomotion. In particular, a MMP-deprived cell is able to repolarize and follow the micropattern geometry, while a full MMP activity leads to a secondary track expansion by degrading the matrix structure. Finally, we confirm that cell movement within a subnuclear structure can be achieved either by pericellular proteolysis or by a significant deformation of cell nucleus.
Percivall Pott: tuberculous spondylitis.
Sternbach, G
1996-01-01
Tuberculous spondylitis, also known as Pott's disease, is an entity that produces a characteristic kyphotic deformity, and was described by Sir Percivall Pott in 1779 and 1782. The majority of his patients were infants and young children. Although the incidence of tuberculosis in the industrialized world has since declined dramatically, the number of cases of extrapulmonary disease, though small, has remained relatively unchanged. In developing countries, spondylitis is still generally a disease of children, but in Europe and North America, it more commonly involves older adults. Pott's spondylitis represents a reactivation of latent disease, frequently years after the initial infection. Clinical findings include complaints of back pain and symptoms of fever, chills, weight loss, malaise, and fatigue. Characteristically a late finding, paraplegia is occasionally the initial indicator of spinal involvement. There is an average delay of a year between the onset of symptoms and patient presentation. Plain spinal radiographs usually are the initial diagnostic modality utilized. Computed tomography scanning and magnetic resonance imaging can be used to further define the process. The differential diagnosis includes neoplasm, pyogenic or disseminated fungal infection, and sarcoid arthritis. PMID:8655942
NASA Astrophysics Data System (ADS)
Lykke Jacobsen, Jesper
2015-11-01
In previous work with Scullard, we have defined a graph polynomial P B (q, T) that gives access to the critical temperature T c of the q-state Potts model defined on a general two-dimensional lattice {L}. It depends on a basis B, containing n × m unit cells of {L}, and the relevant root T c(n, m) of P B (q, T) was observed to converge quickly to T c in the limit n,m\\to ∞ . Moreover, in exactly solvable cases there is no finite-size dependence at all. In this paper we show how to reformulate this method as an eigenvalue problem within the periodic Temperley-Lieb (TL) algebra. This corresponds to taking m\\to ∞ first, so that the bases B are semi-infinite cylinders of circumference n. The limit implies faster convergence in n, while maintaining the n-independence in exactly solvable cases. In this setup, T c(n) is determined by equating the largest eigenvalues of two topologically distinct sectors of the transfer matrix. Crucially, these two sectors determine the same critical exponent in the continuum limit, and the observed fast convergence is thus corroborated by results of conformal field theory. We obtain similar results for the dense and dilute phases of the O(N) loop model, using now a transfer matrix within the dilute periodic TL algebra. Compared with our previous study, the eigenvalue formulation allows us to double the size n for which T c(n) can be obtained, using the same computational effort. We study in details three significant cases: (i) bond percolation on the kagome lattice, up to n max = 14; (ii) site percolation on the square lattice, to n max = 21; and (iii) self-avoiding polygons on the square lattice, to n max = 19. Convergence properties of T c(n) and extrapolation schemes are studied in details for the first two cases. This leads to rather accurate values for the percolation thresholds: p c = 0.524 404 999 167 439(4) for bond percolation on the kagome lattice, and p c = 0.592 746 050 792 10(2) for site percolation on the square lattice.
Nature of ordering in Potts spin glasses
NASA Astrophysics Data System (ADS)
Banavar, Jayanth R.; Cieplak, Marek
1989-09-01
The zero-temperature scaling approach is applied to the three-state Potts spin glass. Our results suggest that the +/-J model has a lower critical dimensionality greater than 3, whereas for the Gaussian model this dimensionality is slightly less than 3. The T=0 scaling exponents are estimated in D=2 and 3. The results are based mostly on exact transfer-matrix calculations and on a Monte Carlo quenching procedure.
NASA Astrophysics Data System (ADS)
Jacobsen, Jesper Lykke; Salas, Jesús; Sokal, Alan D.
2003-09-01
We study the chromatic polynomial P G ( q) for m× n triangular-lattice strips of widths m≤12P,9F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such strips in the Fortuin-Kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q-plane in the limit n→∞. We recompute the limiting curve obtained by Baxter in the thermodynamic limit m, n→∞ and find new interesting features with possible physical consequences. Finally, we analyze the isolated limiting points and their relation with the Beraha numbers.
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)
Dai, Yan-Wei; Hu, Bing-Quan; Zhao, Jian-Hui; Zhou, Huan-Qiang
2010-09-01
The ground-state fidelity per lattice site is computed for the quantum three-state Potts model in a transverse magnetic field on an infinite-size lattice in one spatial dimension in terms of the infinite matrix product state algorithm. It is found that, on the one hand, a pinch point is identified on the fidelity surface around the critical point, and on the other hand, the ground-state fidelity per lattice site exhibits bifurcations at pseudo critical points for different values of the truncation dimension, which in turn approach the critical point as the truncation dimension becomes large. This implies that the ground-state fidelity per lattice site enables us to capture spontaneous symmetry breaking when the control parameter crosses the critical value. In addition, a finite-entanglement scaling of the von Neumann entropy is performed with respect to the truncation dimension, resulting in a precise determination of the central charge at the critical point. Finally, we compute the transverse magnetization, from which the critical exponent β is extracted from the numerical data.
Radiological evaluation of Pott puffy tumor
Wells, R.G.; Sty, J.R.; Landers, A.D.
1986-03-14
The Pott puffy tumor represents frontal osteomyelitis with subperiosteal (pericranial) abscess, secondary to frontal sinusitis. Pott puffy tumor is one of several potential complications of infection of a frontal sinus. Computed tomography (CT) and radionuclide bone imaging have proved to be invaluable tools in the diagnosis of frontal sinusitis, osteomyelitis, and intracranial infection. This article details the radionuclide bone imaging and findings on CT in three children with Pott puffy tumor, as well as the clinical features and pathophysicological mechanisms.
Li, Jonathan F.; Lowengrub, John
2014-01-01
There are numerous biological examples where genes associated with migratory ability of cells also confer the cells with an increased fitness even though these genes may not have any known effect on the cell mitosis rates. Here, we provide insight into these observations by analyzing the effects of cell migration, compression, and contact inhibition on the growth of tumor cell clusters using the Cellular Potts Model (CPM) in a monolayer geometry. This is a follow-up of a previous study (Thalhauser et al., Biol. Direct, 2010, 5:21) in which a Moran-type model was used to study the interaction of cell proliferation, migratory potential and death on the emergence of invasive phenotypes. Here, we extend the study to include the effects of cell size and shape. In particular, we investigate the interplay between cell motility and compressibility within the CPM and find that the CPM predicts that increased cell motility leads to smaller cells. This is an artifact in the CPM. An analysis of the CPM reveals an explicit inverse-relationship between the cell stiffness and motility parameters. We use this relationship to compensate for motility-induced changes in cell size in the CPM so that in the corrected CPM, cell size is independent of the cell motility. We find that subject to comparable levels of compression, clusters of motile cells grow faster than clusters of less motile cells, in qualitative agreement with biological observations and our previous study. Increasing compression tends to reduce growth rates. Contact inhibition penalizes clumped cells by halting their growth and gives motile cells an even greater advantage. Finally, our model predicts cell size distributions that are consistent with those observed in clusters of neuroblastoma cells cultured in low and high density conditions. PMID:24211749
Dynamic metastability in the two-dimensional Potts ferromagnet
NASA Astrophysics Data System (ADS)
Ibáñez Berganza, Miguel; Petri, Alberto; Coletti, Pietro
2014-05-01
We investigate the nonequilibrium dynamics of the two-dimensional (2D) Potts model on the square lattice after a quench below the discontinuous transition point. By means of numerical simulations of systems with q =12, 24, and 48, we observe the onset of a stationary regime below the temperature-driven transition, in a temperature interval decreasing with the system size and increasing with q. These results obtained dynamically agree with those obtained from the analytical continuation of the free energy [J. L. Meunier and A. Morel, Eur. Phys. J. B 13, 341 (2000), 10.1007/s100510050040], from which metastability in the 2D Potts model results to be a finite-size effect.
Potts glass reflection of the decoding threshold for qudit quantum error correcting codes
NASA Astrophysics Data System (ADS)
Jiang, Yi; Kovalev, Alexey A.; Pryadko, Leonid P.
We map the maximum likelihood decoding threshold for qudit quantum error correcting codes to the multicritical point in generalized Potts gauge glass models, extending the map constructed previously for qubit codes. An n-qudit quantum LDPC code, where a qudit can be involved in up to m stabilizer generators, corresponds to a ℤd Potts model with n interaction terms which can couple up to m spins each. We analyze general properties of the phase diagram of the constructed model, give several bounds on the location of the transitions, bounds on the energy density of extended defects (non-local analogs of domain walls), and discuss the correlation functions which can be used to distinguish different phases in the original and the dual models. This research was supported in part by the Grants: NSF PHY-1415600 (AAK), NSF PHY-1416578 (LPP), and ARO W911NF-14-1-0272 (LPP).
Local Autoencoding for Parameter Estimation in a Hidden Potts-Markov Random Field.
Song, Sanming; Si, Bailu; Herrmann, J Michael; Feng, Xisheng
2016-05-01
A local-autoencoding (LAE) method is proposed for the parameter estimation in a Hidden Potts-Markov random field model. Due to sampling cost, Markov chain Monte Carlo methods are rarely used in real-time applications. Like other heuristic methods, LAE is based on a conditional independence assumption. It adapts, however, the parameters in a block-by-block style with a simple Hebbian learning rule. Experiments with given label fields show that the LAE is able to converge in far less time than required for a scan. It is also possible to derive an estimate for LAE based on a Cramer–Rao bound that is similar to the classical maximum pseudolikelihood method. As a general algorithm, LAE can be used to estimate the parameters in anisotropic label fields. Furthermore, LAE is not limited to the classical Potts model and can be applied to other types of Potts models by simple label field transformations and straightforward learning rule extensions. Experimental results on image segmentations demonstrate the efficiency and generality of the LAE algorithm. PMID:27019491
Chemical Equilibrium Models for the S3 State of the Oxygen-Evolving Complex of Photosystem II.
Isobe, Hiroshi; Shoji, Mitsuo; Shen, Jian-Ren; Yamaguchi, Kizashi
2016-01-19
We have performed hybrid density functional theory (DFT) calculations to investigate how chemical equilibria can be described in the S3 state of the oxygen-evolving complex in photosystem II. For a chosen 340-atom model, 1 stable and 11 metastable intermediates have been identified within the range of 13 kcal mol(-1) that differ in protonation, charge, spin, and conformational states. The results imply that reversible interconversion of these intermediates gives rise to dynamic equilibria that involve processes with relocations of protons and electrons residing in the Mn4CaO5 cluster, as well as bound water ligands, with concomitant large changes in the cluster geometry. Such proton tautomerism and redox isomerism are responsible for reversible activation/deactivation processes of substrate oxygen species, through which Mn-O and O-O bonds are transiently ruptured and formed. These results may allow for a tentative interpretation of kinetic data on substrate water exchange on the order of seconds at room temperature, as measured by time-resolved mass spectrometry. The reliability of the hybrid DFT method for the multielectron redox reaction in such an intricate system is also addressed. PMID:26717045
The Pott's puffy tumor: a dangerous sign for intracranial complications.
Ketenci, Ibrahim; Unlü, Yaşar; Tucer, Bülent; Vural, Alperen
2011-12-01
The Pott's puffy tumor is a subperiosteal abscess of the frontal bone associated with osteomyelitis. The purpose of this article is to alert the physician to the severe complications of this entity. The records of six patients were reviewed retrospectively. There were four adults and two adolescents. Nasal endoscopy showed edematous, polypoid mucosa in middle meatus in three and nasal polyps in the rest. At initial admission, two had orbital subperiosteal abscess, but normal cranial CT findings. During hospitalization, three experienced frontal lobe abscess and one frontal cerebritis. Endoscopic sinus surgery was performed in all with external drainage of Pott's puffy tumor in addition to antibiotherapy. Three patients underwent craniotomy/craniectomy for removal of frontal lobe abscesses. One patient with frontal lobe abscess died. Pott's puffy tumor may result in potentially dangerous intracranial complications. Early diagnosis and treatment are essential to reduce morbidity and mortality. PMID:21660452
Mathews, William Christopher; Cachay, Edward Rafael; Agmas, Wollelaw; Jackson, Christopher
2015-09-01
The study aim is to compare anal intraepithelial neoplasia (AIN) progression and regression rates in a cytology inception cohort to estimates based on the subcohort referred for ≥1 high-resolution anoscopies (HRAs).A cytology-based retrospective cohort was assembled including the anal cytology histories and invasive anal cancer (IAC) outcomes of all HIV-infected adults under care between 2001 and 2012. A 3-state Markov model (
Mathews, William Christopher; Cachay, Edward Rafael; Agmas, Wollelaw; Jackson, Christopher
2015-01-01
Abstract The study aim is to compare anal intraepithelial neoplasia (AIN) progression and regression rates in a cytology inception cohort to estimates based on the subcohort referred for ≥1 high-resolution anoscopies (HRAs). A cytology-based retrospective cohort was assembled including the anal cytology histories and invasive anal cancer (IAC) outcomes of all HIV-infected adults under care between 2001 and 2012. A 3-state Markov model (
Potts ferromagnet: Transformations and critical exponents in planar hierarchical lattices
NASA Astrophysics Data System (ADS)
Hauser, Paulo R.; Curado, Evaldo M. F.
1988-07-01
We prove that the duality transformation for a Potts ferromagnet on two-rooted planar hierarchical lattices (HL) preserves the thermal eigenvalue. This leads to a relation between the correlation length critical exponents υ of a HL and its corresponding dual lattice. Using hyperscaling, we show that their specific heat critical exponents α coincide. For a smaller class of HL—namely of diamond and tress types—we prove that another transformation also preserves υ and α.
Pott puffy tumor in a 4-year-old boy presenting in status epilepticus.
Strony, Robert J; Dula, David
2007-11-01
Pott puffy tumor is an osteomyelitis of the frontal bone with the development of a subperiosteal abscess manifesting as a puffy swelling of the forehead or scalp. It is believed to occur as a complication of frontal sinusitis. The modern antibiotic era has made it a rarely encountered entity. This case describes a 4-year-old boy who presented in status epilepticus secondary to Pott puffy tumor. PMID:18007214
The Pott's puffy tumor: an unusual complication of frontal sinusitis, methods for its detection.
Sabatiello, M; Vanhooteghem, O; Mostinckx, S; De La Brassinne, M
2010-01-01
This is a case report of a Pott's puffy tumor, characterized by a subperiosteal abscess associated with frontal bone osteomyelitis, as a consequence of a frontal sinusitis, in a 15-year-old boy. Pott's puffy tumor is a rare condition usually seen as a complication of frontal sinusitis and more commonly described in children. Given that, superficial temporal artery pseudoaneurysms might be interpreted as a cyst or lipoma, it is imperative that physicians be aware of their presentation. PMID:20653869
Pott's puffy tumour: the usefulness of MRI in complicated sinusitis
Bhalla, Vishal; Khan, Nadir; Isles, Matthew
2016-01-01
The sinuses are common sites of infection in children, and if clinical presentation is delayed, there is a high risk of complications including intracranial spread. We present a case of a 5-year-old boy who presented with non-specific symptoms of sinusitis. He went on to develop osteomyelitis of the frontal bone and a subperiosteal abscess known as Pott's puffy tumour. Whilst computed tomography provides an excellent initial imaging, this case report emphasizes the advantages of magnetic resonance imaging, especially when there is extensive involvement of the sinuses with an absence of ionizing radiation. Prompt surgical treatment is imperative as there is a potential for significant morbidity if not quickly diagnosed and treated. PMID:27001196
Miliary tuberculosis disease complicated by Pott's abscess in an infant: Seven year follow-up
Bayhan, Gulsum Iclal; Tanir, Gonul; Gayretli Aydın, Zeynep Gokce; Yildiz, Yasemin Tasci
2015-01-01
A 20-month-old boy presented with 1-year history of persistent fever, cough, and progressive abdominal distention. Abdominal ultrasonography showed hepatomegaly and multiple calcifications in the liver and spleen. Thoracic computed tomography showed multiple mediastinal lymph nodes and consolidation in both lungs. Additionally, there was a 2-cm thick retroperitoneal soft tissue mass destroying the T7-8 and L1-L2 vertebral bodies. The patient was preliminarily diagnosed with miliary tuberculosis (TB) and Pott's disease, and began administering anti-TB treatment consisting of isoniazid, rifampin, ethambutol, and pyrazinamide. Acid-resistant bacilli analysis and mycobacterial culture of the biopsy specimen of Pott's abscess were positive. Mycobacterial culture and PCR of gastric aspirate were also positive. The patient's condition progressively improved with anti-TB treatment and he received 12 months of antiTB therapy. At the end of the treatment all of the patient's symptoms were relieved and he was well except for kyphosis. Miliary TB complicated by Pott's abscess is a very rare presentation of childhood TB. The presented case shows that when Pott's abscess is diagnosed and surgically corrected without delay, patients can recover without squeal. PMID:25983412
NASA Astrophysics Data System (ADS)
Guebels, Corentin Alain Pierre Nicolas
The microstructural changes that occur in metals and alloys due to deformation and heat treatment are often characterized according to the macroscale deformation process (i.e. cold or hot working). The general problem of this type of characterization is that it only distinguishes the general microstructural trends. For many decades, these microstructural phenomena have been described empirically or with limited experimental verification. This shortcoming is apparent for recrystallization and abnormal grain growth processes. Understanding and characterizing the thermal and mechanical processes that compete to control grain boundary kinetics and the subsequent microstructural evolution is critical. These include but are not limited to: the input and recovery of deformation energy, the influence of deformation energy on grain boundary migration, the mechanisms controlling the nucleation of new grains, and the effect of second-phase particles. The present work introduces a new temporal scaling method and investigates the conditions in which some grain boundaries may become unpinned in an otherwise stable, pinned microstructure and extends work done by E. Holm. The temporal scaling method contributes to resolving some of the limitations of Monte Carlo Potts (MCP) simulations in the investigation of the conditions and mechanisms that distinguish recrystallization from dynamic abnormal grain growth (DAGG). Grain boundary unpinning is then investigated for the case of an idealized spherical grain and for a polycrystalline microstructure. The mechanisms of grain boundary pinning and grain growth inhibition by second-phase particles are well known. The influence of simulation temperature on grain boundary unpinning is investigated numerically using a 3D Monte Carlo Potts approach. MCP based models are commonly implemented to simulate microstructural evolution. However, the numerical implementations of recrystallization and other deformation-induced phenomena often elude
Une localisation exceptionnelle de la tuberculose vertébrale Mal de Pott sous-occipital
Yahyaoui, Sana; Majdoub, Senda; Zaghouani, Houneida; Fradj, Hosni Ben; Bakir, Dejla; Bouajina, Elyes; Kraiem, Chakib
2013-01-01
Le mal de Pott est la forme la plus commune de la tuberculose osseuse touchant essentiellement le rachis dorso-lombaire. La localisation sous-occipitale reste exceptionnelle. Le diagnostic de cette entité est le plus souvent tardif ce qui expose à des complications graves. Les radiographies standard ne sont parlantes qu’à un stade tardif de la maladie, d'où l'intérêt de l'imagerie moderne notamment la tomodensitométrie (TDM) et l'imagerie par résonance magnétique (IRM) qui permettent un diagnostic précoce. Nous rapportons un nouveau cas de tuberculose sous-occipitale. Le diagnostic était posé sur l'imagerie en coupe et confirmé histologiquement à la biopsie transorale. Sont rappelés les aspects en imagerie de cette localisation particulière du mal de Pott. PMID:23819005
Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q
NASA Astrophysics Data System (ADS)
Huang, Yuan; Chen, Kun; Deng, Youjin; Jacobsen, Jesper Lykke; Kotecký, Roman; Salas, Jesús; Sokal, Alan D.; Swart, Jan M.
2013-01-01
We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of q. This unexpected result is proven rigorously by using a Peierls argument to measure the entropic advantage of sublattice long-range order. Additional numerical data are obtained using transfer matrices, Monte Carlo simulation, and a high-precision graph-theoretic method.
q-state Potts-glass neural network based on pseudoinverse rule
Xiong Daxing; Zhao Hong
2010-08-15
We study the q-state Potts-glass neural network with the pseudoinverse (PI) rule. Its performance is investigated and compared with that of the counterpart network with the Hebbian rule instead. We find that there exists a critical point of q, i.e., q{sub cr}=14, below which the storage capacity and the retrieval quality can be greatly improved by introducing the PI rule. We show that the dynamics of the neural networks constructed with the two learning rules respectively are quite different; but however, regardless of the learning rules, in the q-state Potts-glass neural networks with q{>=}3 there is a common novel dynamical phase in which the spurious memories are completely suppressed. This property has never been noticed in the symmetric feedback neural networks. Free from the spurious memories implies that the multistate Potts-glass neural networks would not be trapped in the metastable states, which is a favorable property for their applications.
Elnaim, Abdel Latif K
2011-04-01
Pott's disease of the spine with psoas abscess is currently rare form of Extra- pulmonary tuberculosis (TB) in the developed countries, however it is still seen in areas where TB is endemic. We describe a rare case if not the first (according to our knowledge) of bilateral ruptured psoas abscess with extensive tissue necrosis and pelvic organs exposure with limited neurological deficit presented late in young girl. In this case Pott's disease was associated with extensive tissue necrosis exposing pubic bones, urinary bladder and psoas muscle. PMID:22468071
Vanderveken, O M; De Smet, K; Dogan-Duyar, S; Desimpelaere, J; Duval, E L I M; De Praeter, M; Van Rompaey, D
2012-01-01
We report a case of Pott's puffy tumour, a subperiosteal abscess of the frontal bone associated with an underlying frontal osteomyelitis, in a 5-year-old boy. Ultrasonography played a crucial role in the diagnosis of our patient, suggesting the presence of a Pott's puffy tumour with epidural abscess by showing a subperiosteal abscess associated with erosion of the frontal bone. Subsequently, the diagnosis of Pott's puffy tumour with epidural abscess was confirmed by contrast-enhanced CT scanning. Prompt neurosurgical intervention with drainage of abscesses and debridement of bone sequestrate, together with prolonged antibiotic therapy, significantly contributes to a favorable outcome. PMID:22896932
[Anterior instrumentation of spine in tuberculous spondylitis: Pott's disease: case report].
Farage, Luciano; Martins, Johnny Wesley Gonçalves; Farage Filho, Miguel
2002-03-01
We report a case of a surgical treatment with anterior instrumentation in tuberculous spondylitis (Pott's disease), in a 71 years old woman, that was in treatment for pulmonary tuberculosis, with lumbar pain, progressive disability to walk, kyphotic deformity and vesical dysfunction. Magnetic resonance image presents a lesion in the bodies of T12 and L1, with paravertebral abscess. The patient was treated surgically by transthoracic-abdominal approach. The vertebral bodies were cut off and the spine were instrumented anteriorly with a mesh cage and a Z plate. This procedure permits a good arthrodesis and a immediately stabilization of the spine, without any complication of the infection. The patient was seen a year after the surgery and is free of infection, without motor deficit, pain or reminiscent kyphosis. PMID:11965425
38 CFR 13.3 - State legislation.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2010-07-01 2010-07-01 false State legislation. 13.3... ADMINISTRATION, FIDUCIARY ACTIVITIES § 13.3 State legislation. Field facility Directors are authorized to... regarding any proposed legislation relating to fiduciary matters will be taken without the approval of...
46 CFR 309.3 - Stated valuation.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 8 2013-10-01 2013-10-01 false Stated valuation. 309.3 Section 309.3 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION EMERGENCY OPERATIONS VALUES FOR WAR RISK INSURANCE § 309.3 Stated valuation. A stated valuation represents just compensation for the vessel to which it applies computed...
46 CFR 309.3 - Stated valuation.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 8 2010-10-01 2010-10-01 false Stated valuation. 309.3 Section 309.3 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION EMERGENCY OPERATIONS VALUES FOR WAR RISK INSURANCE § 309.3 Stated valuation. A stated valuation represents just compensation for the vessel to which it applies computed...
46 CFR 309.3 - Stated valuation.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 8 2011-10-01 2011-10-01 false Stated valuation. 309.3 Section 309.3 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION EMERGENCY OPERATIONS VALUES FOR WAR RISK INSURANCE § 309.3 Stated valuation. A stated valuation represents just compensation for the vessel to which it applies computed...
46 CFR 309.3 - Stated valuation.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 8 2012-10-01 2012-10-01 false Stated valuation. 309.3 Section 309.3 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION EMERGENCY OPERATIONS VALUES FOR WAR RISK INSURANCE § 309.3 Stated valuation. A stated valuation represents just compensation for the vessel to which it applies computed...
Weinmann, Andreas; Storath, Martin
2015-01-01
Signals with discontinuities appear in many problems in the applied sciences ranging from mechanics, electrical engineering to biology and medicine. The concrete data acquired are typically discrete, indirect and noisy measurements of some quantities describing the signal under consideration. The task is to restore the signal and, in particular, the discontinuities. In this respect, classical methods perform rather poor, whereas non-convex non-smooth variational methods seem to be the correct choice. Examples are methods based on Mumford–Shah and piecewise constant Mumford–Shah functionals and discretized versions which are known as Blake–Zisserman and Potts functionals. Owing to their non-convexity, minimization of such functionals is challenging. In this paper, we propose a new iterative minimization strategy for Blake–Zisserman as well as Potts functionals and a related jump-sparsity problem dealing with indirect, noisy measurements. We provide a convergence analysis and underpin our findings with numerical experiments.
[Anterior approach of cervical spine in Pott's disease. Apropos of 7 cases].
Achouri, M; Hilmani, S; Lakhdar, H; Ait Ben Ali, S; Naja, A; Ouboukhlik, A; el Kamar, A; el Azhari, A; Boucetta, M
1997-01-01
This study reports 7 cases of cervical Pott's disease, gathered during 6 years in the department of neuro-surgery of Ibn Rochd U.H.C. 4 females and 3 males, aged between 9 and 52 years were included. All the patients complained of cervicobrachial pain and weakness of the limbs. Clinical features were: deterioration of general status, rachidian syndrome and neurological impairement with motor and sensitive deficit. Radiological analysis found a destructive and extensive lesion, cervical kyphosis from 10 degrees to 60 degrees, retropharyngeal abscess and intraspinal canal extension of infection. Diagnosis was confirmed by histological study in all cases. In addition to antituberculous therapy and preoperative cervical traction in 4 cases, all the patients had spinal fusion using an anterior approach. Post operative immobilization in a cervical collar varied from 9 to 12 months. All 7 patients had full neurological recovery, 6 patients had an excellent bony fusion and cervical kyphosis was corrected. For the remaining patient, the bone graft was mobilized without neurological disorders. This study confirms anterior arthrodesis efficiency. This procedure in conjunction with preoperative traction, allowed stabilization of the spine and healing of vertebral lesions with excellent kyphosis correction. PMID:9452797
Medical-surgical treatment of progressive tuberculous (Pott's) paraplegia in Gabon.
Loembe, P M
1995-10-01
The present study deals with the results of the medical-surgical treatment of 22 patients with Pott's tetraplegia or paraplegia. Seventeen had progressive tetraplegia-paraplegia which failed to respond solely to medical treatment. On admission, four patients exhibited an acute onset tetraplegia-paraplegia, and one had a 'spinal tumour syndrome'. In addition to antituberculous therapy, seven patients had anterior spinal surgery, consisting of four corporectomies, two anterior debridments and grafting, and one debridment alone. Moreover, one patient had a posterior interbody fusion, four had laminotomies, and 10 had laminectomies. The causes of the spinal cord or cauda equina compression, as was determined at operation, were extradural abscess in eight patients, bony compressions in 11, arachnoiditis in two, and posterior neural arch tuberculosis in one patient. Neurological recovery began between 10 and 21 days postoperatively. The mean length of follow-up was 42.36 months (range 8-144 months). Fourteen patients were found to be functionally and neurologically normal at follow-up examinations (63%). Eighty-two percent recovered sufficiently to walk unaided. Two patients were left paralysed and unable to walk. Two patients were able to get about on crutches. The onset of objective improvement soon after surgical decompression suggests a causal effect. It was concluded that early neural decompression and spinal stabilisation provided the maximum potential for neurological recovery. PMID:8848312
From Potts Hill (Australia) to Pune (India): The journey of a radio astronomer
NASA Astrophysics Data System (ADS)
Swarup, Govind
2006-06-01
In this paper I recapitulate my initiation into the field of radio astronomy during 1953-1955 at CSIRO, Australia; the transfer of thirty-two parabolic dishes of six-feet (1.8-m) diameter from Potts Hill, Sydney, to India in 1958; and their erection at Kalyan, near Bombay (Mumbai), in 1963-1965. The Kalyan Radio Telescope was the first modern radio telescope built in India. This led to the establishment of a very active radio astronomy group at the Tata Institute of Fundamental Research, which subsequently built two world-class radio telescopes during the last forty years and also contributed to the development of an indigenous microwave antenna industry in India. The Ooty Radio Telescope, built during 1965-1970, has an ingenious design which takes advantage of India's location near the Earth's Equator. The long axis of this 530 m × 30 m parabolic cylinder was made parallel to the Equator, by placing it on a hill with the same slope as the geographic latitude (11 degrees), thus allowing it to track celestial sources continuously for 9.5 hours every day. By utilizing lunar occultations, the telescope was able to measure the angular sizes of a large number of faint radio galaxies and quasars with arc-second resolution for the first time. Subsequently, during the 1990s, the group set up the Giant Metrewave Radio Telescope (GMRT) near Pune in western India, in order to investigate certain astrophysical phenomena which are best studied at decimetre and metre wavelengths. The GMRT is an array of thirty fully-steerable parabolic dishes of 45 m diameter, which operates at several frequencies below 1.43 GHz. These efforts have also contributed to the recent international proposal to construct the Square Kilometre Array (SKA).
Non-Hodgkin's lymphoma “masquerading” as Pott's disease in a 13-year old boy
Adegboye, Olasunkanmi Abdulrasheed
2011-01-01
Lymphomas are malignant neoplasms of the lymphoid lineage. They are broadly classified as either Hodgkin disease or as non-Hodgkin lymphoma (NHL). Burkitt's lymphoma, a variety of NHL, is significantly most common in sub-Saharan Africa, where it accounts for approximately one half of childhood cancers. Lymphoblastic lymphoma is less common. A case of paravertebral high grade non-Hodgkin's lymphoma (lymphoblastic lymphoma) “masquerading” as Pott's disease in a 13-year-old child is reported. The present report was informed by the unusual presentation of this case and the intent of increasing the index of diagnostic suspicion. A brief appraisal is provided of the clinical parameters, management strategies and challenges. AT was a 13-year boy that presented on account of a slowly evolving and progressively increasing hunch on the back and inability to walk over 4 and 8 months duration, respectively. There was subsequent inability to control defecation and urination. There was no history of cough. He and his twin brother lived with their paternal grandfather who had chronic cough with associated weight loss. The grandfather died shortly before the child's admission. The child had no BCG immunization. The essential findings on examination were in keeping with lower motor neurons (LMN) paralysis of the lower limbs. The upper limbs appeared normal. There was loss of cutaneous sensation from the umbilicus (T10) downward. There was a firm, (rather tense), non-tender non-pulsatile, smooth swelling over the mid-third of the back (T6-L1) the mass had no differential warmth. It measures about 20×12 cm. Chest radiograph showed no active focal lung lesion, but the thoraco-lumbar spine showed a vertebral planner at L1 and a wedged collapse of T11-T12 vertebrae. There was sclerosis of the end plates of all the vertebral bodies with associated reduction in the bone density. He had an excision biopsy on the 90th day on admission, following which his clinical state rapidly
Tuberculose ostéoarticulaire (mal de Pott exclu): à propos de 120 cas à Abidjan
Gbané-Koné, Mariam; Koné, Samba; Ouali, Boubacar; Djaha, Kouassi Jean -Mermoz; Akoli, Ekoya Ondzala; Nseng, Ingrid Nseng; Eti, Edmond; Daboiko, Jean Claude; Touré, Stanislas André; Kouakou, N'zué Marcel
2015-01-01
Introduction La tuberculose ostéoarticulaire (TOA) représente 2 à 5% de l'ensemble des tuberculoses. Elle demeure d'actualité surtout dans les pays à forte endémicité tuberculeuse. L'objectif était de déterminer la prévalence, les aspects topographiques, radiologiques de la TOA en milieu hospitalier ivoirien. Méthodes Les auteurs rapportent une expérience de 11 ans, à travers une étude rétrospective de 120 dossiers de patients atteints de la tuberculose ostéoarticulaire (le mal de Pott est exclu de cette étude). N'ont pas été inclus dans l’étude les dossiers ne comportant pas d'imagerie. Résultats L'atteinte extra vertébrale représentait 09,2% de la tuberculose ostéoarticulaire. Il s'agissait de 54 hommes et 66 femmes, l’âge moyen était de 43,13 ans. On notait 123 cas d'ostéoarthrites, et 8 cas d'ostéites des os plats. L'atteinte des membres inférieurs prédominait dans 91,87% des cas. La hanche était la première localisation (45,04%), suivie du genou (25,19%). Les atteintes étaient multifocales dans 20% des cas. L'atteinte osseuse était associée à une tuberculose pulmonaire dans 05,83% des cas. Des localisations inhabituelles ont été rapportées: poignet (n = 2), branches ischiopubiennes (n = 4), atteinte sternoclaviculaire (n = 4), médiopieds (n = 2). Les lésions radiologiques étaient avancées (stades III et IV) dans 55,73% des cas. A la TDM, la prévalence des abcès était de 77%. Un geste chirurgical a été réalisé sur 16 articulations (2 épaules, 13 genoux, une cheville). Conclusion La TOA des membres est peu fréquente contrairement à l'atteinte vertébrale. La hanche est la principale localisation. Le retard au diagnostic explique l’étendue des lésions anatomoradiologiques. PMID:26587129
Diffusion tensor imaging observation in Pott's spine with or without neurological deficit
Abbas, Sohail; Jain, Anil Kumar; Saini, Namita Singh; Kumar, Sudhir; Mukunth, Rajagopalan; Kumar, Jaswant; Kumar, Pawan; Kaur, Prabhjot
2015-01-01
Background: Diffusion tensor imaging (DTI) is based upon the phenomenon of water diffusion known as “Brownian motion.” DTI can detect changes in compressed spinal cord earlier than magnetic resonance imaging and is more sensitive to subtle pathological changes of the spinal cord. DTI observation in compressed and noncompressed spinal cord in tuberculosis (TB) spine is not described. This study presents observations in Pott's spine patients with or without neural deficit. Materials and Methods: Thirty consecutive cases of TB spine with mean age of 32.1 years of either sexes with paradiscal lesion, with/without paraplegia divided into two groups: Group A: (n = 15) without paraplegia and group B: (n = 15) with paraplegia were evaluated by DTI. The average fractional anisotropy (FA) and mean diffusivity (MD) values were calculated at 3 different sites, above the lesion (SOL)/normal, at the lesion and below SOL for both groups and mean was compared. Visual impression of tractography was done to document changes in spinal tracts. Results: The mean canal encroachment in group A was 39.60% and group B 44.4% (insignificant). Group A mean FA values above SOL, at the lesion and below SOL were 0.608 ± 0.09, 0.554 ± 0.14, and 0.501 ± 0.16 respectively. For group B mean FA values above SOL, at the lesion and below SOL were 0.628 ± 0.09, 0.614 ± 0.12 and 0.487 ± 0.15 respectively. There was a significant difference in mean FA above the SOL as compared to the mean FA at and below SOL. P value above versus below the SOL was statistically significant for both groups (0.04), but P value for at versus below the SOL (0.01) was statistically significant only in group B. On tractography, disruption of fiber tract at SOL was found in 14/15 (93.3%) cases of group A and 14/15 cases (93.3%) of group B (6/6 grade 4, 3/3 grade 3 and 5/6 grade 2 paraplegic cases). Conclusion: The FA and MD above the lesion were same as reported for healthy volunteer hence can be taken as control. FA
Jacquin, Hugo; Shakhnovich, Eugene; Cocco, Simona; Monasson, Rémi
2016-01-01
Inverse statistical approaches to determine protein structure and function from Multiple Sequence Alignments (MSA) are emerging as powerful tools in computational biology. However the underlying assumptions of the relationship between the inferred effective Potts Hamiltonian and real protein structure and energetics remain untested so far. Here we use lattice protein model (LP) to benchmark those inverse statistical approaches. We build MSA of highly stable sequences in target LP structures, and infer the effective pairwise Potts Hamiltonians from those MSA. We find that inferred Potts Hamiltonians reproduce many important aspects of ‘true’ LP structures and energetics. Careful analysis reveals that effective pairwise couplings in inferred Potts Hamiltonians depend not only on the energetics of the native structure but also on competing folds; in particular, the coupling values reflect both positive design (stabilization of native conformation) and negative design (destabilization of competing folds). In addition to providing detailed structural information, the inferred Potts models used as protein Hamiltonian for design of new sequences are able to generate with high probability completely new sequences with the desired folds, which is not possible using independent-site models. Those are remarkable results as the effective LP Hamiltonians used to generate MSA are not simple pairwise models due to the competition between the folds. Our findings elucidate the reasons for the success of inverse approaches to the modelling of proteins from sequence data, and their limitations. PMID:27177270
First-Order Transition in a Spin Model for Self-Organization
NASA Astrophysics Data System (ADS)
Bauvin, R.; Kamp, Y.
The paper examines the emergence of self-organization in a population where tandem recruitment is combined with individual memory. The time evolution is modeled as a two-dimensional spin system with local interaction along the time axis and a mean-field interaction along the other axis. We generalize a previous result obtained with this model from the case of two sources to the multisource situation and show a twofold connection with the Potts model. First, when individual memory exceeds a critical value, a phase transition sets in, which is second order for two sources but first order beyond, similarly to the mean-field theory of the Potts model. In addition, the self-organization problem considered here relies on a special case of the one-dimensional nearest-neighbor Potts model with external field, which is shown to be explicitly solvable.
Osmanagic, Azra; Emamifar, Amir; Christian Bang, Jacob; Jensen Hansen, Inger Marie
2016-01-01
BACKGROUND Pott's disease (PD) or spinal tuberculosis is a rare condition which accounts for less than 1% of total tuberculosis (TB) cases. The incidence of PD has recently increased in Europe and the United States, mainly due to immigration; however, it is still a rare diagnosis in Scandinavian countries, and if overlooked it might lead to significant neurologic complications. CASE REPORT A 78-year-old woman, originally from Eastern Europe, presented to the emergency department with a complaint of nausea, vomiting, weight loss, and severe back pain. On admission she was febrile and had leukocytosis and increased C-reactive protein. Initial spinal x-ray was performed and revealed osteolytic changes in the vertebral body of T11 and T12. Magnetic resonance imaging (MRI) of the spine illustrated spondylitis of T10, T11, and T12, with multiple paravertebral and epidural abscesses, which was suggestive of PD. Polymerase chain reaction (PCR) of the patient's gastric fluid was positive for Mycobacterium tuberculosis (MT). Based on MRI and PCR findings, standard treatment for TB was initiated. Results of the spine biopsy and culture showed colonies of MT and confirmed the diagnosis afterwards. Due to the instability of the spine and severe and continuous pain, spine-stabilizing surgery was performed. Her TB was cured after nine months of treatment. CONCLUSIONS PD is an important differential diagnosis of malignancy that should be diagnosed instantly. History of exposure to TB and classic radiologic finding can help make the diagnosis. PMID:27272065
Simulated Tempering and Swapping on Mean-Field Models
NASA Astrophysics Data System (ADS)
Bhatnagar, Nayantara; Randall, Dana
2016-08-01
Simulated and parallel tempering are families of Markov Chain Monte Carlo algorithms where a temperature parameter is varied during the simulation to overcome bottlenecks to convergence due to multimodality. In this work we introduce and analyze the convergence for a set of new tempering distributions which we call entropy dampening. For asymmetric exponential distributions and the mean field Ising model with an external field simulated tempering is known to converge slowly. We show that tempering with entropy dampening distributions mixes in polynomial time for these models. Examining slow mixing times of tempering more closely, we show that for the mean-field 3-state ferromagnetic Potts model, tempering converges slowly regardless of the temperature schedule chosen. On the other hand, tempering with entropy dampening distributions converges in polynomial time to stationarity. Finally we show that the slow mixing can be very expensive practically. In particular, the mixing time of simulated tempering is an exponential factor longer than the mixing time at the fixed temperature.
NASA Astrophysics Data System (ADS)
Adams, Stefan; Briceño, Raimundo; Marcus, Brian; Pavlov, Ronnie
2016-02-01
We develop a new pressure representation theorem for nearest-neighbour Gibbs interactions and apply this to obtain the existence of efficient algorithms for approximating the pressure in the 2-dimensional ferromagnetic Potts, multi-type Widom-Rowlinson and hard-core models. For Potts model, our results apply to every inverse temperature but the critical. For Widom-Rowlinson and hard-core models, they apply to certain subsets of both the subcritical and supercritical regions. The main novelty of our work is in the latter.
32 CFR 1903.3 - State law applicable.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 32 National Defense 6 2011-07-01 2011-07-01 false State law applicable. 1903.3 Section 1903.3 National Defense Other Regulations Relating to National Defense CENTRAL INTELLIGENCE AGENCY CONDUCT ON AGENCY INSTALLATIONS § 1903.3 State law applicable. (a) Unless specifically addressed by the...
32 CFR 1903.3 - State law applicable.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 32 National Defense 6 2010-07-01 2010-07-01 false State law applicable. 1903.3 Section 1903.3 National Defense Other Regulations Relating to National Defense CENTRAL INTELLIGENCE AGENCY CONDUCT ON AGENCY INSTALLATIONS § 1903.3 State law applicable. (a) Unless specifically addressed by the...
32 CFR 1903.3 - State law applicable.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 32 National Defense 6 2014-07-01 2014-07-01 false State law applicable. 1903.3 Section 1903.3 National Defense Other Regulations Relating to National Defense CENTRAL INTELLIGENCE AGENCY CONDUCT ON AGENCY INSTALLATIONS § 1903.3 State law applicable. (a) Unless specifically addressed by the...
32 CFR 1903.3 - State law applicable.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 32 National Defense 6 2013-07-01 2013-07-01 false State law applicable. 1903.3 Section 1903.3 National Defense Other Regulations Relating to National Defense CENTRAL INTELLIGENCE AGENCY CONDUCT ON AGENCY INSTALLATIONS § 1903.3 State law applicable. (a) Unless specifically addressed by the...
32 CFR 1903.3 - State law applicable.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 32 National Defense 6 2012-07-01 2012-07-01 false State law applicable. 1903.3 Section 1903.3 National Defense Other Regulations Relating to National Defense CENTRAL INTELLIGENCE AGENCY CONDUCT ON AGENCY INSTALLATIONS § 1903.3 State law applicable. (a) Unless specifically addressed by the...
Benli, I T; Kiş, M; Akalin, S; Citak, M; Kanevetçi, S; Duman, E
2000-04-01
Classic procedure in the treatment of vertebral tuberculosis is drainage of the abscess, curettage of the devitalized vertebra and application of antituberculous chemotherapy regimen. Posterior instrumentation results are encouraging in the prevention or treatment of late kyphosis; however, a second stage operation is needed. Recently, posterolateral or transpedicular drainage without anterior drainage or posterior instrumentation following anterior drainage in the same session is preferred to avoid kyphotic deformity. Seventy-six patients with spinal tuberculosis were operated in the 1st Department of Orthopaedics and Traumatology, Ankara Social Security Hospital, between January 1987 and January 1997. There were four children in our series. Average follow-up period was 36.1 +/- 14.5 months and the average age at the time of operation was 40.8 +/- 15.2 years. This study reports the surgical results of 45 patients with Pott's disease who had anterior radical debridement with anterior fusion and anterior instrumentation [14 patients with Z-plate and 31 patients with Cotrel-Dubousset-Hopf (CDH system)]. The results are compared with those of 8 patients who had posterolateral drainage and posterior fusion, 12 patients who had only anterior drainage and anterior strut grafting and, 11 patients who had posterior instrumentation following anterior radical debridement in the same session in terms of fusion rates, correction of kyphotic deformity, recurrence rate and clinical results. All patients had one year consecutive triple drug therapy. Preoperative 23.2 degrees +/- 12.5 degrees local kyphosis angle was lowered to 6.1 degrees +/- 6.9 degrees with a correction rate of 77.4 +/- 22.3%. When the other three groups which had been instrumented were compared, the correction rates in the local kyphosis angle values were not statistically different and the variation in loss of correction at the last follow-up was also statistically insignificant. The sagittal contour of the
Mutual information in classical spin models
NASA Astrophysics Data System (ADS)
Wilms, Johannes; Troyer, Matthias; Verstraete, Frank
2011-10-01
The total many-body correlations present in finite temperature classical spin systems are studied using the concept of mutual information. As opposed to zero-temperature quantum phase transitions, the total correlations are not maximal at the phase transition, but reach a maximum in the high-temperature paramagnetic phase. The Shannon mutual information and the Renyi mutual information in both Ising and Potts models in two dimensions are calculated numerically by combining matrix product state algorithms and Monte Carlo sampling techniques.
On the nature of a supposed water model
Heckmann, Lotta Drossel, Barbara
2014-08-15
A cell model that has been proposed by Stanley and Franzese in 2002 for modeling water is based on Potts variables that represent the possible orientations of bonds between water molecules. We show that in the liquid phase, where all cells are occupied by a molecule, the Hamiltonian of the cell model can be rewritten as a Hamiltonian of a conventional Potts model, albeit with two types of coupling constants. We argue that such a model, while having a first-order phase transition, cannot display the critical end point that is postulated for the phase transition between a high- and low-density liquid. A closer look at the mean-field calculations that claim to find such an end point in the cell model reveals that the mean-field theory is constructed such that the symmetry constraints on the order parameter are violated. This is equivalent to introducing an external field. The introduction of such a field can be given a physical justification due to the fact that water does not have the type of long-range order occurring in the Potts model.
NASA Astrophysics Data System (ADS)
Palachanis, Dimitrios; Szabó, András; Merks, Roeland M. H.
2015-12-01
Computational modeling is helpful for elucidating the cellular mechanisms driving biological morphogenesis. Previous simulation studies of blood vessel growth based on the cellular Potts model proposed that elongated, adhesive or mutually attractive endothelial cells suffice for the formation of blood vessel sprouts and vascular networks. Because each mathematical representation of a model introduces potential artifacts, it is important that model results are reproduced using alternative modeling paradigms. Here, we present a lattice-free, particle-based simulation of the cell elongation model of vasculogenesis. The new, particle-based simulations confirm the results obtained from the previous cellular Potts simulations. Furthermore, our current findings suggest that the emergence of order is possible with the application of a high enough attractive force or, alternatively, a longer attraction radius. The methodology will be applicable to a range of problems in morphogenesis and noisy particle aggregation in which cell shape is a key determining factor.
A novel dynamics combination model reveals the hidden information of community structure
NASA Astrophysics Data System (ADS)
Li, Hui-Jia; Li, Huiying; Jia, Chuanliang
2015-09-01
The analysis of the dynamic details of community structure is an important question for scientists from many fields. In this paper, we propose a novel Markov-Potts framework to uncover the optimal community structures and their stabilities across multiple timescales. Specifically, we model the Potts dynamics to detect community structure by a Markov process, which has a clear mathematical explanation. Then the local uniform behavior of spin values revealed by our model is shown that can naturally reveal the stability of hierarchical community structure across multiple timescales. To prove the validity, phase transition of stochastic dynamic system is used to indicate that the stability of community structure we proposed is able to describe the significance of community structure based on eigengap theory. Finally, we test our framework on some example networks and find it does not have resolute limitation problem at all. Results have shown the model we proposed is able to uncover hierarchical structure in different scales effectively and efficiently.
NASA Astrophysics Data System (ADS)
Jeppesen, Claus; Flyvbjerg, Henrik; Mouritsen, Ole G.
1989-11-01
Monte Carlo computer-simulation techniques are used to elucidate the equilibrium phase behavior as well as the late-stage ordering dynamics of some two-dimensional models with ground-state ordering of a high degeneracy Q. The models are Q-state Potts models with anisotropic grain-boundary potential on triangular lattices-essentially clock models, except that the potential is not a cosine, but a sine function of the angle between neighboring grain orientations. For not too small Q, these models display two thermally driven phase transitions, one which takes the system from a low-temperature Potts-ordered phase to an intermediate phase which lacks conventional long-range order, and another transition which takes the system to the high-temperature disordered phase. The linear nature of the sine potential used makes it a marginal case in the sense that it favors neither hard domain boundaries, like the standard Potts models do, nor a wetting of the boundaries, as the standard clock models do. Thermal fluctuations nevertheless cause wetting to occur for not too small temperatures. Specifically, we have studied models with Q=12 and 48. The models are quenched from infinity to zero as well as finite temperatures within the two low-temperature phases. The order parameter is a nonconserved quantity during these quenches. The nonequilibrium ordering process subsequent to the quench is studied as a function of time by calculating the interfacial energy, ΔE, associated with the entire grain-boundary network. The time evolution of this quantity is shown to obey the growth law, ΔE(t)~t-n, over an extended time range at late times. It is found that the zero-temperature dynamics is characterized by a special exponent value which for the Q=48 model is n~=0.25 in accordance with earlier work. However, for quenches to finite temperatures in the Potts-ordered phase there is a distinct crossover to the classical Lifshitz-Allen-Cahn exponent value, n=(1/2, for both values of Q. This
NASA Astrophysics Data System (ADS)
Ishimoto, Yukitaka; Morishita, Yoshihiro
2014-11-01
In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, and the cellular Potts model. So far, in any case, pressures have not neatly been dealt with and the curvatures of the cell boundaries have been even omitted through their approximations. We focus on these quantities and formulate them in the vertex model. Thus, a model with the curvatures is constructed, and its algorithm for simulation is provided. The possible extensions and applications of this model are also discussed.
Structural changes in the S3 state of the oxygen evolving complex in photosystem II
NASA Astrophysics Data System (ADS)
Hatakeyama, Makoto; Ogata, Koji; Fujii, Katsushi; Yachandra, Vittal K.; Yano, Junko; Nakamura, Shinichiro
2016-05-01
The S3 state of the Mn4CaO5-cluster in photosystem II was investigated by DFT calculations and compared with EXAFS data. Considering previously proposed mechanism; a water molecule is inserted into an open coordination site of Mn upon S2 to S3 transition that becomes a substrate water, we examined if the water insertion is essential for the S3 formation, or if one cannot eliminate other possible routes that do not require a water insertion at the S3 stage. The novel S3 state structure consisting of only short 2.7-2.8 Å Mnsbnd Mn distances was discussed.
7 CFR 1900.3 - State, district, and county office employees.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 12 2010-01-01 2010-01-01 false State, district, and county office employees. 1900.3... AGRICULTURE PROGRAM REGULATIONS GENERAL Delegations of Authority § 1900.3 State, district, and county office... laws, for and on behalf of, and in the name of the United States of America or the Farmers...
7 CFR 1900.3 - State, district, and county office employees.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 12 2011-01-01 2011-01-01 false State, district, and county office employees. 1900.3... AGRICULTURE PROGRAM REGULATIONS GENERAL Delegations of Authority § 1900.3 State, district, and county office... laws, for and on behalf of, and in the name of the United States of America or the Farmers...
28 CFR 904.3 - State criminal history record screening standards.
Code of Federal Regulations, 2012 CFR
2012-07-01
... III System. (a) The State Criminal History Record Repository or an authorized agency in the receiving... 28 Judicial Administration 2 2012-07-01 2012-07-01 false State criminal history record screening... STATE CRIMINAL HISTORY RECORD SCREENING STANDARDS § 904.3 State criminal history record...
28 CFR 904.3 - State criminal history record screening standards.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 28 Judicial Administration 2 2013-07-01 2013-07-01 false State criminal history record screening... STATE CRIMINAL HISTORY RECORD SCREENING STANDARDS § 904.3 State criminal history record screening standards. The following record screening standards relate to criminal history record information...
28 CFR 904.3 - State criminal history record screening standards.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 28 Judicial Administration 2 2014-07-01 2014-07-01 false State criminal history record screening... STATE CRIMINAL HISTORY RECORD SCREENING STANDARDS § 904.3 State criminal history record screening standards. The following record screening standards relate to criminal history record information...
28 CFR 904.3 - State criminal history record screening standards.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 28 Judicial Administration 2 2010-07-01 2010-07-01 false State criminal history record screening... STATE CRIMINAL HISTORY RECORD SCREENING STANDARDS § 904.3 State criminal history record screening standards. The following record screening standards relate to criminal history record information...
28 CFR 904.3 - State criminal history record screening standards.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 28 Judicial Administration 2 2011-07-01 2011-07-01 false State criminal history record screening... STATE CRIMINAL HISTORY RECORD SCREENING STANDARDS § 904.3 State criminal history record screening standards. The following record screening standards relate to criminal history record information...
NASA Astrophysics Data System (ADS)
Komura, Yukihiro; Okabe, Yutaka
2016-03-01
We present new versions of sample CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm. In this update, we add the method of GPU-based cluster-labeling algorithm without the use of conventional iteration (Komura, 2015) to those programs. For high-precision calculations, we also add a random-number generator in the cuRAND library. Moreover, we fix several bugs and remove the extra usage of shared memory in the kernel functions.
NASA Astrophysics Data System (ADS)
Schlijper, A. G.; van Bergen, A. R. D.; Smit, B.
1990-01-01
We present and demonstrate an accurate, reliable, and computationally cheap method for the calculation of free energies in Monte Carlo simulations of lattice models. Even in the critical region it yields good results with comparatively short simulation runs. The method combines upper and lower bounds on the thermodynamic limit entropy density to yield not only an accurate estimate of the free energy but a bound on the possible error as well. The method is demonstrated on the two- and three-dimensional Ising models and the three-dimensional, three-states Potts model.
Forini, Francesca; Ucciferri, Nadia; Kusmic, Claudia; Nicolini, Giuseppina; Cecchettini, Antonella; Rocchiccioli, Silvia; Citti, Lorenzo; Iervasi, Giorgio
2015-01-01
Mitochondria are major determinants of cell fate in ischemia/reperfusion injury (IR) and common effectors of cardio-protective strategies in cardiac ischemic disease. Thyroid hormone homeostasis critically affects mitochondrial function and energy production. Since a low T3 state (LT3S) is frequently observed in the post infarction setting, the study was aimed to investigate the relationship between 72 h post IR T3 levels and both the cardiac function and the mitochondrial proteome in a rat model of IR. The low T3 group exhibits the most compromised cardiac performance along with the worst mitochondrial activity. Accordingly, our results show a different remodeling of the mitochondrial proteome in the presence or absence of a LT3S, with alterations in groups of proteins that play a key role in energy metabolism, quality control and regulation of cell death pathways. Overall, our findings highlight a relationship between LT3S in the early post IR and poor cardiac and mitochondrial outcomes, and suggest a potential implication of thyroid hormone in the cardio-protection and tissue remodeling in ischemic disease. PMID:26561807
Katamea, Tina; Mukuku, Olivier; Luboya, Oscar Numbi
2014-01-01
Les formes latentes de tuberculose chez la femme enceinte sont associées à un risque élevé de passage à une forme active qui augmente le risque de transmission de la mère infectée à l'enfant dans les 3 premières semaines de vie. Nous rapportons un cas de Gibbosité vertébrale congénitale évoquant un mal de Pott chez un nourrisson de mère tuberculeuse, observé à Lubumbashi, en République Démocratique du Congo. PMID:25478046
Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results
NASA Astrophysics Data System (ADS)
Van Liedekerke, P.; Palm, M. M.; Jagiella, N.; Drasdo, D.
2015-12-01
In this paper we present an overview of agent-based models that are used to simulate mechanical and physiological phenomena in cells and tissues, and we discuss underlying concepts, limitations, and future perspectives of these models. As the interest in cell and tissue mechanics increase, agent-based models are becoming more common the modeling community. We overview the physical aspects, complexity, shortcomings, and capabilities of the major agent-based model categories: lattice-based models (cellular automata, lattice gas cellular automata, cellular Potts models), off-lattice models (center-based models, deformable cell models, vertex models), and hybrid discrete-continuum models. In this way, we hope to assist future researchers in choosing a model for the phenomenon they want to model and understand. The article also contains some novel results.
Omarjee, Saleha; Walker, Bruce D.; Chakraborty, Arup; Ndung'u, Thumbi
2014-01-01
Viral immune evasion by sequence variation is a major hindrance to HIV-1 vaccine design. To address this challenge, our group has developed a computational model, rooted in physics, that aims to predict the fitness landscape of HIV-1 proteins in order to design vaccine immunogens that lead to impaired viral fitness, thus blocking viable escape routes. Here, we advance the computational models to address previous limitations, and directly test model predictions against in vitro fitness measurements of HIV-1 strains containing multiple Gag mutations. We incorporated regularization into the model fitting procedure to address finite sampling. Further, we developed a model that accounts for the specific identity of mutant amino acids (Potts model), generalizing our previous approach (Ising model) that is unable to distinguish between different mutant amino acids. Gag mutation combinations (17 pairs, 1 triple and 25 single mutations within these) predicted to be either harmful to HIV-1 viability or fitness-neutral were introduced into HIV-1 NL4-3 by site-directed mutagenesis and replication capacities of these mutants were assayed in vitro. The predicted and measured fitness of the corresponding mutants for the original Ising model (r = −0.74, p = 3.6×10−6) are strongly correlated, and this was further strengthened in the regularized Ising model (r = −0.83, p = 3.7×10−12). Performance of the Potts model (r = −0.73, p = 9.7×10−9) was similar to that of the Ising model, indicating that the binary approximation is sufficient for capturing fitness effects of common mutants at sites of low amino acid diversity. However, we show that the Potts model is expected to improve predictive power for more variable proteins. Overall, our results support the ability of the computational models to robustly predict the relative fitness of mutant viral strains, and indicate the potential value of this approach for understanding viral immune evasion
On multiscale approaches to three-dimensional modelling of morphogenesis
Chaturvedi, R; Huang, C; Kazmierczak, B; Schneider, T; Izaguirre, J.A; Glimm, T; Hentschel, H.G.E; Glazier, J.A; Newman, S.A; Alber, M.S
2005-01-01
In this paper we present the foundation of a unified, object-oriented, three-dimensional biomodelling environment, which allows us to integrate multiple submodels at scales from subcellular to those of tissues and organs. Our current implementation combines a modified discrete model from statistical mechanics, the Cellular Potts Model, with a continuum reaction–diffusion model and a state automaton with well-defined conditions for cell differentiation transitions to model genetic regulation. This environment allows us to rapidly and compactly create computational models of a class of complex-developmental phenomena. To illustrate model development, we simulate a simplified version of the formation of the skeletal pattern in a growing embryonic vertebrate limb. PMID:16849182
Draft of M2 Report on Integration of the Hybrid Hydride Model into INL's MBM Framework for Review
Tikare, Veena; Weck, Philippe F.; Schultz, Peter A.; Clark, Blythe; Glazoff, Michael; Homer, Eric
2014-07-01
This report documents the development, demonstration and validation of a mesoscale, microstructural evolution model for simulation of zirconium hydride {delta}-ZrH{sub 1.5} precipitation in the cladding of used nuclear fuels that may occur during long-term dry storage. While the Zr-based claddings are manufactured free of any hydrogen, they absorb hydrogen during service, in the reactor by a process commonly termed ‘hydrogen pick-up’. The precipitation and growth of zirconium hydrides during dry storage is one of the most likely fuel rod integrity failure mechanisms either by embrittlement or delayed hydride cracking of the cladding. While the phenomenon is well documented and identified as a potential key failure mechanism during long-term dry storage (NUREG/CR-7116), the ability to actually predict the formation of hydrides is poor. The model being documented in this work is a computational capability for the prediction of hydride formation in different claddings of used nuclear fuels. This work supports the Used Fuel Disposition Research and Development Campaign in assessing the structural engineering performance of the cladding during and after long-term dry storage. This document demonstrates a basic hydride precipitation model that is built on a recently developed hybrid Potts-phase field model that combines elements of Potts-Monte Carlo and the phase-field models. The model capabilities are demonstrated along with the incorporation of the starting microstructure, thermodynamics of the Zr-H system and the hydride formation mechanism.
Star-triangle relation for a three-dimensional model
Bazhanov, V.V. Institute for High Eenrgy Physics, Protvino, Moscow Region ); Baxter, R.J. Australian National Univ., Canberra )
1993-06-01
The solvable sl(n)-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising-type model on the body-centered cubic lattice with two- and three-spin interactions. The corresponding local Boltzmann weights obey a number of simple relations, including a restricted star-triangle relation, which is a modified version of the well-known star-triangle relation appearing in two-dimensional models. It is shown that these relations lead to remarkable symmetry properties of the Boltzmann weight function of an elementary cube of the lattice, related to the spatial symmetry group of the cubic lattice. These symmetry properties allow one to prove the commutativity of the row-to-row transfer matrices, bypassing the tetrahedron relation. The partition function per site for the infinite lattice is calculated exactly. 20 refs., 4 figs.
Random matrix theory and classical statistical mechanics: Spin models
NASA Astrophysics Data System (ADS)
Meyer, H.; Angles D'Auriac, J.-C.
1997-06-01
We present a statistical analysis of spectra of transfer matrices of classical lattice spin models; this continues the work on the eight-vertex model of the preceding paper [H. Meyer, J.-C. Anglès d'Auriac, and J.-M. Maillard, Phys. Rev. E 55, 5261 (1997)]. We show that the statistical properties of these spectra can serve as a criterion of integrability. It also provides an operational numerical method to locate integrable varieties. In particular, we distinguish the notions of integrability and criticality, considering the two examples of the three-dimensional Ising critical point and the two-dimensional three-state Potts critical point. For complex spectra, which appear frequently in the context of transfer matrices, we show that the notion of independence of eigenvalues for integrable models still holds.
app_hybridPotts-phasefield.cpp
Energy Science and Technology Software Center (ESTSC)
2012-09-12
This application simulates microstructural and compositional evolution in two-phase, two-component systems. It is designed to run within the SPPARKS solver and combines the kMC with solution to the Cahn-Hilliard Eq. for phase field.
Super-Resolution Using Hidden Markov Model and Bayesian Detection Estimation Framework
NASA Astrophysics Data System (ADS)
Humblot, Fabrice; Mohammad-Djafari, Ali
2006-12-01
This paper presents a new method for super-resolution (SR) reconstruction of a high-resolution (HR) image from several low-resolution (LR) images. The HR image is assumed to be composed of homogeneous regions. Thus, the a priori distribution of the pixels is modeled by a finite mixture model (FMM) and a Potts Markov model (PMM) for the labels. The whole a priori model is then a hierarchical Markov model. The LR images are assumed to be obtained from the HR image by lowpass filtering, arbitrarily translation, decimation, and finally corruption by a random noise. The problem is then put in a Bayesian detection and estimation framework, and appropriate algorithms are developed based on Markov chain Monte Carlo (MCMC) Gibbs sampling. At the end, we have not only an estimate of the HR image but also an estimate of the classification labels which leads to a segmentation result.
Cell-based computational modeling of vascular morphogenesis using Tissue Simulation Toolkit.
Daub, Josephine T; Merks, Roeland M H
2015-01-01
Computational modeling has become a widely used tool for unraveling the mechanisms of higher level cooperative cell behavior during vascular morphogenesis. However, experimenting with published simulation models or adding new assumptions to those models can be daunting for novice and even for experienced computational scientists. Here, we present a step-by-step, practical tutorial for building cell-based simulations of vascular morphogenesis using the Tissue Simulation Toolkit (TST). The TST is a freely available, open-source C++ library for developing simulations with the two-dimensional cellular Potts model, a stochastic, agent-based framework to simulate collective cell behavior. We will show the basic use of the TST to simulate and experiment with published simulations of vascular network formation. Then, we will present step-by-step instructions and explanations for building a recent simulation model of tumor angiogenesis. Demonstrated mechanisms include cell-cell adhesion, chemotaxis, cell elongation, haptotaxis, and haptokinesis. PMID:25468600
Turnover control of photosystem II: Use of redox-active herbicides to form the S[sub 3] state
Bocarsly, J.R.; Brudvig, G.W. )
1992-12-02
The O[sub 2]-evolving center of photosystem II, which contains an active-site tetramanganese-oxo cluster, catalyzes the four-electron oxidation of two water molecules to dioxygen, with the concomitant production of four H[sup +] and four electrons. During catalytic turnover, the manganese-oxo cluster steps through five intermediate oxidation states, which are known as the S[sub i] states (i = 0-4). While methods have been found to manipulate the system into S[sub 1] and S[sub 2] in high yields, efficient production of the S[sub 3] state in good yield at high concentration has not yet been achieved. Previous methods have suffered from the requirement of low protein concentration so that actinic flashes are saturating; the use of temperature to control S-state advancement under continuous illumination, which can lead to S-state scrambling; or the use of herbicides that bind to the Q[sub B] site and restrict the system to one turnover. The authors describe here a method for the high-yield production of the S[sub 3] state in highly-concentrated samples of photosystem II, through the use of electron-accepting herbicides which bind to the Q[sub B] site. Redox-active herbicides can be used, in principle, to limit S-state cycling to any desired number of turnovers, given the appropriate herbicide. This work has fundamental methodological implications not only for the study of photosystem II but also for other multistate redox protein systems.
Crawling and Gliding: A Computational Model for Shape-Driven Cell Migration
Niculescu, Ioana; Textor, Johannes; de Boer, Rob J.
2015-01-01
Cell migration is a complex process involving many intracellular and extracellular factors, with different cell types adopting sometimes strikingly different morphologies. Modeling realistically behaving cells in tissues is computationally challenging because it implies dealing with multiple levels of complexity. We extend the Cellular Potts Model with an actin-inspired feedback mechanism that allows small stochastic cell rufflings to expand to cell protrusions. This simple phenomenological model produces realistically crawling and deforming amoeboid cells, and gliding half-moon shaped keratocyte-like cells. Both cell types can migrate randomly or follow directional cues. They can squeeze in between other cells in densely populated environments or migrate collectively. The model is computationally light, which allows the study of large, dense and heterogeneous tissues containing cells with realistic shapes and migratory properties. PMID:26488304
Crawling and Gliding: A Computational Model for Shape-Driven Cell Migration.
Niculescu, Ioana; Textor, Johannes; de Boer, Rob J
2015-10-01
Cell migration is a complex process involving many intracellular and extracellular factors, with different cell types adopting sometimes strikingly different morphologies. Modeling realistically behaving cells in tissues is computationally challenging because it implies dealing with multiple levels of complexity. We extend the Cellular Potts Model with an actin-inspired feedback mechanism that allows small stochastic cell rufflings to expand to cell protrusions. This simple phenomenological model produces realistically crawling and deforming amoeboid cells, and gliding half-moon shaped keratocyte-like cells. Both cell types can migrate randomly or follow directional cues. They can squeeze in between other cells in densely populated environments or migrate collectively. The model is computationally light, which allows the study of large, dense and heterogeneous tissues containing cells with realistic shapes and migratory properties. PMID:26488304
On the critical parameters of the q ≤ 4 random-cluster model on isoradial graphs
NASA Astrophysics Data System (ADS)
Beffara, V.; Duminil-Copin, H.; Smirnov, S.
2015-12-01
The critical surface for the random-cluster model with cluster-weight q≥slant 4 on isoradial graphs is identified using parafermionic observables. Correlations are also shown to decay exponentially fast in the subcritical regime. While this result is restricted to random-cluster models with q≥slant 4, it extends the recent theorem of (Beffara and Duminil-Copin 2012 Probl. Theory Relat. Fields 153 511-42) to a large class of planar graphs. In particular, the anisotropic random-cluster model on the square lattice is shown to be critical if \\frac{{p}{{v}}{p}{{h}}}{(1-{p}{{v}})(1-{p}{{h}})}=q, where p v and p h denote the horizontal and vertical edge-weights respectively. We also mention consequences for Potts models.
Tikare, Veena; Hernandez-Rivera, Efrain; Madison, Jonathan D.; Holm, Elizabeth Ann; Patterson, Burton R.; Homer, Eric R.
2013-09-01
Most materials microstructural evolution processes progress with multiple processes occurring simultaneously. In this work, we have concentrated on the processes that are active in nuclear materials, in particular, nuclear fuels. These processes are coarsening, nucleation, differential diffusion, phase transformation, radiation-induced defect formation and swelling, often with temperature gradients present. All these couple and contribute to evolution that is unique to nuclear fuels and materials. Hybrid model that combines elements from the Potts Monte Carlo, phase-field models and others have been developed to address these multiple physical processes. These models are described and applied to several processes in this report. An important feature of the models developed are that they are coded as applications within SPPARKS, a Sandiadeveloped framework for simulation at the mesoscale of microstructural evolution processes by kinetic Monte Carlo methods. This makes these codes readily accessible and adaptable for future applications.
An approach to collective behavior in cell cultures: modeling and analysis of ECIS data
NASA Astrophysics Data System (ADS)
Rabson, David; Lafalce, Evan; Lovelady, Douglas; Lo, Chun-Min
2011-03-01
We review recent results in which statistical measures of noise in ECIS data distinguished healthy cell cultures from cancerous or poisoned ones: after subtracting the ``signal,'' the 1 /fα noise in the healthy cultures shows longer short-time and long-time correlations. We discuss application of an artificial neural network to detect the cancer signal, and we demonstrate a computational model of cell-cell communication that produces signals similar to those of the experimental data. The simulation is based on the q -state Potts model with inspiration from the Bak-Tang-Wiesenfeld sand-pile model. We view the level of organization larger than cells but smaller than organs or tissues as a kind of ``mesoscopic'' biological physics, in which few-body interactions dominate, and the experiments and computational model as ways of exploring this regime.
An agent based multi-optional model for the diffusion of innovations
NASA Astrophysics Data System (ADS)
Laciana, Carlos E.; Oteiza-Aguirre, Nicolás
2014-01-01
We propose a model for the diffusion of several products competing in a common market based on the generalization of the Ising model of statistical mechanics (Potts model). Using an agent based implementation we analyze two problems: (i) a three options case, i.e. to adopt a product A, a product B, or non-adoption and (ii) a four option case, i.e. the adoption of product A, product B, both, or none. In the first case we analyze a launching strategy for one of the two products, which delays its launching with the objective of competing with improvements. Market shares reached by each product are then estimated at market saturation. Finally, simulations are carried out with varying degrees of social network topology, uncertainty, and population homogeneity.
Bayesian approaches to spatial inference: Modelling and computational challenges and solutions
NASA Astrophysics Data System (ADS)
Moores, Matthew; Mengersen, Kerrie
2014-12-01
We discuss a range of Bayesian modelling approaches for spatial data and investigate some of the associated computational challenges. This paper commences with a brief review of Bayesian mixture models and Markov random fields, with enabling computational algorithms including Markov chain Monte Carlo (MCMC) and integrated nested Laplace approximation (INLA). Following this, we focus on the Potts model as a canonical approach, and discuss the challenge of estimating the inverse temperature parameter that controls the degree of spatial smoothing. We compare three approaches to addressing the doubly intractable nature of the likelihood, namely pseudo-likelihood, path sampling and the exchange algorithm. These techniques are applied to satellite data used to analyse water quality in the Great Barrier Reef.
Monaco, James P; Tomaszewski, John E; Feldman, Michael D; Hagemann, Ian; Moradi, Mehdi; Mousavi, Parvin; Boag, Alexander; Davidson, Chris; Abolmaesumi, Purang; Madabhushi, Anant
2010-08-01
In this paper we present a high-throughput system for detecting regions of carcinoma of the prostate (CaP) in HSs from radical prostatectomies (RPs) using probabilistic pairwise Markov models (PPMMs), a novel type of Markov random field (MRF). At diagnostic resolution a digitized HS can contain 80Kx70K pixels - far too many for current automated Gleason grading algorithms to process. However, grading can be separated into two distinct steps: (1) detecting cancerous regions and (2) then grading these regions. The detection step does not require diagnostic resolution and can be performed much more quickly. Thus, we introduce a CaP detection system capable of analyzing an entire digitized whole-mount HS (2x1.75cm(2)) in under three minutes (on a desktop computer) while achieving a CaP detection sensitivity and specificity of 0.87 and 0.90, respectively. We obtain this high-throughput by tailoring the system to analyze the HSs at low resolution (8microm per pixel). This motivates the following algorithm: (Step 1) glands are segmented, (Step 2) the segmented glands are classified as malignant or benign, and (Step 3) the malignant glands are consolidated into continuous regions. The classification of individual glands leverages two features: gland size and the tendency for proximate glands to share the same class. The latter feature describes a spatial dependency which we model using a Markov prior. Typically, Markov priors are expressed as the product of potential functions. Unfortunately, potential functions are mathematical abstractions, and constructing priors through their selection becomes an ad hoc procedure, resulting in simplistic models such as the Potts. Addressing this problem, we introduce PPMMs which formulate priors in terms of probability density functions, allowing the creation of more sophisticated models. To demonstrate the efficacy of our CaP detection system and assess the advantages of using a PPMM prior instead of the Potts, we alternately
Monaco, James P.; Tomaszewski, John E.; Feldman, Michael D.; Hagemann, Ian; Moradi, Mehdi; Mousavi, Parvin; Boag, Alexander; Davidson, Chris; Abolmaesumi, Purang; Madabhushi, Anant
2010-01-01
In this paper we present a high-throughput system for detecting regions of carcinoma of the prostate (CaP) in HSs from radical prostatectomies (RPs) using probabilistic pairwise Markov models (PPMMs), a novel type of Markov random field (MRF). At diagnostic resolution a digitized HS can contain 80K×70K pixels — far too many for current automated Gleason grading algorithms to process. However, grading can be separated into two distinct steps: 1) detecting cancerous regions and 2) then grading these regions. The detection step does not require diagnostic resolution and can be performed much more quickly. Thus, we introduce a CaP detection system capable of analyzing an entire digitized whole-mount HS (2×1.75 cm2) in under three minutes (on a desktop computer) while achieving a CaP detection sensitivity and specificity of 0.87 and 0.90, respectively. We obtain this high-throughput by tailoring the system to analyze the HSs at low resolution (8 µm per pixel). This motivates the following algorithm: Step 1) glands are segmented, Step 2) the segmented glands are classified as malignant or benign, and Step 3) the malignant glands are consolidated into continuous regions. The classification of individual glands leverages two features: gland size and the tendency for proximate glands to share the same class. The latter feature describes a spatial dependency which we model using a Markov prior. Typically, Markov priors are expressed as the product of potential functions. Unfortunately, potential functions are mathematical abstractions, and constructing priors through their selection becomes an ad hoc procedure, resulting in simplistic models such as the Potts. Addressing this problem, we introduce PPMMs which formulate priors in terms of probability density functions, allowing the creation of more sophisticated models. To demonstrate the efficacy of our CaP detection system and assess the advantages of using a PPMM prior instead of the Potts, we alternately incorporate
NASA Astrophysics Data System (ADS)
Alber, Mark; Chen, Nan; Glimm, Tilmann; Lushnikov, Pavel M.
2006-05-01
The cellular Potts model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. We derive a continuous limit of a discrete one-dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified numerically by comparing Monte Carlo simulations for the CPM with numerics for the Keller-Segel model.
Defect-phase-dynamics approach to statistical domain-growth problem of clock models
NASA Technical Reports Server (NTRS)
Kawasaki, K.
1985-01-01
The growth of statistical domains in quenched Ising-like p-state clock models with p = 3 or more is investigated theoretically, reformulating the analysis of Ohta et al. (1982) in terms of a phase variable and studying the dynamics of defects introduced into the phase field when the phase variable becomes multivalued. The resulting defect/phase domain-growth equation is applied to the interpretation of Monte Carlo simulations in two dimensions (Kaski and Gunton, 1983; Grest and Srolovitz, 1984), and problems encountered in the analysis of related Potts models are discussed. In the two-dimensional case, the problem is essentially that of a purely dissipative Coulomb gas, with a sq rt t growth law complicated by vertex-pinning effects at small t.
Zhao, Ningning; Basarab, Adrian; Kouame, Denis; Tourneret, Jean-Yves
2016-08-01
This paper proposes a joint segmentation and deconvolution Bayesian method for medical ultrasound (US) images. Contrary to piecewise homogeneous images, US images exhibit heavy characteristic speckle patterns correlated with the tissue structures. The generalized Gaussian distribution (GGD) has been shown to be one of the most relevant distributions for characterizing the speckle in US images. Thus, we propose a GGD-Potts model defined by a label map coupling US image segmentation and deconvolution. The Bayesian estimators of the unknown model parameters, including the US image, the label map, and all the hyperparameters are difficult to be expressed in a closed form. Thus, we investigate a Gibbs sampler to generate samples distributed according to the posterior of interest. These generated samples are finally used to compute the Bayesian estimators of the unknown parameters. The performance of the proposed Bayesian model is compared with the existing approaches via several experiments conducted on realistic synthetic data and in vivo US images. PMID:27187959
Proper encoding for snapshot-entropy scaling in two-dimensional classical spin models
NASA Astrophysics Data System (ADS)
Matsueda, Hiroaki; Ozaki, Dai
2015-10-01
We reexamine the snapshot entropy of the Ising and three-states Potts models on the L ×L square lattice. Focusing on how to encode the spin snapshot, we find that the entropy at Tc scales asymptotically as S ˜(1 /3 )lnL that strongly reminds us of the entanglement entropy in one-dimensional quantum critical systems. This finding seems to support that the snapshot entropy after the proper encoding is related to the holographic entanglement entropy. On the other hand, the anomalous scaling Sχ˜χηlnχ for the coarse-grained snapshot entropy holds even for the proper encoding. These features originate in the fact that the largest singular value of the snapshot matrix is regulated by the proper encoding.
Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains
NASA Astrophysics Data System (ADS)
Formentin, M.; Külske, C.; Reichenbachs, A.
2012-01-01
We extend the construction by Külske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that for a degenerate non-reversible chain this CLT approximation is not enough, and that the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.
Bridges in the random-cluster model
NASA Astrophysics Data System (ADS)
Elçi, Eren Metin; Weigel, Martin; Fytas, Nikolaos G.
2016-02-01
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By introducing a classification of edges based on their relevance to the connectivity we study the stability of clusters in this model. We prove several exact relations for general graphs that allow us to derive unambiguously the finite-size scaling behavior of the density of bridges and non-bridges. For percolation, we are also able to characterize the point for which clusters become maximally fragile and show that it is connected to the concept of the bridge load. Combining our exact treatment with further results from conformal field theory, we uncover a surprising behavior of the (normalized) variance of the number of (non-)bridges, showing that it diverges in two dimensions below the value 4cos2 (π /√{ 3}) = 0.2315891 ⋯ of the cluster coupling q. Finally, we show that a partial or complete pruning of bridges from clusters enables estimates of the backbone fractal dimension that are much less encumbered by finite-size corrections than more conventional approaches.
Rajchl, Martin; Baxter, John S H; McLeod, A Jonathan; Yuan, Jing; Qiu, Wu; Peters, Terry M; Khan, Ali R
2016-01-01
The incorporation of intensity, spatial, and topological information into large-scale multi-region segmentation has been a topic of ongoing research in medical image analysis. Multi-region segmentation problems, such as segmentation of brain structures, pose unique challenges in image segmentation in which regions may not have a defined intensity, spatial, or topological distinction, but rely on a combination of the three. We propose a novel framework within the Advanced segmentation tools (ASETS)(2), which combines large-scale Gaussian mixture models trained via Kohonen self-organizing maps, with deformable registration, and a convex max-flow optimization algorithm incorporating region topology as a hierarchy or tree. Our framework is validated on two publicly available neuroimaging datasets, the OASIS and MRBrainS13 databases, against the more conventional Potts model, achieving more accurate segmentations. Each component is accelerated using general-purpose programming on graphics processing Units to ensure computational feasibility. PMID:26072170
A MULTISCALE, CELL-BASED FRAMEWORK FOR MODELING CANCER DEVELOPMENT
JIANG, YI
2007-01-16
Cancer remains to be one of the leading causes of death due to diseases. We use a systems approach that combines mathematical modeling, numerical simulation, in vivo and in vitro experiments, to develop a predictive model that medical researchers can use to study and treat cancerous tumors. The multiscale, cell-based model includes intracellular regulations, cellular level dynamics and intercellular interactions, and extracellular level chemical dynamics. The intracellular level protein regulations and signaling pathways are described by Boolean networks. The cellular level growth and division dynamics, cellular adhesion and interaction with the extracellular matrix is described by a lattice Monte Carlo model (the Cellular Potts Model). The extracellular dynamics of the signaling molecules and metabolites are described by a system of reaction-diffusion equations. All three levels of the model are integrated through a hybrid parallel scheme into a high-performance simulation tool. The simulation results reproduce experimental data in both avasular tumors and tumor angiogenesis. By combining the model with experimental data to construct biologically accurate simulations of tumors and their vascular systems, this model will enable medical researchers to gain a deeper understanding of the cellular and molecular interactions associated with cancer progression and treatment.
Study of the attractor structure of an agent-based sociological model
NASA Astrophysics Data System (ADS)
Timpanaro, André M.; Prado, Carmen P. C.
2011-03-01
The Sznajd model is a sociophysics model that is based in the Potts model, and used for describing opinion propagation in a society. It employs an agent-based approach and interaction rules favouring pairs of agreeing agents. It has been successfully employed in modeling some properties and scale features of both proportional and majority elections (see for instance the works of A. T. Bernardes and R. N. Costa Filho), but its stationary states are always consensus states. In order to explain more complicated behaviours, we have modified the bounded confidence idea (introduced before in other opinion models, like the Deffuant model), with the introduction of prejudices and biases (we called this modification confidence rules), and have adapted it to the discrete Sznajd model. This generalized Sznajd model is able to reproduce almost all of the previous versions of the Sznajd model, by using appropriate choices of parameters. We solved the attractor structure of the resulting model in a mean-field approach and made Monte Carlo simulations in a Barabási-Albert network. These simulations show great similarities with the mean-field, for the tested cases of 3 and 4 opinions. The dynamical systems approach that we devised allows for a deeper understanding of the potential of the Sznajd model as an opinion propagation model and can be easily extended to other models, like the voter model. Our modification of the bounded confidence rule can also be readily applied to other opinion propagation models.
Monte Carlo simulation of classical spin models with chaotic billiards
NASA Astrophysics Data System (ADS)
Suzuki, Hideyuki
2013-11-01
It has recently been shown that the computing abilities of Boltzmann machines, or Ising spin-glass models, can be implemented by chaotic billiard dynamics without any use of random numbers. In this paper, we further numerically investigate the capabilities of the chaotic billiard dynamics as a deterministic alternative to random Monte Carlo methods by applying it to classical spin models in statistical physics. First, we verify that the billiard dynamics can yield samples that converge to the true distribution of the Ising model on a small lattice, and we show that it appears to have the same convergence rate as random Monte Carlo sampling. Second, we apply the billiard dynamics to finite-size scaling analysis of the critical behavior of the Ising model and show that the phase-transition point and the critical exponents are correctly obtained. Third, we extend the billiard dynamics to spins that take more than two states and show that it can be applied successfully to the Potts model. We also discuss the possibility of extensions to continuous-valued models such as the XY model.
Observation of Rydberg blockade effects at very high n, n ~ 300 , using strontium n1F3 states
NASA Astrophysics Data System (ADS)
Zhang, Xinyue; Dunning, F. B.; Yoshida, Shuhei; Burgdörfer, Joachim
2015-05-01
Rydberg blockade at very high n, n ~ 300 , is examined using strontium n1F3 Rydberg atoms excited in a small volume defined by two tightly-focused crossed laser beams. Measurements of the number distribution of Rydberg atoms created show deviations from a Poisson distribution revealing sizeable blockade effects. The statistics of the number distribution are studied using a Monte Carlo method in which the interaction between strontium Rydberg atoms is evaluated by solving the Schrödinger equation within a two-active-electron model. The strength of blockade is analyzed in detail with respect to the alignment of two atoms relative to the laser polarizations. With careful control of the experimental parameters the probability for creating one, and only one, Rydberg atom, P(1) , in the excitation volume can be sufficiently large, P(1) > 0 . 6 , as to enable detailed studies of strongly-coupled Rydberg atom pairs. Research supported by the NSF, the Robert A. Welch Foundation, and the FWF (Austria).
Simple model for multiple-choice collective decision making.
Lee, Ching Hua; Lucas, Andrew
2014-11-01
We describe a simple model of heterogeneous, interacting agents making decisions between n≥2 discrete choices. For a special class of interactions, our model is the mean field description of random field Potts-like models and is effectively solved by finding the extrema of the average energy E per agent. In these cases, by studying the propagation of decision changes via avalanches, we argue that macroscopic dynamics is well captured by a gradient flow along E. We focus on the permutation symmetric case, where all n choices are (on average) the same, and spontaneous symmetry breaking (SSB) arises purely from cooperative social interactions. As examples, we show that bimodal heterogeneity naturally provides a mechanism for the spontaneous formation of hierarchies between decisions and that SSB is a preferred instability to discontinuous phase transitions between two symmetric points. Beyond the mean field limit, exponentially many stable equilibria emerge when we place this model on a graph of finite mean degree. We conclude with speculation on decision making with persistent collective oscillations. Throughout the paper, we emphasize analogies between methods of solution to our model and common intuition from diverse areas of physics, including statistical physics and electromagnetism. PMID:25493831
Simple model for multiple-choice collective decision making
NASA Astrophysics Data System (ADS)
Lee, Ching Hua; Lucas, Andrew
2014-11-01
We describe a simple model of heterogeneous, interacting agents making decisions between n ≥2 discrete choices. For a special class of interactions, our model is the mean field description of random field Potts-like models and is effectively solved by finding the extrema of the average energy E per agent. In these cases, by studying the propagation of decision changes via avalanches, we argue that macroscopic dynamics is well captured by a gradient flow along E . We focus on the permutation symmetric case, where all n choices are (on average) the same, and spontaneous symmetry breaking (SSB) arises purely from cooperative social interactions. As examples, we show that bimodal heterogeneity naturally provides a mechanism for the spontaneous formation of hierarchies between decisions and that SSB is a preferred instability to discontinuous phase transitions between two symmetric points. Beyond the mean field limit, exponentially many stable equilibria emerge when we place this model on a graph of finite mean degree. We conclude with speculation on decision making with persistent collective oscillations. Throughout the paper, we emphasize analogies between methods of solution to our model and common intuition from diverse areas of physics, including statistical physics and electromagnetism.
Building toy models of proteins using coevolutionary information
NASA Astrophysics Data System (ADS)
Cheng, Ryan; Raghunathan, Mohit; Onuchic, Jose
2015-03-01
Recent developments in global statistical methodologies have advanced the analysis of large collections of protein sequences for coevolutionary information. Coevolution between amino acids in a protein arises from compensatory mutations that are needed to maintain the stability or function of a protein over the course of evolution. This gives rise to quantifiable correlations between amino acid positions within the multiple sequence alignment of a protein family. Here, we use Direct Coupling Analysis (DCA) to infer a Potts model Hamiltonian governing the correlated mutations in a protein family to obtain the sequence-dependent interaction energies of a toy protein model. We demonstrate that this methodology predicts residue-residue interaction energies that are consistent with experimental mutational changes in protein stabilities as well as other computational methodologies. Furthermore, we demonstrate with several examples that DCA could be used to construct a structure-based model that quantitatively agrees with experimental data on folding mechanisms. This work serves as a potential framework for generating models of proteins that are enriched by evolutionary data that can potentially be used to engineer key functional motions and interactions in protein systems. This research has been supported by the NSF INSPIRE award MCB-1241332 and by the CTBP sponsored by the NSF (Grant PHY-1427654).
NASA Astrophysics Data System (ADS)
Kawashima, Yoshiyuki; Colarusso, Pina; Zhang, K. Q.; Bernath, Peter; Hirota, Eizi
1998-11-01
The ν1and ν3bands of D11BO and the ν1band of D10BO were observed by using an infrared diode laser spectrometer. The DBO molecule was generated by an ac discharge in a mixture of BCl3, D2, O2, and He. As inferred previously, a strong Coriolis interaction was in fact found to take place between the ν1and ν2+ ν3states, and an analysis of the observed ν1spectra, which explicitly took into account this Coriolis interaction, predicted the pure rotational transition frequencies of DBO in the ν1state. Pure rotational lines were then detected by microwave spectroscopy, confirming the validity of the infrared assignment. In the microwave experiment DBO molecules were generated by a discharge in a mixture of B2D6and O2. The three fundamental bands and a hot band of D11BO, as well as the ν1and ν3bands of D10BO, were subsequently recorded in emission with a Fourier transform infrared spectrometer. DBO molecules were generated by the reaction of D2with HBO at temperatures above 800°C in a ceramic tube furnace. All of the observed spectra were simultaneously subjected to a least-squares analysis to obtain molecular parameters in the ground, ν1, ν2, ν3, and ν2+ ν3states. The results thus obtained improved the force field and molecular structure of the HBO/DBO molecules reported in a previous study (Y. Kawashima, Y. Endo, and E. Hirota, 1989,J. Mol. Spectrosc.133, 116-127).
Entanglement Properties of a Quantum Lattice-Gas Model on Square and Triangular Ladders
NASA Astrophysics Data System (ADS)
Tanaka, Shu; Tamura, Ryo; Katsura, Hosho
2014-03-01
In this paper, we review the entanglement properties of a quantum lattice-gas model according to our previous paper [S. Tanaka, R. Tamura, and H. Katsura, Phys. Rev. A 86, 032326 (2012)]. The ground state of the model under consideration can be exactly obtained and expressed by the Rokhsar-Kivelson type quantum superposition. The reduced density matrices of the model on square and triangular ladders are related to the transfer matrices of the classical hard-square and hard-hexagon models, respectively. In our previous paper, we investigated the entanglement properties including the entanglement entropy, the entanglement spectrum, and the nested entanglement entropy. We found that the entanglement spectra are critical when parameters are chosen so that the corresponding classical model is critical. In order to further investigate the entanglement properties, we also considered the nested entanglement entropy. As a result, the entanglement properties of the model on square and triangular ladders are described by the critical phenomena of the Ising model and the three-state ferromagnetic Potts model in two dimension, respectively.
Completely packed O(n) loop models and their relation with exactly solved coloring models.
Wang, Yougang; Guo, Wenan; Blöte, Henk W J
2015-03-01
We investigate the completely packed O(n) loop model on the square lattice, and its generalization to an Eulerian graph model, which follows by including cubic vertices which connect the four incoming loop segments. This model includes crossing bonds as well. Our study was inspired by existing exact solutions of the so-called coloring model due to Schultz and Perk [Phys. Rev. Lett. 46, 629 (1981)], which is shown to be equivalent with our generalized loop model. We explore the physical properties and the phase diagram of this model by means of transfer-matrix calculations and finite-size scaling. The exact results, which include seven one-dimensional branches in the parameter space of our generalized loop model, are compared to our numerical results. The results for the phase behavior also extend to parts of the parameter space beyond the exactly solved subspaces. One of the exactly solved branches describes the case of nonintersecting loops and was already known to correspond with the ordering transition of the Potts model. Another exactly solved branch, describing a model with nonintersecting loops and cubic vertices, corresponds with a first-order, Ising-like phase transition for n>2. For 1
Completely packed O (n ) loop models and their relation with exactly solved coloring models
NASA Astrophysics Data System (ADS)
Wang, Yougang; Guo, Wenan; Blöte, Henk W. J.
2015-03-01
We investigate the completely packed O (n ) loop model on the square lattice, and its generalization to an Eulerian graph model, which follows by including cubic vertices which connect the four incoming loop segments. This model includes crossing bonds as well. Our study was inspired by existing exact solutions of the so-called coloring model due to Schultz and Perk [Phys. Rev. Lett. 46, 629 (1981), 10.1103/PhysRevLett.46.629], which is shown to be equivalent with our generalized loop model. We explore the physical properties and the phase diagram of this model by means of transfer-matrix calculations and finite-size scaling. The exact results, which include seven one-dimensional branches in the parameter space of our generalized loop model, are compared to our numerical results. The results for the phase behavior also extend to parts of the parameter space beyond the exactly solved subspaces. One of the exactly solved branches describes the case of nonintersecting loops and was already known to correspond with the ordering transition of the Potts model. Another exactly solved branch, describing a model with nonintersecting loops and cubic vertices, corresponds with a first-order, Ising-like phase transition for n >2 . For 1
Duality methods in networks, computer science models, and disordered condensed matter systems
NASA Astrophysics Data System (ADS)
Mitchell, Joseph Dan
In this thesis, I explore lattice independent duality and systems to which it can be applied. I first demonstrate classical duality on models in an external field, including the Ising, Potts, and x -- y models, showing in particular how this modifies duality to be lattice independent and applicable to networks. I then present a novel application of duality on the boolean satsifiability problem, one of the most important problems in computational complexity, through mapping to a low temperature Ising model. This establishes the equivalence between boolean satisfiability and a problem of enumerating the positive solutions to a Diophantine system of equations. I continue by combining duality with a prominent tool for models on networks, belief propagation, deriving a new message passing procedure, dual belief propagation. In the final part of my thesis, I shift to propose and examine a semiclassical model, the two-component Coulomb glass model, which can explain the giant magnetoresistance peak present in disordered films near a superconductor-insulator transition as the effect of competition between single particle and localized pair transport. I numerically analyze the density of states and transport properties of this model.
Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
NASA Astrophysics Data System (ADS)
Shi, Qian-Qian; Wang, Hong-Lei; Li, Sheng-Hao; Cho, Sam Young; Batchelor, Murray T.; Zhou, Huan-Qiang
2016-06-01
Geometric entanglement (GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. In this paper we outline a systematic method to compute GE for two-dimensional (2D) quantum many-body lattice models based on the translational invariant structure of infinite projected entangled pair state (iPEPS) representations. By employing this method, the q -state quantum Potts model on the square lattice with q ∈{2 ,3 ,4 ,5 } is investigated as a prototypical example. Further, we have explored three 2D Heisenberg models: the antiferromagnetic spin-1/2 X X X and anisotropic X Y X models in an external magnetic field, and the antiferromagnetic spin-1 X X Z model. We find that continuous GE does not guarantee a continuous phase transition across a phase transition point. We observe and thus classify three different types of continuous GE across a phase transition point: (i) GE is continuous with maximum value at the transition point and the phase transition is continuous, (ii) GE is continuous with maximum value at the transition point but the phase transition is discontinuous, and (iii) GE is continuous with nonmaximum value at the transition point and the phase transition is continuous. For the models under consideration, we find that the second and the third types are related to a point of dual symmetry and a fully polarized phase, respectively.
Ashkin-Teller model and diverse opinion phase transitions on multiplex networks
NASA Astrophysics Data System (ADS)
Jang, S.; Lee, J. S.; Hwang, S.; Kahng, B.
2015-08-01
Multiplex networks (MNs) have become a platform of recent research in network sciences because networks in many real-world systems interact and function together. One of the main scientific issues in MNs is how the interdependence changes the emerging patterns or phase transitions. Until now, studies of such an issue have concentrated on cluster-breakdown phenomena, aiming to understand the resilience of the system under random failures of edges. These studies have revealed that various phase transition (PT) types emerge in MNs. However, such studies are rather limited to percolation-related problems, i.e., the limit q →1 of the q -state Potts model. Thus, a systematic study of opinion formation in social networks with the effect of interdependence between different social communities, which may be seen as the study of the emerging pattern of the Ising model on MNs, is needed. Here we study a well-known spin model called the Ashkin-Teller (AT) model in scale-free networks. The AT model can be regarded as a model for interacting systems between two species of Ising spins placed on respective layers in double-layer networks. Our study shows that, depending on the interlayer coupling strength and a network topology, unconventional PT patterns can also emerge in interaction-based phenomena: continuous, discontinuous, successive, and mixed-order PTs and a continuous PT not satisfying the scaling relation. The origins of such rich PT patterns are elucidated in the framework of Landau-Ginzburg theory.
Dynamical systems approach to the study of a sociophysics agent-based model
Timpanaro, Andre M.; Prado, Carmen P. C.
2011-03-24
The Sznajd model is a Potts-like model that has been studied in the context of sociophysics [1,2](where spins are interpreted as opinions). In a recent work [3], we generalized the Sznajd model to include assymetric interactions between the spins (interpreted as biases towards opinions) and used dynamical systems techniques to tackle its mean-field version, given by the flow: {eta}{sub {sigma}} = {Sigma}{sub {sigma}}'{sup M} = 1{eta}{sub {sigma}}{eta}{sigma}'({eta}{sub {sigma}}{rho}{sigma}'{yields}{sigma}-{sigma}'{rho}{sigma}{yields}{sigma}').Where hs is the proportion of agents with opinion (spin){sigma}', M is the number of opinions and {sigma}'{yields}{sigma}' is the probability weight for an agent with opinion {sigma} being convinced by another agent with opinion {sigma}'. We made Monte Carlo simulations of the model in a complex network (using Barabasi-Albert networks [4]) and they displayed the same attractors than the mean-field. Using linear stability analysis, we were able to determine the mean-field attractor structure analytically and to show that it has connections with well known graph theory problems (maximal independent sets and positive fluxes in directed graphs). Our dynamical systems approach is quite simple and can be used also in other models, like the voter model.
Dynamical systems approach to the study of a sociophysics agent-based model
NASA Astrophysics Data System (ADS)
Timpanaro, André M.; Prado, Carmen P. C.
2011-03-01
The Sznajd model is a Potts-like model that has been studied in the context of sociophysics [1,2] (where spins are interpreted as opinions). In a recent work [3], we generalized the Sznajd model to include assymetric interactions between the spins (interpreted as biases towards opinions) and used dynamical systems techniques to tackle its mean-field version, given by the flow: ησ = ∑ σ' = 1Mησησ'(ησρσ'→σ-σ'ρσ→σ'). Where hs is the proportion of agents with opinion (spin) σ', M is the number of opinions and σ'→σ' is the probability weight for an agent with opinion σ being convinced by another agent with opinion σ'. We made Monte Carlo simulations of the model in a complex network (using Barabási-Albert networks [4]) and they displayed the same attractors than the mean-field. Using linear stability analysis, we were able to determine the mean-field attractor structure analytically and to show that it has connections with well known graph theory problems (maximal independent sets and positive fluxes in directed graphs). Our dynamical systems approach is quite simple and can be used also in other models, like the voter model.
Ashkin-Teller model and diverse opinion phase transitions on multiplex networks.
Jang, S; Lee, J S; Hwang, S; Kahng, B
2015-08-01
Multiplex networks (MNs) have become a platform of recent research in network sciences because networks in many real-world systems interact and function together. One of the main scientific issues in MNs is how the interdependence changes the emerging patterns or phase transitions. Until now, studies of such an issue have concentrated on cluster-breakdown phenomena, aiming to understand the resilience of the system under random failures of edges. These studies have revealed that various phase transition (PT) types emerge in MNs. However, such studies are rather limited to percolation-related problems, i.e., the limit q→1 of the q-state Potts model. Thus, a systematic study of opinion formation in social networks with the effect of interdependence between different social communities, which may be seen as the study of the emerging pattern of the Ising model on MNs, is needed. Here we study a well-known spin model called the Ashkin-Teller (AT) model in scale-free networks. The AT model can be regarded as a model for interacting systems between two species of Ising spins placed on respective layers in double-layer networks. Our study shows that, depending on the interlayer coupling strength and a network topology, unconventional PT patterns can also emerge in interaction-based phenomena: continuous, discontinuous, successive, and mixed-order PTs and a continuous PT not satisfying the scaling relation. The origins of such rich PT patterns are elucidated in the framework of Landau-Ginzburg theory. PMID:26382347
Phase transition in a spatial Lotka-Volterra model
Szabo, Gyorgy; Czaran, Tamas
2001-06-01
Spatial evolution is investigated in a simulated system of nine competing and mutating bacterium strains, which mimics the biochemical war among bacteria capable of producing two different bacteriocins (toxins) at most. Random sequential dynamics on a square lattice is governed by very symmetrical transition rules for neighborhood invasions of sensitive strains by killers, killers by resistants, and resistants by sensitives. The community of the nine possible toxicity/resistance types undergoes a critical phase transition as the uniform transmutation rates between the types decreases below a critical value P{sub c} above that all the nine types of strains coexist with equal frequencies. Passing the critical mutation rate from above, the system collapses into one of three topologically identical (degenerated) states, each consisting of three strain types. Of the three possible final states each accrues with equal probability and all three maintain themselves in a self-organizing polydomain structure via cyclic invasions. Our Monte Carlo simulations support that this symmetry-breaking transition belongs to the universality class of the three-state Potts model.
Phase transition in a spatial Lotka-Volterra model
NASA Astrophysics Data System (ADS)
Szabó, György; Czárán, Tamás
2001-06-01
Spatial evolution is investigated in a simulated system of nine competing and mutating bacterium strains, which mimics the biochemical war among bacteria capable of producing two different bacteriocins (toxins) at most. Random sequential dynamics on a square lattice is governed by very symmetrical transition rules for neighborhood invasions of sensitive strains by killers, killers by resistants, and resistants by sensitives. The community of the nine possible toxicity/resistance types undergoes a critical phase transition as the uniform transmutation rates between the types decreases below a critical value Pc above that all the nine types of strains coexist with equal frequencies. Passing the critical mutation rate from above, the system collapses into one of three topologically identical (degenerated) states, each consisting of three strain types. Of the three possible final states each accrues with equal probability and all three maintain themselves in a self-organizing polydomain structure via cyclic invasions. Our Monte Carlo simulations support that this symmetry-breaking transition belongs to the universality class of the three-state Potts model.
Modeling Of Microstructure Evolution Of BCC Metals Subjected To Severe Plastic Deformation
Svyetlichnyy, Dmytro; Majta, Janusz; Muszka, Krzysztof; Lach, Lukasz
2011-01-17
Prediction of microstructure evolution and properties of ultrafine-grained materials is one of the most significant, current problems in materials science. Several advanced methods of analysis can be applied for this issue: vertex models, phase field models, Monte Carlo Potts, finite element method (FEM) discrete element method (DEM) and finally cellular automata (CA). The main asset of the CA is ability for a close correlation of the microstructure with the mechanical properties in micro- and meso-scale simulation. Joining CA with the DEM undoubtedly improves accuracy of modeling of coupled phenomena during the innovative forming processes in both micro- and macro-scale. Deformation in micro-scale shows anisotropy, which connected with that the polycrystalline material contains grains with different crystallographic orientation, and grain deformation is depended from configuration of directions of main stresses and axis of grain. Then, CA and DEM must be joint solutions of crystal plasticity theory. In the present model, deformation in macro-scale is transferred to meso-sale, where a block contains several, score or hundreds grains, and then is applied in micro-scale to each grain. Creation of low-angle boundaries and their development into high-angle boundaries are simulated by the cellular automata on the base of calculations using finite element method and crystal plasticity theory. The idea proposed in this study and particular solutions are discussed for the case of ultrafine-grained low-carbon steel.
Genetic demixing and evolution in linear stepping stone models
NASA Astrophysics Data System (ADS)
Korolev, K. S.; Avlund, Mikkel; Hallatschek, Oskar; Nelson, David R.
2010-04-01
Results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population are reviewed and extended. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation with additional terms describing mutations. Although the stepping stone model was first proposed for population genetics, it is closely related to “voter models” of interest in nonequilibrium statistical mechanics. The stepping stone model can also be regarded as an approximation to the dynamics of a thin layer of actively growing pioneers at the frontier of a colony of micro-organisms undergoing a range expansion on a Petri dish. The population tends to segregate into monoallelic domains. This segregation slows down genetic drift and selection because these two evolutionary forces can only act at the boundaries between the domains; the effects of mutation, however, are not significantly affected by the segregation. Although fixation in the neutral well-mixed (or “zero-dimensional”) model occurs exponentially in time, it occurs only algebraically fast in the one-dimensional model. An unusual sublinear increase is also found in the variance of the spatially averaged allele frequency with time. If selection is weak, selective sweeps occur exponentially fast in both well-mixed and one-dimensional populations, but the time constants are different. The relatively unexplored problem of evolutionary dynamics at the edge of an expanding circular colony is studied as well. Also reviewed are how the observed patterns of genetic diversity can be used for statistical inference and the differences are highlighted between the well-mixed and one-dimensional models. Although the focus is on two alleles or variants, q -allele Potts-like models of gene segregation are considered as well. Most of the analytical results are checked with simulations and could be tested against recent spatial
Spatial Modeling of Drug Delivery Routes for Treatment of Disseminated Ovarian Cancer.
Winner, Kimberly R Kanigel; Steinkamp, Mara P; Lee, Rebecca J; Swat, Maciej; Muller, Carolyn Y; Moses, Melanie E; Jiang, Yi; Wilson, Bridget S
2016-03-15
In ovarian cancer, metastasis is typically confined to the peritoneum. Surgical removal of the primary tumor and macroscopic secondary tumors is a common practice, but more effective strategies are needed to target microscopic spheroids persisting in the peritoneal fluid after debulking surgery. To treat this residual disease, therapeutic agents can be administered by either intravenous or intraperitoneal infusion. Here, we describe the use of a cellular Potts model to compare tumor penetration of two classes of drugs (cisplatin and pertuzumab) when delivered by these two alternative routes. The model considers the primary route when the drug is administered either intravenously or intraperitoneally, as well as the subsequent exchange into the other delivery volume as a secondary route. By accounting for these dynamics, the model revealed that intraperitoneal infusion is the markedly superior route for delivery of both small-molecule and antibody therapies into microscopic, avascular tumors typical of patients with ascites. Small tumors attached to peritoneal organs, with vascularity ranging from 2% to 10%, also show enhanced drug delivery via the intraperitoneal route, even though tumor vessels can act as sinks during the dissemination of small molecules. Furthermore, we assessed the ability of the antibody to enter the tumor by in silico and in vivo methods and suggest that optimization of antibody delivery is an important criterion underlying the efficacy of these and other biologics. The use of both delivery routes may provide the best total coverage of tumors, depending on their size and vascularity. PMID:26719526
Domain-size heterogeneity in the Ising model: Geometrical and thermal transitions.
de la Rocha, André R; de Oliveira, Paulo Murilo C; Arenzon, Jeferson J
2015-04-01
A measure of cluster size heterogeneity (H), introduced by Lee et al. [Phys. Rev. E 84, 020101 (2011)] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of H to these clusters and, moreover, present new results for the geometric domains for both d=2 and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transitions. An alternative interpretation for the scaling of H that does not introduce a new exponent is also proposed. PMID:25974445
Domain-size heterogeneity in the Ising model: Geometrical and thermal transitions
NASA Astrophysics Data System (ADS)
de la Rocha, André R.; de Oliveira, Paulo Murilo C.; Arenzon, Jeferson J.
2015-04-01
A measure of cluster size heterogeneity (H ), introduced by Lee et al. [Phys. Rev. E 84, 020101 (2011), 10.1103/PhysRevE.84.020101] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of H to these clusters and, moreover, present new results for the geometric domains for both d =2 and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transitions. An alternative interpretation for the scaling of H that does not introduce a new exponent is also proposed.
NASA Astrophysics Data System (ADS)
Jedrychowski, M.; Bacroix, B.; Salman, O. U.; Tarasiuk, J.; Wronski, S.
2015-08-01
The work focuses on the influence of moderate plastic deformation on subsequent partial recrystallization of hexagonal zirconium (Zr702). In the considered case, strain induced boundary migration (SIBM) is assumed to be the dominating recrystallization mechanism. This hypothesis is analyzed and tested in detail using experimental EBSD-OIM data and Monte Carlo computer simulations. An EBSD investigation is performed on zirconium samples, which were channel-die compressed in two perpendicular directions: normal direction (ND) and transverse direction (TD) of the initial material sheet. The maximal applied strain was below 17%. Then, samples were briefly annealed in order to achieve a partly recrystallized state. Obtained EBSD data were analyzed in terms of texture evolution associated with a microstructural characterization, including: kernel average misorientation (KAM), grain orientation spread (GOS), twinning, grain size distributions, description of grain boundary regions. In parallel, Monte Carlo Potts model combined with experimental microstructures was employed in order to verify two main recrystallization scenarios: SIBM driven growth from deformed sub-grains and classical growth of recrystallization nuclei. It is concluded that simulation results provided by the SIBM model are in a good agreement with experimental data in terms of texture as well as microstructural evolution.
Synergy of cell–cell repulsion and vacuolation in a computational model of lumen formation
Boas, Sonja E. M.; Merks, Roeland M. H.
2014-01-01
A key step in blood vessel development (angiogenesis) is lumen formation: the hollowing of vessels for blood perfusion. Two alternative lumen formation mechanisms are suggested to function in different types of blood vessels. The vacuolation mechanism is suggested for lumen formation in small vessels by coalescence of intracellular vacuoles, a view that was extended to extracellular lumen formation by exocytosis of vacuoles. The cell–cell repulsion mechanism is suggested to initiate extracellular lumen formation in large vessels by active repulsion of adjacent cells, and active cell shape changes extend the lumen. We used an agent-based computer model, based on the cellular Potts model, to compare and study both mechanisms separately and combined. An extensive sensitivity analysis shows that each of the mechanisms on its own can produce lumens in a narrow region of parameter space. However, combining both mechanisms makes lumen formation much more robust to the values of the parameters, suggesting that the mechanisms may work synergistically and operate in parallel, rather than in different vessel types. PMID:24430123
Liu, R M; Zhuo, W Z; Dong, S; Lu, X B; Gao, X S; Qin, M H; Liu, J-M
2016-03-01
In this work, we investigate the phase transitions and critical behaviors of the frustrated J(1)-J(2)-J(3) Ising model on the square lattice using Monte Carlo simulations, and particular attention goes to the effect of the second-next-nearest-neighbor interaction J(3) on the phase transition from a disordered state to the single stripe antiferromagnetic state. A continuous Ashkin-Teller-like transition behavior in a certain range of J(3) is identified, while the four-state Potts-critical end point [J(3)/J(1)](C) is estimated based on the analytic method reported in earlier work [Jin, Sen, and Sandvik, Phys. Rev. Lett. 108, 045702 (2012)]. It is suggested that the interaction J(3) can tune the transition temperature and in turn modulate the critical behaviors of the frustrated model. Furthermore, it is revealed that an antiferromagnetic J(3) can stabilize the staggered dimer state via a phase transition of strong first-order character. PMID:27078299
Fan, D.; Geng, C.; Chen, L.Q.
1997-03-01
The local kinetics and topological phenomena during normal grain growth were studied in two dimensions by computer simulations employing a continuum diffuse-interface field model. The relationships between topological class and individual grain growth kinetics were examined, and compared with results obtained previously from analytical theories, experimental results and Monte Carlo simulations. It was shown that both the grain-size and grain-shape (side) distributions are time-invariant and the linear relationship between the mean radii of individual grains and topological class n was reproduced. The moments of the shape distribution were determined, and the differences among the data from soap froth. Potts model and the present simulation were discussed. In the limit when the grain size goes to zero, the average number of grain edges per grain is shown to be between 4 and 5, implying the direct vanishing of 4- and 5-sided grains, which seems to be consistent with recent experimental observations on thin films. Based on the simulation results, the conditions for the applicability of the familiar Mullins-Von Neumann law and the Hillert`s equation were discussed.
Loth, E.; Tryggvason, G.; Tsuji, Y.; Elghobashi, S. E.; Crowe, Clayton T.; Berlemont, A.; Reeks, M.; Simonin, O.; Frank, Th; Onishi, Yasuo; Van Wachem, B.
2005-09-01
Slurry flows occur in many circumstances, including chemical manufacturing processes, pipeline transfer of coal, sand, and minerals; mud flows; and disposal of dredged materials. In this section we discuss slurry flow applications related to radioactive waste management. The Hanford tank waste solids and interstitial liquids will be mixed to form a slurry so it can be pumped out for retrieval and treatment. The waste is very complex chemically and physically. The ARIEL code is used to model the chemical interactions and fluid dynamics of the waste.
NASA Astrophysics Data System (ADS)
Ge, M. L.; et al.
1996-09-01
The Table of Contents for the full book PDF is as follows: * Preface * Part I: Satellite Meeting of STATPHYS-19 * Boundary Yang-Baxter in the RSOS/SOS Representation * Quantum Domains in Ferromagnetic Anisotropic Heisenberg Chains * The Generalized Chiral Clock Model and its Phase Diagram * Algebraic Solution of the Coincidence Problem for Crystals and Quasicrystals * Reflection Equations and Surface Critical Phenomena * Fully Packed Loop Models * Quantum Field Theories in terms of Group-Valued Local Fields: An Overview * C-Statiscal Transition Transforms of the Heisenberg Spin Chain and Braided Symmetry * U(1)-Invariant Local and Integrable Lattice Formulation of the Massive Thirring Model * Corner Transfer Matrices and Novel Polynomials * Rigorous and Numerical Results on Two-Dimensional Oriented Self-Avoiding Walks * The Price for Quantum Group Symmetry: Chiral Versus 2D WZNW Model * Integrable Zn-Chiral Potts Model : The Missing Rapidity-Momentum Relation * Dilute Algebras and Solvable Lattice Models * Falicov-Kimball Model: Ground States and Flux Phase Problem * Mutual Exclusion Statistics in the Exactly Solvable Model of the Mott Metal-Insulator Transition * Quantum Group and the Hofstadter Problem * Domain Walls in the Spin-S Quantum Ising Chain * Quantization of Nonultralocal Models - Generalization of the Theorem for the Multiple Coproduct * Multipoint Functions(Form-factors) of Quantum sine-Gordon Field with Boundary * Three-Dimensional Vertex Model * Probability of Phase Separation and Two Point Temperature Correlation Functions for the Bose Gas with Delta Interaction * On the Fundamental Invariant of the Hecke Algebra Hn(q) * Ternary Z3-Graded Algebras and New Gauge Theories * Thermodynamics of Integrable Quantum Chains : Free Energy and Correlation Lengths * Quantum Integrable Systems and Classical Discrete Nonlinear Dynamics * Quantum Jacobi-Trudi Formula and Analytic Bethe Ansatz * On Boundary Condition of Single Particle and the Spectrum of Many
Boussac, Alain; Rutherford, A William; Sugiura, Miwa
2015-01-01
The site for water oxidation in Photosystem II (PSII) goes through five sequential oxidation states (S0 to S4) before O2 is evolved. It consists of a Mn4CaO5-cluster close to a redox-active tyrosine residue (YZ). Cl- is also required for enzyme activity. By using EPR spectroscopy it has been shown that both Ca2+/Sr2+ exchange and Cl-/I- exchange perturb the proportions of centers showing high (S=5/2) and low spin (S=1/2) forms of the S2-state. The S3-state was also found to be heterogeneous with: i) a S=3 form that is detectable by EPR and not sensitive to near-infrared light; and ii) a form that is not EPR visible but in which Mn photochemistry occurs resulting in the formation of a (S2YZ)' split EPR signal upon near-infrared illumination. In Sr/Cl-PSII, the high spin (S=5/2) form of S2 shows a marked heterogeneity with a g=4.3 form generated at low temperature that converts to a relaxed form at g=4.9 at higher temperatures. The high spin g=4.9 form can then progress to the EPR detectable form of S3 at temperatures as low as 180K whereas the low spin (S=1/2) S2-state can only advance to the S3 state at temperatures≥235 K. Both of the two S2 configurations and the two S3 configurations are each shown to be in equilibrium at ≥235 K but not at 198 K. Since both S2 configurations are formed at 198 K, they likely arise from two specific populations of S1. The existence of heterogeneous populations in S1, S2 and S3 states may be related to the structural flexibility associated with the positioning of the oxygen O5 within the cluster highlighted in computational approaches and which has been linked to substrate exchange. These data are discussed in the context of recent in silico studies of the electron transfer pathways between the S2-state(s) and the S3-state(s). PMID:25843552
NASA Astrophysics Data System (ADS)
Yunus, ćaǧın; Renklioǧlu, Başak; Keskin, Mustafa; Berker, A. Nihat
2016-06-01
The spin-3/2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d =3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d =3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.
NASA Astrophysics Data System (ADS)
Morin-Duchesne, Alexi
Lattice models such as percolation, the Ising model and the Potts model are useful for the description of phase transitions in two dimensions. Finding analytical solutions is done by calculating the partition function, which in turn requires finding eigenvalues of transfer matrices. At the critical point, the two dimensional statistical models are invariant under conformal transformations and the construction of rational conformal field theories, as the continuum limit of these lattice models, allows one to compute the partition function at the critical point. Many researchers think however that the paradigm of rational conformal conformal field theories can be extended to include models with non diagonalizable transfer matrices. These models would then be described, in the scaling limit, by logarithmic conformal field theories and the representations of the Virasoro algebra coming into play would be indecomposable. We recall the construction of the double-row transfer matrix DN (λ, u) of the Fortuin-Kasteleyn model, seen as an element of the Temperley-Lieb algebra. This transfer matrix comes into play in physical theories through its representation in link modules (or standard modules). The vector space on which this representation acts decomposes into sectors labelled by a physical parameter d, the number of defects, which remains constant or decreases in the link representations. This thesis is devoted to the identification of the Jordan structure of DN(λ, u) in the link representations. The parameter β = 2 cos λ = -(q + q-1) fixes the theory : for instance β = 1 for percolation and 2 for the Ising model. On the geometry of the strip with open boundary conditions, we show that DN(λ, u) has the same Jordan blocks as its highest Fourier coefficient, FN. We study the non-diagonalizability of FN through the divergences of some of the eigenstates of ρ(F N) that appear at the critical values of λ. The Jordan cells we find in ρ(DN(λ, u)) have rank 2 and
18 CFR 740.3 - State applications.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 18 Conservation of Power and Water Resources 2 2012-04-01 2012-04-01 false State applications. 740.3 Section 740.3 Conservation of Power and Water Resources WATER RESOURCES COUNCIL STATE WATER... for completing the application; (2) The criteria to be used by the Council in assessing need for...
18 CFR 740.3 - State applications.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 18 Conservation of Power and Water Resources 2 2013-04-01 2012-04-01 true State applications. 740.3 Section 740.3 Conservation of Power and Water Resources WATER RESOURCES COUNCIL STATE WATER... for completing the application; (2) The criteria to be used by the Council in assessing need for...
18 CFR 740.3 - State applications.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 18 Conservation of Power and Water Resources 2 2014-04-01 2014-04-01 false State applications. 740.3 Section 740.3 Conservation of Power and Water Resources WATER RESOURCES COUNCIL STATE WATER... for completing the application; (2) The criteria to be used by the Council in assessing need for...
18 CFR 740.3 - State applications.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 18 Conservation of Power and Water Resources 2 2011-04-01 2011-04-01 false State applications. 740.3 Section 740.3 Conservation of Power and Water Resources WATER RESOURCES COUNCIL STATE WATER... for completing the application; (2) The criteria to be used by the Council in assessing need for...
18 CFR 740.3 - State applications.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 18 Conservation of Power and Water Resources 2 2010-04-01 2010-04-01 false State applications. 740.3 Section 740.3 Conservation of Power and Water Resources WATER RESOURCES COUNCIL STATE WATER... for completing the application; (2) The criteria to be used by the Council in assessing need for...
Kinetic model of particle-inhibited grain growth
NASA Astrophysics Data System (ADS)
Thompson, Gary Scott
made in 2-D and 3-D Monte Carlo-Potts Model simulations, it was concluded that the decrease in growth rate constant was most likely due to the removal of grain boundary curvature by particles.
A Framework for Efficient Structured Max-Margin Learning of High-Order MRF Models.
Komodakis, Nikos; Xiang, Bo; Paragios, Nikos
2015-07-01
We present a very general algorithm for structured prediction learning that is able to efficiently handle discrete MRFs/CRFs (including both pairwise and higher-order models) so long as they can admit a decomposition into tractable subproblems. At its core, it relies on a dual decomposition principle that has been recently employed in the task of MRF optimization. By properly combining such an approach with a max-margin learning method, the proposed framework manages to reduce the training of a complex high-order MRF to the parallel training of a series of simple slave MRFs that are much easier to handle. This leads to a very efficient and general learning scheme that relies on solid mathematical principles. We thoroughly analyze its theoretical properties, and also show that it can yield learning algorithms of increasing accuracy since it naturally allows a hierarchy of convex relaxations to be used for loss-augmented MAP-MRF inference within a max-margin learning approach. Furthermore, it can be easily adapted to take advantage of the special structure that may be present in a given class of MRFs. We demonstrate the generality and flexibility of our approach by testing it on a variety of scenarios, including training of pairwise and higher-order MRFs, training by using different types of regularizers and/or different types of dissimilarity loss functions, as well as by learning of appropriate models for a variety of vision tasks (including high-order models for compact pose-invariant shape priors, knowledge-based segmentation, image denoising, stereo matching as well as high-order Potts MRFs). PMID:26352450
Lattice models and integrability: a special issue in honour of F Y Wu
NASA Astrophysics Data System (ADS)
Guttmann, A. J.; Jacobsen, J. L.
2012-12-01
published in the April issue of Physical Review Letters (PRL) of the same year [4], and in September 1967, Wu moved to Northeastern University to join Lieb's group. Wu taught at Northeastern for 39 years until his retirement in 2006 as the Matthews Distinguished University Professor of Physics. Over the years, Wu has published more than 230 papers and monographs, and he continues to publish after retirement. Most of his research since 1967 is in exact and rigorous analyses of lattice models and integrable systems, which is the theme of this special issue. In 1968, after Wu's arrival at Northeastern, Lieb and Wu obtained the exact solution of the ground state of the one-dimensional Hubbard model and published the result in PRL [5], a work which has since become highly important after the advent of high-temperature superconductivity. This Lieb-Wu paper and Wu's 1982 review of the Potts model in Reviews of Modern Physics [37] are among the most cited papers in condensed matter physics. Later in 1968 Lieb departed Northeastern for MIT. As a result, the full version of the solution was not published until 34 years later [38] when Lieb and Wu collaborated to work on the manuscript on the occasion of Wu's 70th birthday. Wu spent the summer of 1968 at Stony Brook as the guest of C N Yang. Working with Yang's student, C Fan, he extended the Pfaffian solution of the Ising model to general lattices and termed such models 'free-fermion', a term now in common use [6]. In 1972, Wu visited R J Baxter, whom he had met earlier in 1968 at MIT, in Canberra, Australia, with the support of a Fulbright grant. They solved the triangular-lattice Ising model with 3-spin interactions [7], a model now known as the Baxter-Wu model. It was an ideal collaboration. While Baxter derived the solution algebraically, Wu used graphical methods to reduce the problem to an Ashkin-Teller model, which greatly simplifies the presentation. While in Canberra, Wu also studied the 8-vertex model on the honeycomb
Steinkamp, Mara P.; Winner, Kimberly Kanigel; Davies, Suzy; Muller, Carolyn; Zhang, Yong; Hoffman, Robert M.; Shirinifard, Abbas; Moses, Melanie; Jiang, Yi; Wilson, Bridget S.
2013-01-01
Ovarian cancer relapse is often characterized by metastatic spread throughout the peritoneal cavity with tumors attached to multiple organs. In this study, interaction of ovarian cancer cells with the peritoneal tumor microenvironment was evaluated in a xenograft model based on intraperitoneal injection of fluorescent SKOV3.ip1 ovarian cancer cells. Intra-vital microscopy of mixed GFP-red fluorescent protein (RFP) cell populations injected into the peritoneum demonstrated that cancer cells aggregate and attach as mixed spheroids, emphasizing the importance of homotypic adhesion in tumor formation. Electron microscopy provided high resolution structural information about local attachment sites. Experimental measurements from the mouse model were used to build a three-dimensional cellular Potts ovarian tumor model (OvTM) that examines ovarian cancer cell attachment, chemotaxis, growth, and vascularization. OvTM simulations provide insight into the relative influence of cancer cell–cell adhesion, oxygen availability, and local architecture on tumor growth and morphology. Notably, tumors on the mesentery, omentum, or spleen readily invade the “open” architecture, while tumors attached to the gut encounter barriers that restrict invasion and instead rapidly expand into the peritoneal space. Simulations suggest that rapid neovascularization of SKOV3.ip1 tumors is triggered by constitutive release of angiogenic factors in the absence of hypoxia. This research highlights the importance of cellular adhesion and tumor microenvironment in the seeding of secondary ovarian tumors on diverse organs within the peritoneal cavity. Results of the OvTM simulations indicate that invasion is strongly influenced by features underlying the mesothelial lining at different sites, but is also affected by local production of chemotactic factors. The integrated in vivo mouse model and computer simulations provide a unique platform for evaluating targeted therapies for ovarian cancer
Lebensohn, Ricardo A; Lee, Sukbin; Rollett, Anthony D
2009-01-01
A viscoplastic approach using the Fast Fourier Transform (FFT) method for obtaining local mechanical response is utilized to study microstructure-property relationships in composite materials. Specifically, three-dimensional, two-phase digital materials containing isotropically coarsened particles surrounded by a matrix phase, generated through a Kinetic Monte Carlo Potts model for Ostwald ripening, are used as instantiations in order to calculate the stress and strain rate fields under uniaxial tension. The effects of the morphology of the matrix phase, the volume fraction and the contiguity of particles, and the polycrystallinity of matrix phase, on the stress and strain rate fields under uniaxial tension are examined. It is found that the first moments of the stress and strain rate fields have a different dependence on the particle volume fraction and the particle contiguity from their second moments. The average stresses and average strain rates of both phases and of the overall composite have rather simple relationships with the particle volume fraction whereas their standard deviations vary strongly, especially when the particle volume fraction is high, and the contiguity of particles has a noticeable effect on the mechanical response. It is also found that the shape of stress distribution in the BCC hard particle phase evolves as the volume fraction of particles in the composite varies, such that it agrees with the stress field in the BCC polycrystal as the volume of particles approaches unity. Finally, it is observed that the stress and strain rate fields in the microstructures with a polycrystalline matrix are less sensitive to changes in volume fraction and contiguity of particles.
Maciorowski, Anthony F.
1974-01-01
The collection of Pottsiella erecta in western Lake Erie in August 1972 represents the first reported occurrence of this species in the Great Lakes and a 110 km northward extension of its known range.
Pott's Disease? AIDS-Associated Mycobacterium heckeshornense Spinal Osteomyelitis and Diskitis
Graf, Paul C. F.
2014-01-01
Acid-fast bacillus (AFB) spinal osteomyelitis in a patient with AIDS is often presumed to be caused by reactivated Mycobacterium tuberculosis. However, other AFB pathogens can mimic M. tuberculosis and, to ensure appropriate and adequate therapy, should be considered by clinicians. We present a case of aggressive spinal osteomyelitis caused by Mycobacterium heckeshornense in an AIDS patient; a review of the literature is also included. PMID:25428153
Kula, Serdar; Atasayan, Vildan
2015-10-01
Despite advances in the medical treatment of children with pulmonary arterial hypertension that have resulted in improved health quality and life expectancy, the progression of the disease is still the main problem for some patients. Because of this undesirable condition, the search for new treatment strategies continues for pediatric cardiologists. At this point, the Eisenmenger physiology is the main target because of the long-life expectancy and more stable hemodynamics of patients with Eisenmenger syndrome. Therefore, some invasive procedures may be used for conversion to Eisenmenger physiology with the aim of decompressing the right ventricle. PMID:26477721
Emir, Suna; Erdem, Arzu Y; Demir, Haci A; Kaçar, Ayper; Tunç, Bahattin
2012-01-01
Paravertebral tumors may interfere with the radiological and clinical features of spinal tuberculosis. We report a case of a 3-year-old boy with spinal tuberculosis who was initially misdiagnosed as having a paraspinal tumor. The diagnosis of tuberculosis was made on the basis of intraoperative findings and confirmed by histopathology. This case highlights the importance of awareness of the different radiographic features of spinal tuberculosis, which can mimic a spinal malignancy. In order to avoid delayed diagnosis, pediatricians and radiologists must be aware of spinal tuberculosis, which may interfere with other clinical conditions. PMID:23439455
[Medico-surgical treatment of Pott's disease. Our attitude in Gabon].
Loembe, P M
1994-11-01
Twenty-six of 95 adults treated for tuberculous spondylitis, between 1982 and 1993, underwent surgery. Twenty-one exhibited neurological deficits: radicular deficits: 4, and progressive spinal cord syndromes: 17 (incomplete, 13, complete, of acute onset: 4). Vertebral body compression fracture was the most prominent finding. Indications for surgery were neurologic: 11, mechanical: 1, etiologic: 1, and mixed: 13. Twelve patients had vertebrectomies, 3 laminotomies and 11 laminectomies. The average follow-up was 23 months. The neurological recovery was complete in 16 cases, partial in 4 cases and unchanged in one case. Bony consolidation occurred after 3-5 months. The medicosurgical treatment produced a very high cure rate, so rapidly, that it became the treatment of choice in our setting. Moreover, that allows to specify the diagnosis. Anterior decompression and fusion is recommended in the cervical and lumbar spine. In the thoracic segment, significant kyphosis is infrequent, so that surgical correction is rarely necessary. Laminotomy may occasionally be indicated for posterior decompression for abscess. Laminectomy is now preferred for uncommon cases of thoracolumbar posterior compression by tuberculous arachnoiditis or associated posterior vertebral tuberculosis. Indications for open biopsy are discussed. PMID:7874618
[Is there a place for surgery in Pott's disease in adults? Our experience in Gabon].
Loembe, P M; Chouteau, Y
1994-01-01
Tuberculous spondylitis treatment in developing nations remains controversial. We report our experience, working in a Center where appropriate medical and human structures are available. 22 of 78 adults treated at Jeanne-Ebori Hospital (Gabon), for tuberculous spondylitis, between August 1982 and June 1992, underwent surgery. The average age was 48 years (range, twenty-six to sixty-eight years). Eighteen patients had neurological complications: progressive spinal cord lesions: 15 cases (tetraplegia: 3, paraplegia: 11, tetraparesis: 1) and radicular syndromes (3 cases). The patients were seen in advanced stages of the disease with bone destruction, associated with collapse of vertebrae in ten cases. Indications for surgery were: neurologic in eleven cases, mechanical in one case, and mixed in ten cases (neurologic and mechanical: 5, etiologic and mechanical: 3, etiologic and neurologic: 2). Anterior approach were performed in 10 cases, posterior approach in 12 cases, generally, following an initial three weeks course of antituberculous therapy. The average length of time spent in hospital including rehabilitation had been 10.4 weeks. The average follow-up was 23.7 months (range: 8 months to 8 years). All patients obtained fusion, and stability was achieved after 3-5 months. The neurological recovery was complete in 9 cases, partial in 8 cases, unchanged in one case. All patients were considered medically cured. The analysis of material and socio economic difficulties obliges us to reduce the treatment length by favoring surgical intervention in relatively advanced lesions. Moreover, that allows to specify the diagnosis. PMID:7753296
Psoas abscess secondary to Pott's disease--an unusual presentation in a young child.
Afzal, Atif; Arshad, Muhammad; Ashraf, Omer
2006-04-01
Psoas abscess in neonates and infants are rare. Primary psoas abscesses are said to be more common in young children. Limping, fever and abdominal pain has been described to be the way psoas abscesses usually present. The authors describe the unusual presentation and successful treatment of a young child with a unilateral psoas abscess secondary to advanced spondylodiscitis. PMID:16711345
NASA Astrophysics Data System (ADS)
Fawzy, Wafaa M.
2010-10-01
applied to analysis and fitting the observed high resolution infrared spectra of the O 2sbnd HF/O 2sbnd DF and O 2sbnd N 2O complexes. Test input file for simulation and fitting the high resolution infrared spectrum of the O 2sbnd DF complex is provided. Program summaryProgram title: TSIG_COMP Catalogue identifier: AEGM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGM_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.: 10 030 No. of bytes in distributed program, including test data, etc.: 51 663 Distribution format: tar.gz Programming language: Fortran 90, free format Computer: SGI Origin 3400, workstations and PCs Operating system: Linux, UNIX and Windows (see Restrictions below) RAM: Case dependent Classification: 16.2 Nature of problem: TSIG_COMP calculates frequencies, relative intensities, and expectation values of the various quantum numbers and parities of bound states involved in allowed ro-vibrational transitions in semi-rigid planar weakly-bonded open-shell complexes. The complexes of interest contain a free radical in a Σ3 state and a closed-shell partner, where the electron-spin-electron-spin interaction, electron-spin rotation interaction, and centrifugal forces significantly modify the spectral patterns. To date, ab initio methods are incapable of taking these effects into account to provide accurate predictions for the ro-vibrational energy levels of the complexes of interest. In the TSIG_COMP program, the problem is solved by using the proper effective Hamiltonian and molecular basis set. Solution method: The program uses a Hamiltonian operator that takes into account vibration, end-over-end rotation, electron-spin-electron-spin and electron-spin rotation interactions as well as the various centrifugal distortion terms. The Hamiltonian operator
ERIC Educational Resources Information Center
Chiang, Rachelle Johnsson; Meagher, Whitney; Slade, Sean
2015-01-01
Background: The Whole School, Whole Community, Whole Child (WSCC) model calls for greater collaboration across the community, school, and health sectors to meet the needs and support the full potential of each child. This article reports on how 3 states and 2 local school districts have implemented aspects of the WSCC model through collaboration,…
NASA Technical Reports Server (NTRS)
James, G. K.; Ajello, J. M.; Kanik, I.; Slevin, J.; Franklin, B.; Shemansky, D.
1993-01-01
The electron-atomic hydrogen scattering system is an important testing ground for theoretical models and has received a great deal of attention from experimentalists and theoreticians alike over the years. A complete description of the excitation process requires a knowledge of many different parameters, and experimental measurements of these parameters have been performed in various laboratories around the world. As far as total cross section data are concerned it has been noted that the discrepancy between the data of Long et al. and Williams for n = 2 excitations needs to be resolved in the interests of any further refinement of theory. We report new measurements of total cross sections and atomic line polarizations for both n=2 and n=3 excitations at energies from threshold to 2000 eV...
Classical Monte Carlo Study for Antiferro Quadrupole Orders in a Diamond Lattice
NASA Astrophysics Data System (ADS)
Hattori, Kazumasa; Tsunetsugu, Hirokazu
2016-09-01
We investigate antiferro quadrupole orders in a diamond lattice under magnetic fields by Monte Carlo simulations for two types of classical effective models. One is an XY model with Z3 anisotropy, and the other is a two-component ϕ4 model with a third-order anisotropy. We confirm that the universality class of the zero-field transition is that for the three-dimensional XY model. Magnetic field corresponds to a Z3 field in the effective model, and under this field, we find that collinear and canted antiferro-quadrupole orders compete. Each phase is characterized by symmetry breaking in the sector of (sublattice Z2) otimes (reflection Z2 for the order parameter). When Z3 anisotropy and magnetic field vary, it turns out that this system is a good playground for various multicritical points; bicritical and tetracritical points emerge in a finite field. Another important finding is about the scaling of parasitic ferro quadrupole order at the zero-field critical point. This is the secondary order parameter induced by the primary antiferro order, and its critical exponent β' = 0.815 clearly differs from the expected value that is twice the value for the primary order parameter. The corresponding correlation length exponent is also different, ν' = 0.597(12). We also discuss relation of the present effective quadrupole models with the 3-state Potts model as well as implication to understanding of orbital orders in Pr-based 1-2-20 compounds.
7 CFR 718.3 - State committee responsibilities.
Code of Federal Regulations, 2012 CFR
2012-01-01
... AGRICULTURE FARM MARKETING QUOTAS, ACREAGE ALLOTMENTS, AND PRODUCTION ADJUSTMENT PROVISIONS APPLICABLE TO... digital images. (b) The State committee shall submit to the Deputy Administrator requests to deviate...
7 CFR 718.3 - State committee responsibilities.
Code of Federal Regulations, 2013 CFR
2013-01-01
... AGRICULTURE FARM MARKETING QUOTAS, ACREAGE ALLOTMENTS, AND PRODUCTION ADJUSTMENT PROVISIONS APPLICABLE TO... digital images. (b) The State committee shall submit to the Deputy Administrator requests to deviate...
7 CFR 718.3 - State committee responsibilities.
Code of Federal Regulations, 2011 CFR
2011-01-01
... AGRICULTURE FARM MARKETING QUOTAS, ACREAGE ALLOTMENTS, AND PRODUCTION ADJUSTMENT PROVISIONS APPLICABLE TO... digital images. (b) The State committee shall submit to the Deputy Administrator requests to deviate...
7 CFR 718.3 - State committee responsibilities.
Code of Federal Regulations, 2010 CFR
2010-01-01
... AGRICULTURE FARM MARKETING QUOTAS, ACREAGE ALLOTMENTS, AND PRODUCTION ADJUSTMENT PROVISIONS APPLICABLE TO... digital images. (b) The State committee shall submit to the Deputy Administrator requests to deviate...
7 CFR 718.3 - State committee responsibilities.
Code of Federal Regulations, 2014 CFR
2014-01-01
... AGRICULTURE FARM MARKETING QUOTAS, ACREAGE ALLOTMENTS, AND PRODUCTION ADJUSTMENT PROVISIONS APPLICABLE TO... digital images. (b) The State committee shall submit to the Deputy Administrator requests to deviate...
Energy Science and Technology Software Center (ESTSC)
2002-03-28
This code is a FORTRAN code for three-dimensional Monte Carol Potts Model (MCPM) Recrystallization and grain growth. A continuum grain structure is mapped onto a three-dimensional lattice. The mapping procedure is analogous to color bitmapping the grain structure; grains are clusters of pixels (sites) of the same color (spin). The total system energy is given by the Pott Hamiltonian and the kinetics of grain growth are determined through a Monte Carlo technique with a nonconservedmore » order parameter (Glauber dynamics). The code can be compiled and run on UNIX/Linux platforms.« less
ERIC Educational Resources Information Center
Freeman, Thomas J.
This paper discusses six different models of organizational structure and leadership, including the scalar chain or pyramid model, the continuum model, the grid model, the linking pin model, the contingency model, and the circle or democratic model. Each model is examined in a separate section that describes the model and its development, lists…
ten Cate, Jacob M
2015-01-01
Developing experimental models to understand dental caries has been the theme in our research group. Our first, the pH-cycling model, was developed to investigate the chemical reactions in enamel or dentine, which lead to dental caries. It aimed to leverage our understanding of the fluoride mode of action and was also utilized for the formulation of oral care products. In addition, we made use of intra-oral (in situ) models to study other features of the oral environment that drive the de/remineralization balance in individual patients. This model addressed basic questions, such as how enamel and dentine are affected by challenges in the oral cavity, as well as practical issues related to fluoride toothpaste efficacy. The observation that perhaps fluoride is not sufficiently potent to reduce dental caries in the present-day society triggered us to expand our knowledge in the bacterial aetiology of dental caries. For this we developed the Amsterdam Active Attachment biofilm model. Different from studies on planktonic ('single') bacteria, this biofilm model captures bacteria in a habitat similar to dental plaque. With data from the combination of these models, it should be possible to study separate processes which together may lead to dental caries. Also products and novel agents could be evaluated that interfere with either of the processes. Having these separate models in place, a suggestion is made to design computer models to encompass the available information. Models but also role models are of the utmost importance in bringing and guiding research and researchers. PMID:25871413
OpenACC programs of the Swendsen-Wang multi-cluster spin flip algorithm
NASA Astrophysics Data System (ADS)
Komura, Yukihiro
2015-12-01
We present sample OpenACC programs of the Swendsen-Wang multi-cluster spin flip algorithm. OpenACC is a directive-based programming model for accelerators without requiring modification to the underlying CPU code itself. In this paper, we deal with the classical spin models as with the sample CUDA programs (Komura and Okabe, 2014), that is, two-dimensional (2D) Ising model, three-dimensional (3D) Ising model, 2D Potts model, 3D Potts model, 2D XY model and 3D XY model. We explain the details of sample OpenACC programs and compare the performance of the present OpenACC implementations with that of the CUDA implementations for the 2D and 3D Ising models and the 2D and 3D XY models.
Non linear identities between unitary minimal Virasoro characters
NASA Astrophysics Data System (ADS)
Taormina, Anne
Non linear identities between unitary minimal Virasoro characters at low levels (m = 3, 4, 5) are presented as well as a sketch of some proofs. The first identity gives the Ising model characters (m = 3) as bilinears in tricritical Ising model characters (m = 4), while the second one gives the tricritical Ising model characters as bilinears in the Ising model characters and the six combinations of m = 5 Virasoro characters which do not appear in the spectrum of the three state Potts model.
MODEL DEVELOPMENT - DOSE MODELS
Model Development
Humans are exposed to mixtures of chemicals from multiple pathways and routes. These exposures may result from a single event or may accumulate over time if multiple exposure events occur. The traditional approach of assessing risk from a single chemica...
Xtoys: Cellular automata on xwindows
Creutz, M.
1995-08-15
Xtoys is a collection of xwindow programs for demonstrating simulations of various statistical models. Included are xising, for the two dimensional Ising model, xpotts, for the q-state Potts model, xautomalab, for a fairly general class of totalistic cellular automata, xsand, for the Bak-Tang-Wiesenfield model of self organized criticality, and xfires, a simple forest fire simulation. The programs should compile on any machine supporting xwindows.
Diffusion of two brands in competition: Cross-brand effect
NASA Astrophysics Data System (ADS)
Laciana, C. E.; Gual, G.; Kalmus, D.; Oteiza-Aguirre, N.; Rovere, S. L.
2014-11-01
We study the equilibrium points of a system of equations corresponding to a Bass based model that describes the diffusion of two brands in competition. To increase the understanding of the effects of the cross-brand parameters, we perform a sensitivity analysis. Finally, we show a comparison with an agent-based model inspired in the Potts model. Conclusions include that both models give the same diffusion curves only when the cross coefficients are not null.
Three-body interactions in sociophysics and their role in coalition forming
NASA Astrophysics Data System (ADS)
Naumis, Gerardo G.; Samaniego-Steta, F.; del Castillo-Mussot, M.; Vázquez, G. J.
2007-06-01
An study of the effects of three-body interactions in the process of coalition formation is presented. In particular, we modify a spin glass model of bimodal propensities and also a Potts model in order to include a particular three-body Hamiltonian that reproduces the main features of the required interactions. The model can be used to study conflicts, political struggles, political parties, social networks, wars and organizational structures. As an application, we analyze a simplified model of the Iraq war.
NASA Astrophysics Data System (ADS)
Li, Qin; Zhao, Yongxin; Wu, Xiaofeng; Liu, Si
There can be multitudinous models specifying aspects of the same system. Each model has a bias towards one aspect. These models often override in specific aspects though they have different expressions. A specification written in one model can be refined by introducing additional information from other models. The paper proposes a concept of promoting models which is a methodology to obtain refinements with support from cooperating models. It refines a primary model by integrating the information from a secondary model. The promotion principle is not merely an academic point, but also a reliable and robust engineering technique which can be used to develop software and hardware systems. It can also check the consistency between two specifications from different models. A case of modeling a simple online shopping system with the cooperation of the guarded design model and CSP model illustrates the practicability of the promotion principle.
Parameters for pyrethroid insecticide QSAR and PBPK/PD models for human risk assessment.
Knaak, James B; Dary, Curtis C; Zhang, Xiaofei; Gerlach, Robert W; Tornero-Velez, R; Chang, Daniel T; Goldsmith, Rocky; Blancato, Jerry N
2012-01-01
), and Colmenarejo (2003). QikProp(Schrodinger, LLC) was used to obtain Fu values for calculating partition coefficients and for calculating permeation constants (Caco-2, MDCK, and logBBB). ADMET Predictor (Simulations Plus Inc.) provided Vm~,x and Km values for the hydroxylation of drugs/pyrethroids by human liver recombinant cytochrome P450 enzymes making the values available for possible use in PBPK/PD models.The Caco-2 permeability constants and CYP3A4 Vmax and Km values are needed in PBPK/PD models with GI ACAT sub models. Modeling work by Chang et al.(2009) produced rate constants (kcat) for the hydrolysis of pyrethroids by rat serumcarboxylesterases. The skin permeation model of Potts and Guy (1992) was used topredict K, values for the dermal absorption of the 15 pyrethroids.The electrophysiological studies by Narahashi (1971) and others (Breckenridgeet al. 2009; Shafer et al. 2005; Soderlund et al. 2002; Wolansky and Harrill 2008)demonstrated that the mode of action of pyrethroids on nerves is to interfere with the changes in sodium and potassium ion currents. The pyrethroids, being highly lipid soluble, are bound or distributed in lipid bilayers of the nerve cell membrane and exert their action on sodium channel proteins. The rising phase of the action potential is caused by sodium influx (sodium activation), while the falling phase is caused by sodium activation being turned off, and an increase in potassium efflux(potassium activation). The action of allethrin and other pyrethroids is caused by an inhibition or block of the normal currents. An equation by Tatebayashi and Narahashi (1994) that describes the action of pyrethroids on sodium channels was found in the literature. This equation, or some variation of it, may be suitable for use in the PD portion of pyrethroid PBPK models. PMID:22610175
The scaling state in two-dimensional grain growth
Mulheran, P.A. . Dept. of Physics)
1994-11-01
A new model of normal grain growth in two-dimensional systems is derived from considerations of Potts model simulations. This Randomly Connected Bubble model is based on Hillert's theory and combines the essential topological features of the grain boundary network with the action of capillarity. It successfully predicts what the scaling state of the network should be and explains why the system evolves into this state. The implications for grain growth in real materials are also discussed.
Models, Part IV: Inquiry Models.
ERIC Educational Resources Information Center
Callison, Daniel
2002-01-01
Discusses models for information skills that include inquiry-oriented activities. Highlights include WebQuest, which uses Internet resources supplemented with videoconferencing; Minnesota's Inquiry Process based on the Big Six model for information problem-solving; Indiana's Student Inquiry Model; constructivist learning models for inquiry; and…
Yost, S.A.
1991-05-01
Radom matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous bosonic models. Two choices of integration slice are investigated. One leads to a perturbative structure which is reminiscent of, and perhaps identical to, the usual Hermitian matrix models. Another leads to an eigenvalue reduction which can be described by a two component plasma in one dimension. A stationary point of the model is described.
Yost, S.A. . Dept. of Physics and Astronomy)
1992-09-30
In this paper, random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous bosonic models. Two choices of integration slice are investigated. One leads to a perturbative structure which is reminiscent of, and perhaps identical to, the usual Hermitian matrix models. Another leads to an eigenvalue reduction which can be described by a two-component plasma in one dimension. A stationary point of the model is described.
Capturing the state transitions of seizure-like events using Hidden Markov models.
Guirgis, Mirna; Serletis, Demitre; Carlen, Peter L; Bardakjian, Berj L
2011-01-01
The purpose of this study was to investigate the number of states present in the progression of a seizure-like event (SLE). Of particular interest is to determine if there are more than two clearly defined states, as this would suggest that there is a distinct state preceding an SLE. Whole-intact hippocampus from C57/BL mice was used to model epileptiform activity induced by the perfusion of a low Mg(2+)/high K(+) solution while extracellular field potentials were recorded from CA3 pyramidal neurons. Hidden Markov models (HMM) were used to model the state transitions of the recorded SLEs by incorporating various features of the Hilbert transform into the training algorithm; specifically, 2- and 3-state HMMs were explored. Although the 2-state model was able to distinguish between SLE and nonSLE behavior, it provided no improvements compared to visual inspection alone. However, the 3-state model was able to capture two distinct nonSLE states that visual inspection failed to discriminate. Moreover, by developing an HMM based system a priori knowledge of the state transitions was not required making this an ideal platform for seizure prediction algorithms. PMID:22254742
Models-3 is a third generation air quality modeling system that contains a variety of tools to perform research and analysis of critical environmental questions and problems. These tools provide regulatory analysts and scientists with quicker results, greater scientific accuracy ...
This presentation presented information on entrainment models. Entrainment models use entrainment hypotheses to express the continuity equation. The advantage is that plume boundaries are known. A major disadvantage is that the problems that can be solved are rather simple. The ...
NASA Technical Reports Server (NTRS)
Rubesin, Morris W.
1987-01-01
Recent developments at several levels of statistical turbulence modeling applicable to aerodynamics are briefly surveyed. Emphasis is on examples of model improvements for transonic, two-dimensional flows. Experience with the development of these improved models is cited to suggest methods of accelerating the modeling process necessary to keep abreast of the rapid movement of computational fluid dynamics into the computation of complex three-dimensional flows.
Bayesian segmentation of hyperspectral images
NASA Astrophysics Data System (ADS)
Mohammadpour, Adel; Féron, Olivier; Mohammad-Djafari, Ali
2004-11-01
In this paper we consider the problem of joint segmentation of hyperspectral images in the Bayesian framework. The proposed approach is based on a Hidden Markov Modeling (HMM) of the images with common segmentation, or equivalently with common hidden classification label variables which is modeled by a Potts Markov Random Field. We introduce an appropriate Markov Chain Monte Carlo (MCMC) algorithm to implement the method and show some simulation results.
Exploring new frontiers in statistical physics with a new, parallel Wang-Landau framework
Vogel, Thomas; Li, Ying Wai; Wuest, Thomas; Landau, David P
2014-01-01
Combining traditional Wang Landau sampling for multiple replica systems with an exchange of densities of states between replicas we describe a general framework for simulations on massively parallel Petaflop supercomputers. The advantages and general applicability of the method for simulations of complex systems are demonstrated for the classical 2D Potts spin model featuring a strong first-order transition and the self-assembly of lipid bilayers in amphiphilic solutions in a continuous model.